Perception of Whole-Body Vibrations: From basic ... · PDF filePerception of Whole-Body Vibrations: From basic experiments to eﬀects of seat and steering-wheel vibrations on the

Perception of Whole-Body Vibrations:From basic experiments to effects of seat andsteering-wheel vibrations on the passenger‘s

comfort inside vehicles

Vom Fachbereich Physik derUniversitt Oldenburg

zur Erlangung des Grades eines

Doktors der Naturwissenschaften (Dr. rer. nat.)

angenommene Dissertation

Michael A. Bellmann

geboren am 20. November 1972in Brake

Erstreferent: Prof. Dr. rer. nat. V. Mellert

Korreferent: Prof. Dr. rer. nat. Dr. med. B. Kollmeier

Korreferent: Dr. rer. nat. R. Weber

Tag der Disputation: 05. Juli 2002

Contents

Zusammenfassung (Summary) III

Introduction 1

1 Theory 6

1.1 Evaluation and production of vibration . . . . . . . . . . . . 6

1.1.1 Different ways to produce vibrations . . . . . . . . . 7

1.1.2 Vibration isolation . . . . . . . . . . . . . . . . . . . 11

1.1.3 Whole-body vibration standards . . . . . . . . . . . 16

1.2 Psychophysics and sensoric physiology . . . . . . . . . . . . 28

1.2.1 Sensation threshold . . . . . . . . . . . . . . . . . . 28

1.2.2 Psychophysical measuring methods . . . . . . . . . . 33

1.2.3 Physiology of the skin (sense of touch) . . . . . . . . 42

2 Simulator 46

2.1 Vibration-Floor . . . . . . . . . . . . . . . . . . . . . . . . 47

2.1.1 General description . . . . . . . . . . . . . . . . . . 47

2.1.2 Dynamic performance of the vibration-floor . . . . . 50

2.1.3 Vibration performance . . . . . . . . . . . . . . . . . 53

2.2 Sound & Vibration Reproduction System . . . . . . . . . . . 57

3 Experiments on the perception of vibrations 62

3.1 Measuring set-up and stimuli . . . . . . . . . . . . . . . . . 63

3.2 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3 Exp. 1: Psychometric Function . . . . . . . . . . . . . . . . 66

II CONTENTS

3.4 Parameters which influence the perception thresholds . . . . 69

3.4.1 Stimulus duration . . . . . . . . . . . . . . . . . . . 70

3.4.2 Audible sound . . . . . . . . . . . . . . . . . . . . . 74

3.5 Exp. 2: Perception Threshold . . . . . . . . . . . . . . . . . 81

3.6 Exp. 3: Just Noticeable Differences (JND) . . . . . . . . . . 86

3.6.1 Just Noticeable Differences in Level (JNDL) . . . . . 87

3.6.2 Just Noticeable Differences in Frequency (JNDF) . . 90

3.7 Exp. 4: Equal-Vibration Level Contours (EVLC) . . . . . . . 92

3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4 Objective description of comfort inside cars 103

4.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . 104

4.2 Calculation of the objective signal parameters . . . . . . . . 105

4.3 Subjective quality judgements . . . . . . . . . . . . . . . . . 112

4.4 Results of the correlation analysis . . . . . . . . . . . . . . . 113

4.4.1 Seat vibrations . . . . . . . . . . . . . . . . . . . . . 114

4.4.2 Steering-wheel vibrations . . . . . . . . . . . . . . . 124

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5 Psychophysical measurements on a car seat 134

5.1 Measurement set-up . . . . . . . . . . . . . . . . . . . . . . 135

5.2 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.3 Exp. 1: Perception Threshold . . . . . . . . . . . . . . . . . 140

5.4 Exp. 2: Just Noticeable Differences in Level (JNDL) . . . . . 143

5.5 Exp. 3: Influence of level on seat vibration assessments . . . 145

5.6 Exp. 4: Influence of sound on seat vibration ratings . . . . . 148

5.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Summary and conclusion 154

References 166

A Supplements for the vibration standards i

B Supplements for the simulator vii

C List of results x

Zusammenfassung(Summary)

Die zunehmende Technisierung, z.B. am Arbeitsplatz, und die Tendenz zueinem immer hoheren Grad an Mobilitat haben zum Teil erhebliche Be-lastungen auf den Menschen und seiner Umwelt zur Folge. So ist derMensch vermehrt vielfaltigen Ganzkorpervibrationen im Alltag ausgesetzt,die z.B. durch Verkehr oder Bautatigkeiten verursacht werden. ”Ihre Wirkun-gen sind weniger sinnesspezifische Uberlastungen, vielmehr belastigen sieden Menschen im Sinne eines Zustandes verminderten Wohlbefindens odersie beeintrachtigen seine Leistung” (Meloni, 1991). Bestehende Normen,z.B. die ISO 2631-1/2, verwenden meist sinusformige Anregungen und be-schreiben die Grundlagen der Wahrnehmung von Vibrationen in Gebauden,wie etwa die Perzeptionsschwellen. Existierende Literaturdaten fur Perzep-tionsschwellen (einige sind zusammengefasst in Griffin, 1990) zeigen zumTeil erhebliche Abweichungen zu den Normwerten. Es bestehen aber auchdeutliche Unterschiede untereinander, die sich teilweise auf die verwende-ten Messmethoden zuruckfuhren lassen (Griffin, 1990). Auerdem existierenfast keine oder nur luckenhafte Angaben in der Literatur zu grundlegendenFragen der Vibrationswahrnehmung, wie z.B. die Frage nach den geradewahrnehmbaren Unterschieden in der Amplitude oder Frequenz (JNDL undJNDF). Aus diesen Grunden wurden einige grundlegende Experimente zurVibrationswahrnehmung mit bewahrten und neuen Messmethoden aus derPsychoakustik durchgefuhrt.

Ein bekanntes Beispiel fur eine simultane Einwirkung von Schall und Vibra-tionen auf den Menschen sind Fahrzeuge. Es ist bekannt, dass der Komfortbzw. Diskomfort, der durch Schall und Vibrationen im Fahrzeuginnerenverursacht wird, sehr entscheidend fur die Akzeptanz eines Fahrzeuges ist.In der Fahrzeugindustrie ist man daher zunehmend bemuht, den Komfortund die Qualitat im Bezug auf die wahrnehmbaren Innengerausche und

IV Zusammenfassung

Vibrationen zu erhohen. Es ware wunschenswert, die Eigenschaften derakustischen und vibratorischen Signale, die fundamental wichtig fur diesubjektive Qualitatsbewertung sind, zu kennen. Damit ware es moglich,die Qualitatsurteile nicht nur objektiv zu beschreiben, sondern auch bed-ingt Vorhersagen aus einfachen objektiven Aufnahmen der Schall- und Vi-brationssignalen uber den Komfort zu treffen. Aus den oben genanntenGrunden muss die Wahrnehmung von synthetisch einfachen bis hin zu realkomplexen Ganzkorpervibrationen untersucht werden.

Fur die in dieser Arbeit durchgefuhrten Experimente sind zwei Simula-toren entwickelt und gebaut worden: Zum einen ist fur eine reine ver-tikale Anregung der Probanden mit Ganzkorpervibrationen das ’Vibration-Floor’ konstruiert worden. Mit dem ’Vibration-Floor’ wurde in Kapitel 3Grundlagenforschung, bezogen auf die Wahrnehmung von sinusformigenGanzkorpervibrationen in vertikaler Richtung, durchgefuhrt. Zum anderenist das bestehende ’Sound & Vibration Reproduktion System c©’ fur die An-wendung in der Fahrzeugindustrie bezogen auf Sitz-und Lenkradvibrationen,sowie auf die Innenraumakustik (siehe Kapitel 5) modifiziert und optimiertworden. Dieses System kann sowohl synthetische als auch real gemessene,komplexe Lenkrad- als auch Sitzvibrationen in alle drei Richtungen subjek-tiv realistisch wiedergeben. Die Vorteile der in dieser Arbeit entwickeltenSimulatoren sind, dass sie unter psychophysikalischen Gesichtspunkten op-timiert sind und somit unter anderem kein bzw. kaum horbaren Schall beider Produktion bzw. Reproduktion von Vibrationen erzeugen.

Im Fokus dieser Arbeit standen zwei, wie oben erwahnt, unterschiedlicheBereiche: Im ersten Teil wurde die Wahrnehmung von vertikalen sinusfor-migen Vibrationen im Frequenzbereich von 5 bis 80 Hz auf einem starrenStuhl untersucht (Kapitel 3). Es wurden die Perzeptionsschwelle, sowie diepsychometrische Funktion, gerade wahrnehmbare Unterschiede im Beschleu-nigungspegel und in der Frequenz, sowie die Kurven gleicher Vibrationswahr-nehmung mit neuen und zuverlassigen psychophysikalischen Messmethodenaus der Psychoakustik ermittelt. Es zeigt sich, dass die Perzeptionsschwellefur vertikale Ganzkorpervibrationen nahezu konstant im Bereich ab 8 bis63 Hz ist. Oberhalb von 63 Hz sinken die gemessene Perzeptionsschwellenleicht, was wahrscheinlich auf Knochenleitung (Korperschall) zuruckzufuhrenist. Im Gegensatz zur Perzeptionsschwelle steigt die Kurve gleicher Vibra-tionswahrnehmung mit ca. 2.3 dB/Oktave im Bereich von 6 bis 63 Hz an,obwohl der Referenzreiz (sinusformige Ganzkorpervibration mit f = 20 Hzund LV ib = 100 dB) nur ca. 10 dB oberhalb der Perzeptionsschwelle liegtund damit schwellennahe ist. Der Unterschied zwischen diesen beiden unter-schiedlichen Kurvenverlaufen lasst sich nicht mit einer frequenzabhangigenJNDL erklaren, die frequenzunabhangig in diesem Frequenz- und Pegelbe-

Zusammenfassung V

reich bei ca. 1.5 dB liegt. Die JNDFs steigen im Gegensatz dazu frequenz-abhangig mit zunehmenden Frequenzen an.

Der zweite experimentelle Teil beschaftigt sich mit einem sehr praxisna-hen und anwendungsbezogenen Gebiet aus der Fahrzeugindustrie (Kapitel4). Durch Multikanalaufnahmen der Lenkrad- und Sitzvibrationen, sowiedes Schallfeldes in diversen Fahrzeugenklassen, sollten objektive Metho-den zur Beschreibung des subjektiven Komforts im Fahrzeug erarbeitet undverbessert werden. Dazu wurden zeitgleich zu den objektiven Messungendie subjektiven Qualitats- und Komfortbeurteilungen durch professionelleSubjektiv-Tester aus der Fahrzeugindustrie ermittelt. Aus den vibro-akus-tischen Multikanalaufnahmen werden Parameter aus bestehenden Normen(z.B. ISO 2631-1/2, ISO 5349-1/2, DIN 4051-1/2 und VDI 2057-1/2/3),sowie Signalparameter aus der Fahrzeugindustrie fur die Lenkrad- und Sitzvi-brationen berechnet und mit den subjektiven Bewertungen korreliert. DieKorrelationsanalyse ergibt, dass psychophysikalisch motivierte und spektraleinfach gewichtete Vibrationsparameter besser fur die Beschreibung des sub-jektiven Komforts geeignet sind. Dieser Befund gilt jedoch nur fur dieLenkradvibrationen. Fur die Sitzvibrationen korrelieren spektral ungewichtete,dafur aber spektral begrenzte Parameter um dominante Motorordnungen(zweite Motorordnung) besser mit den subjektiven Komfortbeurteilungen.Der tieffrequente Vibrationsenergieanteil ist ebenfalls fur die Bewertung derLenkradvibrationen wichtig. Auerdem zeigt sich fur die Lenkrad- und Sitzvi-brationen, dass die subjektiven Bewertungen pegelabhangig sind.

In dem letzten Experimentalteil wurden grundlegende und weiterfuhrendeExperimente zur Wahrnehmung von Sitzvibrationen auf einem realen Fahr-zeugsitz im Labor wiederholt bzw. durchgefuhrt (Kapitel 5). Mit diesen Ex-perimenten soll die Lucke zwischen den Grundlagen, die mit sinusformigenReizen ermittelt worden sind (Kapitel 3), und der praxisorientierten Anwen-dung im Fahrzeug (Kapitel 4) geschlossen werden. Fur die unterschiedlichenExperimente wurden sowohl (synthetisch einfache) sinusformige Sitzvibra-tionen, als auch in realen Fahrzeugen aufgenommene, komplexe vibro-akusti-sche Signale verwendet. Es lassen sich einige grundlegende Befunde, ge-messen auf einem starren Stuhl, bestatigen. So sind die Perzeptionsschwellenebenfalls frequenzunabhangig in dem untersuchten Frequenzbereich auf einem(gepolsterten) Fahrzeugsitz. Die ermittelten JNDLs sind ebenfalls frequen-zunabhangig und betragen ca. 1.5 dB. Auerdem kann gezeigt werden, dassdie Unterschiede in den subjektiven Bewertungen auf gerade wahrnehm-bare Unterschiede im Beschleunigungspegel (JNDL) zuruckzufuhren sind.Desweiteren zeigt sich, dass ein zusatzlicher akustischer Reiz einen nichtunerheblichen Einfluss auf die Bewertung der Sitzvibrationen besitzt.

Introduction

The human body is exposed to various whole-body vibrations from differentsources, e.g., at workshop in industry or in daily life traffic while travel-ing and in many other situations. Whole-body vibrations occur when thehuman body (standing, lying, sitting) is in contact with a vibrating sur-face. Oscillations in the frequency range from 1 to 80 Hz (and sometimeshigher) are called vibrations in existing standards (e.g., ISO 2631-1, 1997;VDI 2057-1, 1987). For higher frequencies the human body becomes lessand less sensitive, see Fig. 1.9. Movements with frequencies below 1 Hz aredenoted as motions and the excitation with such low frequency movementsproduce motion sickness (see Chapter 1.1.3). The perception of whole-bodyvibrations is often coupled with the hearing of low-frequency sound (soundbelow 20 Hz is called infrasound) because a vibrating structure or surfaceusually emits sound, as well. ”The effects of whole-body vibrations do notcause primary damage to the organs of perception, however they are oftenannoying and reduce the well-being of humans in daily life” (Meloni, 1991).It is just briefly noted that vibrations with high magnitudes and with a longexposure can also have health risks for humans. The effects of vibrationson the health of humans - e.g., whole-body and hand-arm transmitted vi-brations - was discussed in many studies and was frequently reported (forexample, Martin, 1984; Griffin, 1990; Dupuis & Hartung, 1998). Neverthe-less, there is a gap of knowledge of human response to vibrations at lowmagnitudes around the perception threshold. Whether a motion or vibra-tion causes annoyance, discomfort or interferes with activities depends onmany factors - including the characteristics of the presented vibrations likefrequency components and levels, characteristics of the exposed person andmany other aspects of the environment. Therefore it is difficult or impossi-ble to summarize all effects, to define a standard with limits and standardvalues for all conditions and for the whole frequency and level range. Ad-ditionally, human responses to vibrations are varied and differ greatly overtime and from one person to the other. Therefore a vibration limit is mean-

2 Introduction

ingless without the specification of the relevant criterion stating with whichprobability a specified effect is prevented by the limit.

The interest in human response to vibration becomes more and more pub-lic because the number of mechanized sources of vibrations have increasedand the number of exposed persons has risen. Additionally, the quality oflife becomes more important. The vibration exposure in daily life is usuallyaround or a bit higher than the perception threshold. For example, notonly health aspects (like safety belt or airbag) are important componentsof the acceptability of a vehicle but also the (dis-) comfort caused by seatand steering-wheel, as well as the interior sound has become very importantover the last years. The benefit of better information and knowledge aboutthe perception of vibrations and the human response to vibrations allows toimprove designs so that comfort would increase and the annoyance experi-enced from excessive vibrations would be reduced. Therefore, we have toinvestigate the perception of these combined, complex stimuli in the rangeof human perception thresholds and comfort to evaluate the effects of suchenvironmental stresses on the human body.

This study focuses on three different aspects of the perception of whole-bodyvibrations with low magnitudes which are around or somewhat above theperception thresholds. The first aspect focuses on basic experiments on theperception of whole-body vibrations just with vertical sinusoidal (artificial)excitations (Chapter 3). In the second part of this thesis the comfort or dis-comfort caused by vibrations in passenger cabins of vehicles is investigated(comprising usually of components in more than one direction, Chapter 4).Therefore multi-channel recordings of the seat and the steering-wheel vi-brations are made in various real cars of various types. The objective is tocalculate objective parameters of vibration signals that are more suitable todescribe a good or a poor quality assessments of subjective-testers. However,the knowledge of the perception of simple artificial stimuli in one directioncannot easily be transformed to the perception of special applications withcomplex broadband (real) vibrations like in the cabin of a vehicle. Thereforebasic experiments, which take into account aspects and knowledge of theChapter 3 and 4, are made with simple artificial and complex (broadband)real vibration signals on a real, cushioned car seat in the laboratory (Chap-ter 5). The objectives are to find a correlation between basic parametersand a special application of the perception of vibrations inside a car.

Many experimental studies in the laboratory use sinusoidal vibrations or ex-citations to investigate the human response to vibration because it is easy toproduce such vibrations and the description of the vibration signals is possi-ble with simple parameters. Additionally, it is possible to study the responseto a single frequency of motion with a sinusoidal excitation. In practice,

Introduction 3

on the other hand, not only periodic narrow band and sinusoidal vibrationsoccur but also vibration exposures with broadband signals to random char-acteristics are often encountered during work, travel and leisure time. Thesesignals are also stochastic and they contain transient events sometimes, es-pecially in a passenger cabin in a vehicle. It is frequently reported in theliterature that the human body is more sensitive for random, stochastic vi-brations (for example, Dupuis & Hartung, 1971; Mansfield & Griffin, 2000).The interesting frequency ranges vary according to the environment and theeffect. Effects of whole-body vibrations on health, activities, perception andcomfort is often associated with frequencies from 1 to 100 Hz. At lower fre-quencies the principal effect of the oscillation is a kind of motion sickness.Above 100 Hz the sensitivity of the human body decreases because of phys-iological reasons (Chapter 1.2). Additionally, the human ear gets more andmore sensitive for stimuli with increasing frequency. That is the reason whyvibrations and sounds emitted from vibrating surfaces are mostly perceivedas audible cues for frequencies above 100 Hz, respectively. The degree ofannoyance for the humans depends on many factors, as mentioned before.One important effect is the coupling between the human body and the vi-brating surface. For example, dominant vibrations transmitted through theseats of vehicles are often in the frequency range below 30 Hz. But there aremany other frequency components on the floor of a vehicle or in a buildingat higher frequencies. The degree to which vibration is transmitted to thehuman body depends on many factors, especially on the vibration frequencyor on the weight of the subject who is sitting on a cushioned or a rigid seat.Therefore attempts to summarize and to describe the knowledge merely byrecommending the avoidance of some vibration frequency, or by defining asingle curve, which represents all responses and effects of the humans toall frequencies, level ranges and conditions, is probably not possible. Ad-ditionally, such a standard mostly represents an insufficient compromise ofthe effects of vibrations on the body.

Chapter 1 gives an overview of the existing standards for the perception ofwhole-body vibrations and describes some methods for the description andthe evaluation of vibrations. Additionally, different principles of systems toproduce vibrations are presented with their advantages and disadvantages.Furthermore, the physiological aspects, which have an influence on the per-ception of vibrations, are briefly described.

Existing standards, e.g., ISO 2631-1/2 and VDI 2057-1/2/3, refer to sinu-soidal excitations on the base of the perception of vibrations in buildings.These standards address perception thresholds of whole-body vibrations inall directions, equal-comfort contours and the influence of exposure on theperception of vibration among other things. Literature data (e.g., Meloni,

4 Introduction

1991; Griffin, 1990; Parsons & Griffin, 1988; Meister, 1937) on the per-ception of sinusoidal whole-body vibrations show considerable differences tothe existing standards. Additionally, data from different laboratories deviatefrom each other too, probably due to differences in the psychophysical mea-suring method (some data are summarized in Fig. 3.3, Chapter 3). Besides,details are missing in the literature for basic experiments and parameterswhich are well known in psychoacoustics like Just Noticeable Differences(JND) in level or in frequency (Chapter 3). The reasons for the lack ofbasic knowledge are manifold. On one hand the perception of vibration isinfluenced by many factors, as mentioned before. Not only the couplingand contact area between the vibrating system (surface) and the humanbody are of decisive importance but also the posture of the subjects, addi-tional cues like sound and visual components, activities of the subjects andthe context of presented vibrations probably have an influence. Thereforesome investigations are found for special applications in the literature. It isdifficult or impossible to generalize this knowledge for the basic perceptionof vibration, for example, perception thresholds on different cushioned andrigid seats. On the other hand systems are needed, which can produce (si-nusoidal as well as broadband) vibrations in a reliable fashion and withoutany additional disturbing components like sound. The simulators, which areused for the production of just vertical vibrations (’vibration-floor’, Chap-ter 2.1) and for the reproduction of real sound and vibration (whole-bodyvibrations as well as hand-arm transmitted) signals recorded in idle runningcars (’Sound & Vibration Reproduction System c©’, Chapter 2.2), are pre-sented in Chapter 2. Both simulators are constructed and developed underpsychophysical aspects. This means that both systems do not emit audiblesound for low frequencies during the production of vibrations and emit justlow sound pressures around the auditory threshold for higher frequencies,among other things.

In Chapter 3 basic experiments on the perception of sinusoidal verticalwhole-body vibrations are conducted with new and reliable psychoacous-tic measuring methods on a rigid seat. These measuring methods shouldminimize the influence of measuring parameters on the results. First thepsychometric function is measured for a sinusoidal vertical excitation of5 Hz (Chapter 3.3). Additionally, the whole shape of the psychometricfunction is fitted with the measured data with a maximum likelihood fit. Inthe second experiment perception thresholds only in the vertical directionare measured (Chapter 3.5). But before this experiment is conducted withmany subjects, the influence of some measuring parameters, like the expo-sure time, the measuring method and the influence of an additional audiblesound, on the perception threshold are investigated (Chapter 3.4). There-

Introduction 5

after the Just Noticeable Differences in Level (JNDL, Chapter 3.6.1) and inFrequency (JNDF, Chapter 3.6.2) are determined. In the last experimentequal-vibration level contours, which are comparable to equal-loudness levelcontours in psychoacoustics, are determined with a fixed reference stimulus(Chapter 3.7). Broadband vibration signals could be spectrally weightedwith such psychophysically motivated curves to find objective parameterswhich are perhaps better suited for the description of the perception ofvibration than spectrally unweighted parameters.

In Chapter 4 methods for improving the objective description of subjectivecar vibration quality assessments are investigated. It is well known that in-terior sound and vibration in cars impair the subjective comfort. Objectivesignal parameters, which describe and are able to predict subjective assess-ments of sound and vibration, are desirable. One testing method in carindustry is to judge the quality of booming noise, seat and steering-wheelvibrations by professional subjective-testers. In Chapter 4 seat and steering-wheel vibrations as well as sound are recorded in cars belonging to differentcar classes (small, middle and upper middle class) in idle running conditionssimultaneously with the subjective ratings. From the 19 channel-recordingsobjective signal parameters for the seat and steering-wheel vibrations arecalculated, which correlate significantly with the subjective ratings, andconsequently describe the subjective vibration comfort. Psychophysicallymotivated parameters (from existing standards, e.g., ISO 2631-1/2 andISO 5349-1/2), as well as signal parameters from the car industry are con-sidered for the classification of seat and steering-wheel vibrations. They arecorrelated with the comfort ratings of subjective-testers (Chapter 4.4).

The results of the basic experiments on the perception of whole-body vi-brations (Chapter 3) and of the application inside a car according to thecomfort (Chapter 4) are not easy to compare with each other. Parameters,which could help to understand and to describe the deficiency between basicknowledge and special applications, are desirable. Therefore simple exper-iments with (artificial) sinusoidal and (real) broadband seat vibrations areconducted on a real cushioned car seat in the laboratory (Chapter 5). Theseat is similar to the seats used in Chapter 4. First basic experiments likeperception thresholds and JNDL (according to Chapter 3) on the perceptionof vertical whole-body vibrations are repeated. Thereafter, broadband seatvibration signals recorded in real cars are changed in level or are presented inpresence of additional audible stimuli to investigate the influence of vibrationlevel and of sound on the subjective ratings of the seat vibrations accord-ing to Chapter 4. Additionally, the influence of the individual perceptionof vibration like JNDLs on the judgement behaviors of subjective-testers isinvestigated.

Chapter 1

Theory

1.1 Evaluation and production of vibration

Hearing of low frequency sound (sound below 20 Hz called infrasound) withhigh levels is always coupled with the perception of vibrations. These in-frasounds and vibrations1 are usually annoying and reduce the well-beingof humans in daily life. Therefore, it is necessary to specify standards toimprove comfort and reduce the annoyance experienced from excessive vi-brations. Especially standards are needed for the living quarters and for theworking environments. But before such standards are specified basic knowl-edge must be collected. Vibrating (moving) systems and a standardizedevaluation are necessary to investigate the perception of whole-body vibra-tions. Furthermore, the physiological aspects on the perception of vibrationmust be taken into account.

In practice, the human body is exposed to various kinds of vibrations, whichare transmitted by different parts into the body, e.g., in vehicles, by hands,feet, backside etc. These different sensations of vibrations can be sepa-rated into two big sections, the perception of whole-body vibrations andthe perception of hand-arm transmitted vibrations. This study is focusedon the first aspect, the perception of whole-body vibrations (Chapter 3)but also regards hand-arm transmitted vibrations (Chapter 4). For thesereasons the physical and physiological fundamentals on the perception, pro-duction, measurement and evaluation methods of whole-body vibrations arepresented in this chapter. Additionally, in Chapter 1.1.3 the state-of-the-

1The frequency range from 1 to 80 Hz is important for the perception of vibration(Chapter 1.1.3)

1.1. Evaluation and production of vibration 7

art about existing international and national standards on the perception ofwhole-body vibration are briefly discussed.

1.1.1 Different ways to produce vibrations

Various systems use different principles to produce vibrations. The advan-tages and disadvantages of these systems are briefed to motivate which prin-ciples for the simulators (vibrating systems) are used in this study (Chap-ter 2). Most technical constructions of moving and vibrating systems ormachinery were developed for structure vibration tests during world war II.The aim of this sector was and is still to test the stability and capacity ofdifferent parts and equipments structures used in the aerospace technology.In the meantime, such developed systems, which produce vibrations, andappendant measuring methods are used in nearly all public parts of industry(transport, car, packaging and agricultural industries), applied research onthe perception of vibration and structural research of materials. Not onlysinusoidal stimuli are used but also stochastic and transient vibrations toverify systems, materials etc. Malfunctions of materials can be found withsuch stimuli due to vibrating strains (e.g., from the resonance frequency ofa rotating machinery).

Fig. 1.1: Electro-dynamic exciter calledshaker (adapted fromBruel & Kjær, 1967).

There are a lot of possibilities to produce vibrations using pneumatic, hy-draulic, electro-dynamic and many other systems. The familiar versions arei) straight stimulated, ii) electro-hydraulic and iii) electro-dynamic exciter.These systems have advantages and disadvantages and are optimized fordifferent tasks. The simplest system is the straight stimulated exciter (i).The testing material is shaken by an eccentric arm, which is moved by arotational motor. With such a system high magnitudes and high forces canbe produced. But there are two big disadvantages: Firstly, it is only possibleto produce periodic (sinusoidal) stimuli and secondly, just a small frequency

8 Chapter 1. Theory

range is usable (Fig. 1.2). In the literature many variations of these sys-tems are found but today this principle is no longer used because of theconstrained movement. The next type of exciter is the electro-hydraulicversion (ii). With this system very high masses can be moved. Additionally,there is no lower frequency limit (frequencies down to DC are possible) andvery high magnitudes and displacements are possible (1 m and more). Butthis system is practically not usable for frequencies above f = 30 Hz withadequate output (power) because of the supineness of the oil and system.Other disadvantages are the costs and structural expenses. Furthermore,such a gear produces a lot of noise (L = 85 dB(A) and more), which makesthis exciter unsuitable for the research on human response to vibrations. Thelast system is the electro-dynamic exciter, called ’shaker’ (iii). The shakerwas developed in the early sixties and is based on the electro-hydraulicsystems. There are two versions of electro-dynamic shakers possible: (a)’moving-magnet’ and (b) ’moving-coil’ systems. The foundations are thesame. Fig.1.1 clarifies the ’moving coil’ option. The coil is energized bya power supply and induces a magnetic counter field. The two magneticfields (from the magnet and the induced one) affect a magnetic repulsionbetween the magnet and the coil. The motion of the coil or magnet is pro-portional to the induced magnetic field upwards and downwards. Thereforethe vibrating table - often called shaker-table which is fixed on the movingelement and centered by springs moves, as well. The utilizable force of thesystem depends on the diameter of the coil, the number of coil windings andthe magnetic field strength, as well as the magnetic field of the permanentmagnet. With a system like this vibrations can be produced in a broadbandfrequency range. The disadvantages are the cooling of the coil and theproblems of centering device of the moving system (more information is in,e.g., Bruel & Kjær, 1967; Booth, 1958).

Today the electro-dynamic and electro-hydraulic exciters are used in theindustry depending on the tasks of the vibrating system. Fig. 1.2 gives anoverview about the frequency ranges of the different exciter principles (sum-marized in Booth, 1958). For the electro-hydraulic exciter, the disadvan-tages are that they produce noise by high constructional outlay. Therefore,electro-dynamic exciters are used for producing vibrations in this study sincethey do not emit a lot of sound and a high frequency range from about 5 Hzup to some kHz can be produced (Chapter 2).

All electro-dynamic exciters - shakers - have similar transfer functions andacceleration-frequency-characteristics, which are based on typical (electro-mechanical) properties of the used materials (e.g., described in Booth,1958). If a constant current I is loaded to a coil the moving part of theshaker moves consequently with a constant force F . The real acceleration of


Fig. 1.2: Frequency ranges ofdifferent systems to produce vi-brations (adapted from Booth,1958).

the vibrating system is a function of frequency and can be separated into fourregions A to D with two main resonances: the suspension resonance and themoving element resonance (Fig. 1.3). The first (suspension) resonance is of-ten called ’electro-mechanical’ resonance or ’electronical’ resonance becauseof the influence of mechanical and electronical elements on this resonance(e.g., described in Zollner & Zwicker, 1993). The equivalent circuit of anelectro-dynamic transducer is shown in Fig. 1.4 (left) with only electroni-cal elements2. The size of the displacement of the shaker-table below thefirst resonance depends on the stiffness of the mechanical ’spring’ (centeringdevice), which means that at low frequencies a constant displacement3 ispossible in region A. If the input signal increases in frequency the resonanceof the total volume of the system in conjunction with the spring affects thespring or suspension resonance (region B). Above this region the masses ofthe moving elements of the system (shaker-table, test items) dominate themotions of the shaker-table and a region (C) of constant acceleration affili-ates. For higher frequencies the different parts of the moving elements havetheir resonances and the higher frequency range show a peak-trough struc-

2The mechanical elements are transduced into electronical elements in Fig. 1.4.3Constant displacement x indicates an increase of 12 dB/octave because a = δ2x/δt2.

10 Chapter 1. Theory

Fig. 1.3: Acceleration as a function of frequency if the current in coil is constantover the frequency (adapted from Booth, 1958).

ture (region D). This main resonance is mostly an axial resonance, which isproduced by the moving elements in the axial direction, and limits the higherusable frequency range of such vibrating systems. These resonances are pro-duced solely by the mechanical properties of the moving elements. A simpleequivalent mechanical circuit is shown for just one additional mass (shaker-table) in Fig. 1.4 (right). If test items are mounted on the shaker the simplemodel in Fig. 1.4 is extended by more mass-spring elements. Therefore anelectro-dynamic exciter can be described by a simple model with at least twodifferent resonances: an ’electro-mechanical’ and a mechanical resonance.The sizes and properties of the electronical and mechanical elements set theacceleration-frequency-characteristics of an exciter.

The acceleration-frequency-characteristics depend on different material prop-erties of the coil and magnet as well as the mechanical elements like the’spring’ and additional masses, as mentioned above. For example, for ahigh-performance shaker with a low resistance the spring resonance will benearly completely suspended because of the electrical attenuation effect.Such an attenuation effect is affected by the low internal resistance of thepower-amplifier. This leads to a short-circuit of the induced inverse volt-age in the coil if the coil moves in a constant magnetic field. Because ofthe proportionality of the inverse voltage and the velocity, the movementin this region (B) takes place with constant velocity (increasing with nearly6 dB/octave). In a higher frequency range, where the movement (motion)depends on mass, a range with constant acceleration is given. But due


Fig. 1.4: The equivalent circuit of an electro-dynamic transducer (left) and anequivalent mechanical circuit of the appendant moving-element (right). In theleft figure the mechanical elements of an electro-dynamic exciter (like centeringdevice) are transferred into electronical elements. If a constant current I is loadedto a coil the moving part of the shaker is moving consequently with a constantforce F . A simple model to characterize the resonance of the moving element(shaker-table) is shown in the right figure. This figure is based on pictures fromZollner & Zwicker (1993).

to the low ohmic resistance of the coil windings, this region is very smalland the induction of the coil delivers a decreasing acceleration level (withabout 6 dB/octave). With damping materials the performance factor ofthe system can be regulated and thus the frequency range with constantacceleration increases (region C). More information about electro-dynamictransducer are summarized in, e.g., Bruel & Kjær (1967); Zollner & Zwicker(1993); Harris & Crede (1976)

Electro-dynamic shakers can be used for an active (a) or a re-active (b)excitation of a movable system or machine. In the first case the shakeris fixed on a rigid high mass (e.g., foundation) and innervates the movingpart of the system. In the second case the shaker is used as an ’inertial’shaker, which is just fixed on the moving part of a movable system. If theshaker runs (produces vibration) the moving element is stimulated, as well(reactive). Both principles are used in this study to produce whole-bodyvibrations (Chapter 2). The advantages and disadvantages, as well as thesimulators, which produce whole-body vibrations are explained in Chapter 2.

1.1.2 Vibration isolation

Vibration isolation is a prominent problem. Additionally, isolation mech-anisms are used for the constructions of the simulators which are usedin this study for the production of whole-body vibrations. That is why


Fig. 1.5: Simple model of a single degree-of-freedom damped self-oscillating mass-spring system. On the left side the ’passive’ vibration isolation principle and onthe right side the ’active’ principle are shown.

a short overview about the vibration isolation mechanism is presented inthis subsection. The vibration isolation problem is often solvable with theknowledge of the resonance frequency of the vibrating system. The basicproblems and solutions of vibration isolation will be discussed based on asimple model (damped self-oscillating mass-spring system): A simple singledegree-of-freedom model is realized by a moving mass mounted on a springand a damping module that isolates the moving mass from the foundation(Fig. 1.5). The vibration isolation differs according to the active and thepassive isolation principles. In the first case the moving (vibrating) systemis ’passive’ isolated by the spring-damping module (called ’isolator’) fromthe environment (perhaps foundation) and protects the moving mass fromdisturbing motions from the foundation, like vibrations from buildings, traf-fic or subsonic noise. On the other hand the environment is ’active’ isolatedfrom the vibrating mass or system by the isolator. In this case the functionof an isolator is to reduce the magnitude of force transmitted from the mov-ing (vibrating) mass to its foundation. Theoretically, the moving mass andthe foundation should be dynamic rigid masses. Additionally, the foundationshould have an infinite mass. Both suppositions are not possible because


all bodies are more or less elastic and have finite masses. For these reasonsthe foundation has a factor of about 10 times higher mass than the movingmass in practical experience (Harris & Crede, 1976).

The quality of isolation depends on the excitation, the resonance frequencyfR, the damping material and factor D, the size (geometry) and the weightm of the moving mass (test item), and the spring constant c (’stiffness’of the spring). A simple damped self-oscillating mass-spring system have asimple equation of motion (Eq. 1.1 or , e.g., Harris & Crede). The differentialequation of the motion changes a bit if a constant excitation F = F0·sin(ωt)occurs, Eq. 1.2:

m · d2x

dt2+ D · dx

dt+ c · x = 0 (1.1)

with a constant excitation, respectively:

m · d2x

dt2+ D · dx

dt+ c · x = F0 · sin(ωt) (1.2)

However, under physical aspects only a finite isolation is possible. Thereforea compromise between the isolation effect and the stability of the wholesystem must be found. The excitation bandwidth and the bilateral isolationas well as the slide in only one direction (moving axis) are assured becausethe softer the spring (’stiffness’) the better the isolation at frequencies abovef =

√2 · fR, whereas the resonance frequency decreases with decreasing

spring constant (Eq. 1.4). Additionally, the stiffness of the spring influencesthe stability of the system construction. Based on Eq. 1.1 and assuming thatthe motion (displacement) x is sinusoidal x = x0 · cos(ωt) with ω = 2πfthe resonance frequency f0 is calculated by Eq. 1.4:

f0 =12π

· 2

√c

m=

1T

(1.3)

c =E ·A

d

with

E = dynamical elastic modulus

A = support area

d = thickness of the material

c = spring constant

T = cycle duration


The spring constant depends on dynamic elastic modulus (E-modulus),which differs, depending on frequency, from the static E-modulus if damp-ing occurs. For this reason Eq. 1.4 are not applied for calculation of theresonance frequency and displacement x (of the moving body) of undampedvibration isolation (e.g., for steel springs after Harris & Crede, 1976), re-spectively.

fR =5√x

(1.4)

Theoretically, undamped systems vibrate infinitely but in reality, in all sys-tems, a mechanical damping with a damping factor D occurs, which isdescribed by the mechanical loss factor η (after Veit, 1996):

η = 2 ·D (1.5)

Fig. 1.6: The absolute (left) and relative (right) transmissibility for the rigidlyconnected viscous-damped isolation system as a function of ω/ω0 and criticaldamping ζ(= d/dc) (defined in Harris & Crede, 1976). The absolute transmis-sibility is the ratio x0/u0 for foundation motion excitation (left Fig.1.5) and theratio FT /F0 for mass force excitation (right Fig.1.5). The relative transmissibilitydescribes the motion between the mass and the foundation (i.e., the deflection ofthe isolator). (The figure is adapted from Harris & Crede, 1976).


In the case of passive isolation, the standing wave ratio of the relative mov-ing mass displacement δ = x− u and the foundation vibration amplitude uindicates the vibration isolation and is called ’relative (displacement) trans-missibility TR’ (Fig. 1.5). The ratio of dynamic excited force F0 of movingbody to the transmitted force FT is used in active isolation case, which isequal to the ratio x0/u0. This ratio is called ’absolute transmissibility TA’and implies a measurement of the reduction of transmitted force or motionafforded by an isolator. The absolute and relative transmissibility curvesof a (viscous) 1-dimensional damped self-oscillating mass-spring system areshown as a function of frequency ratio ω/ω0 in Fig. 1.6 (after Harris &Crede, 1976).

Whereas, if only the displacement x of a constrained oscillating motion ofan excited mechanical system with a force F (= F0 ·sin(ωt)) is subjected tothe unbalance v (= ω

ω0− ω0

ω ) a symmetric curve is drawn with a maximumat the eigenfrequency (resonance frequency) ω0. The resonant curve couldbe strong inflate or flat depending on the damping factor D and ratio of

1

x

1−180

−150

−120

−90

−60

−30

0

ω/ω0

ψ [°

]

ζ increases m increases

Fig. 1.7: Resonance curves drawn for different fractions of critical damping ζ ofa constrained motion of an excited mechanical system (upper figure). The phaseshift between the excited force and the constrained motion is shown in the lowerfigure.


critical damping ζ= d/dc (with dc = 2 ·√

c ·m) (Veit, 1996). The phaseshift between the constrained motion and the excited force depends on thefrequency and the critical damping (Fig. 1.7). This figure shows a symmetricresonant curve because the behavior of the whole system is figured. Ifthe behavior of every single variable of a mass-spring system is separatelyplotted, unsymmetric curves will be obtained.

The isolation I of an isolator depends on the frequency ratio f/fR anddamping factor D and is calculable after Eq. 1.6:

I = 100 ·

[1−

√1 + η2

[1 + ( ffR

)2]2 + η2

](1.6)

Eq. 1.6 show that the isolation I depends on physically qualified ampli-tude resonance above f =

√fR; therefore the isolation decreases. Realistic

moving (vibrating) systems are not always describable by a simple singledegree-of-freedom damped self-oscillating mass-spring system, that is whyadditional fixed bodies with discrete masses and springs produce more reso-nances therefore it is often useful to upgrade such simple models for specialtasks. Furthermore for dynamically soft materials (like steel) the frequencydependence on the ’impedance’ Z of the structure must be taken into ac-count.

1.1.3 Whole-body vibration standards

This section gives an overview of the existing standards and regulations formeasuring and evaluating whole-body vibrations with national (German) andinternational character mainly from the German Institute for Standardization’(DIN; ”Deutsches Institut fur Normung e.V.”), the Club of German Engi-neers (VDI; ”Verein Deutscher Ingenieure”) and the International StandardsOrganization (ISO). In different nations various other national standards likethe British Standards (BS) or the American National Standards (ANS) exist.Users of any standards should base their work on the full documents andnot on this summarized study.

The word ’standard’ has many different meanings and interpretations in-cluding defined evaluation procedures, limits, indications of what individu-als may expect (suggest attributes), quality or acceptability, etc. Severalexisting standards on human response to vibration exhibit a confusing mix-ture of objectives: there has been a tendency to produce human vibrationstandards which partially define a vibration evaluation procedure and par-tially define a vibration limit. In several standards incomplete knowledge


and uncertainty has been reflected in the definition of ambiguous evaluationprocedures with rigid limits, rather than unambiguous evaluation procedureswith uncertain limits. ”Since a limit is meaningless without the evaluationprocedure, it is clear that a standardization of procedures is a prerequisiteto the standardized limits” (Griffin, 1990). When the two possible principlefunctions of standards are separated in this way it also becomes clear thata standard does not even need to define limits. Additionally, humans areexposed to vibrations at varying locations and conditions which is anotheraspect of standards: limits, which take into account all situations worldwide,will probably not be optimal for many local areas or specific activities (likein industry, traffic, daily life, buildings, etc.).

The first German guideline (standard) was the VDI 2057 edited in 1963. TheISO (International Standards Organization) published the first internationalstandard (ISO 2631) in 1974. Thence the German VDI guidelines wererevised in order to find a concordance with the ISO standard. The latestversion of the VDI 2057 (’Effect of mechanical vibrations on human beings4,1987’) is separated into four parts:

• Part 1: Fundamentals - Classifications - Terms

• Part 2: Evaluation

• Part 3: Assessment

• Part 4: Measurements and assessment of workshop places in buildings

The second published guideline in German language was the DIN 4150 (’Vi-brations in buildings5, 1975’). It was made for architects and engineers whowork in the building trade. This standard is based on the VDI 2057 andon some other standards from the building trade. Additionally, the VDI2057 takes into account that vibrating surfaces emit sound (infrasound andaudible sound).

This study refers to the following evaluation and analysis methods from the(ISO 2631-1, 1997; ISO 2631-2, 1989) because those standards are morecommon and the guidelines in German language have high concordancewith them.

The ISO 2631 was published in 1974 ”[...] in order to give ’numerical’ valuesfor limits of exposure to vibrations transmitted from solid surfaces, e.g., inbuildings to the human body in a frequency range from 1 to 80 Hz” (ISO2631-1, 1997). This ISO (’Evaluation of human exposure to whole-bodyvibration’) is separated into three main parts:

4”Einwirkung mechanischer Schwingungen auf den Menschen” in German5”Erschutterungen im Bauwesen” in German


• Part 1: General requirements

• Part 2: Continuous and shock-induced vibration in buildings (1 to80 Hz).

• Part 3: Evaluation of human exposure to whole-body z-axis verticalvibration in the frequency range 0.1 to 1 Hz.

In the last nearly 30 years, some complete revisions of the standard havebeen made which considered knowledge from present studies to eliminateremaining ambiguity and replace those aspects which are untenable or un-necessary. The last revisions are: from 1997 for the Part 1 and from 1989for the Part 2 whereas the committee starts with a new revision in the year2000 for Part 2.

The ISO 2631 defines methods for quantification, evaluation and analysison human response to whole-body vibrations concerning different aspects:

1. Health risk

2. Comfort and Perception

3. Motion Sickness

Thereby the first two items indicate vibrations in a frequency range from 1to 80 Hz whereas the third item considers vibrations from 0.1 to 0.5 Hz orfrom 0.1 to 1 Hz. The following presented methods are only applicable forperiodic, randomized and transient vibrations signals (sinusoidal or complex)but not for evaluation of extreme magnitudes – single shocks which occurin ,e.g., vehicle accidents.

The first part of ISO 2631 gives an overview of the used symbols and sub-scripts, vibration axes, frequencies and magnitudes. Additionally, ISO 2631-1 defines measuring methods and analysis parameters which depend on thetime and frequency domain, psychophysically motivated weighting functions,etc. The second part of the ISO 2631-2 defines how the methods of the’basic standard’ should be extended to allow the assessment of building vi-brations. Limits of acceptability of vibrations in various building types andperception thresholds in all three directions (x/y/z-axes) for whole-body vi-brations are included in this part as well. The principal frequency weightingsare based on the specified curves in the ISO 2631-1.

The physical force of vibrations is measurable as acceleration a [m/s2], ve-locity v [m/s] or displacement x [m]. – The conversion into these differentcomponents is given by the temporal integration or derivation. – The accel-eration a is used for the representation of vibration parameters and signals in


Tab. 1.1: Most relevant parameters for vibration time signals (adapted fromMeloni (1991).

Parameter Definition

mean x = 1N

∑x(i)

standard deviation τ =[

1N

∑[x(i)− x]2

] 12

root-mean-square r.m.s =[

1N

∑x2(i)

] 12

crest factor peakvaluerms

root-mean-quad value r.m.q. =[

1N

∑x4(i)

] 14

Vibration Dose Value V DV =[

TS

N

∑x4(i)

] 14

estimated Vibration Dose Value eV DV =[(

1.4(r.m.s))4

TS

] 14

nearly all present studies. Whereas an acceleration level of LV ib = 140 dBcorresponds to an acceleration of a = 10 m/s2 ≈ g. The following measure-ment and evaluation methods for human response to vibrations are definedin the present ISO 2631.

The evaluation of a vibration signal is possible in the time domain or in thefrequency domain. In the time domain an analysis points out parameterslike: peak value , standard deviation, root mean square value (rms), runningrms, crest factor, energy equivalent rms, estimated Vibration Dose Value(eVDV), root-mean-quad value (rmq) or Vibration Dose Value (VDV). Theevaluations and weightings in the frequency domain can be realized via aFast Fourier Transformation (FFT) or in the power spectrum. The mostimportant parameters are summarized in Tab. 1.1. Whereas the period TS

of the vibration time signal with a frequency fs is sampled with N = TS ·fs

values for x(i).Not only the physical variables like magnitude and frequency are importantbut also exogenous variables: e.g., posture and body-size of the subjects,exposure and endogenous variables: e.g., age and gender have influence onthe perception of vibrations (Meloni, 1991).

Human are able to discriminate six different kinds of vibrations which are


specified in ISO 2631-1 and VDI 2057-2: three translational directions, thatmeans vibrations in x-, y- and z-direction (basicentric axis), as well as threerotational directions: around the x- (roll), the y- (pitch) and the z-axis(yaw). The basicentric axes are defined according to the orientation of thebody with respect to gravity (Fig. 1.8 after ISO 2631-1).

The vibrations should be measured at the contact area with the human body.The disturbance variables or quantity, for example the body-resonances orinteraction effects, between the human body and the moving surface arenot taken into account. The evaluation of vibration is defined by the speci-fication of the rms value of the acceleration a in m/s2 for translational andfor rotational vibrations in rad/s2, Eq. 1.7:

aw =

[1T

T∫0

a2w(t)dt

] 12

(1.7)

with

w = weighting factor for different conditions

a2w(t) = instantaneous frequency-weighted acceleration

T = integration time for running averaging

Fig. 1.8: The orientation ofthe basicentric axes to thegravitational field, specifiedin, e.g., ISO 2631-1 (1997);VDI 2057-2 (1987).


Vibration signals with more than one frequency component should be sub-divided into 1/3 octave steps. The acceleration is described by the currentcenter frequency fc. The measured vibrations are weighted for differentconditions, e.g., body-posture or measuring position of the vibrations, withdifferent frequency weightings W . Therefore the ith center frequency cor-responds to the principal frequency weighting factor Wi. – Weighting fac-tors are frequency dependent and they respond to filter functions whichare the inverted standardized perception threshold curves after ISO 2631-2 (Fig. 1.9). – The weighting factors given in Fig. A.1 and Tab. A.1 inAppendix A shall be used for a conversion of 1/3 octave band data. Theoverall weighted acceleration aw shall be determined in accordance with thefollowing equation (Eq. 1.8) or its digital equivalent in the time or frequencydomain:

aw =

[∑i

(Wi · ai)2] 1

2

(1.8)

with

Wi = frequency weighting factor for the ith center frequency of the

ith 1/3 octave band

ai = rms acceleration of the ith 1/3 octave band

If the vibration signal includes vibrational components in more than onedirection, the vibration total value aV of the weighted rms accelerationsdetermined from vibrations in orthogonal coordinate-systems, is calculatedas follows:

aV = (k2xa2

wx + k2ya2

wy + k2za2

wz)12 (1.9)

with

awx, awy, awz = weighted rms accelerations with respect to the orthogonal

axes x, y or z, respectively

k2x, k2

y, k2z = multiplying factors for special axes

The rms acceleration is not useful if the crest factor of a given transientvibration signal is high because the human body is more sensitive to changesin the vibration signal. Furthermore, the rms value does not exceedinglypoint out the peaks in a signal. Instead of the rms value the running rmsvalue aw(t0) (i), Eq. 1.10 is used with short durations τ if transient vibrations


occur:

aw(t0) =

[1τ

t0∫t0−τ

a2w(t)dt

] 12

(1.10)

or the Vibration Dose Value VDV (ii), sometimes called fourth-power vibra-tion dose, which is more sensitive for peak values, is used if high peak valuesoccur in the vibration signal (like shock conditions):

V DV =

[ T∫0

a4w(t)dt

] 14

(1.11)

The VDV is a method of assessing the cumulative effects (i.e. dose) ofvibrations. If the crest factor is low (i.e. less than 6.0), the estimated Vi-bration Dose Value (eVDV) is sometimes used to calculate the approximatevibration dose value from the rms of the frequency-weighted accelerations(arms) and the exposure time t in seconds:

eV DV = 1.4 · arms · t1/4 (1.12)

When more than one stimulus is presented the total VDV must be calculatedfrom the fourth root of the sum of the fourth powers of individual vibrationdose values:

V DVtotal =

[∑i

V DV 4i

] 14

(1.13)

Rotational vibration exposures should be assessed in terms of translationalvibration occurring over the principal contact area with the human body. Inappendix A the Tab. A.3 shows the root-mean-square accelerations whichproduce a vibration dose value of 15 m/s1.75. This value is a kind of upperlimit for human bodies and is specified in the BS 6841 (1987a) for sinusoidalexcitation in a frequency range from 0.5 to 80 Hz for durations from 1 s upto 8 h.

This section only deals with universal evaluation methods for the humanresponse to whole-body vibration until here. The following part handles thespecial evaluation methods for the perception and comfort sensation whichare specified in ISO 2631-1. The highest (rms) acceleration in one directionfor measured vibrations is the equivalent stimulus for the used signal. ”Fiftypercent of alert, fit persons can just detect a Wk weighted vibration witha peak magnitude of about 0.015 m/s2” (ISO 2631-1, 1997). There is alarge interindividual variation in the ability to perceive vibrations so that


the interquatile range of response may extend from about 0.01 m/s2 to0.02 m/s2. ISO 2631-2 specifies these predictions for the perception ofvibrations in buildings and defines standardized perception thresholds inx/y/z-directions in a frequency range from 1 to 80 Hz, Fig. 1.9.

1 1.6 2.5 4 6.3 10 16 25 40 63 1000.001

0.0031

0.01

0.031

0.1

0.316

1

Acc

eler

atio

n [m

/s2 ]

1 1.6 2.5 4 6.3 10 16 25 40 63 10060

70

80

90

100

110

120

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

x,y−axis base curve z−axis base curve combined−direction criteria curve

1 1.6 2.5 4 6.3 10 16 25 40 63 1000.001

0.0031

0.01

0.031

0.1

0.316

1

Acc

eler

atio

n [m

/s2 ]

1 1.6 2.5 4 6.3 10 16 25 40 63 10060

70

80

90

100

110

120

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

x,y−axis base curve z−axis base curve combined−direction criteria curve

Fig. 1.9: Building vibration x/y- and z-axis base curve (perception thresholdsdefined in ISO 2631-2 (1989); VDI 2057-2 (1987)) for acceleration levels on theleft y scale and for accelerations on the right y scale. In addition the buildingvibration combined direction (x/y/z-axis) acceleration curve which should be usedwhen the direction of the human occupants varies or is unknown with respect tothe most interfering or annoying vibrations.

The human body has the same sensitivity for vibrations in x- and y-directionsafter existing standards like ISO 2631-1 ( Fig. 1.9). The most sensitive fre-quency range for horizontal vibrations is from 0.1 to 2 Hz (a = 0.0036 m/s2)and increases with increasing frequency with 6 dB/octave This slope corre-sponds to a proportionality between the perception and a constant velocity.In the vertical direction the human body is more sensitive than for hori-zontal vibrations in the frequency range from 3 Hz upwards. Between 4and 8 Hz the human body has the highest sensitivity for vertical vibrations.The base curve increases or decreases for higher or lower frequencies with6 dB/octave, respectively. For vibrations where the direction of the humanoccupants varies or is unknown a combined base curve from the horizon-


1 1.6 2.5 4 6.3 10 16 25 40 63 1000.001

0.0031

0.01

0.031

0.1

0.316

1

Acc

eler

atio

n [m

/s2 ]

1 1.6 2.5 4 6.3 10 16 25 40 63 10060

70

80

90

100

110

120

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

1 1.4

2

4

8

16

32

60

90

curve = 128

Fig. 1.10: Combined-direction criteria curves (this represents a combination forthe worst case for all three axes). Curves are shown corresponding to the variousmultiplying factors given in A.4 after ISO 2631-2 (1989).

tal and vertical curve should be used with respect to the most interferingor annoying vibration (Fig. 1.9). ”Those combined standard base curvescould be used for preliminary investigations to decide whether further in-vestigation is necessary” (ISO 2631-2, 1989). Moreover, state-to-the-artinformation on results of surveys on the magnitudes of building vibrationfound to be satisfactory with respect to human response is presented inFig. 1.10 (and Tab. A.4 in Appendix C). The curves in Fig. 1.10 are basedon basic weighting curves and perception thresholds for no specific vibrationdirection. Sometimes these curves are called equivalent-comfort contoursand are based on the perception threshold which is multiplied with constantfactors.

It is just briefly noted that in some countries the z- and x/y- base curvesare used rather than the provisional combined weighting curve (e.g., inVDI 2057-2, 1987). These curves are summarized in Fig A.2 (in Ap-pendix A). In addition, a second difference between the ISO 2631 andthe VDI 2057 is the application of the parameter ’vibration force K’ (inGerman ”Schwingungsstarke”) instead of frequency weighted accelerationsaw for evaluation of vibration signals. The ’vibration force K’ depends on


the frequency, as well. Withal the frequency weighted acceleration awz cor-responds to a vibration force KZ, whereas KX and KY indicate awx andawy, respectively. The relation between the frequency weighted accelerationafter ISO 2631-1 and the VDI 2057-2 is given by Eq. 1.15:

KX = 28 · awx

m/s2

KY = 28 · awy

m/s2

KZ = 20 · awz

m/s2(1.14)

The K values specified in VDI 2057-2 are based on the 1/3 octave spectrumof a vibration signal with a frequency weighting of:

1 Hz ≤ f ≤ 2 Hz : KX = 28 · ax

m/s2

KY = 28 · ay

m/s2

2 Hz ≤ f ≤ 80 Hz : KX = 56 · ax

m/s2· Hz

f

KY = 56 · ay

m/s2· Hz

f

1 Hz ≤ f ≤ 4 Hz : Kz = 20 · az

m/s2·√

f/Hz

4 Hz ≤ f ≤ 8 Hz : KZ = 20 · az

m/s2

8 Hz ≤ f ≤ 80 Hz : KZ = 160 · az

m/s2· Hz

f(1.15)

The (center) frequency fc and the rms value a should be used in Eq. 1.16.If the direction of the vibration signal, which is transmitted to the humanbody, is unknown a combined base curve from the horizontal and verticalcurve can be used (Eq. 1.16). The calculated vibration parameter is calledKB-value:

1 Hz ≤ f ≤ 2 Hz : KB = 28 · a

m/s2


2 Hz ≤ f ≤ 8 Hz : KB = 33.5 · a

m/s24√

Hz/f

8 Hz ≤ f ≤ 80 Hz : KB = 160 · az

m/s2· Hz

f(1.16)

In reference to comfort the acceptable values of vibration magnitude de-pends on many factors which vary with each application like the passengerexpectations with regards to trip duration and the type of activities pas-sengers expect to accomplish. Therefore, a special limit is not defined inISO 2631. The values approximate indications of likely reactions to variousmagnitudes of overall vibration total values in public transport6 (Tab. 1.2).

Tab. 1.2: Approximate magnitudes of overall (rms) vibration total values (aV

in m/s2) in public transport. Scale of vibratory (dis-)comfort adapted from ISO2631-1 (1997).

weighted acceleration aV [m/s2] (Dis-) comfort categories

< 0.315 not uncomfortable

0.315 to 0.63 a little uncomfortable

0.5 to 1 fairly uncomfortable

0.8 to 1.6 uncomfortable

1.25 to 2.5 very uncomfortable

> 2 extremely uncomfortable

Guidelines for the effect of whole-body vibration on health is provided in ISO2631-1, as well as for vibration transmitted by the seat. The assessment isbased on the largest measured translational component of the frequencyweighted acceleration. This value should be compared with the health cau-tion zone in Fig. 1.11 specified in ISO 2631-1. Assuming responses arerelated to energy, two different daily energy-equivalent vibration are indi-cated in different studies - the dashed (Eq. 1.17) and dotted (Eq. 1.18) line,

6Given in ISO 2631-1 (1997).


respectively:

aw,e =

[∑a2

wi · Ti∑Ti

] 12

(1.17)

aw,e =

[∑a4

wi · Ti∑Ti

] 14

(1.18)

with

aw,e = equivalent vibration magnitude

awi = vibration magnitude for exposure duration Ti

The lower and upper dotted lines correspond to vibration dose values of 8.5and 17, respectively.

Fig. 1.11: Health guidance caution zones (adapted from the ISO 2631-2, 1989).


1.2 Psychophysics and sensoric physiology

In this PhD thesis, psychophysical experiments on the perception of whole-body vibrations are conducted in Chapter 3 to 5. Therefore, a short overviewabout basics of psychophysics and sensoric physiology is given in this section.Additionally, psychophysical measuring methods, which are used for thefollowing experiments, are briefed, as well.

1.2.1 Sensation threshold

In the 19th century the knowledge about the functioning of the sense or-gans was very limited. The sensoric physiology was started to investigatethe relation between the subjective sensation (perception) and the objectivestimulus. The goal was to find objective parameters which can describe andforecast the subjective perception of a sensory stimulus. At the beginningof these investigations is the intensity-dimension of the sensation and theclassification which is called psychophysics ( described in, e.g., Zwicker &Fastl, 1999; Schmidt & Thews, 1995). The central concept of the psy-chophysics is to determine the sensoric (intensity-) thresholds, which can beseparated into two groups: 1) absolute threshold: smallest detectable inten-sity or magnitude of a special stimulus that produce a subjective sensation.2) difference threshold or just noticeable differences. Those differences arethe relative difference thresholds in a stimulus magnitude. The relation (rel-ative difference threshold ∆ϕ/ϕ) between the absolute detected differencesof the magnitude (∆ϕ) and the magnitude (ϕ) of a stimulus is a constantratio (as proposed by E.H. Weber). This law is stated by Eq. 1.19:

∆ϕ

ϕ= c or ∆ϕ = c · ϕ (1.19)

The boundary of the application of the Weber-law is around the absolutethreshold of a special stimulus because the quotient ∆ϕ/ϕ is not constant.The Weber-law does not generally hold at the absolute thresholds, i.e. theconstant c rises. For example, the Weber-quotient does not deliver a con-stant ratio until the stimuli are 40 dB above the absolute threshold in psy-choacoustics (Fig.1.12). Probably the reason is that the (sensation) percep-tion is superposed by stochastic processes, called internal noise. For stimulinear the thresholds the Weber-law must be modified by a constant n whichtakes into account the internal noise, Eq. 1.20:

∆ϕ

ϕ + n= c or ∆ϕ = c · (ϕ + n) (1.20)

1.2. Psychophysics and sensoric physiology 29

The constant n represents the internal noise and the spontaneous activityof the nerve fibers, respectively. If ϕ increases, the influence of n is notimportant, but if ϕ decreases n gets more and more important.

Absolute threshold The absolute threshold can be explained with such aconstant: the absolute threshold is the stimulus which is significantly higherthan the stimulus caused by spontaneous activity. This psychophysical the-

Fig. 1.12: Weber-quotient and Weber-law:1) Relation between theoutput stimuli magnitude(ϕ) and the stimuliincrement (∆ϕ) (JustNoticeable Difference’JND’ in the forcesense: ∆ϕ

ϕ= const.).

2) Dependence of theWeber-quotient (∆ϕ/ϕ)from the output stimulusmagnitude ,e.g., foracoustic stimuli. 3)Revision of the Weber-quotient with a constantn for close-by thresholdstimuli (adapted fromSchmidt & Thews, 1995).


ory is applicable in the ’sensory decision theory’ or ’signal detection theory’(SDT). Furthermore, the sensory signal detection theory assumes that thedetermination of thresholds does not only depend on the sensoric selectiv-ity but also regards the subjective decision processes. That means, that astimulus with a fixed neural excitation around the absolute threshold is notalways distinguishable between a perception (sensation) of a stimulus anda spontaneous activity of the nerve fiber. This problem does not exist formagnitudes above the absolute threshold.

Usually, biological systems (like the ear or the sense of touch) are variablesin the reaction of a fixed stimulus, so that, e.g., stimuli magnitudes belowthe absolute threshold are detectable, as well. It is customary in the psy-chophysics to define the absolute threshold as the level (for example, soundpressure level or acceleration level) at which the stimulus (sound or vibra-tion) is detected with a probability of 50% (Gelfand, 1998). That means50% of all presented stimuli with a fixed parameter, like the level, the stim-ulus is detected and in 50% it is not. Therefore the absolute threshold isequivalent with a correct response-probability of P (L) = 50% of the psycho-metric function. Therefore, psychophysical measuring methods with severalrepetitions such as the like method of constant stimuli, alternative forcechoice (AFC) methods, method of limits, etc. are often used to measurethe absolute threshold. With some of these measuring methods it is possibleto measure not only absolute thresholds but also difference thresholds andmany other psychophysical parameter (Chapter 1.2.2).

Psychometric function The psychometric function characterizes the sub-jective response behavior of an individual (subject) or group of individuals(mean of subjects) depending on the force of a given stimulus parameterin a psychophysical experiment. For example, the given correct response-probability P (L) to detect a stimulus is printed as a function of the level,Fig 1.13. This means that the psychometric function shows the probability(percentage) of correct responses for different stimulus levels (or magnitudeϕ as in Fig 1.13). Therefore in such measurements a lot of stimuli withdifferent levels must be presented to a subject with some stimulus repeti-tions. The interpolated function of the measured data is called psychometricfunction7 and is often well fitted as a cumulated shape of the normal dis-tribution (integral of the Gauss distribution). Functions like this are oftencalled ’ogive’. If the stimulus level is printed as a function of the relative (de-termined) incidence in terms of probability values (z-values) then the valuesare ordered in a straight line (Fig. 1.13), as well. This fact is of theoretical

7looks often like a S


interest since it shows that a statistical process is qualified by fluctuationsof the sensation. The probability P (L) (detected stimulus) results from arelative occurrence of correct responses at, e.g., a fixed stimulus level L.

Fig. 1.13: Psychometric function: 1) The relative incidence ordered by the stim-ulus magnitude. 2) The s-shapes of the psychometric function corresponds oftento the integral of the Gauss distribution curve (ogive). The psychometric func-tion becomes a straight line, if the relative incidence is transformed into z-values(adapted from Schmidt & Thews, 1995).

Many time-consuming measurements at many different levels must be con-ducted to get the whole shape of a psychometric function, which describesthe dependence of, i.e., the perception of vibration on the presented ac-celeration level (Chapter 3.3). A second possibility is to measure somepoints, especially around the expected absolute threshold, and to make aconformance (’fit’) of the whole shape by using a model-function or cost-function. Some of the presented stimuli with varied objective parameter(here the level) are detectable for the subjects and some are not, there-fore this measurement can be understood as a Bernoulli-experiment witha correct response-probability P (L). It is possible to fit the whole shapeof the psychometric function with just some measured points by using acost-function (sometimes called model-function), as mentioned before. Inthis study a maximum likelihood fit is used to fit the psychometric functionto the measured data. For example, in Chapter 3.3 the method of constantstimuli is used with three (A = 3) given intervals for each trial for the de-termination of the psychometric function. This means that three intervalsare presented in one trial, whereas just one interval includes a stimulus withvarying level and the other two intervals comprise no signal. The task ofthe subjects is to say if they feel a vibration and then to mark that inter-


val, in which they felt the vibration. The number of intervals A per trialstates the probability P (L) to guess the correct interval – the probability toguess the correct interval is P (L) = (1/A)·100%. – Therefore, the followingmodified logistical model-function for the maximum likelihood fit is used inChapter 3.3, Eq.1.22:

y =1A·(

1 + (A− 1)

1 + eL50−L

s

)(1.21)

s =A− 1

4 ·A · slope

with free parameters

L50 = Level of 50% correct detected stimuli [dB]

slope = Slope of the psychometric function at L50 [%/dB]

The fitted psychometric function can be characterized or described by thetwo free parameters of the model-function, respectively: the level of the50% point of correctly detected stimuli (L50) and the slope parameter sof the function at this point. The level L50 has the highest slope and isthe central point of the logistical function. That means that L50 is notalways the point with 50% correct response-probability (P (L) = 50%) butthe probability between P (L) = 100% (all presented stimuli are detected)and the probability to detect by chance.

The exact real intraindividual errors are not possible to determine for suchmeasurements because just a random (spot) sample for all presented stimulilevels is used. The errors, which are given by the used measuring method, arenot really known either. But a minimal error estimation can be calculatedfor the measured data because a probability P (L) for the variance of aBernoulli-experiment is given by Eq. 1.22:

τ2P = P (L) · (1− P (L)) (1.22)

The number of correctly detected stimuli R is binominal (Bernoulli) dis-tributed for a given random (spot) sample N . A good approximation ofthe minimal error estimation for the Bernoulli distribution can be calculatedwith the relative occurrence of correct responses R/N by Eq. 1.23:

τP =1N·√

P · (1− P ) (1.23)


These errors are just the minimal error estimations (lower boundary), whereasthe real errors are slightly larger than the calculated (shown) errorbars.

1.2.2 Psychophysical measuring methods

The psychophysics deals with how humans (sometimes animals, as well)perceive the physical stimuli impinging upon their sense organs like the earor the skin (Gelfand, 1998). Therefore, the subject actually perceive (sen-sitivity) and the manner in which they respond (response proclivity) mustbe distinguished. Usually in psychophysics the experimenters are interestedin sensory capability (sensitivity). ”The response proclivity reflects not onlythe subject‘s sensitivity, but also the biases and criteria that affect how theyrespond” (Gelfand, 1998). However, measured thresholds and other psy-chophysical results are therefore more or less biased by the used measuringmethod and the response behavior of the subjects. The primary goal isto find out the relationships between the presented stimulus and how thesubjects perceive this stimulus or objective parameters (like the level) ofthe stimulus which are suited to describe the subjective perception. Fur-thermore the objectives are to minimize the bias of the method for speciallyselected stimuli and experiments and to get constant and repeatable results.In the last four decades numerous investigations were made in psychoacous-tics to clarify the influence of some measuring parameters on experimentswith audible stimuli.

In this subsection the measuring methods, which are used for the psy-chophysical experiments in Chapters 3 to 5, are presented and the advan-tages and disadvantages of those methods are briefly discussed. Most ofthe used methods are reliable techniques which are developed and are oftenused in psychoacoustics. A good overview and a discussion of many detailsfor psychophysical experiments is given in, e.g., Gelfand (1998).

Method of constant stimuli ”The method of constant stimuli involvesthe presentation of various stimulus levels to the subject in random or-der” (Gelfand, 1998). Therefore, this method is a nonsequential procedure.Which means that the presented stimuli with varying levels (or other signalparameters) are not presented in ascending or in descending order. The taskof the subjects is to indicate whether the stimulus presentation has been per-ceived during each trial. The range of the varying parameter, like the level,is fixed, which based upon pilot experiments or previous experience, for allsubjects (Gelfand, 1998). For example, for psychometric function measure-ments an equal number of stimuli are presented at each level because the


aim is to determine the probability (P (L)) to detect a stimulus with a fixedlevel, as mentioned before. The step-size of the variation of the parametermust be fixed, as well. The difficulty is to set the step-size because too largestep-sizes may place the highest indetectable presentation at a level with a10% probability of correct response, and the lowest detectable presentationat a level with a 90% probability of correct response. For such measureddata it is difficult or impossible to fit the whole shape of the psychometricfunction. Therefore some of the presented levels must be (i) around the ex-pected absolute threshold, (ii) below – and not detectable for all subjects –and (iii) some must be above the estimated absolute threshold, respectively.

The advantage of the method of constant stimuli, as opposed to the meth-ods of limits and adjustments, is the higher precision of the measure-ment. However, the method of constant stimuli is also applicable for variousother experiments above the absolute threshold such as difference thresholdmeasurements or the equal-loudness level contour measurements. In suchmeasurements the relation between a subjective sensation (perception) andan objective signal parameter is investigated, as well. For example, for mea-suring the equal-loudness level contours the subjects have to compare twodifferent stimuli with, e.g., different frequencies and different levels. Thetask for the subjects is to say which of the perceived stimuli is, e.g., ’louder’.The point of subjective equality (PSE) is that point at which the two differ-ent stimuli are subjectively equal in their perception. But the method hassome disadvantages, as well. It is very inefficient because a very large num-ber of trials are needed to obtain results and this is very time-consuming.Another disadvantage of the method of constant stimuli is that the pre-sented level range for the determination of, e.g., the equal-loudness levelcontours has a considerable influence on the measured data because in therun-up to the measurements it is not known where the PSE of the subjects(individuals) is ranged. This influence or bias is called the ’range effect’and is described for the equal-loudness level contours by Gabriel (1996)and Reckhardt et al. (1997). These range effects could have an influence ofabout 15 dB on the equal-loudness level contours by using the same methodbut with different presented level ranges (Reckhardt et al., 1997).

Adaptive alternative force choice (AFC) method In Chapter 3 anadaptive A - AFC x up - y down measuring method (Levitt, 1971) is used forthe determination of the perception threshold of vertical sinusoidal whole-body vibrations (Chapter 3.5) and the measurements of the just noticeabledifferences in level and in frequency (Chapter 3.6). The advantages of anadaptive procedure is that the level at which a particular stimulus is pre-sented to a subject depends on the response of the subject to the previous


stimuli (e.g., described in Levitt, 1971). The adaptive procedure can becombined with some other measuring methods like AFC-methods (Levitt,1971). Additionally, an adaptive AFC measuring method is very fast be-cause just one position (probability P(L)) on the psychometric function ismeasured. Moreover, many studies in psychoacoustics report about the highrepeatability of such methods.

In an A - AFC method A intervals are presented to the subjects duringone trial, whereas A − 1 of these intervals include the reference stimuliand one interval implies the test stimulus. The task of the subjects isto mark that interval which includes the test stimulus. For example, for anabsolute threshold measurement the reference stimuli includes no detectablesignals and the test stimulus is a signal with a fixed frequency and with avariable level (for example, in Chapter 3.5). Therefore the subjects haveto mark that interval in which they are able to detect (hear or perceive) astimulus . If they cannot detect a stimulus they must choose one interval(alternative force choice). The option x up - y down characterizes thechanging (adapting) procedure of the varying stimulus parameter. Thatmeans that the parameter range, which is presented to the subjects, is notfixed but would be influenced by the response behavior of the subjects,as mentioned before. ”The up-down strategy tends to converge on thatstimulus level at which the probability of a down response sequence equalsthe probability of an up responses sequence2 (Levitt, 1971). For example,for a 1 up - 2 down strategy the probability of obtaining an up sequence isP (X)[1−P (X)]+[1−P (X)] whereas P (X) is the probability of a positiveresponse at the stimulus level. This means that after 2 correctly detectedtest stimuli the parameter decreases (down sequence) which is characterizedby [P (X)]2. The level increases (up sequences) if (i) 1 test stimulus is notdetected (or a wrong interval is marked) [1−P (X)] or (ii) if the test stimulusis correctly detected one time (P (X)) and the next stimulus is not detected([1−P (X)] ·P (X)) thereafter. Therefore the strategy converges on a fixedcorrectly detected probability. For example, Eq. 1.24:

2-down sequence = 1-up sequence[P (X)

]2 = P (X) ·[1− P (X)] +

[1− P (X)

][P (X)

]2 = P (X)−[P (X)

]2 + 1− P (X)[P (X)

]2 = 0.5

P (X) = 2√

0.5 = 0.707 (1.24)

With the variation of the up-down sequences (procedure) different positions(probability P(X)) on the psychometric function could be measured. Some


Tab. 1.3: ”Response groupings for transformed up-down strategies. Entry 1corresponds to the simple up-down procedure” (adapted from Levitt, 1971).

Response sequence Response groupings

up

group

down

group

Probability of a se-quence from downgroup = P (down])

Probability of positiveresponse at conver-gence

1 1 P (X) P (X) = 0.5

1 2 [P (X)]2 P (X) = 0.707

2 1 [1− P (X)] + P (X) P (X) = 0.293

1 3 [P (X)]3 P (X) = 0.794

1 4 [P (X)]4 P (X) = 0.841

common up-down sequences, which are often used for psychophysical ex-periments, are summarized in Tab. 1.3 which is adapted from Levitt (1971).

’Adaptive’ means that the initial step-size of the test stimulus parameter(e.g., the level as in Chapter 3) is halved after each upper reversal to a fixedfinal step-size. The advantage of the adaptive option is that the parameterrange of the starting condition can be very large. Additionally, no priorknowledge of where the threshold (or the PSE) is located is required. Usuallya large initial step-size is used and then the step-size becomes smaller asthe threshold approach. Therefore a lot of stimuli are presented around theindividual‘s threshold. The method stops after a fixed number of reversalswith the (smallest) final step-size. The individual result (e.g., the perceptionthreshold) is in this study the median of the values taken from the reversalswith the final step-size. The order of the test and reference stimuli should berandomized to prohibit order effects. A schematic overview of an adaptiveAFC 1 up - 2 down measuring method is given in Fig 1.14.

Interleaved measuring method In Chapter 3.7 an adaptive 2 - AFC in-terleaved 1 up - 1 down method (Buus et al., 1997) is used for the measure-ment of the equal-vibration level contours (Chapter 3.7). The option ’in-terleaved’ means that several measurements with different test stimuli (in


-34

-32

-30

-28

-26

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

No. of presentation

Att

enu

atio

n [

dB

]

76

78

80

82

84

86

88

90

92

94

96

98

100

102

104

106

108

110

ending step-size

Threshold:median value of the reversals

with the ending step-size

initial step-size

Fig. 1.14: Schematic overview of an adaptive AFC 1 up - 2 down measuringmethod. After two correctly detected test stimuli the level of the test-signaldecreases and if the test stimulus is not detected the level increases. The resultis the median value of the reversals with the final step-size.

Chapter 3.7 sinusoidal vibration signals with different test-frequencies) anddifferent starting conditions for the variable stimulus parameter (e.g., theinitial level of the test vibrations) are measured simultaneously in one mea-suring procedure, whereas each test stimulus is compared to the same refer-ence stimulus. This measuring method was presented by Buus et al. (1997)for loudness experiments and minimizes the influence of several measuringparameters on the results. A study of Reckhardt et al. (1998) shows thatthis measuring method minimizes the range effect on equal-loudness levelcontours therefore this method is used for the determination of the equal-vibration level contours (Chapter 3.7). The advantages of this method isthat the subjects do not know which test stimulus with which variable levelwill be presented in the next trial (presentation). Fig. 1.15 gives a schematicoverview of this method with four different test stimuli which are measuredin one method trial simultaneously. The order of the test and the referencestimulus, as well as the order of the different test stimuli are randomized toprohibit order effects. The starting conditions of the test-stimuli should bevery high and the order of the starting conditions should be randomized toprohibit range effects, as well. With the adaptive 2 - AFC 1 up - 1 downmethod the point of subjective equality (PSE, P (L) = 50%) is determined.


1 2 3 4 5 6 7 8

0.031

0.056

0.1

0.178

0.316

0.56

Acc

eler

atio

n [m

/s2 ]

1 2 3 4 5 6 7 8

90

95

100

105

110

115

Nr. of Presentation

Acc

eler

atio

n le

vel [

dB]

Test−Frequency 1 Test−Frequency 2 Test−Frequency 3 Test−Frequency 4

Fig. 1.15: Illustrationof an interleavedmeasuring method.Typical data for thismeasuring methodwith four differenttest stimuli (e.g., test-frequencies) which areused in one measuringprocedure.

Psychophysical connections

The psychophysical laws and relationships link the objective parameter of astimulus (for example, the magnitude) and the subjective sensation. Twofamous competing descriptions exist in the literature: the Fechner- and theStevens-law. The Fechner-law is often called Weber-Fechner-law because itis based on the description from E. H. Weber and is the most importantlaw in psychophysics. The Weber-Fechner-law defines that a logarithmicallyincreasing stimulus magnitude ϕ yields a linear increase of the subjectivesensation (perception) Ψ (Eq. 1.25).

Ψ = k · log10(ϕ

ϕo) with k = const. (1.25)

The Weber-Fechner-law needs some basic requirements: the detection thresh-olds are based on the same detection level (DL) of the increase of the sen-sation level (SL), which means that the same magnitude increment deliversthe same perceptual increase for low and high magnitudes. This relation wasfound for some sensory systems, like the human ear. The decibel-scale is awell known example for the Fechner relation in psychoacoustics. However,the just noticeable differences in level (JNDL) are about 1 dB. This findingis valid for broadband signals over a large level range but for narrow bandsignals (or pure tones) the JNDLs are higher than 1 dB for low magnitudes(around the absolute threshold) and decrease for higher magnitudes (e.g.,Zwicker & Fastl, 1999). This deviation is often called ’near miss to Weber‘slaw’ in the literature and originates from a special excitation of the basilarmembrane by sinusoidal signals (pure tones).


The other description between the objective stimulus magnitude and theperception is called the ’Stevens potential-law’. After this law the rela-tion can be described by a potential function and a variable potential α(EQ. 1.26). The basic principle of such a measurement is to determine aproportional correlation between the objective and subjective data (see, forexample, Kießling et al., 1997).

Ψ = k · (ϕ− ϕo)α with k = const. (1.26)

The Fechner relation describes the noticeable differences of stimuli ratherthan the subjective perceptual force. As opposed to this the Stevens-lawpoints out that the perceptual force should be valued directly instead of theFechner-law. The Fechner- and Stevens-law need different scales for thedescription of the perceptual magnitude. For example, the Stevens-law usesa direct scaling of the perceptual magnitude like twice or half of a referencemagnitude. This scale is called a ’rational-scale’. In comparison, Fechneruses an indirect scaling method from the detection levels which just possesthe rank of a ’ordinal-scale’. A good example for the Weber-Fechner-lawand the Stevens-law is the determination of the psychoacoustic parameterloudness N . The loudness describes the perceived intensity (magnitude)of noise. The subjective loudness N depends on the presented level ofthe stimulus in psychoacoustics. There are different methods of subjectiveloudness scaling (ratio and categorical). One way to determine the influenceis to estimate the loudness with a ratio-scale by subjects which was proposedby S. S. Stevens. The unit of this scale is [sone] and 1 sone is defined asthe loudness of a 1 kHz pure tone of 40 dB SPL (Eq. 1.27).

N =

(I

I0

)α

(1.27)

I is the magnitude (intensity) of the stimulus and I0 is the magnitude of areference stimulus at 1 kHz with a level of 40 dB which corresponds to aloudness of N = 1 sone, as mentioned before. The exponent α is 0.3, if alarge number of subjects is used. A pure tone with 1 kHz of 2 sone has aloudness which is subjective twice as strong as the 1 sone tone. This signalhas a level of 50 dB SPL because an increase by 10 dB doubles the loudnessabove 40 dB SPL for a 1 kHz tone8. This reflects the fact that the relationbetween the ratio scaled loudness and the sound pressure is a power law.The Stevens potential-law (1.27) is reached, if the estimated numbers ofthe loudness are figured as a function of the presented level.

8An increase of 10 dB corresponds to an increase of the intensity of a factor 10 and100.3 = 2.


Another way to investigate the subjective loudness sensation (perception) isto use an indirect scaling method with categorical scales (like the ’WurzburgerHorfeldskalierung’ according to Heller, 1985, which uses 50 different cate-gories or the ’Oldenburger Horflachenskalierung’ according to Hohmann andKollmeier, 1995, which uses 11 different categories9). The relation betweenthe loudness in categorical units and the level of the test stimulus is astraight line. This finding obtains just in the middle level range. Whichmeans that the perceived subjective loudness N increases in proportion tothe logarithm of the magnitude I. Differences of the logarithm of the loud-ness N in sone just occur at very low and very high levels (e.g., diagrammedin Kießling et al., 1997). Therefore the sone scale can be described withthe Weber-Fechner law, as well, if the logarithm of the estimated numbersis used instead of the numbers themselves. However, the relation betweenthe objective parameter and the subjective perception of a stimulus is usu-ally describable by the Weber-Fechner-law in psychophysics, as mentionedbefore. Some more examples and more details can be found in many text-books about psychophysics and psychoacoustics (e.g., Kießling et al., 1997;Zwicker & Fastl, 1999).

Integrated sensoric physiology

The modern sensoic physiology often investigates integrating problems, whichform the background of physiological and perceptual processes. With suchan integrated sensoric physiology it is possible to control experimental re-sults of the (objective) sensoric physiology like the differences between theabsolute sensation thresholds and the neuronal thresholds. For example,the psychometric functions are determined on two different positions on thehand: finger tip and palm. The hypothesis (see above) for this experiment is,that the threshold is exceeded if the excitation of the sense is distinguishablefrom the internal noise n (spontaneous activity) of the nerve fibers. Thishypothesis can be proved in the limits of the integrated sensoric physiology(Fig. 1.16, which is based on a figure in Schmidt & Thews, 1995). Theogive-shape of the psychometric function shows that perception is a kind ofstatistical process at low magnitudes below and around the absolute thresh-old. The consequential question is: Is the spontaneous activity a functionof the variability of the nerve fibers or a transmission problem in the centralnervous system (CNS) ? It is possible to measure the derivative of selectednerve fibers ,e.g., RA-sensors10 (grey line in Fig. 1.16) with methods of themicro-neurography. The psychometric functions for the nerve fiber and the

9This scaling method is qualified for measurements with persons with impaired hearing.10RA-sensors: ’rapidly adapting’ sensors (Chapter 1.2.3).


measured threshold show no significant differences for the finger tip. Thispoints out, that a part of the variation can be ascribed to the nerve ac-tivity. But for the palm it is totally different. The threshold curve for theRA-sensors in the palm looks like the curve of the sensors in the finger tipbut the psychometric functions of the subjects are shifted in the magnituderange (shift to the right side, which means to higher magnitudes). Thisis maybe an indicator of an additional information loss in the CNS or an

Fig. 1.16: Absolute thresh-olds of rapidly adaptingreceptors (RA-receptors) inthe skin and the appendantpsychometric function. A)Psychophsycially deter-mined absolute perceptionthreshold and simultaneouslymeasured derivative of theskin afferences in a micro-neurographical experiment.B) Innervation density of theRA-receptors at different po-sitions on the palm (adaptedfrom Schmidt & Thews,1995).


Tab. 1.4: Resonance frequencies fR of the human body with an impairment ofhealth (Martin, 1984).

Part of the body Frequency range [Hz]

viscera and venter 3main resonance of a standing man 4 to 6resonance of the pelvis 10 to 12head 20eyes 40 to 100

addition of spontaneous activity in the CNS. This means that the sensationlevel (perception threshold) in a sensoric system does not only depend onthe sensitivity of the sensors but also on the transmission reliability in theCNS and in the special nerve fiber, respectively.

1.2.3 Physiology of the skin (sense of touch)

The somato-visceral sensoric system has three main prediction-inputs: fromthe skin, the inner organs and the motion system. The psychophysicalanalysis of the skin (sense of touch) characterizes the qualities: pressure,skin contact and vibration as well as the perception thresholds, positionsof contact and the dependence of the subjective intensity sensation of thestimuli force. The force of contact is measurable with contact hairs aftervon Frey: on the hand, a force of F = 10−5 N and an amplitude of 1 µmis detectable at a frequency of f = 200 Hz, respectively.

The human body does not have receptors (sensors) just for the percep-tion of vibration. Therefore, the perception of vibration (whole-body orhand-arm transmitted) must be a concomitant of a particular excitationsample of the sensor of touch. This is influenced by the transient stimula-tion of all innervated mechano-receptors (Schmidt & Thews, 1995). Themechano-receptors are in the skin or in the muscle spindles for deep lyingvibration-receptors like the Pacinian corpuscles. The task of the sensors isto transmit the received stimulus to the CNS. The muscle spindles are alsoresponsible for the detection of position conditions and time-dependent po-sition changes of the human body. The translation of the sensations takesplace via afferent nerve fibers which have diameters of approx. 5 to 12 µmand line velocities of 30 to 70 m/s. The absolute threshold of perception isnarrowly coupled with the frequency of the vibration. In addition, the inner-vation of the skin is influenced by different factors like thickness of the skin,surrounding cellular tissue (fat, etc.) and the density of the receptors (e.g.,


described in Schmidt & Thews, 1995; Iggo, 1973). The body temperaturehas an influence on the thresholds, as well. For example, a temperature dif-ference of 4◦C from the normal skin temperature of 36◦C of human bodyis leading to an increase of the absolute perception threshold (Weitz, 1941).Additionally, the biomechanical behavior of the human body influences theperception of whole-body vibrations through body resonances. These reso-nances are in a range from about some Hz up to 100 Hz. An overview aboutresonance of the human body is given in Tab. 1.4 in respect to impairmentsof health. Additionally, the body resonances depend on the direction andthe transmittance of vibrations into the human body. A simple theoreticalmodel of the resonance frequencies fR of the human body is given Fig. 1.17.Numerous investigations were conducted in the field of occupational safetyand health on the basis of the knowledge of health impairment caused bybody resonance.

Four different types of mechano-receptors with group II Aβ-afferent nervefibers are found in the hairless skin of mammals: SA-I - (type 1), SA-II -(type 2), RA- and PC-sensors which can be characterized by their responsebehavior of stimuli excitability and their morphology:

Fig. 1.17: Simple theoreti-cal model of the resonancefrequencies fR of the humanbody.


• SA-I and II are ’slowly adapting’ sensors. These sensors produce actionpotentials in afferent fibers if a long stimulus occurs, especially fromthe weight of the body on the feet during a walk.

• RA signs the ’rapidly adapting’ sensors, which only response on movingskin-stimulus.

• PCs are the ’Pacinian corpuscles’ which are very rapidly adapting sen-sors.

In the hairless skin Merkel‘s discs are SA-I-, Ruffini‘s endings are SA-II- andMeissner‘s corpuscles are RA-receptors. Hair-follicles act like RA-sensorsin the skin with hairs instead of Meissner‘s corpuscles. Fig.1.18 gives anoverview about the hairless skin (based on a figure in Griffin, 1990).

The classical psychophysical qualities pressure, contact area and vibrationcan be attached to the slowly (type I and II), rapidly adapting sensors andPacinian-corpuscles. A mechanical ramp stimulus is used to characterizethe four different sensor-types (Fig. 1.19). The time domain of the stim-ulus shows parts with constant skin deformation S (proportional to theintensity), constant velocity v (dS/dt) and with constant acceleration a(d2S/dt2). Fig. 1.19 indicates that SA-I/II-sensors give responses (firing-and spiking-rate) for constant deformations S (pressure, intensity), RA-sensors for velocity v and PC-sensors for the acceleration a. SA-I sensors

Fig. 1.18: ”Cross-section of skin showing the dermis and epidermis” (adaptedfrom Griffin, 1990).


are specialized for stimuli which are orthogonal to the skin surface and SA-II-sensors for strain-stimuli. Therefore the four different sensors are specializedfor deformation (intensity), velocity and acceleration.

The reaction time of PC-sensors are in a range of 0, 02 to 0.025 s and less.This corresponds to frequencies f of 40 to 50 Hz and higher. The Meissnercorpuscles – RA-sensors – are able to detect stimuli in a frequency range of 5to 50 Hz and SA-sensors are specialized for detecting low frequency stimuli:SA-I-sensors < 5 Hz and SA-II-sensors from 8 to 16 Hz after Lofvenberg &Johansson (1984).

The cutan mechano-receptors are specialized for different stimuli qualities(S, v and a) as mentioned before. The innervation density of the mechano-sensitive afferent nerve fibers in the skin is responsible for the topologicalstrictness of the sense of touch. The skin area, which is innervated by astimulus with a defined intensity, is called the ’receptive array’. For example,only one afferent nerve fiber is joint with two to ten vicinal Meissner‘scorpuscles in a human finger. In contrast, 30 hair-follicles are innervated byjust one nerve fiber. In the human hand the receptive arrays for RA- andSA-I-afferent have a size of about 12 mm2. These arrays are the smallestin the human body. The receptive arrays for the SA-II- and PC-afferent areabout a factor ten times higher. However, the size of the receptive arrays isnot important for topological resolution but rather the innervation-densityof afferent fibers per cm2 in the skin. In some parts of the human handthe topological resolution is highly correlated with the density of SA-I- andRA-afferent but not of SA-II- and PC-sensors.

SA-I

SA-II

RA

PC

Merkel’sDisk

Ruffini’sending

Meissner’scorpuscle

Paciniancorpuscle

2

2

dtSd

dtdS

S

Fig. 1.19: Stimulus response-behavior of mechano-sensorsin the skin of mammals. Thecharacteristical spiking ratepatterns (i.e. sequences ofaction-potentials in afferentnerve fibers) of the four typessusceptible sensors in the hair-less skin (e.g., hand) areshown for a mechanical rampstimulus. (Figure based on adiagram in Schmidt & Thews,1995).

Chapter 2

Simulator

Reliable systems, which produce vibrations in just one direction (e.g., ver-tical), are necessary for basic studies on human perception of whole-bodyvibration in one direction at first. A combination and interaction of vibra-tions in more than one direction can be investigated with systems, whichproduce vibrations in more than one direction, to verify the findings ofthe investigations with an excitation in just one direction thereafter. Thelack of detailed information on basic aspects on the perception of verti-cal vibrations possibly indicates a lack of facilities to conduct research onthese issues. Facilities designed for this purpose tend to have problems withsimulating the dominance of vertical vibrations unless these machines arevery heavy, bulky and expensive. Often hydraulic systems are used whichemit audible sound with a level of 85 dB(A) and more in running condition(Chapter 1.1.1). With such hydraulic systems investigations on the percep-tion of vibration separated from sound are difficult and investigation aboutthe influence of audible stimuli on the perception of vibrations are impossi-ble. Smaller, cheaper but reliable systems are needed with very low emittedsound pressure.

In this chapter the two used systems (simulators) for the production ofwhole-body vibration, which are constructed and modified for the applica-tion in this study, are presented. Both systems contain electro-dynamicexciters, called shaker, and are developed for different tasks and experi-ments. The first simulator is based on the active excitation principle and isoptimized for the production of only vertical whole-body-vibrations (Chap-ter 2.1) to conduct basic experiments on the perception of vertical vibrations(Chapter 3). The second simulator is a system to reproduce real sound andvibration (whole-body, as well as hand-arm transmitted vibration) signals

2.1. Vibration-Floor 47

recorded in idle running cars (Chapter 2.2). These features are needed inChapter 5 to investigate the perception of seat-vibrations and the influenceof sound on the subjective comfort caused by seat-vibrations in cars. It ispossible to produce vibrations in all three dimensions (x/y/z-axes) simul-taneously or separately with this simulator. A re-active principle is used forthis system.

2.1 Vibration-floor: a system that producesvertical whole-body vibrations

A reliable system that produces only vertical vibrations (called ’vibration-floor’) is needed for the investigations on the perception of vertical whole-body vibrations in Chapter 3. The description and construction of thevibration-floor, which is developed for this study, is presented in this section.The features like the exciter and the springs (suspensions) are described indetail. Performance characteristics are discussed including the transfer func-tion and a surface vibration comparison, as well. The system is capable ofproducing vertical vibrations up to 3 m/s2 in a frequency range from 5 to200 Hz in a reliable fashion. The vibrating system is constructed to pro-duce whole-body vibrations and simultaneously emits no or very low soundpressures which are not audible for low frequencies and around the auditorythreshold for higher frequencies.

2.1.1 General description

The requirements for such a system include:

• the capability to produce the range of frequencies and accelerationlevels which are dominant for human perception and comfort research

• to produce vibrations just in one direction (in this case vertical)

• to be as silent as possible and to avoid interaction between sound andvibration during psychophysical measurements.

The vibration-floor contains all itemized features and comprises of the fol-lowing parts (Fig. 2.1): (i) cage, (ii) table, (iii) springs, (iv) electro-dynamicexciter (called ’shaker’), (v) seat, (vi) control equipment and (vii) measur-ing equipment. A schematic view and a picture of the system are shown inFig 2.1 and 2.2.

48 Chapter 2. Simulator

ShakerShakerSuspensions

Seat

Table

Cage

100

1000

Fig. 2.1: Two schematic views of the vibration-floor. On the left side the systemis shown from the front and on the right side from the side. The whole system ismounted on a rigid floor (foundation) with screws. The seat / chair is removable.The whole system has linear guides for motions in only vertical (z-) direction.

The system is located in a 3×4.5×6 m3 room with sound absorbing materialsplaced on the walls to obtain a silent measuring environment. The room isbuilt on a separate foundation from the rest of the building. Therefore thevibration-floor is protected against ambient vibrations (passive isolation),like subsonic noise. The 1×1 m2 stainless steel table (called ’shaker-table’)is fitted into a cage which supports the legs with 16 linear guides (steelrollers). These rollers prohibit motions in horizontal plane (x/y-direction,Fig. 2.2). The cage has a high mass and is fixed tightly to the ground. Theweight of the table is supported by four pneumatic springs of type BoschBagzylinder x1, placed under each leg of the shaker-table. The surface of thevibration-floor is designed as a square grid to reduce the surface area and tomake attaching objects (chairs, accelerometers) to the surface easier. Thevibration-floor is excited from below the central point by an electro-dynamicexciter (active excitation principle). Different types of chairs and seats canbe fixed on the shaker-table.

Electro-dynamic exciter The electro-dynamic exciter is a TIRAVib type52120 device from TIRA GmbH. The max. exciting force is F = 222 Nfor sinusoidal signals and F = 150 Neff for noise signals. The frequencyrange is 2 Hz to 3 kHz for sinusoidal and 10 Hz to 2 kHz for noise signals.


Fig. 2.2: Picture of thevibration-floor which was de-veloped for this study at theUniversity of Oldenburg.

The maximum acceleration for the unattached tip is 100 g (≈ 1000 m/s2)for sinusoidal and 70 g (≈ 700 m/s2) for noise signals. Peak to peakdisplacement is x = ± 10 mm when the tip is unattached to the table. Themax. acceleration and displacement decrease with increasing mass attachedto the system.

Seat Different types of chairs: rigid chairs as well as real car or aircraftseats can be fixed to the shaker-table. For the performance assessmenttests, a rigid wooden chair (same chair as in Chapter 3) was fixed to thesurface with the central of gravity directly above the central point of thetable.

Control equipment The control and excitation signals are generated byMatlab from Mathworks, running on a IBM compatible PC. The generatedsignals are then transmitted digitally from the RME Digi 96/Pro soundcardvia optical cable to a Sony TA-E 2000 ESD Digital Processing Control Pre-Amplifier with a 32 kHz D/A converter. The signals are transmitted tothe main power-amplifier afterwards. The power-amplifier is a A50150 from


TIRA, with a power of 500 VA and a frequency bandwidth from 2 Hz to20 kHz. The control equipment of the vibration-floor is shown in Fig. 2.3and 3.1.

Signal generator:PC with digital sound card

(RME DIGI 96/Pro)

Pre-amplifier andD/A Converter

(Sony TA-E 2000 ESD)

Power amplifier(TIRA A50150)

Shaker(TIRA 52120)

Fig. 2.3: Control diagram of the vibration-floor.

Measuring equipment For performance tests, four triaxial accelerometers(PCB M356A15 from Piezotronics) plus one triaxial seatcushion accelerom-eter (MMF KB 103SV) are placed at different positions on the table surfaceand on other parts of the system such as the chair and the cage. The dataare collected and analyzed by a SQLab II System with the ArtemiS 3.01.100software package from HEAD acoustics running on an IBM Thinkpad. Fur-ther data analysis are made by using Matlab version 5.3.

The mass of the shaker-table is nearly m = 50 Kg. For this reason theweight of the subjects must be considered because the weight (additionalmass) has an influence on the performance of the vibration-floor. Therefore,a calibration must be transduced for each subjects to get parameters forthe controlling of the vibration-floor for psychophysical experiments (like inChapter 3). An overview of the different measuring positions on the systemis given in Fig. 2.4. The vibration performance of the system is describablewith these nine different positions on the table and two additional positionsat the seat. The position ’bottom’ on the bottom of the seat is taken as thereference position for the following measurements (as well as in Chapter 3).

2.1.2 Dynamic performance of the vibration-floor

The measured performance of the vibration-floor is described in detail in thissection. For the performance tests, the sampling frequency is 1.5 kHz foracceleration and 32 kHz for acoustic signals. The Discreet Fourier Transform(DFT) size for data analysis is 1500 samples for acceleration and 32000samples for the acoustics.

Background conditions The background conditions in the laboratory aremeasured to verify if they have any effects on the performance of the systemand on the subjects during psychophysical measurements, e.g., an additional


97 8

1 2 3

4 65

Front

Rear

Right

Left

Cushion

Bottom

Seat

Fig. 2.4: Measuring positions on the vibration-floor to describe and control thevibrations on the system and on the seat.

cue for the perception of whole-body vibrations. First, the backgroundvibrations in the laboratory are measured on the system at the referenceposition in vertical (z-)direction. The vibrations are indicated as accelerationlevel LV ib [dB] and as acceleration a [m/s2]. In Fig. 2.5 the accelerationlevel LV ib on the left y-axis and the acceleration a on the right scale of the

5 10 20 40 80 160

0.001

0.01

Acc

eler

atio

n [m

/s2 ]

5 10 20 40 80 160

60

70

80

90

Acc

eler

atio

n Le

vel [

dB]

Frequency [Hz]

ISO 2631−2 vertical background vibrations

Fig. 2.5: Measured background vibrations in the laboratory on the vibration-floorat the reference position (dash-dotted line) in vertical (z-) direction. Additionally,the perception threshold after ISO 2631-2 is shown.


S

ound

Pre

ssur

e Le

vel [

dB]

Frequency [Hz]

0

10

20

30

40

50

(ISO 389−7)audible threshold

16 Hz

100 1000 0

10

20

30

40

63 Hz

100 1000

125 Hz

emitted sound from

the vibration−floor

Fig. 2.6: Measured background noise (dash-dotted line) in the laboratory. Addi-tionally, the auditory threshold after ISO 389-7 is shown (upper left figure, dottedline). Background noise with emitted sound from the vibration-floor running at16 Hz (upper right), 63 Hz (lower left) and 200 Hz (lower right) with an accel-eration level of LV ib = 100 dB (a = 0.1 m/s2), which is above the perceptionthreshold of vertical whole-body vibration, is diagrammed, as well. There are somepeak in the spectra, when the shaker is running with 63 and 125 Hz, which areabove the background noise.

y-axis are plotted as a function of frequency. In addition to the backgroundvibrations the standard perception threshold for vertical vibrations specifiedin ISO 2631-2 is shown. The vibration levels are always minimum 10 dBbelow the perception threshold, except for 4 Hz, therefore no influence onpsychophysical measurements are expected. The background vibrations inthe horizontal plane are less than the plotted vertical background vibrationsand have no influence on the following measurements, too.

The ambient sound pressure level, when the shaker is off, is shown in Fig. 2.6.The sound pressure is measured in at the level of the head of a subject.The plotted background spectrum (dash-dotted line, upper left figure) hassome ranges where the sound pressure level (SPL) is above the standardaudible threshold (dotted line) which is specified in ISO 389-7, as well. This


background noise is particularly audible above 100 Hz and has a level ofL = 33 dB(A). For comparison the sound pressure levels, when the shakerproduces vibrations with three different frequencies (16, 63 and 125 Hz),is plotted in Fig. 2.6, as well. The emitted sound pressure is measuredat the same position as the background noise. The sound emitted by thevibration-floor does not differ from the background noise of the laboratoryduring the production of a sinusoidal vibration with f = 16 Hz with aminimal acceleration a = 0.1 m/s2 (LV ib = 100 dB)1 (upper right figure).Furthermore, there are no differences between the background noise andthe emitted sound for vibrations up to a frequency of f = 50 Hz whichis not shown in Fig. 2.6. However, the emitted sound and the backgroundsound is probably not audible for the subjects. Therefore, no influence of theemitted sound on experiments of the perception of whole-body vibrations upto an acceleration level of LV ib = 100 dB is expected. If the accelerationlevel increases the emitted sound of the vibration-floor could increase, aswell. Therefore, an influence of the emitted sound (especially for frequencycomponents above 100 Hz) on experiments cannot be predicted. For higherfrequencies some more peaks are observable above the background curve forsinusoidal vibrations with an acceleration level of LV ib = 100 dB, especiallyfor higher vibration frequencies (63, 125 and 200 Hz) at 200 and 400 Hz.Additionally, for the reproduction of vibrations with 63 Hz, the vibration-floor emits narrow band sound around 63 Hz with a sound pressure of about40 dB. The fact that the vibration-floor emits sound which is maybe audible,especially for 63 Hz, could have a disturbing influence on measurementsof the perception threshold even at low acceleration levels. Therefore, inChapter 3.4 the influence of the emitted sound from the vibration-flooron the perception threshold will be investigated. If the acceleration levelincreases the sound pressure of the disturbing noise will be increased, aswell.

2.1.3 Vibration performance

The following figures show in detail the vibration performance of the systemin three parts. First, the influence of the linear guidance on the horizontalvibrations (x/y-axis) is shown in Fig. 2.7. Then the transfer function ofthe system is given (Fig. 2.8). And finally, the vibration levels on the seatand the shaker-table measured at different positions are compared for thedescription of the vibration distribution on the vibration-floor (Fig. 2.9).

1An acceleration level of LV ib = 100 dB is slightly above the perception threshold ofvertical whole-body vibrations.


5 10 20 40 80 160

0.001

0.01

0.1

Acc

eler

atio

n [m

/s2 ]

5 10 20 40 80 160

60

70

80

90

100

Acc

eler

atio

n Le

vel [

dB]

Frequency [Hz]

x−axisy−axisz−axis

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0.001

0.01

0.1

Acc

eler

atio

n [m

/s2 ]

5 10 20 40 80 160

60

70

80

90

100

Acc

eler

atio

n Le

vel [

dB]

Frequency [Hz]


Fig. 2.7: Vibrationsmeasured on position5 (center of the table)in three directions dur-ing a vertical broad-band excitation.

Vibrations in different directions The vibration-floor is linear conductedwith rollers to move only in the vertical-direction. Fig. 2.7 shows the vibra-tion levels measured with a triaxial accelerometer at the center of the tablesurface (position 5). The excitation signal is a pink noise. Comparison ofthe vibration levels for the three dimensions reveals that the accelerationlevels of the vibrations in the vertical (z-) direction are about 15 dB higherthan the vibrations in the horizontal (x- and y-axes) plane. The difference inthe vibration levels are also 15 dB at other points of the shaker-table whichis not presented in Fig. 2.7. The human body is more sensitive to verti-cal vibrations than to x/y- vibrations at low magnitudes (especially at andaround the perception thresholds) which is reported frequently in the litera-ture (e.g., Griffin, 1990; Bellmann, 1999). These findings are also specifiedin existing standards (e.g., ISO 2631-2, 1989; VDI 2057-2, 1987). Thereforean influence of the horizontal vibrations on the vertical vibrations, especiallyfor the perception threshold, are not expected. Moreover, there is proba-bly no influence of the horizontal vibrations on experiments with verticalvibrations which are above the perception threshold.

Transfer function The transfer function is measured with a pink noise(2 < f < 1000 Hz) in vertical direction as input vibration signal at theposition 5 (Fig. 2.8). The transfer function takes into account the coher-ence function. That is the reason why the transfer function is just printedwhen the input and output signals are highly correlated (error e ≤ 0.15,specified in Wilken & Wempen, 1986). The vibration-floor shows a typi-cal acceleration-frequency-characteristics of an electro-dynamic system, forcomparison see Fig. 1.3 in Chapter 1.1.1. The spring and coil resonance


6.3 10 16 25 40 63 100 160−25

−20

−15

−10

−5

0

5

10

15

20

25

Frequency [Hz]

Mag

nitu

de [d

B]

electro−mechanical resonance(caused by the coil and the springs)

moving element resonances(caused by the shaker−table)

Fig. 2.8: Trans-fer function of thevibration-floor invertical directionmeasured at position5 (center of table)with pink noise asinput signal. Thetransfer function isjust printed wherethe input and outputsignals are highlycorrelated (Wilken &Wempen, 1986).

is at about fR = 11 Hz (first maximum) and is called electro-mechanicalresonance because of the influence of mechanical and electronic factors(Fig. 1.3). The first moving element resonance2 is at about fR1 = 80 Hz andis called the mechanical resonance because just the mass of the shaker-tableand the mass of the subject sets this resonance of 1-dimensional dampedself-oscillating mass-spring-system. At fR1 = 80 Hz the shaker-table hasthe first grid resonance with a maximum displacement at the edge of thetable and a minimum in the center of the table, as well (Fig. 2.9). Above thefirst mechanical resonance (moving element resonance) the transfer functionshows a typical peak valley structure. The next maximum at 160 Hz is thefirst harmonic of the moving element resonance (fRn = n · fR1 [Hz], withn = 2, 3, 4, ...).

Vibrations at Different Positions A comparison of the measured verti-cal vibrations at different positions3 are drawn for a broadband excitation inFig. 2.9 (input signal is a pink noise again). There are no significant differ-ences in the spectra up to a frequency of 50 Hz. Above 50 Hz the measuredcurves deviate from each other and from the first shaker-table resonancewhere the center of the shaker-table does not move in contrast with theedge of the table. This can be observed especially at about fR1 = 80 Hz.

It is necessary to know which acceleration level is produced or reproduced at

2The input and output signals are not correlated at fR1 = 80 Hz. That is why thetransfer function is not plotted around fR1 = 80 Hz.

3From the front to the back - position 2, 5 and 8 -, from the right to the left - 4, 5,6 - and the two diagonals


Acc

eler

atio

n Le

vel [

dB]

Frequency [Hz]

60

70

80

90

100

front − back

left − right

5 10 20 40 80 16060

70

80

90

100

front right − back left

5 10 20 40 80 160

front left − back right

Fig. 2.9: Comparison of the vertical spectra measured at different positions: 2,5 and 8 - from the front to the back of the shaker-table (upper right), 4, 5, 6 -from the right to the left (upper left) and the two diagonals (lower left and right).The solid curve marks the measured spectra at position 5.

different positions on the vibration-floor for experiments on the perceptionof vertical whole-body vibrations. Therefore a set of tests are made withsinusoidal excitation with frequencies which are varied in 1/3rd octave stepsfrom 5 to 200 Hz (comparable with measuring stimuli in Chapter 3). Thevibration levels recorded by the accelerometer fixed under the seat bottomare taken as reference with an acceleration level of LV ib = 100 dB. Therespective acceleration levels [dB] on various positions of the vibration-floorsurface at 8 and 16 Hz are summarized in Fig. 2.10. For test-frequenciesof 31.5, 63, 160 and 200 Hz the figures are summarized in Fig. B.1 inAppendix A. For frequencies of 8 and 16 Hz the acceleration levels at dif-ferent positions on the shaker-table and at the seat show no considerabledifferences (≤ 1.5 dB) to the reference (seat bottom). Especially, the accel-eration levels on the seat and at the front side of the shaker table (position2), which are the contact areas between the human body and the vibration-floor (feet is position 2 and fundament is seat cushion), do not deviate fromeach other. For higher frequencies the differences between the different po-sitions increase slightly, especially on the shaker-table around the movingelement resonances.

In conclusion, the vibration-floor is capable of producing just vertical vibra-

2.2. Sound & Vibration Reproduction System 57

Fig. 2.10: Comparison of the acceleration levels [dB] on various positions of thevibration floor for 8 and 16 Hz. The excitation stimulus is a sinusoidal vibrationwith an acceleration level of LV ib = 100 dB (see position seat bottom).

tions silently. This means that there is no influence of horizontal vibrationsexpected on the results of experiments with vertical vibrations. Furthermore,the emitted sound of the vibration-floor during the production of vibrationswith frequencies up to 50 Hz with an acceleration level of LV ib = 100 dBis not audible for humans, whereas the emitted sound for higher vibrationsmay be audible. If the acceleration level increases for the produced vibra-tions, the emitted sound may be audible but with very low sound pressures.For this reasons, it is possible to use the vibration-floor for research on per-ception of vertical whole-body vibration in a silent environment and in abroadband frequency range.

2.2 Sound & Vibration Reproduction System

In Chapter 5 psychophysical measurements are conducted with interior soundand vibrations which are recorded in real cars. The ’Sound & Vibration Re-production System c©4’, called SVRS, was developed for the facsimile of inte-rior sound and seat vibrations of helicopters and aircrafts at the itap GmbHin cooperation with the University of Oldenburg (Acoustics). This system ismodified for the realistic reproduction of interior sound, seat- and steering-wheel vibrations in idle running cars during this study. Several studies ofsubjective comfort or quality assessments in cars or aircrafts confirm that thecombination of sound and vibrations, which are presented simultaneously,are important (e.g., Quehl, 2000). This system is psychophysically optimizedfor a realistic reproduction of recorded interior noise (’booming noise’), as

4 c© by the institute of technical and applied physics; itap GmbH ”Institut fur techni-sche und angewandte Physik GmbH”


Fig. 2.11: Schematic view of the Sound & Vibration Reproduction System c©

(SVRS) developed at the itap GmbH in cooperation with the University of Old-enburg. The SVRS is used in Chapter 5 to reproduce recorded seat vibrations.

well as seat and steering-wheel vibrations simultaneously, e.g., from vehiclesor aircrafts (Remmers & Bellmann, 2000).

The simulator consists primarily of three components: A so-called ’vibration-pad’ is used for the production and reproduction of the seat vibrations(whole-body vibrations). The steering-wheel vibrations are produced by aseparate vibrating system. Sound can be alternatively reproduced by head-phones or special tuned loudspeaker orders, depending on the specificationof the recorded sound signals. The vibration-pad consists of a rigid baseplate. Electro-dynamic exciters (called Paraseats from Emphaser Inc. witha force of F = 35 Neff ) with different resonance frequencies are fixed sep-arately for all three directions on the base plate. Therefore different springsand incremental masses are used to modify the shaker so that each shakerhas a different resonance frequency (resonance frequency ranges from 15to 55 Hz). The seat is removable. The whole system is mounted on aPU-foam (Diepoelast 2.2 c© from PUR Service GmbH & Co. KG) with re-silient and damping properties in all three directions (x/y/z-axes) (Tab. B.1in Appendix B). Therefore the vibration-pad could be described as a 3-dimensional damped self-oscillating mass-spring system. The resonance fre-quencies of the vibration-pad are at about fR ≈ 8 Hz for nearly all threedirections. The produced vibrations are transmitted from a real car seatand the base plate to the subjects by the feet, backside and fundamental,


Fig. 2.12: Photo of the Sound & Vibration Reproduction System c©. In this casethe acoustics is reproduced by headphones and a subwoofer.

like in Chapter 5. Additionally, a special mass-spring system with a realsteering-wheel allows to produce steering-wheel vibrations in all three direc-tions separately from the vibration-pad. The vibration-pad and the movablesteering-wheel system are capable of producing and reproducing vibrations inthe frequency range from about 10 to 500 Hz with a maximum accelerationof aeff = 2 m/s2 for noise signals and nearly aeff = 2 m/s2 for sinusoidalsignals. The acoustic reproduction, which is often called booming noise inthe car industry, is possible by headphones in connection with a subwooferfor the low frequency noise or with different loudspeakers and loudspeakerorders (e.g., dolby surround c© 5.1, Remmers & Bellmann). A schematicview of the system and some pictures of the system are diagrammed inFig. 2.11, 2.12 and 2.13.

The frequency range of the steering-wheel system and the vibration-pad islinearized with integrated parametric equalizer, which are in the pre-amplifier(Sony TA-E 2000 ESD Digital Processing Control Amplifier,) in a frequencyrange from 10 to 100 Hz. The control diagram of the system, as well asthe optimization and validation procedure of the SVRS with two profes-sional subjective-testers with long term experience from the car industryare briefly summarized (Fig. B.2 in Appendix B). Psychophysical pre-tests


Fig. 2.13: A second photo of the Sound & Vibration Reproduction System c©.In this case the acoustics is reproduced by flexural wave loudspeaker in NXT c©

technology and a subwoofer.

Fig. 2.14: Flexural waveloudspeaker in NXT c© tech-nology for a psychoacousti-cally motivated interior soundreproduction in cars.


result that the application of flexural wave loudspeaker (near-field loud-speaker) in NXT c© technology for the reproduction of the interior car sounddeals with a realistic reproduction of the interior sound. Those loudspeak-ers which produce flexural waves inside the panel consist of a panel with asmall electro-dynamic shaker on a fixed position. This loudspeaker radiatessound to both sides of the panel (dipole). The application of flexural waveloudspeaker needs multi-channel recordings of the sound particle velocitycomponents of the interior sound field in comparison to a reproduction ofrecordings of an artificial head with headphones. The frequency range ofthese loudspeakers depends on the size, the centering device of the panelsand the excitation force of the ’mini’ exciter. It is possible to produce soundfrom 40 Hz to 12 kHz with such a loudspeaker which is shown in Fig. 2.14in detail.

This Sound & Vibration Reproduction System c© has the advantage that,e.g., a comparison of different types of cars or situations with the samemeasurement set-up in the laboratory is possible. Additionally, each sin-gle parameter (sound, seat and steering-wheel vibrations) could be variedseparately. This feature is useful for different studies in practice, e.g., pro-totyping or sound and vibration design in the car or aircraft industry. Withsimilar systems, investigations were conducted in different sections, like de-velopment of a comfort-index for interior sound and vibration in aircraftsand helicopters (e.g., Quehl, 2000). The ’vibro-acoustic’ specifications ofthe simulator are summarized in Tab. B.2 in Appendix A and in Remmers& Bellmann (2000).

Chapter 3

Basic experiments on theperception of vertical whole-body vibrations on a rigid seat

The motivation for the basic experiments in this chapter is that human be-ings encounter vibrations everywhere: in buildings, vehicles, aircrafts, etc.,in their daily activities. Unfortunately, there is a lack of knowledge onmany aspects concerning the human response to vibrations (introduction).There are some standards usually for the perception of whole-body vibrationand for the health risks in buildings (e.g., ISO 2631-2 (1989); DIN 4051-2 (1999); VDI 2057-2 (1987), Chapter 1.1.3). These standards address,for example, perception thresholds of whole-body vibrations in different di-rections or equivalent-comfort contours. Existing data in literature (e.g.,Meister, 1937; Griffin, 1990; Meloni, 1991) for the perception thresholds ofsinusoidal whole-body vibrations show considerable differences to the exist-ing standards. The data from different laboratories (some are summarizedin Fig.3.3) exhibit deviations also, probably due to differences of the usedpsychophysical measuring method and other measuring parameters. Addi-tionally, incomplete details exist in the literature for basic experiments forthe description of human perception of whole-body vibration, for example,’Just Noticeable Differences’ (JND) in frequency and in level.

The following basic experiments on the perception of sinusoidal verticalwhole-body vibration for seated subjects are conducted with new and reli-able psychoacoustic measuring methods in detail:

3.1. Measuring set-up and stimuli 63

1) Psychometric function

2) Perception thresholds in vertical direction (z-axis)

3) Just Noticeable Differences (JND) in level and in frequency

4) Equal-Vibration Level Contours (EVLC, comparable with equal-loudnesslevel contours in psychoacoustics)

3.1 Measuring set-up and stimuli

Whole-body vibrations are produced by using the so-called ’vibration-floor’for the basic experiments in this chapter. This system is optimized for theproduction and reproduction of vertical (z-axis) vibrations according to psy-chophysical aspects (Chapter 2.1). For example, just low sound pressure isemitted, which is not audible for low frequencies up to 50 Hz and aroundthe auditory threshold for higher frequencies, during the production of vibra-tions (Fig. 2.6). A rigid wooden chair is fixed to the surface with the centralof gravity directly above the center point of the vibration-floor. The chairhas a small backrest but no armrests (Fig.2.2). A masking audible noisewith a level of L = 69 dB(A) is used which is presented via headphones(HDA 200 from Sennheiser) to the subjects. Further information about thevibration-floor can be found in Chapter 2.1.

Sinusoidal vibration signals are used varying in duration from 1 to 4 s whichare separated by a break of 500 ms in the following experiments. Initialand end ramps (Hanning time-windows) with a duration of 10% of thestimulus duration are used for a soft transposition. The test frequenciesvary in 1/3rd octave steps from 5 to 200 Hz. All stimuli are producedby using an AFC-package1 for Matlab on an IBM compatible computer.The AFC-package controls the used measuring method, as well. With amodification of the control and configuration files (user-, set- and config-file)different up-down procedures as well as interval numbers and other optionslike adaptive and interleaved can be realized. For the following experiments,I modified the control and configuration files of the AFC-package. Thevibrating system is located in a 3× 4.5× 6 m3 room with sound absorbingmaterials placed on the walls to obtain a nearly silent measuring environment(background noise: L = 33 dB(A), Chapter 2.1). The measurement set-upis unchanged for the following experiments in this chapter and is shownin Fig. 3.1. All experiments are repeated for each test subject at leastthree times on three different days. Results are represented as the overallaveraged rms values (mean values, Eq. 1.7) with inter- and intraindividual

1The AFC-package was developed at the University of Oldenburg, c©Stephan Ewert

64 Chapter 3. Experiments on the perception of vibrations

Fig. 3.1: Measurement set-up for the basic experiments on the perception ofvertical whole-body vibrations (lower figure). Additionally, the control diagramof the measurement set-up is shown (upper figure). The measurement set-up isunchanged for the following experiments, except for the measuring methods whichrun on the PC.

standard deviations. The data are usually indicated as acceleration levelLV ib [dB] and as acceleration a [m/s2] thus an acceleration of a = 10 m/s2

corresponds to an acceleration level of LV ib = 140 dB. In the following plotsthe acceleration level LV ib is usually located on the left and the accelerationa on the right scale of the y-axis as a function of frequency. The measuringposition at the bottom of the rigid chair is used as reference (Chapter 2.1).

3.2 Subjects

All subjects are healthy (aged between 23 and 33 years with a mean of28 years) and most of them are students of the University of Oldenburg.The number of subjects varies from 8 to 17 for the different experiments.The specific numbers of the participants in these experiments are given inthe following sections where the experiments are presented. Anthropometric

3.2. Subjects 65

(endogenous and exogenous) data are recorded from each subject like body-size and weight. Additionally, the Body Mass Index ’BMI’ and the RohrerIndex ’RI’ are calculated using Eq. 3.1 and Eq. 3.2 (adapted from Garrow& Webster, 1985). All averaged anthropometric data (indicated as meanwith interindividual standard deviation and median value) of the subjectsare summarized in Tab. 3.1.

BMI =Weight [Kg]

(Body-size [m])2=[Kg

m2

](3.1)

RI =Weight [Kg]

(Body-size [m])3=[Kg

m3

](3.2)

All experiments refer to seated subjects. The posture of the subjects isnormal and preferably comfortable on the seat: feet on the rigid shaker-tableof the vibration-floor, sitting with an upstanding upper part of the body,leaning with the backside against the backrest. During the measurementsthe posture is not monitored by cameras or similar devices but the subjectshave been instructed to sit in the same way during the whole experimentand it is assumed that they do.

Tab. 3.1: Anthropometric and other personal (exogenous and endogenous) dataof the subjects for the basic experiments in this chapter.

Parameter Mean Medium

age [a] 28.2 ± 2.4 29

body-size [m] 1.77 ± 0.1 1.80

weight [Kg] 71.9 ± 12.3 72

BMI [Kg/m2] 22.9 ± 2.7 22.4

RI [Kg/m3] 13.0 ± 1.6 12.9


3.3 Experiment 1: Psychometric function

Before the perception threshold for vertical whole-body vibrations is mea-sured in a broadband frequency range (Chapter 3.5) the psychometric func-tion for a vertical (sinusoidal) excitation of 5 Hz is determined. The psycho-metric function describes the response behavior of an individual (subject)or group of individuals (mean of subjects) depending on the force of apresented stimulus in a psychophysical experiment (here implemented bythe correct response-probability P (L) subjected to the stimulus accelera-tion level, Chapter 1.2.2). With this measurement the dependence of thedetected vibration on the acceleration level should be investigated.

The psychometric function is measured for f = 5 Hz for 14 subjects (2female and 12 male). The measuring method is a constant stimulus methodwith three given intervals for each trial (Chapter 1.2.2). Two of the threeintervals include no signal; one interval applies a stimulus with varying leveland a fixed test-frequency of f = 5 Hz. The task of the subjects is tomark that interval, in which they felt a vibration. The presented levels LV ib

vary from 75 to 90 dB (obviously below and above the expected perceptionthreshold2) in 1.5 dB steps. A step-size of 1.5 dB is used because a studyof Morioka & Griffin (2000) reports that the just noticeable difference inlevel for 5 Hz is nearly about 1 to 1.5 dB. Therefore all presented stimuliabove the individual threshold are distinguishable for each subject. Thestimulus duration of the signals are 2 s because there is an influence of thestimulus duration on the perception of vibration for low frequencies up toan excitation of 2 s (Chapter 3.4.1).

The probability P (L) results from a relative occurrence of true (correct)responses at a presented stimulus level L. Therefore, each level LV ib ispresented N = 24 times. The order of the presented levels and the or-der of null- and test-signal are randomized to prohibit order effects. Manytime-consuming measurements at many different levels are necessary to pro-duce the whole shape of the psychometric function, as mentioned before inChapter 1.2.1. A second possibility is to measure some points on the psy-chometric function and to find a conformance (’fit’) of the whole shape byusing a model-function or cost-function. In this study a maximum likelihoodis used to get the whole shape of the psychometric function. For the usedmeasurement design the probability P (L) to detect by chance the right in-terval is 1/3 = 33% because the number of intervals A is three, whereas justone interval comprises a stimulus. The modified logistical model-function,which is described in Eq. 1.22, is used for the maximum likelihood fit. The

2The level range is chosen from data in the literature and from earlier pre-experiments.

3.3. Exp. 1: Psychometric Function 67

P

roba

bilit

y P

(L)

of c

orre

ct r

espo

nse

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0

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100 Sub.12

75 78 81 84 87 90

Sub.13

0

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40

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80

100 Sub.9

Sub.10

75 78 81 84 87 90

Sub.14

Sub.11

Fig. 3.2: Measured individual psychometric functions for 14 subjects, as well asthe overall averaged data of all subjects presented as ’mean’ (upper left figure).Additionally, the minimal error estimation of the measured data are shown aserrorbars. For comparison, the calculated curves from a maximum likelihood fitare plotted, as well.

fitted psychometric function (Fig. 3.2) can be characterized or be describedwith the level L50 and the slope of the function at this point (Chapter 1.2.1).The L50 point has the highest slope of the fitted curve and is the central


point of the logistical function. The logistical function, which is used in thissection, is modified (Eq. 1.22) so that the function starts at the probabilityto detect by chance the correct response (P(L)=33%) and increases to aprobability of P(L)=100% which means that all stimuli with the fixed levelare correctly detected. Therefore the L50 is not the point with P(L)=50%’correct response-probability’ but nearly with P (L) = 66%3 in this case.

The measured single data for the 14 subjects are plotted, as well as the fit-ted curves in Fig.3.2. Additionally, the minimal error estimations (Eq. 1.23)for the measured data are shown as errorbars, because the real error is notknown. These errors are just the minimal error estimations (Chapter 1.2.1).The fitted curve begins at about P (L) = 33% right detected stimuli prob-ability and increases rapidly to a probability of P (L) = 100% in less than10 dB. There are considerable differences between the 14 subjects in theshape of the measured data and the fitted psychometric functions. The re-sults (mean values inclusive standard deviations) of some subjects like sub.11, 13 and 14 are very interesting because the correct response-probabilityP(L) for acceleration levels between 76.5 to 79.5 dB is systematically be-low the probability to detect by chance the correct response (P(L)=33%)sometimes. The reason for these findings is not clear but no further analysisabout these findings are made. The individual position of L50 varies from79.7 to 85 dB with a slope of 8 to 28%/dB (Fig. 3.2). In the upper leftfigure the fitted psychometric function labeled as ’mean’ is calculated fromthe averaged single results of all subjects. This curve indicates a mean psy-chometric function of the participants in this experiment (L50 = 82.9 dB,slope = 0.11%/dB).

With the knowledge of the individual and average fitted psychometric func-tions the differences between different positions on the curve could be calcu-lated because some psychophysical measuring methods for the determinationof the threshold do not measure the 50% point of the psychometric function(Chapter 1.2.2). For example, it is possible to compare the results of thismeasurement and the results of the perception threshold measurements for5 Hz with an adaptive 3 - AFC 1 up - 2 down measuring method which isused in Chapter 3.4. However, there are no literature data for the psycho-metric function of vibration signals hence the findings of this experimentcannot be compared to other data.

3The mean probability between the 100% (all presented stimuli are detected) and theprobability to detect by chance (33%) the right response.

3.4. Parameters which influence the perception thresholds 69

3.4 Parameters which influence theperception threshold

In the last section the psychometric functions for 5 Hz are measured. Thesemeasurements are very time consuming. Therefore a common procedure inthe literature is to measure just a fixed position on the psychometric functionfor many different test frequencies with different psychophysical measuringmethods. Some of the literature data for the perception thresholds forseated subjects in the frequency range from 5 to 80 Hz are summarized inFig. 3.3, as well as the standardized perception threshold specified in ISO2631-2 (1989) and VDI 2057-2 (1987). The literature data show consid-erable differences to existing standards. Moreover, the data from differentlaboratories deviate from each other too, probably due to differences inthe methods of acquiring the data, stimulus duration and other measuringparameters (like background noise during the measurements and stimulusduration). For example, in the literature the stimulus duration for exper-iments on the perception of vibration at low frequencies varies from 1 upto 15 s (some are summarized in Fig. 3.3, too) and sometimes longer butthere are no results for systematic investigations about the influence of theduration on the perception threshold for low frequencies (e.g., 5 Hz). If thestimulus duration is too long the results may be biased since the attentionand concentration of the subjects decreases with increasing overall measure-ment time. However, if the stimulus duration is shorter than the integrationtime of the mechano receptor or CNS the perception threshold is probablybiased, as well. Additionally, the different psychophysical measuring meth-ods used might have an influence on the data. However, before measuringthe perception threshold in a broadband frequency range (Chapter 3.5) twomain questions should be answered in this section:

• Which parameter influences the perception threshold ?

• Which psychophysical measuring method should be used ?

Therefore two experiments are conducted to investigate the parameter (i)stimuli duration and (ii) additional audible sound on the perception thresh-olds of vertical whole-body vibrations. Moreover, the results of the stimuliduration experiment are compared to the data of the measured (fitted)psychometric functions (Chapter 3.3) to verify if the used psychophysicalmeasurement delivers repeatable and constant results to the prior findings.


5 10 20 40 80 160

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/s2 ]

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eler

atio

n Le

vel [

dB]

ISO 2631−2 ‘89 Reiher & Mesiter ‘31 Miwa ‘69 McKay ‘71 Benson & Dilnot ‘81 Parsons & Griffin ‘88 Parsons & Griffin ‘88

Fig. 3.3: Perception thresholds for vertical sinusoidal whole-body vibrations areshown from different studies - Parsons and Griffin, 1988; Benson & Dilnot, 1981;McKay, 1971; Miwa, 1969 and Reiher & Meister, 1931 (some data are based onan illustration in Griffin, 1991) - in comparison to existing standard data (definedin ISO 2631-2 and VDI 2057-2). The literature data are measured particularlywith different measuring methods.

3.4.1 Stimulus duration

It is well known that the stimulus duration influences the perception curveswhich decrease slightly with increasing vibration exposure up to 1 s and differjust a bit with further increase in duration (ISO 2631-1, 1997; VDI 2057-2,1987). These results are verified in the literature for test frequencies of f =16 Hz (Parsons & Griffin, 1988). But there is no validation for the durationdependence on the threshold for low frequencies. However, a duration of 1 scorresponds to just 5 sinusoidal waveforms for a test frequency of 5 Hz. Thenumber of waveforms decreases even more if ramps (e.g., Hanning-window)for a soft closure and break are used. The question is: How long is theminimal stimulus duration for lower frequencies to minimize the influence ofthe duration on the perception thresholds and, therefore, delivers constantand repeatable results ?

For this reason, the perception thresholds are measured with different stim-ulus durations at 5, 12.5 and 16 Hz. An adaptive 3 - AFC 1 up - 2 down


measuring method (Levitt, 1971, Chapter 1.2.2) is used with sinusoidal vi-bration signals of 5 Hz with 1, 2 and 4 s stimulus duration and of 12.5and 16 Hz with 1 and 2 s for the test-stimulus. This method of takingmeasurements is used because literature data in psychoacoustics for mea-suring audible thresholds report that this method produces repeatable re-sults. Furthermore, an adaptive AFC measuring method is very fast becausejust one position on the psychometric function is measured (Chapter 1.2.2).This method used determines the 70.7% point of the psychometric func-tion. The 70.7% criterion is often used in psychoacoustics for measuringthe auditory threshold and differs a bit from the common definition of theabsolute threshold which is usually the 50% point of the psychometric func-tion. Therefore the results should be a bit higher than the expected resultswith the 50% criterion. But with the knowledge of the psychometric func-tion (Chapter 3.3) the differences between the 50% and 70.7% criterioncan be determined. ’Adaptive’ means that the initial step-size of 8 dB ishalved after each upper reversal to a final step-size of 1 dB. The individualthreshold is the median of the values taken from the last four reversals withthe final step-size of 1 dB. Eight subjects (3 female and 5 male) take partin this experiment with three repetitions. Three intervals are presented forthe subjects in this experiment, whereas two intervals contain no signals(reference stimuli) and the third interval implies the test-stimuli. The taskfor the subjects is to mark that interval in which they felt a vibration. Thethree intervals are marked with an optical cue for the discrimination and theorder of the test and the reference stimuli are randomized to prohibit ordereffects. The initial acceleration level of the test-stimulus is LV ib = 110 dB,a = 0.316 m/s2.

5 12.5 1682

84

86

88

90

92

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

1 s2 s4 s

Fig. 3.4: Averaged meanvalues inclusive interindi-vidual standard deviationsand median values for theperception thresholds ofeight subjects at frequen-cies of 5, 12.5 and 16 Hz.The stimuli durations is 1,2 s or 4 s, respectively.The data with an expo-sure of 1 and 4 s and theresults for the median val-ues are slightly shifted fora better illustration.


A

ccel

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l [dB

]

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1 s2 s4 s

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Fig. 3.5: Individual perception thresholds for eight different subjects at frequenciesof 5, 12.5 and 16 Hz with various stimulus durations of 1, 2 s and 4 s for verticalsinusoidal whole-body vibration, respectively. The data with an exposure of 1 and4 s are slightly shifted for a better illustration. Additionally, in the upper left figurethe overall mean values (’mean’) inclusive interindividual standard deviations ofall subjects are summarized.

For comparison, the averaged mean inclusive interindividual standard de-viations and the median value of all subjects are shown in Fig. 3.4. Theresults for an exposure of 1 and 4 s and the results of the median valuesare slightly shifted in the frequency range for a better illustration. Thereare no significant differences between the mean and the median values ofthe measured perception thresholds with different stimuli durations. Themean and median values for the single data of the individuals are not pre-sented in Fig. 3.4 but there are no differences observed. Therefore, just themean values are analyzed in the following. Fig. 3.5 includes the individualmean values (mean value of the three repetitions of each subject) inclusivethe intraindividual standard deviations and the overall mean values with theinterindividual standard deviations (upper left figure). The intraindividualstandard deviations are very small (between 0.5 and 1.3 dB), except forsubject 1. Additionally, there is a tendency for almost all subjects that the


perception thresholds decrease for increasing stimulus duration from 1 to2 s, except for 16 Hz. An increasing stimulus duration from 2 to 4 s yieldsno systematic different results for 5 Hz. The mean values for all subjectsreflect these findings. However, the decreasing perception thresholds for in-creasing exposure are not statistically significant (T-Test, p > 0.05) for thesummarized data (mean) but the changes in perception threshold between 1and 2 s are statistically significant (T-Test, p < 0.05) for a lot of individualdata for 5 Hz and are particularly significant for 12.5 Hz. For 16 Hz theresults for 1 and 2 s are not statistically significant (T-Test, p > 0.05), nei-ther for the averaged (mean) data nor the individual data. Due to this fact,that there are significant differences between the data of different stimulusdurations for some subjects, a stimulus duration of 2 s is used in the fol-lowing experiments for test frequencies below 16 Hz and 1 s for frequenciesfrom 16 Hz upwards.

Influence of the psychophysical measuring method Back to the begin-ning of this chapter, some points of the psychometric function are measuredwith a method of constant stimuli for 5 Hz (Chapter 3.3). Furthermore thewhole shape of the averaged psychometric function is fitted with a maximum

75 77 79 81 83 85 87 8930

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Pro

babi

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P(L

) of

cor

rect

ans

wer

s

Fitted psychometric function Measured 70.7% point of the psychometric function

Fig. 3.6: Comparison of the fitted (averaged) psychometric function of 8 subjectsand the measured 70.7% point of the psychometric function determined to anadaptive 3 - AFC 1 up - 2 down measuring method for f = 5 Hz.


likelihood fit (Fig. 3.2). Additionally, the perception threshold is measuredwith an adaptive 3 - AFC 1 up - 2 down measuring method for 5 Hz. Thedesign of the used method should deliver the measured 70.7% point of thepsychometric function. Usually, if the influence of the measuring parameterson the results are minimized, both methods should deliver the same resultsreferring to the 70.7% point of the psychometric function. Therefore theaveraged results of all eight subjects, who participated in both measure-ments, are summarized in Fig.3.6. The interindividual standard deviation ispresented for the data measured with the adaptive 3 - AFC 1 up - 2 downmeasuring method, as well. The averaged results show no obvious differ-ences referring to the 70.7% point of the psychometric function. The adap-tive 3 - AFC 1 up - 2 down measuring method yields constant results whichrefers to the measured psychometric functions. Additionally, the adaptive3 - AFC 1 up - 2 down measuring method delivers repeatable results whichis labeled by the low intraindividual standard deviations (Fig. 3.5). Fur-thermore, that method is very fast and minimizes the measuring time forthe subjects so that the experiments could be repeated quickly on differentdays to minimize the influence of the daily form of the subjects. Thereforethis measuring method is used for the following experiments. Furthermore,the expected differences between the 50% and the 70.7% criterion of theabsolute threshold is ranged at about 1.5 dB. This difference is nearly theJNDL for a 5 Hz sinusoidal vibration which is reported from Morioka &Griffin (2000). Such a difference must be considered if the results of thisstudy are compared to literature data which are based on the 50% criterionof the absolute threshold.

3.4.2 Audible sound

The perception threshold of vertical whole-body vibrations (z-axis) is carriedout with and without any additional audible stimuli. This measurement ismade for higher frequencies to investigate the influence of sound, which isprobably emitted by the used vibration-floor, on the perception thresholds(Chapter 2.1.2). The audible stimuli are presented by headphones to thesubjects. First, the perception thresholds are determined without a supple-mentary acoustic stimulus, except for the background noise in the laboratory(L = 33 dB(A) - ’without noise’ condition) and the emitted sound of thevibration-floor. The curves are measured for 11 seated subjects (2 femaleand 9 male). The same measuring method as in Chapter 3.4.1 is used(adaptive 3 - AFC 1 up - 2 down measuring method). The test signals aresinusoidal vibrations with frequencies of 16, 31.5, 63, 125 and 200 Hz. Theinitial acceleration level is LV ib = 110 dB (a = 0.316 m/s2), which is well


16 31.5 63 125 200

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/s2 ]

16 31.5 63 125 200

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Acc

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vel [

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Fig. 3.7: Measured (individual) perception thresholds for 11 subjects. Addition-ally, the averaged data presented as mean (opened circles and bold solid lines)with the interindividual standard deviation and the median values (bold dash dot-ted line) are shown.

detectable but just ’a little bit uncomfortable’ after ISO 2631-1 (Tab.1.2).The stimulus duration of the test-vibrations is 1 s according to the results ofthe findings in the last subsection. The initial and final step-sizes are 8 and1 dB again. The measurement is repeated three times on three differentdays for each subject.

The overall averaged data (mean values, bold solid line) of 11 subjects areshown with the interindividual standard deviations, as well as the individualaveraged data of each subject to give an overview of the differences betweenindividuals (Fig. 3.7). The individual data of each subject are shifted for abetter illustration. Additionally, the averaged median values (bold dash line)of all subjects are drawn in comparison to the mean data. The intraindividualstandard deviations (τ , see Tab. 1.1), which are not presented in this figure,are below 2 dB for all subjects. This result indicates a high repeatability foreach subject. The interindividual standard deviations are about 2.5 dB andincrease above 63 Hz with rising test frequency. Most of the participatingsubjects have nearly the same perception threshold. But the results ofthree subjects show considerable differences to the averaged data, especiallyfor 125 and 200 Hz. Two of them have nearly 10 dB higher perceptionthresholds and one subject shows nearly 5 dB lower results. There are no


significant differences between the averaged mean and median data for allsubjects observable (Fig. 3.7).

The decreasing shape of the perception threshold, which is shown in Fig. 3.7,especially for 63 Hz is not explicable with sensorial properties of the humanbody because the sensitivity of the mechano receptors is constant or de-creases for increasing frequencies (Chapter 1.2.3). A possible reason for thisshape is maybe due to the fact that the subjects get an additional ’audible’cue4 for higher frequencies by the emitted sound of the vibration-floor. It isjust briefly noted that low frequency sound is particularly not distinguishablefrom the perception of a vibration stimulus if the magnitude is around theperception or auditory threshold. It is shown in Chapter 2.1.2 that the emit-ted sound of the vibration-floor features some peaks above the backgroundnoise, especially for 63 Hz.

Sou

nd P

ress

ure

Leve

l [dB

]

Frequency [Hz]

5

10

15

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63 Hz

25 50 100 200 0

5

10

15

125 Hz

25 50 100 200

200 Hz

Fig. 3.8: Difference spectra between the emitted sound of the vibration-floor(running with 16, 63, 125 and 200 Hz) and the background noise in the laboratory.

For a better illustration the difference spectra between the emitted soundfrom the vibration-floor, which is running with 16, 63, 125 and 200 Hz,and the background noise in the laboratory are presented in Fig. 3.8. Thesound pressure of the audible signals is measured in height of the ear ofa sitting subject. The emitted sound from the vibration-floor running at63, 125 and 200 Hz shows components around 200 Hz and around 63 Hz

4Default task: ’In which interval do you felt a vibration/stimulus ?’


which are probably additional audible cues for the participating subjects.Therefore the measurement of the perception threshold is repeated with anaudible stimulus (’with noise’ condition), which should mask the emittedsound of the used simulator. The audible (’masking’) stimulus is presentedby headphones (HDA 200 from Sennheiser) to the subjects. The additionalstimulus is a pink noise (50 Hz < f < 10 kHz) with a sound pressure levelof 69 dB(A). The different literature studies (Meloni, 1991; Baumann et al.,2001a) revealed that there are no influences up to this level on the perceptionthresholds of vertical whole-body vibrations. Above this level an influenceof the sound on the perception of vibration is possible (Meloni, 1991) butthis is not stringent5. Closed headphones are used to prohibit influencesof the sound field (especially for low frequencies) on the performance ofthe vibrating system and to damp the sound pressure of the backgroundand emitted noise for higher frequencies, as well. The mean values andinterindividual standard deviations of the 11 subjects are presented for theperception thresholds without (circles) and with an audible masking noise(squares) in a frequency range from 16 Hz to 200 Hz in Fig. 3.9. The datawithout masking noise are slightly shifted in frequency range for a betterillustration.

A statistical test (T-Test, p < 0.05) delivers no significant differences be-tween the data with and without audible masking noise, except for f =63 Hz. This result points out that the subjects are probably influenced bythe emitted sound of the vibrating system at f = 63 Hz when measurementswere taken but not for the other frequencies. - This finding indicates that theemitted sound from the vibration-floor running with 63 Hz is just noticeablefor the subjects, especially the components around 63 and 200 Hz (Fig. 3.8).- The intraindividual standard deviation is below 1.0 dB and increases slightlyup to about 1.5 dB for higher frequencies for both measurements and in-dicates a good repeatability of the results by the subjects. However, theinterindividual differences increase with rising frequency. Individual data forthe condition ’with noise’ of some subjects are depicted in Fig 3.10. Somesubjects feature an increasing (as expected from the physiological point ofview) a decreasing or an unvarying curve for increasing frequencies. The de-creasing and the unvarying data for higher frequencies cannot be explainedby an additional audible cue for some subjects. A possible reason to explainthe increasing sensitivity of some subjects is the influence of body-bornesound (vibrations which are prefaced in the human body) which providean additional cue for the detection of the vibration signals while measur-ing. This hypothesis is confirmed with proposition of those subjects whoreported after the experiment that they have heard stimuli with high ’si-

5Influence depends on the masking sound and the vibration signal.


16 31.5 63 125 200

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Fig. 3.9: Measured perception thresholds for the condition ’without noise’ (tri-angle) and with an audible (masking) noise ’with noise’ (circles) for 11 subjects.The data without masking noise are slightly shifted in frequency range for a betteroverview.

nusoidal’ frequencies sometimes without an additional acoustic stimulus aswell as with an audible masking noise. An audible cue via air conduction canbe excluded because the subjects carried closed headphones with a dampingeffect of the sound for frequencies above 50 Hz. Additionally, a measure-ment of the sound pressure at the ear of the subject who carried headphones,shows that the levels are below the standard audible threshold specified inISO 389-7. The effect, that an audible stimulus is recognized without anaudible sound via air conduction, is described in the literature as bone con-duction. That means that the inner ear is stimulated by body-borne sound.Griffin (1990) reports that subjects were able to detect a 63 Hz vibration ofa rigid surface on which they were sitting at approximately one-tenth of thenormal vibration magnitude required for feeling by using bone conduction.In medical tests (Rinne and Weber tests) both the bone and air conductionof patients are determined to characterize the hearing of a patient.

It is difficult to verify whether there is an effect of body-borne sound andbone conduction on the perception threshold for higher frequencies (above63 Hz) since the bone conduction is influenced by many factors. The trans-mission of vibration to the body depends especially on the posture and thereare large differences observed between subjects which are reported frequently(Griffin, 1975; Cooper, 1986; Messenger, 1987; Messenger & Griffin, 1989).


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Fig. 3.10: Individual perception thresholds (mean values and intraindividual stan-dard deviations) of some subjects, who are very different, are presented as inFig. 3.9 for the condition ’with noise’ .

Most of the authors measured the seat-to-head transmissibility of the hu-man body from nearly 0 to 25 Hz, but there are no results found for higherfrequencies in the literature. Additionally, the transmission was usually mea-sured for acceleration of 1 m/s2 and more and for broadband shock signals.For these reasons, sinusoidal vibration signals are prefaced by the seat surfaceand the shaker-table of the vibration-floor into the human body (buttocksand feet) with a constant acceleration level6 of LV ib = 95 dB for frequen-cies, which varies in 1/3rd octave steps from 5 to 100 Hz, to measure theseat-to-head transmissibility. The resultant vibrations are picked up at thehead (mastoid and brow) and at the contact area between the seat andthe body of the subjects with an acceleration cushion (position ’cushion’)in Fig. 2.4). Two subjects participated with a ’normal’ posture like in theother experiments (Chapter 3.2). It turns out, that the vertical transmit-ted vibration at the seat surface (position ’cushion’ are transformed intovibrations in all three axes on the head (mastoid) during the measurement.That is why the magnitude of the seat-to-head transmissibility is calculatedwith the vibration total values (Eq. 1.9, with kx = ky = kz = 1 and withspectrally unweighted accelerations in x/y/z-direction, related to the powertransfer function, Fig.C.1).

6This level is nearby the perception threshold in this frequency range.


These vertical seat-to-head transmissibilities show a decreasing magnitudewith increasing frequency from 5 up to 100 Hz. It was not possible tomeasure the vibrations at the head above 100 Hz because the sensitivity ofthe used and usually all prevalent accelerometers are not high enough tomeasure vibrations between 50 or 60 dB. Perhaps laser-scanning vibrometertechniques are better suited for such measurements; but then the headmust be fixed. Additionally, the effects of coupling between the exciterand the head are unknown. Furthermore, it is not really clear what kindof influence the acceleration level on the seat-to-head transmissibility hassince the posture and muscle activity of the subjects probably change withincreasing level. There are some clues found in the literature that the firstmaximum in the seat-to-head transmissibility (which is around 5 Hz) changesslightly with increasing frequency. Furthermore, the human body is a highlynon-linear system which is frequently reported in the literature (e.g., Griffin,1990; Mansfield & Griffin, 1998). That is why this measurement cannoteasily be compared to results which are measured in a higher accelerationlevel range. But the tendencies between the results found in the literatureand the results from this study are nearly the same. Another aspect is thatthere are only few data in the literature (e.g., Queller & Khanna, 1982;Khanna et al., 1976) found in which acceleration levels of the vibrationsat the mastoid or at the brow according to the bone conduction thresholdsare measured. These studies are conducted with frequencies above 200 Hzand report about a decreasing bone conduction threshold with increasingfrequency. The minimum of the bone conduction threshold is in a frequencyrange between 1 to 6 kHz. Additionally, large differences between individualsare observed (Queller & Khanna, 1982).

An influence of the emitted sound from the vibration-floor on the perceptionof vertical whole-body vibrations can be excluded if an additional audible(’masking’) stimulus with a level of L = 69 dB(A) is presented simul-taneously. But whether there is an influence of bone conduction for fre-quencies above 63 Hz is not really clear. Probably, not the felt accelerationsof the test frequency vibrations deliver an additional cue but probably someharmonics or modes in the human body are excited by higher frequencyvibrations which produce a bone conduction stimulus at higher frequencies.For a verification of this hypothesis the basic pure tone bone conductionthresholds after the existing standard (ISO 8253-1, 1989) must be conductedwith special specified exciter on the mastoid. The prefaced vibration intothe head must be recorded with high sensitive accelerometer or with laserscanning vibrometer technics. Additionally, the vibration on the seat mustbe measured simultaneously to get potential influence on the head-to-seatand seat-to-head transmissibility, respectively.

3.5. Exp. 2: Perception Threshold 81

3.5 Experiment 2: Perception threshold

The perception thresholds are determined for 17 subjects (5 females and12 males) considering all or most of all results from the pre-experiments(Chapter 3.4). The measuring method is an adaptive 3 - AFC 1 up - 2 downas in the previous experiment (Levitt, 1971, Chapter 1.2.2). The stimulusduration changes with frequency: 2 s for test frequencies up to 12.5 Hzand 1 s duration for higher frequencies. The test vibrations are sinusoidalstimuli which vary in the frequency range from 5 to 16 Hz in 1/3rd octavesteps and with frequencies of 31.5, 63, 125 and 200 Hz. The measurementswith an exposure of 1 s are taken with an additional acoustic stimulus.The initial and final step-size of the adapting procedure is 8 and 1 dB asbefore. The experiment is conducted for each volunteer three times at threedifferent days. The resultant perception threshold of each measurement isthe median value of the four reversals with the final step-size of 1 dB again.The individual single values for each subject are the averaged (mean) valuesof the three repetitions.

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Fig. 3.11: Averaged mean values and interindividual standard deviations of themeasured perception thresholds with an audible masking noise (opened circles)and without a present noise (closed circles) for 17 subjects (5 female and 12male). The duration varied from 1 s for frequencies above 16 Hz to 2 s for lowerfrequencies. For comparison, the median values of the measured data (bold dashlines) are plotted, as well.


The overall averaged perception thresholds of 17 subjects (5 female, 12male) are presented as mean values with interindividual standard deviationsin Fig 3.11. The open symbols mark the test frequencies with an exposureof 1 s and the closed symbols with 2 s. The test frequencies from 16 to200 Hz are measured in presence of an audible masking noise (pink noise,L = 69 dB(A)) to minimize the influence of the emitted sound from thevibration-floor, like mentioned before in the pre-experiment (Chapter 3.4.2).For comparison, the median values of these measurements are printed inFig. 3.11 as bold dash lines. - The results of the perception threshold forfrequencies above 16 Hz look similar to the results in Fig. 3.9 which arejust measured for 11 subjects (Chapter 3.4.2). - The perception thresholdincreases with increasing frequency between 5 to 8 Hz from about 83.5to 88 dB and it is nearly constant above 8 Hz or it decreases slightly,especially for higher frequencies above 63 Hz. The interindividual standarddeviation increases with increasing frequency from 2.5 to 5 dB at 200 Hzas well as the intraindividual standard deviations which rise slightly fromabout 1 to 1.5 dB. There are no significant differences between the meanand the median values found. Therefore in the following analysis just the

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Fig. 3.12: Individual perception thresholds for the 17 participants are presentedin the frequency range from 5 to 200 Hz. Additionally, the mean values and theinterindividual standard deviations of all subjects are plotted like in Fig. 3.11, aswell.


mean values are used. However there are considerable differences betweenindividuals (Fig. 3.12). The single values as well as the mean values areobliged for a better illustration. The symbols of the presented data aresimilar to the presentation in Fig. 3.11. Some of the 17 subjects show a lowersensitivity, especially for higher frequencies, than the other subjects. Thedifferences in the perception thresholds are about 10 dB. Additionally, twosubjects show a very low perception threshold for 200 Hz at an accelerationlevel of about 80 dB.

Anthropometric Data The measured perception thresholds for verticalwhole-body vibrations (Fig. 3.12) as well as the measured psychometricfunctions (Fig. 3.2) show that there are considerable differences for thedetection of vibrations between individuals. This finding is well known in theliterature and is frequently reported (e.g., Parsons & Griffin, 1988; Meloni,1991; Griffin, 1990). It would be desirable to have objective parameters todescribe and to explain the interindividual differences for the perception ofvibrations. Therefore some collected objective anthropometric (exogenousand endogenous) parameters are correlated with the individual perceptionthreshold (mean values) of the 17 participants to find relations between thesubjective perception of vibration and the objective parameters.

First of all, a correlation analysis between age, weight, body-size, BMI,RI and gender on the one hand and the individual sensitivity (perceptionthreshold) of the 17 subjects on the other hand is conducted to investigatethe influence of anthropometric and other personal data on the perceptionthresholds. – The calculated correlation coefficients between weight, body-size, BMI and RI, as well as between gender and body-size are significant(p < 0.05), as expected, whereas the ones between gender and age arenot, see Tab. C.2. – There are no relations or tendencies found, which arestatistically significant (p > 0.05) between the perception threshold (of eachmeasured frequency) and the personal data age, weight, body-size, BMI, RIand gender, particularly except for higher frequencies at f = 31.5, 63 and125 Hz (Tab. C.2 in appendix C). The calculated correlation coefficients areparticularly significant for those frequencies. The sensitivity of the subjectdecreases with increasing weight, BMI or sometimes age. The reason forthese particularly significant correlation coefficients is unknown. Howeverthe differences between individuals cannot be explained systematically withthe used exogenous and endogenous data. It is very difficult to decidewhether there is an influence of the gender on the perception thresholdbecause the number of female subjects (5), who participated, is too small.These results are similar to several other studies in the literature whichinvestigated the relation between anthropometric and personal data, for


example: gender, weight, body-size, age and body dynamics, and data whichcharacterize the perception of vibration, e.g.: sensitivity (e.g., Griffin &Whitham, 1978; Griffin, 1982; Parsons & Griffin, 1982; Corbridge & Griffin,1986; Griefahn & Brode, 1997), equivalent-comfort contours (e.g., Orboneet al, 1981) and relative discomfort experiments (e.g., Griffin & Whitham,1978).

Seat Pressure Distribution The measured and calculated anthropomet-ric (endogenous and exogenous) data, like age, body-size, etc., are not suit-able to explain the interindividual differences of the measured perceptionthresholds. That is the reason why the seat pressure distribution is mea-sured, as well, to investigate if objective parameters which are calculatedfrom the seat pressure distribution can provide more information about thedifferences between individuals. The seat pressure distributions are mea-sured for 11 of the 17 subjects, who participated in the measurement ofthe perception threshold. The measurements of the seat pressure distribu-tion are conducted in cooperation with Roland Kruse (graduate student atthe University of Oldenburg). The measurement system is a GP SoftMessSystem from GeBiom (Munster, Germany). This system uses 480 resistivesensors (24 × 20) which are mounted on a piece of cloth with a size of56 × 56 cm2. It is possible to read and save the data from each sensor onan IBM compatible computer with a provided software package. GeBiomnumeralizes the repeatability of the measured results of about 5% and thepressure range is separated into 1 mbar steps. Further informations aboutthe measurements and the system can be found in Kruse (2001). The seatpressure distribution is measured at least twice for each subject. 5 objec-tive parameter for the static seat comfort are calculated from the averageddistributions:

• mean and maximum pressure (pmean), (pmax)

• mean and maximum absolute value of the pressure gradient (| 5 p|)

• size of the contact area between the seat and the body

A correlation analysis between the parameters listed above and the percep-tion threshold (mean values at each measured frequency) of 11 subjectspoints out that there are no relations between the objective parameters andthe subjective perception data. The calculated correlation coefficients arenot statistically significant (p > 0.05), except for 6.3, 12.5 Hz and the sizeof contact area, see Tab. C.1 in appendix C. Thus such simple parameterscan also not explain systematically the measured interindividual differences


of the measured perception thresholds. To conclude, in the study of Kruse(2001) some more relevant data for the description of the perception ofvibration - like perception thresholds at 16 and 31.5 Hz from this study andmeasured perception thresholds on real car seats - are used for the corre-lation analysis with several more objective ’comfort’ relevant parameters.Additionally, the seat pressure distribution measurements are described indetail in that study. Furthermore, some more sporadic correlation coeffi-cients between the objective parameters and data for the description of theperception of vibration, which are particularly statistical significant, are listedin that study. But no objective parameters were found which are able toexplain systematically the differences between individuals for the perceptionof vibration, as well.

Literature Data In comparison to data from this study, curves from Par-sons & Griffin (1988); Benson & Dilnot (1981); McKay (1972); Miwa (1968)(some data are based on an illustration in Griffin, 1990), which are deter-mined on rigid seats, are depicted in Fig. 3.13. Additionally, the standardcurve specified in the ISO 2631-2 (1989); VDI 2057-2 (1987) is shown. Theresults from Reiher & Meister (1931), which are based on standing persons,are also included in Fig. 3.13 because they are widely referenced and have

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Fig. 3.13: The perception threshold for vertical sinusoidal whole-body vibration isshown in comparison to several literature data (some are based on an illustrationin Griffin, 1991) and standard data specified in ISO 2631-2.


influenced several existing vibration standards (Chapter 1.1.3).

A detailed comparison of the summarized data is not explicitly possiblebecause the data are determined using different measuring methods (e.g.,method of adjustment, signal detection theory, etc.), threshold criterion7,stimuli durations, systems for the production of vibration, subject groups,etc. For example, the influence of different measuring methods are visiblein data from Parsons & Griffin which show almost the lowest and highestperception curves8 ”[...] lowest curve with signal detection theory for 36subjects, highest curve with method of adjustment for 8 subjects”, Grif-fin, 1990. The measured data in this study look very similar to data fromMcKay (1972) and show no considerable differences to some other literaturedata in the frequency range from 16 Hz upwards. But there are substan-tial differences between the summarized data for the low frequency rangein Fig. 3.13. These varieties for lower frequencies are not explicable withdifferent absolute threshold criteria because the measurement of the psycho-metric function for 14 subjects at 5 Hz show that the differences betweenthe 70.7% and the 50% criterion are just around 1.5 dB. But the varietiesfor different laboratories are max. about 10 dB for 5 Hz. However, thedifferences between the summarized data in Fig. 3.13 for the low frequencyrange are probably explained by the fact that ”[...] lower curves will occurwhen visual or auditory stimuli provide additional cues to the presence ofmotion” (Griffin, 1990). However, on the one hand a part of variability inthresholds between different studies can be explained with used differentsubjects or subject groups (Parsons & Griffin, 1988). But on the other handthe effects of the used measuring method, stimuli duration, audible noiseessentially influence this basic experiment (the influence of some parameterare shown in Chapter 3.4). Finally, all measured data show particular varia-tions to the existing standards (VDI 2057-2, 1987; ISO 2631-2, 1989) whichare influenced and are based on data from Reiher & Meister (1931).

3.6 Experiment 3: Just noticeable differences– effects of level and frequency

The just noticeable differences (JNDs) are the relative difference thresholdsin a stimulus magnitude or frequency. These differences in the magnitudeI or in the frequency f are often signified as difference thresholds in the

7Most of the summarized data used the 50% criterion for the absolute threshold.8Furthermore, Griffin (1976) reports: ”[...] these curves show that the different results

may be mainly attributed to different criterion adopted by the subjects (low value at 63 Hzwere associated with imperfections in the stimulus).”

3.6. Exp. 3: Just Noticeable Differences (JND) 87

literature and have been measured for audible stimuli several times. Therelationship (relative difference threshold ∆I/I or ∆f/f) between the ab-solute detected differences of the magnitude (∆I) or frequency (∆f) andthe magnitude or frequency (I, f) of a stimulus is a constant ratio c (asproposed by E.H. Weber, see Chapter 1.2). This law can be stated as:

∆I

I= c or ∆I = c · I (3.3)

The JNDs are well known for audible stimuli and are important parametersin psychoacoustics because they show, for example, which level differencesin an audible stimulus are distinguishable. This could be an importantparameter for the explanation of differences for heard sounds. But there is alack of studies for vibration stimuli for the JNDs. There are just two studiesfound in the literature for Just Noticeable Differences in Level (JNDL) witha sinusoidal vertical excitation (Bellmann, 1999; Morioka & Griffin, 2000).But both studies used just a limited number of test frequencies (e.g., justfor 5 and 20 Hz). Moreover, there are no data in the literature found for theJust Noticeable Differences in Frequency (JNDF). Therefore the JNDLs andthe JNDFs are measured in this study for test frequencies which are variedin the frequency range from 5 to 50 Hz or 5 to 40 Hz. These differencethresholds are determined in a nearly silent environment (see Chapter 2.1.2)without any additional audible stimuli. This is why the frequency range islimited to 50 Hz. Above 50 Hz an influence of the emitted sound of the’vibration-floor’ is not excluded (Chapter 2.1.2).

3.6.1 Just Noticeable Differences in Level (JNDL)

The JNDLs are measured for vertical whole-body vibrations with an adaptive3 - AFC 1 up - 2 down measuring method (Levitt, 1971, Chapter 1.2.2)with seated subjects. AFC measuring methods are often used to determinethe JNDLs with audible stimuli in psychoacoustic measurements and withvibration stimuli (e.g., Morioka & Griffin, 2000). The initial step-size of4 dB is halved after each upper reversal to a final step-size of 0.25 dB. Thereference stimulus is a sinusoidal vibration of the same frequency as the test-stimulus with an acceleration level of LV ib = 96 dB (a = 0.063 m/s2). Thislevel is about 10 dB above the measured perception threshold for verticalwhole-body vibration (Fig. 3.11). The test-stimuli are varied from 5 to50 Hz in 1/3rd octave steps and have an initial acceleration level of 101 dB(a = 0.112 m/s2). In this experiment the subjects feel three vibrations(intervals, 3 - AFC), two of the intervals include the reference stimulusand one interval comprises the test-stimulus with the same frequency but


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Fig. 3.14: JNDLs are plotted as a function of frequency (left y-axis). On theright y-scale the relative difference thresholds (∆I/I) are denoted. The openedsignals mark an stimulus duration of 1 s and the results with closed symbols aremeasured with 2 s. Additionally, data from Morioka & Griffin (2000) at differentacceleration level for 5 and 20 Hz are shown.

a different (higher) acceleration level. The task for the subjects is to markthat interval in which they felt the vibration with the highest magnitude.This experiment is a decrement method that means that the level of thetest-stimuli cannot be less than the level of the reference stimulus (thatmeans that in the extreme condition all three felt vibrations have the sameacceleration level). 16 subjects (5 females and 11 males) assist in thesemeasurements. The stimuli duration is 2 s for frequencies up to 12.5 Hzand 1 s for frequencies from 12.5 Hz upwards9. The test frequency 12.5 Hzis measured with 1 and 2 s duration to investigate if there are any influencesof the stimulus duration on the JNDLs for that frequency. The results for12.5 Hz are slightly shifted in the frequency range for a better illustration.The relative individual difference threshold is the median of the values takenfrom the last four reversals with the final step-size.

The mean values and the interindividual standard deviations of the JNDLsare represented as a function of frequency for the 16 subjects in Fig. 3.14.Additionally, on the right y-axis the mean values of the relative difference

9according to results of the pre-experiment for perception thresholds in Chapter 3.4


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Fig. 3.15: The absolute difference thresholds (∆I) in level for 16 subjects incomparison to data from Morioka & Griffin (2000) are shown. The data areslightly shifted in frequency range for a better illustration.

thresholds (∆I/I) are plotted. The results show that a level difference ofabout 1.5 dB with a standard deviation of about 0.4 dB is independent offrequency detectable in a frequency range from 5 to 50 Hz. The single dataof the difference thresholds for individuals range from 0.5 dB to 2.5 dB withan intraindividual standard deviation of below 0.4 dB. There are no sig-nificant differences between the measured JNDLs at the eleven frequencies(T-Test, p < 0.01), as well as between a stimulus duration of 1 and 2 s for12.5 Hz.

In the literature just a few data of the JNDLs exist, as mentioned before.Moreover no standard values are specified. In Fig. 3.14 and 3.15 data fromMorioka & Griffin (2000) are presented in comparison to the results of thisstudy. The literature data are measured with a similar method (2 AFC1 up - 3 down, 79.4% of the psychometric function) with higher referenceacceleration levels of 100 and 114 dB (0.1 and 0.5 m/s2) and a stimulus du-ration of 4 s. The results of Morioka & Griffin (2000) are slightly shifted infrequency range for a better illustration (Fig. 3.14 and 3.15). If the JNDLsare independent of the reference magnitude the relative results of Morioka& Griffin should be a bit higher than the results of this study because the


threshold criterion is the 79.4% point of the psychometric function insteadof 70.7% point which is used in this study. But the JNDLs of this study area bit higher than those presented by Morioka & Griffin (2000) (mean values,Fig. 3.14). The data of Morioka & Griffin (2000) show no frequency depen-dence for measured JNDLs at low magnitudes. The differences between thetwo studies are not significant (T-Test,p < 0.05) and could be explained bythe usage of different subject groups or, what is more probable, the JNDLsare not independent of level so that the relative difference thresholds de-crease with increasing reference level. For comparison, the mean values withstandard deviations of the absolute difference thresholds (∆I) are shown inFig. 3.15, as well. The individual absolute difference thresholds vary from0.0037 to 0.021 m/s2 with a mean threshold of 0.0115 m/s2. Moreover,the absolute difference thresholds (∆I) rise with increasing reference mag-nitude, but the relative difference threshold (∆I/I) and the JNDLs decreasea little with increasing reference magnitude.

Some other studies report about JNDLs but those are usually measuredon real car seats like, e.g., Baumann et al. (2001a) and sometimes withreal measured (broadband) vibration signals. The contact areas betweenthe human body and a real car seat or rigid seat are considerable different.Furthermore, a just vertical excitation of a real car seat is almost impossible(Chapter 5.3). Therefore the transmitted vibrations from a real car seatcomprise almost components in more than the vertical direction. That isthe reason why these results are not really comparable to each other. Never-theless, the results of Baumann et al. on a real car seat validate the findingsshown above that a JNDL of 1.5 dB or less (for higher acceleration levels)is detectable.

3.6.2 Just Noticeable Differences in Frequency (JNDF)

The difference thresholds in frequency are measured for the perception ofvertical whole-body vibrations with the same measuring methods as theJNDLs (adaptive 3 - AFC 1 up - 2 down). The reference stimulus is asinusoidal vibration with a fixed frequency fref which is varying in octave-steps from 5 to 40 Hz and the same fixed acceleration level of LV ib =96 dB (a = 0.063 m/s2) as the test-stimulus. The test-stimuli starts with afrequency of ftest = fref + ∆f . The start values for ∆f are determinedin pre-tests and are 12 Hz for 5, 10 and 20 Hz and 25 Hz for 40 Hz. Theinitial step-size of 8 Hz is halved after each upper reversal to a final step-size of 0.25 Hz. The task of the participating volunteers is to mark thatinterval in which they felt the vibration with the highest frequency. Thisexperiment is a decrement measurement (∆f ≥ 0) again. The relative


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Fig. 3.16: The individual JNDFs of six subjects are plotted as a function ofthe test frequency (linear x-scale) as mean values with intraindividual standarddeviations.

individual difference threshold is the median of the values taken from thelast four reversals. Six subjects (1 female and 5 males) participated in thismeasurement, with three repetitions. The stimuli duration is 2 s for 5 and10 Hz, and 1 s for 20 and 40 Hz, respectively, according to results of theprevious experiments (Chapter 3.4).

The individual measured data of the six subjects are plotted in Fig. 3.16 asmean values inclusive intraindividual standard deviations. One subject wasnot able to measure the JNDF for fref = 40 Hz because a decrement of∆f = 25 Hz was not detected. The JNDFs increase frequency depending on0.25 to about 16.7 Hz at 40 Hz, as well as the interindividual standard devia-tions which rise from nearly 0 to about 3.1 Hz. These data show that thereare almost no differences for low frequencies but the differences betweenindividuals in detecting frequency changes increase with rising frequency.The intraindividual standard deviations are very small for low reference fre-quencies and are ranged like the interindividual standard deviations whichdepend on the reference frequency. A correlation analysis points out thatthe correlation coefficient between the reference frequency and the JNDFs isstatistically significant (p < 0.001, r = 0.93∗∗∗). A linear regression curveis calculated according to the correlation analysis. This curve is picturedwith the mean values and the interindividual standard deviations as well asthe single results of the six individuals (mean values of the three repetitions)in Fig. 3.17, as well. A good match between the linear regression and themeasured (averaged) data is listed. Thus, humans are able to differentiate


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Fig. 3.17: The averaged relative difference thresholds (∆f) for six subjects incomparison to the interindividual noticeable frequency differences. Additionally,the linear regression curve is plotted as a function of frequency. The correlationcoefficient between the individual JNDFs and the frequency is significant, r =0.93∗∗∗.

between two vibrations of 5 and 5.4 Hz (∆f = 0.4); above 5 Hz ∆f in-creases in proportion to frequency and is about 0.34 · f − 1.25 Hz. Theequation is just applicable for reference-frequencies between 5 and 40 Hz. Itis not possible to give some propositions about the JNDF for higher or lowerreference frequencies. A comparison to literature data is not possible be-cause no studies about JNDFs for sinusoidal vertical whole-body vibrationsare found in the literature or in existing standards.

3.7 Experiment 4: Equal-vibration levelcontours

The equal-vibration level contours (EVLC) are comparable with the equal-loudness level contours in psychoacoustics. The equal-loudness level con-tours describe the subjective equality of two audible sinusoidal sounds withdifferent frequencies in a level range from the auditory threshold to the ’painthreshold’. These curves are given in phon, whereas the sound pressure level

3.7. Exp. 4: Equal-Vibration Level Contours (EVLC) 93

in dB corresponds to the loudness (level) in phon at a sinusoidal signal off = 1 kHz, and are specified in the ISO 226 (1987). The equal-loudnesslevel curves have a local minimum between 1 kHz and 4 kHz and the curvesincrease with decreasing and rising frequencies. These shapes reflect thatthe human ear is very sensitive to frequencies between 1 and 4 kHz. Fur-thermore, the equal-loudness level contours do not just depend on frequencybut also on level. The shape of the contours at low levels, which are audible,e.g., the 10 and 20 phon curve, are very similar to the shape of the auditorythreshold but for higher levels (e.g., 60 phon curve) the shapes become moreflat.

In existing standards for the perception of vibrations, e.g., VDI 2057-2(1987); ISO 2631-2 (1989), curves above the perception thresholds arespecified for the horizontal plane (x/y-axes) and vertical direction (z-axis)to describe the sensation or perception of whole-body vibrations. Thesecurves are the standardized perception thresholds multiplied with K-values(Fig. 1.10 in Chapter 1.1.3 and Fig. A.2 in Appendix C). Such curvesare from decisive interest for measured vibrations in real situations like inbuildings or transport facilities in daily life where vibrations above the per-ception thresholds usually occur. The measured curves could be used assubmittal for creating psychophysically motivated spectral weighting func-tions for broadband vibration signals by reversing the curves (e.g., Chapter 4or Fig. A.1 in Appendix A). In the literature such curves are sometimes de-noted as equal-subjective vibration intensity (Shoenberger & Harris, 1971)or equivalent-comfort contours (e.g., summarized in Griffin, 1990) becausethe task of the participating subjects was to judge the presented stimuliby their subjective comfort or discomfort sensation. In my opinion thistask might include some problems because there is no standardized defi-nition of comfort or discomfort, specified in an existing standard, so thatthe judgement criteria could differ between subjects. Most of the measuredequivalent-comfort contours for vertical vibrations and with seated subjects,which are published by ,e.g., Dupuis et al., 1972a-c; Griffin (1982); Donati etal. (1983); Corbridge & Griffin (1986) and others, feature a rising curve forincreasing frequency above 8 Hz with a slope of about 6 dB/octave Thesecurves are mostly measured at high accelerations (a ≥ 0.5 m/s2) and showno considerable differences to the specified curves in existing standards (e.g.,VDI 2057-2). But there is a lack of data in the lower acceleration range.Furthermore, the shapes of the equivalent-comfort contours and the per-ception threshold, especially for a vertical excitation, which are publishedin the literature, show particularly no accordance to each other. For thevertical whole-body vibrations, the perception thresholds of some studiesare summarized in Fig. 3.13 and for the equivalent comfort contours some


results of different studies are summarized in Griffin (1990) .

In this study such curves are indicated as equal-vibration level contourssince the level and not the comfort (or discomfort) perception is assessedby the subjects. The task for the subjects is: Which of the two presentedvibrations was stronger ? The equal-vibration level contours (EVLC) aremeasured with an adaptive 2 - AFC interleaved 1 up - 1 down method10

(Buus et al., 1997, Chapter 1.2.2) with 15 subjects (3 female and 12 male).This method is used because recent studies (Buus et al., 1997; Reckhardt etal., 1998) show that this method minimizes the influence of several methodparameters, e.g., the initial starting level of the test stimulus or the presentedlevel range, on equal-loudness level contours and other loudness experimentsin psychoacoustics. There are no studies found in the literature for vibrationexperiments but in the following measurements it can be shown that theinfluence of the initial acceleration level of the test vibration is minimized.

’Interleaved’ means that several adapting measurements with various teststimuli and conditions (here initial acceleration level of the test vibrations)are measured simultaneously in one measurement, whereas each test stimu-lus is compared to the same reference stimulus (see Chapter 1.2.2). In thisexperiment, four different test stimuli are measured simultaneously in onetrial method, (Fig. 1.15). 12 different test frequencies (sinusoidal vibrations)which are varied in 1/3rd octave steps from 5 to 80 Hz11, except for 25, 40and 50 Hz which are used with three different initial acceleration levels: 90,100 and 110 dB. The influence of the presented vibration levels will be in-vestigated with such a large variance of the initial level. The reference stim-ulus is a sinusoidal vertical whole-body vibration with a reference-frequencyfRef = 20 Hz and a fixed reference-level of LV ib = 100 dB and an accel-eration of 0.1 m/s2. It is not possible or easy to compare vibrations, whichdiffer too much in frequency from each other because the perception is toodifferent which is confirmed in pre-tests. For example, the comparison of 5and 80 Hz (minimal and maximal frequency in this experiment) is almostimpossible. Therefore a reference signal of a frequency between is neces-sary. In this experiment 20 Hz is used for the reference stimulus because 5 or80 Hz are two octave below or above 20 Hz. The stimulus duration dependson frequency: below 16 Hz the duration12 is 2 s and above it is 1 s. The ini-tial step-size of each adaptive measurement is 6 dB and decreases to a finalstep-size of 1.5 dB (measured JNDL in Chapter 3.6.1). The method stops

10Selects the 50% point of the psychometric function.11At higher frequencies problems with the emitted sound of the system and bone

conduction could probably occur. That is the reason why 80 Hz is the highest frequency.1216 Hz is measured with 1 and 2 s stimulus duration to verify if this point depends

on the exposure.


5 8 12.5 20 31.5 50 800.031

0.056

0.1

0.178

0.316

0.56

Acc

eler

atio

n [m

/s2 ]

5 8 12.5 20 31.5 50 8090

95

100

105

110

115

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

Ref.: f=20Hz; LVib

=100dB <=> a=0.1m/s2

Mean Initial Level 90 dB Initial Level 100 dB Initial Level 110 dB

Fig. 3.18: Measured data of equal-vibration level contours with various startingconditions (labeled after starting levels) and the overall averaged curve (’mean’).These curves are measured at low magnitudes with a reference of a sinusoidalvertical vibration with a frequency of 20 Hz and a level of a = 0.1 m/s2. Theclosed symbols mark results with a stimulus duration of 2 s and the opened symbolsof 1 s.

after four reversals with the final step-size of 1.5 dB for each test stimulusand from these data the median is calculated. The order of the test andthe reference stimulus, as well as the order of the different test stimuli, arerandomized to prohibit order effects. This experiment is repeated for eachfrequency and for each starting condition three times for each volunteer sothat nine results (three repetitions for three initial acceleration levels) foreach subject and frequency are available for the analysis.

Averaged results of all subjects for different starting conditions (labeledafter levels) are plotted in Fig. 3.18, as well as the mean values (labeled as’mean’) of all measured data inclusive interindividual standard deviations.There are no significant differences between the different starting conditionsto each other and between the starting conditions and the overall mean curve(T-Test, p < 0.001). This figure shows that no influence of the differentstarting conditions on the equal-vibration level contours is recognized withthe used measuring method. The mean values increase depending on thefrequency from 6.3 to 80 Hz. The interindividual standard deviation riseswith increasing or decreasing frequency from fRef = 20 Hz up to 80 Hz


5 8 12.5 20 31.5 50 800.031

0.1

0.316

Acc

eler

atio

n [m

/s2 ]

5 8 12.5 20 31.5 50 8090

95

100

105

110

115

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

Fig. 3.19: Overall mean values inclusive interindividual standard deviations (likein Fig. 3.18) and four individual curves from four subjects with different judgementbehaviors to illustrate the interindividual differences.

or down to 5 dB, respectively. The intraindividual standard deviations areranged between 1 and 2 dB for frequencies up to 31.5 Hz and increaseslightly for higher frequencies. For the reference frequency fRef = 20 Hz theintraindividual standard deviations are below 0.5 dB which indicates a highrepeatability for each subject. The individual differences between subjectsare shown in Fig. 3.19 for four subjects with different judgement behaviors incomparison to the overall mean and the interindividual standard deviation.The intraindividual standard deviations are not printed in Fig. 3.19 for abetter overview but the intraindividual standard deviations are less than2 dB. The measured curves of the participating subjects show considerabledifferences to each other, especially for higher frequencies.

In this (acceleration) level range only a few data exist in literature (e.g.,Howarth & Griffin, 1990) which are presented in Fig. 3.20, as well as themeasured data from the present study13. The data from Howarth & Grif-fin (1990) were obtained with a different reference stimulus and measuringmethod: a narrow band (audible) noise as reference and a method of mag-nitude estimation was used. The contours obtained for magnitude estimates

13Most of the literature data were measured for higher vibration magnitudes (from0.5 m/s2 up to some m/s2). These data are summarized in Griffin and show a frequencydepending increase with approximately 6 dB/octave from nearly f = 8 Hz upwards.


of 50, 100 and 200 (comparing to the reference) that is why the data arenot really comparable to each other. However, the results for a magnitudeestimation of 50 from Howarth & Griffin show no large differences to themeasured equal-vibration level contours of the present study in spite of theused reference stimulus. For higher magnitude estimations (100 and 200)the curves get more and more flat to nearly a constant acceleration levelof LV ib = 110 dB. Additionally, a standard curve specified in VDI 2057-2 (1987) with a multiplying factor of KZ = 0.8 (Fig.A.2), is plotted inFig. 3.20, too. This multiplying factor is used to specify sufficient magni-tudes of building vibrations with respect to human response to vibrations andhave been applied to the standard perception threshold14. This curve showsa frequency depending increase of 6 dB/octave and features considerabledifferences to the summarized measured curves.

5 8 12.5 20 31.5 50 800.031

0.056

0.1

0.178

0.316

0.56

Acc

lera

tion

[m/s

2 ]

5 8 12.5 20 31.5 50 8090

95

100

105

110

115

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

B. Ref.: Vibration (sinusoidal) 20 Hz, LVib

= 100 dB

H&G Ref.: Noise (1/3−Octave−band) fc = 1 kHz, L(A) = 77 dB

ISO with KB = 0.8

Howarth & Griffin ‘90 ISO 2631 −2 ‘89 Data of this study

Fig. 3.20: Data of Fig. 3.18 with literature data (Howarth & Griffin, 1990) andexisting standard (VDI 2057-2, KZ = 0.8) for comparison. The data of Howarth& Griffin (1990) are determined with a different reference stimulus and a methodof magnitude estimation of 50, 100 and 200.

The measured perception threshold, as well as the equal-vibration level con-tours from this study are shown in Fig. 3.21 for a better comparison. The

14Measured equal-vibration level contour coincides in level to the standard curve atfRef = 20 Hz.


5 8 16 31.5 63 125 2000.01

0.017

0.031

0.056

0.1

0.177

0.316

0.56

Acc

eler

atio

n [m

/s2 ]

5 8 16 31.5 63 125 20080

85

90

95

100

105

110

115

Frequency [Hz]

Acc

eler

atio

n Le

vel [

dB]

Ref.: 20Hz, 100 dB = 0.1m/s2

Equal− Vibration Level Contour Perception Threshold

Fig. 3.21: Measured perception threshold of this study in comparison to measuredequal-vibration level contours.

shapes of the perception threshold and the equal-vibration level contourdeviate from each other. As opposed to the perception threshold whichis nearly constant from 8 Hz upwards the equal-vibration level contour in-creases with rising frequency from 6 or 8 Hz, respectively, upwards withnearly 2.3 dB/octave The perception threshold corresponds to a propor-tionality between the perception of the vibration and a constant accelera-tion level. As opposed, the slope of the equal-vibration level contour doesnot show a proportionality between the equal-vibration level sensation anda constant acceleration or a constant changing of the velocity (v = δx/δt)which will be characterized by an 6 dB/octave increase. Furthermore, thereare differences between the presented data at low magnitudes and litera-ture results for higher accelerations a ≥ 0.5 m/s2 and measured health riskcurves (’pain thresholds’, e.g., measured by Magid et al., 1998) which fea-ture such a 6 dB/octave slope. The differences between these curves cannotbe explained by a frequency depending JNDL because these are constantup to 50 Hz at about 1.5 dB or slightly less for acceleration levels between0.1 and 0.5 m/s2. This changing slope in the curves shown is rather aneffect of acceleration on the sensation of vertical whole-vibrations betweenthe perception threshold and the reported equal-vibration level contours at

3.8. Discussion 99

high magnitudes and health risk curves (’pain thresholds’).

3.8 Discussion

Basic experiments on the perception of vertical whole-body vibrations forseated subjects are conducted using new and reliable methods in psychoa-coustics. In the first experiment the psychometric function is measured in alevel range from 75 to 90 dB for vertical whole-body vibrations. This curveincreases from P (L) = 33% (probability to detect by chance) to 100% (allstimuli detected) in less than 10 dB. A maximum likelihood fit shows a goodconsistence to the measured data and points out that the slope is 10.7 %/dBat the central point L50 = 82.9 dB of the averaged logistical function. Theinterindividual differences are very large for the slopes and the L50, as well.Additionally, with the knowledge of the psychometric function the differ-ences between 50% and 70.7% threshold criterion can be determined. Thedifference is about 1.5 dB which is nearly the just noticeable difference inlevel.

Before the perception thresholds are measured in a broadband frequencyrange two pre-experiments about parameter, which could influence the per-ception thresholds, are conducted. In the first pre-experiment, the durationdependence of the perception threshold is measured. The perception thresh-old decreases with increasing stimulus duration up to an exposure of 2 s andis nearly unchanged for frequencies below 16 Hz afterwards. This tendencyis not significant for the averaged data of all subjects but is nearly always sig-nificant for the individual measured data (p < 0.05). For 16 Hz an exposureof 1 s gives similar results with longer stimulus durations. For this reasonthe succeeding experiments are conducted with a stimulus duration of 2 sfor vibrations between 5 and 12.5 Hz and of 1 s for higher vibrations. Fur-thermore, the 70.7% point of the psychometric function is repeatable withan adaptive 3 AFC 1 up - 2 down method which is used in the following ex-periments (Fig. 3.6). Additionally, the perception thresholds are measuredwithout (just background noise, L = 33 dB(A) - ’silent’ condition) and withan audible (’masking’) component (pink noise, L = 69 dB(A)) in the fre-quency range from 16 to 200 Hz in the second pre-experiment. No influenceof an additional audible stimulus on the perception threshold is observable,except for 63 Hz. This measured data is influenced in the ’silent’ conditionby the emitted sound of the vibration-floor which is used for the productionof vibration (Fig. 2.6). The results indicate that this vibrating system canbe used for measurement on the perception of vertical vibrations withoutany disturbing emitted sound up to a frequency of 63 Hz.


The perception threshold for vertical whole-body vibrations is measured ina frequency range from 5 to 200 Hz taking into account the results of thetwo pre-experiments thereafter. The averaged perception curve increasesfrom 5 to 8 Hz with nearly 7 dB/octave and is constant up to 63 Hz ata level of LV ib = 88 dB. For higher frequencies the perception thresholddecreases a bit to a level of LV ib = 86 dB. This slightly increasing sensitivity- decreasing perception threshold - for 125 and 200 Hz depends probablyon bone conduction threshold. However a measurement of the perceptionthreshold is difficult or maybe impossible even with masking audible noise,if bone conduction influences the perception thresholds for higher frequen-cies. This is probably the reason why no or only a few data above 80 Hzare available for the perception threshold in the literature. However, thepresented perception threshold for vertical whole-body vibrations show nolarger deviations to literature data (Fig 3.13), except for low frequenciesbelow 16 Hz which are often influenced by visual or audible additional cues(e.g., Griffin, 1990, Fig. 3.13). Standards for vertical vibrations show a fre-quency dependent increase from 8 Hz upwards and are up to 50 Hz lowerand then higher as the summarized data, thereafter. Thus the standarddata overestimate or underestimate the vertical whole-body vibrations be-low or above 50 Hz, respectively. The particularly considerable differencesbetween individuals in the perception thresholds in this study are not expli-cable with anthropometric exogenous variables, like weight and body-size,or endogenous variables, like age and gender. These findings verify resultsof different other studies which are found in the literature for some other ex-periments on the perception of whole-body vibrations (Griffin & Whitham,1978; Orbone et al, 1981; Griffin, 1982; Parsons & Griffin, 1982; Corbridge& Griffin, 1986; Griefahn & Brode, 1997; Baumann, 2001b). Additionally,the seat pressure distribution of some participants is measured during themeasurements of the perception thresholds. Objective parameters, whichare calculated from the averaged seat pressure distributions, like mean andmaximum value of the measured pressure or of the pressure gradient, arenot helpful to explain the differences between individuals for the percep-tion of vertical whole-body vibrations (see also the diploma thesis of Kruse,2001). This experiment shows that data from different laboratories with afixed measuring technique and a fixed set-up are needed to get a revision ofthe standard perception threshold which are specified in existing standards(e.g., ISO 2631-2, 1989; VDI 2057-2, 1987). Additionally, future researchesshould investigate the differences between subjects because there are noobjective parameters found to explain the differences yet.

In the third experiment the JNDs (Just Noticeable Differences), also calleddifference thresholds, in level and frequency are measured in a frequency

3.8. Discussion 101

range from 5 Hz to 50 Hz (JNDL) and from 5 Hz to 40 Hz (JNDF) forvertical whole-body vibrations with a reference level of LV ib = 96 dB (cor-responds to a = 0.063 m/s2). The individual JNDLs range from 0.5 to2.5 dB with an overall mean, which is independent of frequency of about1.5 dB with an interindividual standard deviation of 0.4 dB (absolute dif-ference thresholds, ∆L = 0.012 m/s2 ± 0.0035 m/s2, respectively). Theintraindividual standard deviations (τ ≤ 0.4 dB) indicate a high reproducibil-ity of the JNDLs. There are no significant differences between the differ-ence thresholds at the eleven different frequencies (p < 0.01). Additionally,no significant differences are observed for 1 and 2 s stimulus duration for12.5 Hz, except for the intra- and interindividual standard deviations whichincrease slightly for 1 s duration. Studies from literature (e.g., Baumann etal., 2001a), which are measured with nearly the same references level andin the same frequency range, report similar results even though the data aremeasured on a real car seat (with a foam seat surface and a full backrest). Incontrast to these findings, results from Morioka & Griffin (2000) (measuredon a rigid seat, as well), which are measured at 5 and 20 Hz, are in a levelrange from 0.9 to 1 dB ± 0.57 dB at a level of 100 and 114 dB (0.1 and0.5 m/s2 r.m.s.). These data show that the absolute difference thresholdsincrease with increasing stimuli magnitude in contrast to the JNDLs whichdecrease with increasing magnitude of the stimuli. However, the findingsof Morioka & Griffin are independent of frequency. It would be expectedthat the data from Morioka & Griffin (2000) are a bit higher for the relativeJNDLs because a 79.4% criterion instead of a 70.7% (like in this study) isused. The differences between the summarized results point out that theJNDLs probably depend on the reference level.

Furthermore, the JNDFs are measured at the same reference level of LV ib =96 dB. The averaged detectable frequency thresholds increase from about0.4 Hz at 5 Hz with increasing reference frequency to nearly 12.4 Hz at40 Hz. This corresponds to an increase in proportion of frequency of ap-proximately 0.34 · f − 1.25 Hz in the frequency range from 5 to 40 Hz.The intra- and interindividual standard deviations increase noticeable withincreasing frequency (from nearly 0 up to about 3.1 Hz). There are noother data in the literature or values in existing standards found for JNDFswith vibration signals. In comparison to that, measured JNDFs for audiblestimuli in psychoacoustics are constant values of about 1 Hz below 500 Hzand above the JNDFs increase with 0.002 · f which indicates a higher fre-quency sensitivity in changes of frequency for the ear as for the skin (senseof touch).

In the last (fourth) experiment equal-vibration level contours (comparable toequal-loudness level contours) are determined with an adaptive 2 - AFC in-


terleaved 1 up - 1 down measuring method in the frequency range from 5 to80 Hz for vertical whole-body vibration. This measuring method minimizesthe influences of the experimental procedure, e.g., the initial level depen-dence of test vibrations on the results (Fig. 3.18). The equal-vibrationlevel contours are measured approximately 10 dB above the perceptionthreshold - reference stimuli: sinusoidal vibration with fRef = 20 Hz andLRef = 100 dB. The measured curve is constant between 5 and 6.3 Hzand shows an increase of 2.3 dB/octave from 6.3 to 63 Hz. For higherfrequencies the slope increases (6 dB/octave). In the literature only a fewdata for these curves at such low magnitudes exist which are often referredto as equivalent-comfort contours. Data from Howarth & Griffin (1990) areplaced slightly higher or around the equal-vibration level contours due to an-other measuring procedure and using a different reference stimulus (audiblenoise, Fig. 3.20). Therefore these curves are not really comparable with thedata of this study, but both findings show similar tendencies based on thedependence on frequency. The standard curve (KZ = 0.8, defined in VDI2057-2, 1987) increases with 6 dB/octave corresponding to the standardperception threshold in the same frequency range. This slope is more thantwo times higher as the measured data and shows considerable differencesto the presented data.

The shapes of the presented perception threshold and the equal-vibrationlevel contours exhibit considerable differences to each other even though thecontour is measured almost 10 dB above the perception curve (Fig. 3.21).The differences in both curves are not explicable with frequency dependingJNDLs because the difference thresholds in this level and frequency range areindependent of frequency. More equal-vibration level contours are needed,especially with reference acceleration levels between the perception thresholdand the presented equal-vibration level contour with a reference level ofLV ib = 100 dB to investigate the differences in the shape of both presentedcurves.

Chapter 4

Methods for improving theobjective description ofsubjective car vibration qualityassessments

The comfort or discomfort caused by noise and vibrations in passenger cab-ins is a decisive condition for the acceptability of a vehicle. One way to judgeacoustic and vibration quality standards is to employ professional subjective-testers with long term experiences for evaluating the noise and vibrationimpact in the car. One testing method in the car industry is concernedwith the quality of booming noise, seat and steering-wheel vibrations in idlerunning cars. It would be very advantageous to know the properties of noiseand vibration signals which are fundamental to the subjective quality assess-ments. Therefore signal parameters, which are calculated from recordingsof the sound and the vibrations inside cars, are searched in order to describeand forecast the quality judgements.

This study dissects just the objective parameters and the appendant sub-jective assessments of the seat and steering-wheel vibrations. The aim is toimprove the subjective comfort in cars and to find objective parameters forthe recorded vibration signals which are better suited to describe good orpoor quality assessments of subjective-testers. Some clues are proposed indifferent studies in literature (for example, Pielemeier et al, 1999; Wan-SupCheung et al., 1999; Bellmann et al., 2000b). Psychophysically motivatedparameters specified in existing standards (e.g., the ISO 2631-1/2 or theVDI 2057-1/2/3), as well as signal parameters from the car industry are

104 Chapter 4. Objective description of comfort inside cars

considered for classification of seat and steering-wheel vibrations. Thereforethe following investigation presents the status-quo for objective descriptionof the subjective vibration quality assessments to improve the subjectivecomfort in vehicles. The calculated parameters will be correlated with thecomfort ratings of subjective-testers.

4.1 Experimental set-up

The relation between subjective ’comfort’ assessments and objective para-meters of interior car vibrations (seat and steering-wheel vibrations) areevaluated. The testing-sessions in a car comprise subjective judgements ofthe quality of vibration and interior sound, as well as recordings of sound andvibration signals (vibro-acoustic signals) from the seat and steering-wheel aswell as the sound field in a car simultaneously (Chapter 4.2). Hence eachcar is tested in three different idle running conditions:

• without any consumer on (each consumer off)

• with light and rear window heating on (with consumer on) and

• additional running air-condition, if possible

These testing-sessions are a popular tool in car-industry and are used for arevision of the quality of car production. Additionally, the subjective ratingsof the vibro-acoustic quality of a car are a good way for prototyping of newcars and for sound and vibration design. The usage of professional testers isa more common standard in the car industry because the testers know thevariance which possibly occur in a car type (production run). Furthermore,the testers are highly trained subjects who are able to give constant andrepeatable results for the evaluation of different vehicles belonging to thesame car type. Therefore it is possible to evaluate and to supervise theserial production of cars by these testers. The subjective-testers are able torecognize different cars during a testing-session which is confirmed in dryrunnings.

Used Cars The testing-sessions are conducted in cars from three differ-ent car classes (small, middle and upper middle class) with just 4-cylinderengine models. Therefore, it is possible to investigate if the parameters forthe description of the subjective quality of the seat and the steering-wheelvibrations depend on the used car class (type) or if the parameters are globalvariables. The number of the used cars was changed from class to class:

4.2. Calculation of the objective signal parameters 105

for upper middle class NP = 3 petrol and ND = 9 diesel-engine cars aremeasured. For middle class cars NP = 7 and ND = 9 are available for thisanalysis and NP = 8 and ND = 8 for small class. The vehicles in one carclass belong to the same type of car.

Some of the tested cars have no air condition. That is the reason why thetotal number of available data1 are as followed:

• upper middle class cars: nP = 9 / nD = 26

• middle class cars: nP = 18 / nD = 27

• small class cars: nP = 21 / nD = 22

4.2 Calculation of the objective signal para-meters

19 channel signal recordings

The vibro-acoustic signals are recorded with a SQLab II System and the soft-ware package ArtemiS 3.01.100 from HEAD acoustics in combination withan IBM Thinkpad. During the subjective ratings the following vibro-acousticsignals in x/y/z- directions (axes) have been recorded by microphones andaccelerometers simultaneously. In particular:

• Sound pressure p with window-microphones (B&K 4190) at the frontside windows - left (driver‘s side) and right (front-seat passenger‘sside) - in head height of an adult.

• Sound pressure p (two channels) with an artificial head (HMS II fromHEAD acoustics) on the front-seat passenger‘s side.

• Vibration acceleration a at the right back rail of the driver‘s seat -referred to as position ’P1 ’- (PCB 356A15 accelerometer, triaxial).

• Vibration acceleration a at the left front rail of the driver‘s seat -referred to as position ’P2’- (PCB 356A15 accelerometer, triaxial).

• Vibration acceleration a on the driver‘s seat (seat surface) - referredto as position ’P3 ’- (accelerometer cushion MMF KB103SV, triaxial).

1Numbers of signals nP /nD are the product of the number of different used carsNP /ND and the tested conditions.


• Vibration acceleration a at the back-rest of the driver‘s seat (ac-celerometer cushion MMF KB103SV, triaxial) for small and middleclass vehicles and at the head rest of the driver‘s seat (PCB 356A15accelerometer, triaxial) for upper middle class cars - referred to asposition ’P4’.

• Vibration acceleration a at the steering wheel (highest place) - referredto as ’wheel’- (PCB 356A15 accelerometer, triaxial).

The following analysis is restricted to the evaluation of the vibration signalsfrom all four measuring positions (’P1’ to ’P4’) of the seat vibrations and thesteering-wheel vibrations (measuring position ’wheel’). The used measuringpositions of the seat and steering-wheel vibrations in a car are shown inFig. 4.1. The positions ’P2’ to ’P4’ are specified for laboratory methods forevaluating vehicle seat vibrations in the ISO 10326-1 (1992) (Fig. A.3 inAppendix A).

The first step in preparing the signals is to choose (by means of an editor)intervals with no interfering disturbances which inevitably occur during therecordings in the presence of humans in the cabin, especially on the seat.The following calculations are based on these ’clean’ intervals which containjust the interesting signals.

Steering-wheel

’P3’ seat surface

’P2’ front seat rail

Fig. 4.1: Measuring positions for seat (for example ’P2’ and ’P3’) and for steering-wheel (’wheel’) vibrations inside a car.


Analysis of the vibration signals

Averaged vibration spectra, which are calculated from the recorded signals,are the basis for determination of the objective signal parameters. Thoseparameters will be correlated with ratings of the subjective-testers. Firstof all, objective psychophysically motivated signal parameters, which arespectrally weighted and specified in existing standards (e.g., ISO 2631-1,1997; VDI 2057-2, 1987; ISO 5349, 1986), and standard signal parameters,which are usually used in the car industry, are taken for the description ofseat and steering-wheel vibrations. In particular four different parametersare determined:

1. az rms acceleration in z-direction of the spectrally unweighted ac-celerations in the frequency range from 0 to 500 Hz (referred to asunweighted z-acceleration). This objective parameter is determinedjust for seat vibrations (Eq. 4.4).

2. awz rms acceleration in z-direction of the spectrally weighted accel-erations in the frequency range from 0 to 500 Hz (referred to asweighted z-acceleration). This objective parameter is calculated justfor seat vibrations (after ISO 2631-2, Eq. 4.4), as well.

3. a′V unweighted vibration total value (rms acceleration) of the spec-trally unweighted rms accelerations in all three (x/y/z) directions inthe frequency range from 0 to 500 Hz (Eq. 4.2).

4. aV vibration total value (rms acceleration) of the spectrally weightedrms accelerations in all three directions in the frequency range from0 to 500 Hz (after ISO 2631-1, VDI 2057-2 for whole-body vibrationsor ISO 5349-1 for hand-arm transmitted vibrations, Eq. 4.1, Chap-ter 1.1.3).

The rms values instead of the Vibration Dose Values (VDV) are used becausean analysis of the recorded vibration signals points out that the crest factoris below 6 and the vibration signals are nearly stationary. Therefore therms value is the adequate evaluation parameter for the description of thevibrations (Chapter 1.1.3).

After calculating each x/y/z (rms) acceleration separately, the (spectrallyunweighted and weighted) vibration total values a′V and aV are combinedwith the exponent na (related to the energy), weighting factors kj for dif-ferent directions and j = x, y, z, as followed:


aV =[kx

naanawx + ky

naanawy + kz

naanawz

] 1na

(4.1)

a′V =[kx

naanax + ky

naanay + kz

naanaz

] 1na

(4.2)

weighted

awx/y =[∑

i

(Wd,i · ai)2] 1

2

awz =[∑

i

(Wk,i · ai)2] 1

2

awh =[∑

i

(Wh,i · ai)2] 1

2

unweighted

ax/y =[∑

i

a2i

] 12

(4.3)

az =[∑

i

a2i

] 12

(4.4)

ah =[∑

i

a2i

] 12

(4.5)

with

aV = the spectrally weighted vibration total value

a′V = the spectrally unweighted vibration total value

ai = the rms acceleration for the ith frequency component of whole-

body vibrations in x/y/z- directions or hand-arm vibrations

Wd,i = the weighting factor for the ith frequency component of whole-

body vibrations in x/y- direction

Wk,i = the weighting factor for the ith frequency component of whole-

body vibrations in z- direction

Wh,i = the weighting factor for the ith frequency component of hand-

arm vibrations in x/y/z- directions

kj = weighting-factors for the three (j = x/y/z) directions

The weighting factors kj for the three (x/y/z) directions are kx = ky = kz =1, and the exponent is na = 2 according to the recommendation for comfortand perception evaluation after ISO 2631-1 and VDI 2057-2. The spectralweighting functions W for different directions are used according to ISO2631-1, VDI 2057-2 and ISO 5349-1 for the calculation of the weighted rmsaccelerations (vibration total value) aV . The spectral weighting functionsare based on psychophysical experiments. The comparison of the weighting


functions Wd and Wk indicates that the sensitivity of humans for verticalvibrations (z-axis) is higher than for vibrations in the horizontal plane (x- andy-axes) (Fig. 4.3 and Chapter 1.1.3). For hand-arm transmitted vibrationsonly one weighting function Wh exists for all three directions (defined inVDI 2057-2 and ISO 5349-1). Additionally, the weighting functions Wd andWk for whole-body vibrations are used for the calculation of an objectiveevaluation parameter for steering-wheel vibrations in this study. Duringthe correlation analysis it was observed that the objective broadband signalparameters do not always deliver high significant correlation coefficientswith the subjective ratings. Therefore signal parameters are determinedby calculating the (weighted and unweighted) vibration total value aV anda′V , (weighted and unweighted) z-acceleration awz and az, respectively, inspecially selected narrow frequency bands around prominent motor orders(see spectra in Fig. 4.2 and 4.4):

∆B1 = [ 0 ≤ f ≤ 500 Hz]− whole spectrum (0 - 500 Hz)

∆B2 = [10 ≤ f ≤ 35 Hz]− around the 1st and 2nd motor order

∆B3 = [20 ≤ f ≤ 35 Hz]− around the 2nd motor order

∆B4 = [35 ≤ f ≤ 100 Hz]− around the 4th to 6th motor order

∆B5 = [73 ≤ f ≤ 100 Hz]− around 6th motor order

(just for steering-wheel vibrations)

Therefore 15 different parameters for steering-wheel vibrations2 and 16 dif-ferent parameters for each measuring position for seat vibrations3 are at mydisposal for the following analysis. Typical averaged spectra in three dimen-sions (x-, y- and z-direction) of the seat vibrations and the steering-wheelvibrations for 4-cylinder petrol- and diesel-engine cars for each car class(type) are shown in Fig. 4.2 for the seat and in Fig. 4.4 for steering-wheelvibrations. The acceleration values - here as well as in the following figures- are given in arbitrary units [au]. The spectra have a resolution of 2.9 Hzin the frequency range from 3 to 200 Hz. The cutoff frequency f = 200 Hzis used for illustration because there is not a lot energy above 200 Hz in thevibration signals and the sensitivity of the human body also decreases withincreasing frequency.

The spectra of the seat vibrations in Fig. 4.2 exhibit a typical peak-troughstructure which can be interpreted in terms of motor orders (MO). For ex-

2Parameter: spectrally unweighted and weighted (with hand-arm and whole-bodyvibration weighting functions) vibration total value in five different frequency ranges.

3Parameter: spectrally unweighted and weighted z-acceleration and vibration totalvalue in four different frequency ranges.


Frequency [Hz]

Acc

eler

atio

n [a

u]

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10

x−axisy−asisz−axis

0.1

.316

1

3.16

10 Petrol

Diesel

Frequency [Hz]

Acc

eler

atio

n [a

u]

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10


0.1

.316

1

3.16

10 Petrol

Diesel

Frequency [Hz]

Acc

eler

atio

n [a

u]

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10

4 6.3 10 16 25 40 63 100 160

0.1

.316

1

3.16

10


0.1

.316

1

3.16

10 Petrol

Diesel

Fig. 4.2: Typical averaged spectra for seat vibrations of petrol- (left) and diesel-engine models (right) in all three (x-, y- and z-) directions. For each car classone typical petrol and diesel car is shown: upper middle class (top), middle class(middle) and small class (bottom).

ample, a motor with 800 rpm in idle running condition shows the secondorder at about 27 Hz and delivers the most prominent contribution for a 4-cylinder engine. The following even order peaks clearly dominate the higherfrequency region. The distinct vertical vibrations (z-direction) does not giveconsiderably higher accelerations than those in the horizontal plane (x- andy-directions), especially for higher motor orders for almost all investigatedcars from different car classes. The accelerations in x- and y-direction reachparticularly the acceleration values of the vertical (z-axis) around the 2ndmotor order for diesel cars. The y-acceleration (y-axis) gives the highestcontribution at higher motor order for petrol and diesel cars from the uppermiddle and the middle class. The effect of the psychophysically motivatedspectral weighting functions Wd and Wk on the different frequency compo-nents in the three directions is visualized in Fig. 4.3. On the left side theoriginal spectra of the seat vibrations are shown. In comparison to that, theweighted spectra of the same seat vibrations are given in the right figure.


Frequency [Hz]

Acc

eler

atio

n [a

u]

4 6.3 10 16 25 40 63 100 160

0.01

0.1

1

10 spectrally unweighted


4 6.3 10 16 25 40 63 100 160

spectrally weighted

Fig. 4.3: Typical spectrally unweighted spectra (left) in comparison to theweighted (right) spectra by using the weighting functions Wd for x/y- axes andWk for the vertical components for seat vibrations (specified in the VDI 2057-2and the ISO 2631-1).

For steering-wheel vibrations (Fig. 4.4) the co-ordinate system with thex’/y’/z’-axes is used. It differs a bit from the usual definition of the x/y/z-dimensions (cartesian co-ordinate system) in a car. The x’-direction pointstoward the front into the direction of the steering column, the y’-axis ispractically identical to the y-axis and points from right to left and the z’-axis is orthogonal to the x’- and y’-axis and lies in the plane of the steering-wheel. Fig. 4.4 shows a typical example of averaged spectra in the x’-, y’-and z’-dimensions. The shown peak-trough structure can also be related tothe motor orders. The peaks at the second and the sixth motor order (!)are clearly most prominent for nearly all presented spectra. The vibrationsin x’-direction appear to be the strongest in nearly the whole consideredfrequency range. An exception is the frequency range around the first order,where the z’-vibrations sometimes are stronger than those in x’-direction.The vibrations in z’-direction reach the acceleration values in the x’-directionaround the second order. There are considerable differences observable forthe spectra between different types of classes, as well as between diesel- andpetrol-engine cars.

Three clear differences between the seat and steering-wheel vibrations areidentifiable (Fig. 4.2 and 4.4):

1. the measured steering-wheel vibrations (accelerations) around the 2ndmotor order are higher than the seat vibrations.

2. the steering-wheel vibrations contain more energy at higher motororders - e.g., at 6th motor order - than the seat vibrations.

3. the magnitude distribution of the vibrations are varying in all threedirections for steering-wheel and the seat vibrations.


Frequency [Hz]

Acc

eler

atio

n [a

u]

4 6.3 10 16 25 40 63 100 160

0.1

1

10

100

4 6.3 10 16 25 40 63 100 160

0.1

1

10

100

x‘−axisy‘−asisz‘−axis

0.1

1

10

100

Petrol

Diesel

Fig. 4.4: Typical averaged spectra, like the spectra of the seat vibrations inFig. 4.2, for the steering-wheel vibrations of petrol (left) and diesel (right) modelin x’-, y’- and z’-axes at the position ’wheel’ for different car types: upper middleclass (top), middle class (middle) and small class (bottom).

4.3 Subjective quality judgements

In an ordinary testing-session in the car industry, the professional subjective-tester gives his (dis-) comfort ratings of the sound and vibration quality inidle running cars. The ratings are categorically assessed by using a fixed10 point scale which is normally used in the car industry for quality assess-ments of sound and vibrations. The subjective-testers are familiarized withthis scale. The subjective quality judgements are presented in terms of cat-egorical units [cu] which are different from the numbers of the scale used.It turns out that just a limited portion of this scale is normally used for thequality evaluations. However, the categorical units reflect the resolution ofthe categories which are employed by the subjective-testers. Thereby highsubjective ratings indicate a good quality whereas low values denote a poorquality.

4.4. Results of the correlation analysis 113

During a subjective testing-session the evaluation is performed for threedifferent stimuli: the booming noise, the seat and the steering-wheel vibra-tions. These three aspects are rated for three different conditions, thereforenine subjective assessments for each car and for each tester with an air-condition, and six for cars without an air-condition are available for thefollowing analysis.

Two subjective-testers were available for tests in the small and the middleclass vehicles and one subjective-tester for the upper middle class vehicles.The subjective-testers are professional highly trained subjects with a longterm experience. Both testers for small and middle class cars show almostsimilar judgement behaviors which is confirmed with statistical tests. There-fore the subjective assessments are summarized together with the objectiveparameters in the cases of the small and the middle class vehicles.

4.4 Results of the correlation analysisbetween objective signal parameters andsubjective ’comfort’ assessments

The correlation coefficients r (Pearson) are determined for the descriptionof the relation between the subjective judgements and the objective (eval-uation) signal parameters - unweighted and weighted vibration total valuesa′V and aV , as well as z-accelerations az and awz - for seat or steering-wheelvibrations. The statistically significant correlation coefficients rP for petroland rD for diesel models are marked with asterisks (*) according to thelevel of significance4. In addition a linear regression curve between the usedsubjective and objective data is calculated and represented if the respectivecorrelation coefficient is statistically significant. For correlation analysis be-tween the objective vibration parameters and the subjective ratings differentnumbers of data pairs are used (Chapter 4.1). The analysis separated afterthe different car classes enabled one to find objective parameters which areglobal evaluation tools for the subjective quality assessments in cars.

First the correlation analysis is described for middle class vehicles in detail.The findings for the objective description of the subjective judgements formiddle class vehicles are compared to the evaluation parameters which arefound for small and upper middle class vehicles thereafter. Additionally, astatistical test points out that the correlation coefficients are improved fora separate analysis of petrol- and diesel-engine cars. Therefore the results

4* - 5%, ** - 1%, *** - 0.1% level of significance


of the correlation analysis are presented separately after petrol and dieselcars. Parameters from existing standards and usual parameters from the carindustry are used for the correlation analysis.

4.4.1 Seat vibrations

Middle class cars

First the correlation analysis is realized between the subjective ratings andthe objective signal parameters spectrally unweighted and weighted z-acceler-ation (az and awz) for seat vibrations of the middle class cars. The corre-lation coefficients are calculated separately after petrol nP = 36 and dieselcars nD = 54. The relation between the subjective assessments and theobjective parameters, which are calculated in the whole frequency range(∆B1 : 0 ≤ f ≤ 500 Hz), are shown in Fig. 4.5 for the measuring position’P3’.

0 5 10 15 20unweighted z−Acceleration a

z [au]

subj

. Rat

ing

[cu] r

P= −0.59***

nP=36

rD= −0.095

nD=54

↑

↓1 categorical unit [cu]

↑

bette

r

→Regression Petrol

0 2.5 5 7.5 10 12.5unweighted z−Acceleration a

wz [au]

rP= −0.55**

nP=36

rD= −0.19

nD=54

← Regression Petrol

DieselPetrol

Fig. 4.5: Relation between the spectrally unweighted z-accelerations az (left) andthe spectrally weighted z-accelerations awz (right) in the frequency band ∆B1

(whole frequency range) of the driver seat, respectively, and the subjective ratingsfor measuring position ’P3’. Additionally, the correlation coefficients rP / rD andthe total number of data pairs nP / nD are presented.

The relation between the objective and subjective data is not statisticallysignificant for diesel cars (az: rD = −0.01 and awz: rD = −0.19) butit is statistically significant for petrol cars (az: rP = −0.59∗∗∗ and awz:rP = −0.55∗∗). The correlation coefficients are negative which meansthat a higher rating indicates a better quality and less vibrations. Theresults for spectrally unweighted z-acceleration az (left) and the spectrallyweighted z-acceleration awz (right) look very similar, except for the levelrange. The reason for this is that the weighting function Wk exhibits a


low pass characteristic. Therefore just the higher frequency components aredecreased and the lower frequency components, especially around the 2ndmotor order dominate the objective parameter awz. The high correlationcoefficients for petrol cars are effected by just two objective parameters witha high acceleration around 15 au. Therefore it is difficult to derive a generaltendency for petrol cars.

Furthermore, the spectra in Fig. 4.2 show that the vibrations in the horizon-tal plane are also as high as the components in the vertical axis. Therefore,the relation between the objective parameters, which include the acceler-ations in all three directions, like the spectrally unweighted and weightedvibration total values a′V and aV (after Eq. 4.2 and 4.1) and the subjectiveratings are presented in Fig. 4.6 for used petrol and the diesel models. Thevibration total values are calculated in the same frequency range as thevertical (z-) accelerations in Fig. 4.5. The correlation coefficients betweenthe spectrally unweighted vibration total value a′V and the pertinent sub-jective ratings for seat vibrations are statistically high significant for petroland for diesel cars, rP = −0.78∗∗∗ and rD = −0.36∗∗. Using the spec-tral weighting functions Wd and Wk, which are psychophysically motivated,for the calculation of the rms accelerations for x- and y-directions and forz-direction yields the relation between objective and subjective data of theright figure. The correlation coefficient for the investigated petrol models issignificant, rP = −0.55∗ again, but not as high as the correlation coefficientfor the unweighted parameter a′V , rP = −0.78∗∗∗. In comparison to this,the ’clouds’ of points testify that no significant correlation exists betweenthe weighted vibration total value and the subjective rating for diesel models

0 5 10 15 20 25 30unweighted Vibration Total Value a‘

V [au]

subj

. Rat

ing

[cu]

rP= −0.78***

nP=36

rD= −0.36**

nD=54

↑


↑

bette

r

← Regression Diesel


0 2.5 5 7.5 10 12.5weighted Vibration Total Value a

V [au]

rP= −0.55*

nP=36

rD= −0.26

nD=54


DieselPetrol

Fig. 4.6: Relation between the spectrally unweighted and weighted vibration totalvalues a′V , a′V of the driver seat and the subjective ratings like in Fig. 4.5 for thez-accelerations.


(rD = −0.26, Fig. 4.6). Furthermore, the data for spectrally weighted para-meters awz and aV look very similar (Fig 4.5 and 4.6). The reason for thisis that the weighting function Wd decreases the horizontal accelerations (x-and y- directions) more than the z- acceleration by using Wk, so that theweighted parameter aV is dominated by the z-components and is similar tothe parameter awz (see also the weighted spectra in Fig. 4.3).

Fig.4.5 and 4.6 also exhibit a more general trend which applies to the otherinvestigated objective parameters. The correlation coefficients between thesubjective and the objective data increase when spectrally unweighted rmsacceleration parameters, which take into account accelerations of all three(x/y/z) directions, are used. The calculated correlation coefficients betweenthe objective vibration parameters of the driver seat and the subjective rat-ings for nP = 36 and nD = 54 are summarized in Tab. 4.1. The analy-sis is carried out in the indicated frequency ranges of the seat vibrations(columns). The four rows make the distinction between spectrally weightedand unweighted parameters aV , awz, a′V and az.

The parameters (spectrally unweighted vibration total values) from broad-band vibration signals correlate significantly with the subjective ratings ofthe professional testers for petrol and diesel models. Similar high signifi-cant correlation coefficients deliver for parameters from a limited frequencyband between the 1st and 2nd motor order and around the 2nd motororder (Fig. 4.7). The correlation coefficients show no significant tenden-cies with the subjective judgements for the calculated parameters aroundhigher motor orders (not presented in Tab. 4.1). The importance of vi-bration energy at lower frequency for the (dis-) comfort is supported by

0 5 10 15 20 25unweighted Vibration Total Value a‘

V [au]

subj

. Rat

ing

[cu]

rP= −0.69***

nP=36

rD

= −0.3*

nD

=54

↑


↑

bette

r



DieselPetrol

Fig. 4.7: Same relationsas in Fig. 4.6 between thesubjective ratings and thespectrally unweighted vi-bration total values a′V ina narrow frequency rangefrom 10 to 35 Hz (∆B2).


Tab. 4.1: Correlation coefficients between subjective ratings for the driver seatvibrations and spectrally weighted / unweighted vibration total values aV / a′V andz-accelerations awz / az, respectively, at the position ’P3’ for different frequencyranges for middle class vehicles.

Frequency range 0-500 Hz 10-35 Hz 20-35 Hz

Motor order (MO) whole range 1st - 2nd MO 2nd MO

petrol nP = 36 /diesel nD = 54

rP rD rP rD rP rD

unweighted vibrationtotal value a′V

-0.78

***

-0.36

**

-0.69

***

-0.30

*

-0.69

***

-0.26

weighted vibrationtotal value aV

-0.55

***

-0.26 -0.56

***

-0.25 -0.57

***

-0.10

unweighted z-acceleration az

-0.59

***

-0.09 -0.59

***

-0.13 -0.60

***

-0.04

weighted z-acceleration awz

-0.55

***

-0.19 -0.55

***

-0.21 -0.57

***

-0.05

the fact that parameters from the spectrally weighted and from the narrowfrequency band acceleration signals yield significant correlation coefficientswith the subjective parameters (of course with the exception of the highfrequency range from 35 to 100 Hz). In this context, it should be statedthat the weighting functions Wk and Wd exhibit low pass characteristicsand the weighting function Wd decreases the horizontal acceleration (x-and y- direction) more than the z- acceleration by using Wk. However,for the investigated cars, the horizontal accelerations reach the accelerationvalues in z-direction, especially around the prominent 2nd motor order, fordiesel models and in higher motor order spectrum for petrol models. That isthe reason why the spectrally unweighted parameters give significant highercorrelation coefficients with the subjective ratings than spectrally weightedparameters. These findings are tested in a correlation analysis which de-livers nearly the same correlation coefficients by using only the horizontalvibrations for the objective parameters.


The above summarized finding is a contradiction to a study carried out byBellmann et al. (2000b), but the spectra of the used cars in that studyshow that the horizontal vibrations are more than a factor of 3 times lowerthan the vertical seat vibrations. The results show that the horizontal vi-brations are of decisive importance for subjective judgements of the presentcars. Additionally, the usage of objective signal parameters, which con-tain contributions of all three acceleration (x/y/z-) directions instead ofjust one dimensional parameters (especially z-acceleration), provide highercorrelation coefficients. An analysis with diesel and petrol models separatedincreases the correlation coefficients, as well. The various assessment behav-iors (Fig. 4.5 to 4.7) of petrol and diesel models however are not explicablejust with spectral qualities or properties of the seat vibration signals.

The objective acceleration parameters have been calculated for four differentmeasuring points (’P1’ - ’P4’). For the investigated type of car it turns outthat the correlation coefficients are always the highest for parameters ofthe seat vibrations measured at the position ’P3’ which is the contract areabetween the vibrating seat surface and the human body. The measuringposition ’P4’, which is at the backrest of the seat, yields nearly the samecorrelation coefficients between the subjective and objective data.

In the ordinary, subjective assessments, which are given on a categoricalscale, correlate with logarithmic parameters, which is frequently reportedfor measurements in psychoacoustics. It is just briefly noted that logarith-mic objective parameters, which are based on the acceleration level (LV ib),deliver correlation coefficients which are nearly the same by using the (lin-ear) acceleration a. This is verified in statistical tests. This result is notsurprising because the linear acceleration for used seat vibration signals donot differ very much so that the differences in the (logarithmic) accelerationlevel are not large, as well. Moreover, the correlation coefficients betweenthe weighted Vibration Dose Values and the subjective ratings are calcu-lated even though the crest factors are below 6. The statistical test withthe VDV yields in any case lower correlations with the subjective judge-ments than with the objective rms parameters. This correlation coefficientsare not particularly significant but show the same tendencies as parameterswhich are related to the energy (rms), as mention above. This finding isalso frequently reported in literature.

Upper middle class cars

For analysis of the seat vibrations of cars of the upper middle class nP = 9for petrol and nD = 26 for diesel are available. One subjective-tester par-ticipated in the testing-sessions for the evaluation of the quality of booming



V [au]

subj

. Rat

ing

[cu]

rP= −0.92***

nP=9

rD= −0.07

nD=26

↑


↑

bette

r



V [au]

rP= −0.26

nP=9

rD= −0.55**

nD=26


DieselPetrol

Fig. 4.8: The subjective ratings for seat vibrations of the driver seat are presentedas a function of the spectrally unweighted (left) and the weighted (right) vibrationtotal value a′V , a′V for upper middle class cars. The objective parameters arecalculated in the frequency range ∆B1 and the measuring position was ’P1’.

noise, as well as seat and steering-wheel vibrations. The same correlationanalysis between the subjective ratings and the different objective para-meters for seat vibrations, like for middle class cars in Chapter 4.4.1, hasbeen carried out for the vehicles of upper middle class, as well. The re-lation between the subjective ratings and the spectrally unweighted andweighted vibration total value - a′V and aV - for the whole frequency range(∆B1 : 0 ≤ f ≤ 500 Hz) are shown in Fig. 4.8. The subjective ratings arepresented as a function of the same objective parameters as in Fig. 4.8 forthe narrow frequency band between the 1st and 2nd motor order in Fig. 4.9.The seat vibration signals were measured at the measuring position ’P1’(back seat rail).

The relation between the spectrally unweighted vibration total values aV

which is calculated in the whole frequency range (∆B1) and the subjectiveratings is significant for petrol cars, rP = −0.92∗∗∗, but it is not significantfor the diesel cars, rD = −0.07. The correlation increases for diesel cars ifthe psychophysically motivated weighting functions are used for calculationof the weighted vibration total values aV . The correlation coefficient is thensignificant, rD = −0.55∗∗. But the clouds of data for petrol cars show thatthere is no correlation if the spectrally weighted vibration total value is usedinstead of the unweighted parameter, rP = −0.07.

Both correlation coefficients for diesel and for petrol cars become statisti-cally significant between the objective spectrally unweighted vibration totalvalues and the subjective ratings if just a limited frequency band from the1st to the 2nd motor order is used for the calculation of the objective



V [au]

subj

. Rat

ing

[cu]

rP= −0.72*

nP=9

rD= −0.65**

nD=26

↑


↑

bette

r

→Regression Diesel


0 5 10 15 20weighted Vibration Total Value a

V [au]

rP= −0.23

nP=9

rD= −0.54*

nD=26

←Regression Diesel

DieselPetrol

Fig. 4.9: Relation between spectrally unweighted and weighted vibration totalvalues a′V , aV of the driver seat and the subjective ratings like in Fig. 4.8. Thenarrow frequency range between the 1st and 2nd motor order is used for thecalculation of the objective parameters at the position ’P1’.

parameter (Fig. 4.9). The correlation coefficients for the various spectrallyunweighted and weighted rms parameters are also calculated in differentfrequency ranges and are summarized in Tab. 4.2.

The correlation analysis between the objective parameters and the subjectiveratings for seat vibrations of the upper middle class cars points out that theenergy at low frequencies, especially between the 1st and the prominent 2ndmotor order, is of paramount importance for subjective ratings. Additionally,spectrally unweighted parameters deliver in any case for petrol cars and innarrow band frequency ranges for diesel cars higher correlation coefficientswith the judgements than spectrally weighted parameters. The correlationcoefficients between the unweighted vibration total value calculated in thenarrow frequency range ∆B2 and the subjective ratings for seat vibrationsare statistically significant, rP = −0.72∗ and rD = −0.65∗∗ (Tab. 4.2 andFig. 4.9). The measuring position ’P1’ for seat vibrations delivers in anycase the highest correlations between the objective and subjective data.The measuring position ’P2’ (front left seat rail) delivers similar results.The reason why the objective parameters, which are calculated form thevibration signals recorded at the contact area between the human and theseat, do not deliver the highest correlation coefficients with the subjectiveratings is not really clear. A possible reason probably is that the measuringposition ’P3’ for vibrations at the contact area is not the right one on theused car seat for recording the adequate seat vibrations.

The findings of the analysis of the seat vibrations for upper middle classvehicles are similar to the results of the correlation analysis for middle classvehicles (Chapter 4.4.1). However, the correlation coefficients are based


Tab. 4.2: Correlation coefficients between subjective ratings and different objec-tive parameters for driver seat vibrations for upper middle class vehicles like inTab. 4.1 for middle class cars. The measuring position is ’P1’.




rP rD rP rD rP rD


-0.92

***

-0.07 -0.72

*

-0.65

***

-0.65 -0.64

***


-0.26 -0.55

**

-0.23 -0.54

**

-0.22 -0.54

**


-0.41 -0.52

**

-0.27 -0.52

**

-0.27 -0.52

**

raggedright weightedz- acceleration awz

-0.21 -0.53

**

-0.18 -0.53

**

-0.18 -0.53

**

on different measuring positions for seat vibrations in different car types,probably due to the used car seat with different seat rails.

Small class cars

Two subjective-testers assisted for the testing-sessions in the small car class.But their judgement of both testers differ in this case significant which isconfirmed in a statistical test. The reasons for differences in the assessmentsbehavior of the quality of the seat vibrations are probably influenced by thefact that the production run of these cars were new. Furthermore, the testersare not highly trained and are not familiar with the assessments of the seatvibrations of the tested cars of this type. For these reasons, the results ofjust one subjective tester, who delivers the highest correlations, are shownin the following analysis. A second difference to the analysis of the other carclasses is that the optimal measuring position of the seat vibrations dependson the engine type so that the position ’P1’ is used to present the results



V [au]

subj

. Rat

ing

[cu]

rP= −0.31

nP=21

rD= 0.093

nD=22

↑


↑

bette

r


V [au]

rP= −0.79***

nP=21

rD= −0.73***

nD=22



DieselPetrol

Fig. 4.10: Relation between spectrally unweighted (left) and weighted (right)vibration total values a′V , a′V of the driver seat and the subjective ratings forsmall class cars in the whole frequency range. The presented data are from onesubjective-tester and the measuring position was ’P3’ for petrol and ’P1’ for dieselcars.

for diesel-engine cars and ’P3’ is used for petrol cars.

The number of subjective and objective data pairs are nP = 21 for thepetrol and nD = 22 for diesel cars because the data of just one tester areused. The 16 different spectrally weighted signal parameters are calculatedfor seat vibrations like for middle and upper middle class cars, as well. Thesubjective ratings for seat vibrations are given as a function of the spectrallyunweighted and weighting vibration total values in Fig. 4.10 for the wholefrequency range (∆B1). The clouds of data pairs for unweighted parameterstestify that there are no correlations between the subjective and objectivedata. The correlation coefficients are not statistically significant for thepetrol and for diesel cars, rP = −0.31 and rD = −0.09. The relationbetween the subjective ratings and the spectrally weighted vibration totalvalues aV increase by the application of the psychophysically motivatedweighting functions Wk and Wd (Fig.4.10 left). The correlation coefficientsbecome statistically significant, rP = −0.79∗∗∗ and rD = −0.73∗∗∗. Almostthe same correlation coefficients rP and rD result if the spectrally weightedparameters are calculated in a narrow frequency range around the prominent2nd motor order and between the 1st and the 2nd motor order (Fig. 4.11 andTab. 4.3). Additionally, the correlation coefficient for diesel cars is significantfor the unweighted parameter in the narrow frequency band ∆B2.

The correlation coefficients between all the calculated objective parametersin different narrow and broad frequency bands and the appendant subjectivejudgements of the seat vibrations are listed in Tab. 4.3. The results pointout that the energy at low frequencies between the 1st and the 2nd mo-



V [au]

subj

. Rat

ing

[cu]

rP= −0.27

nP=21

rD= −0.72***

nD=22

↑


↑

bette

r

↑Regression Diesel

0 5 10 15 20weighted Vibration Total Value a

V [au]

rP= −0.62**

nP=21

rD= −0.73***

nD=22

↑Regression Diesel

←Regression Petrol

DieselPetrol

Fig. 4.11: The subjective ratings for the seat vibrations in the small class carsare presented as a function of the spectrally unweighted and weighted vibrationtotal values a′V , aV , like in Fig. 4.10. The narrow frequency range around the 1stand 2nd motor order is used for the calculation of the objective parameters at theposition ’P3’ for petrol and ’P1’ for diesel cars.

tor order are very important for the subjective ratings again. This findingis similar to the results of the other car classes. But the summarized re-sults show some more general tendencies for the small class cars: first, thevibrations in the vertical direction (z-acceleration) influence the subjectivequality judgements more than the vibrations in the horizontal plane for thistype of car. The correlation coefficients for the weighted z-accelerations awz

are nearly equal with the correlation coefficients for the weighted vibrationtotal values aV and are higher for the unweighted parameters (Tab. 4.3).This finding is explicable with the presented spectra of the seat vibrationsin Fig. 4.2. The vertical vibrations in this car type dominate the wholefrequency range, especially around the 2nd motor order, so that the vibra-tions in the horizontal plane are not perceptible or are probably maskedby the vertical components. The calculated parameter aV by applicationof the spectral weighting functions deliver similar correlation coefficients asspectrally unweighted parameter for diesel models and higher correlations forpetrol models with the subjective ratings because the weighting function Wd

decreases the horizontal accelerations (x- and y- direction) more than thez- acceleration by using Wk. Therefore the vertical vibrations provide thehighest components for the spectrally weighted vibration total value. Addi-tionally, the weighting functions exhibit low pass characteristics. Thereforethe vertical vibrations at low frequencies are more accentuated than thehorizontal vibrations. Furthermore, the objective parameters for the diesel-engine cars are significantly higher than the data for the petrol-engine carseven though nearly a similar part of the subjective rating scale is used.


Tab. 4.3: Correlation coefficients between the subjective ratings for driver seatvibrations and the spectrally weighted / unweighted vibration total values aV /a′V and z-accelerations awz / az for small class cars, respectively. The correlationcoefficients are for the data of one subjective tester measured at the position ’P1’for diesel cars and at ’P3’ for petrol cars.




rP rD rP rD rP rD


-0.31 -0.09 -0.27 -0.72

***

-0.15 -0.70

***


-0.79

***

-0.73

***

-0.62

**

-0.73

***

-0.30 -0.73

***


-0.59

**

-0.62

**

-0.48

*

-0.73

***

-0.35 -0.73

***

weighted z-acceleration awz

-0.79

***

-0.73

***

-0.63

**

-0.73

***

-0.36 -0.73

***

The analysis of the seat vibrations of the small class cars show that if thevibrations in one direction are expressed clearly the spectra the subjectiveratings are influenced by these components. Additionally, the judgementbehavior of the two professional subjective-tester are particularly significantlydifferent probably due to the fact that the testers are not familiar with the’new’ type of car class. Therefore professional testers who are specialized forsome car types are maybe necessary for the evaluation of subjective qualityof seat vibrations.

4.4.2 Steering-wheel vibrations

Two different types of spectral weighting functions are used for the anal-ysis of the steering-wheel vibrations. First, the accelerations in all threedirections are spectrally weighted with the same weighting function Wh,


which is defined in ISO 5349-1 for hand-arm transmitted vibrations, and arecombined with the weighted vibration total value aV thereafter. It is justbriefly noted that the weighting function Wh exhibit a low pass characteristicand that is why the low frequency components are more accentuated thanthe higher frequency components. A second kind of weighting functions isused for the evaluation of the steering-wheel vibrations in this study. Theweighting functions Wk and Wd for the evaluation of whole-body vibrationsare used for hand-arm vibrations, as well: Wd for horizontal vibrations andWk for vertical vibrations. The weighted and unweighted parameters arecalculated in five different frequency ranges. Therefore 15 different objec-tive parameters are correlated with the subjective ratings in the followinganalysis.

Middle class cars

The relations between nP = 36 (petrol) and nD = 54 (diesel) spectrallyunweighted vibration total values a′V in the frequency band ∆B1 (wholefrequency range) and the subjective ratings for steering-wheel are presentedin Fig. 4.12. The quality of the steering-wheel vibrations are judged bytwo testers who indicate a similar assessment behavior. The unweightedvibration total value a′V is calculated according to Eq. 4.2 by the applicationof the weighting function Wh. The distribution of data shows that there isa correlation between this objective parameter and the subjective rating forpetrol but not for diesel models. The correlation coefficient is significantfor petrol models rP = −0.82∗∗∗ and not significant for diesel models rD =


V [au]

subj

. Rat

ing

[cu]

rP= −0.82***

nP=36

rD= −0.26

nD=54

↑



↑

bette

r

0 25 50 75 100 125 150 175 200weighted Vibration Total Value a

V [au]

rP= −0.83***

nP=36

rD= −0.39**

nD=54



DieselPetrol

Fig. 4.12: Relation between spectrally unweighted and weighted (with Wh) vibra-tion total values a′V , aV in the frequency band: ∆B1 and the subjective ratingsof the steering-wheel vibrations. Additionally, the correlation coefficient rP / rDand the total number of data pairs are shown.


−0.26.

The correlation can be improved by applying the weighting function Wh

for the calculation of the rms accelerations for all three directions for dieselcars. The altered relations between objective and subjective data are shownin Fig. 4.12. The correlation coefficient is almost the same for petrol mod-els, rP = −0.83∗∗∗, and becomes significant with rD = −0.39∗∗ for thediesel models. The spectrally unweighted and weighted vibration total val-ues a′V and aV for the frequency bands - ∆B1, ∆B2, ∆B3, ∆B4 and ∆B5

- are calculated and correlated with the subjective data. In addition theunweighted and weighted vibration total value a′V and aV are calculated forthe frequency band ∆B5 [73 < f < 100 Hz] since the 6th motor order is aprominent component in the spectrum of the steering-wheel vibrations in x-direction (Fig. 4.4). Tab. 4.4 gives an overview of the correlation coefficientsrP and rD for parameters of different frequency bands.

The correlation coefficients between the subjective assessments and theobjective parameters for steering-wheel vibrations increase by using theweighted vibration total values aV - weighted with whole-body vibrationweighting functions Wd and Wk - in contrast to the spectrally unweightedparameter a′V according to prior findings and other studies (e.g., Bellmann etal., 2000b). This result indicates that the frequency energy in the steering-wheel vibration signals is important for the subjective (comfort-) ratingsfor steering-wheel vibrations. Hence the correlation coefficients increaseby using psychophysically motivated weighting functions, which have a lowpass characteristic, and increase or are similar if just a narrow band lim-ited frequency range around the 2nd motor order is used for calculating the


V [au]

subj

. Rat

ing

[cu]

rP= −0.79***

nP=36

rD= −0.42**

nD=54

↑


↑

bette

r




V [au]

rP= −0.83***

nP=36

rD= −0.42**

nD=54



DieselPetrol

Fig. 4.13: Same relations than in Fig.4.12, but with spectrally unweighted andweighted vibration total values a′V and aV (with Wh after ISO 5349-1/2) whichare calculated in a limited frequency range around the 2nd motor order (∆B3).


objective parameters (Fig. 4.13).

However, the correlation coefficients rP and rD for higher frequency bands∆B4 and ∆B5 also show some significant correlations between the sub-jective ratings and the objective parameters (Tab. 4.4). This finding is incontrast with a similar study (e.g., Bellmann et al., 2000b), and the reasonsare not yet clear.

A possible conclusion from these results is that the judgement behaviorsfor steering-wheel vibrations are highly influenced by spectral properties ofthe vibration signals. The vibration signals in the vertical direction (z’-axis)and x’-axis are highly correlated with each other which is confirmed in astatistical test. Additionally, these two components are of equal paramountimportance for the quality assessments of the steering-wheel vibrations. Aseparated correlation analysis between the x’- or z’-acceleration and thesubjective ratings deliver nearly the same correlation coefficients. Further-more, the frequency band around the 2nd motor order is very importantfor subjective assessments of steering-wheel vibrations. Moreover, the cor-relation coefficients between the objective and subjective data increase byusing the spectrally weighted vibration total value aV with psychophysicallymotivated weighting functions for hand-arm Wh and whole-body vibrationsWd and Wk (specified in, e.g., ISO 2631-1, VDI 2057-2 and ISO 5349-1).

Upper middle class cars

Just one subjective-tester participated for the testing-sessions in the uppermiddle class cars . Therefore nP = 9 and nD = 26 objective and subjectivedata are applicable for the following correlation analysis like in Chapter 4.4.1for seat vibrations. The subjective ratings for steering-wheel vibrations arefigured as a function of the spectrally unweighted and weighted vibrationtotal values in the frequency band ∆B1 in Fig. 4.14.

The results for upper middle class cars are similar to the findings of the mid-dle class cars. The correlation coefficients are significant for petrol and dieselcars by using the unweighted parameter a′V , rP = −0.67∗ and rD = −0.47∗.This correlations can be slightly improved by applying the weighting func-tion Wh for the calculation of the rms accelerations for all three directions.Additionally, the correlation coefficients between the subjective assessmentsand the objective parameter for steering-wheel vibrations also increase whenusing the vibration total values aV , weighted with whole-body vibrationweighting functions Wd and Wk, in contrast to the spectrally weightedparameter aV with Wh and the unweighted parameter a′V . The correlationscoefficients are statistically significant rP = −0.74∗ and rD = −0.56∗∗ for


Tab. 4.4: Correlation coefficients rP and rD between the subjective assessmentsand the objective parameters - spectrally weighted (with hand-arm and whole-body vibration weighting functions Wh, Wd and Wk) and unweighted vibrationtotal value aV and a′V - for steering-wheel vibrations of middle class cars.

Frequency range 0-500 Hz 10-35 Hz 20-35 Hz 35-100 Hz

Motor order (MO) whole range 1st - 2nd MO 2nd MO 4th - 6th MO


rP rD rP rD rP rD rP rD

unweighted vibra-tion total value a′V

-0.82

***

-0.26 -0.79

***

-0.42

**

-0.79

***

-0.42

**

-0.80

***

-0.12


(with Wd andWk)

-0.81

***

-0.46

***

-0.81

***

-0.46

***

-0.81

***

-0.45

***

-0.68

***

-0.45

***


(with Wh)

-0.83

***

-0.39

**

-0.83

***

-0.42

**

-0.83

***

-0.42

**

-0.81

***

-0.05

weighted vibration total values with whole-body vibration weighting func-tions (Fig. 4.14 right). These findings indicate that the vertical vibrations

0 100 200 300 400 500 600 700 800unweighted Vibration Total Value a‘

V [au]

subj

. Rat

ing

[cu]

rP= −0.67*

nP=9

rD= −0.47*

nD=26

↑


↑

bette

r ↑Regression Petrol



V [au]

rP= −0.74*

nP=9

rD= −0.56**

nD=26



DieselPetrol

Fig. 4.14: Relation between spectrally unweighted and weighted (with Wd andWk for whole-body vibrations after VDI 2057-2 and ISO 2631-1) vibration totalvalues a′V , aV in the frequency band: ∆B1 of the steering-wheel vibrations andsubjective ratings for upper middle class cars.


0 100 200 300 400 500 600 700 800unweighted Vibration Total Value a‘

V [au]

subj

. Rat

ing

[cu]

rP= −0.65

nP=9

rD= −0.39*

nD=26

↑


↑

bette

r



V [au]

rP= −0.74*

nP=9

rD= −0.5**

nD=26



DieselPetrol

Fig. 4.15: Same relations as in Fig.4.14, but with spectrally weighted vibrationtotal value aV (with Wk and Wd) in a frequency range from 20 to 35 Hz.

for steering-wheel vibrations are more important for the judgements thanthe horizontal vibrations for this car class. Since the whole-body vibrationweighting functions decrease the horizontal vibrations more by application of

Tab. 4.5: Correlation coefficients rP and rD between the subjective assessmentsand the objective parameters - spectrally weighted (with hand-arm and whole-body vibration weighting functions Wh, Wd and Wk) and unweighted vibrationtotal value a′V and aV - for steering-wheel vibrations of the upper middle classcars.




rP rD rP rD rP rD rP DrD


-0.67

*

-0.47

*

-0.65 -0.40

*

-0.65 -0.39

*

-0.96

***

-0.29


(with Wd andWk)

-0.74

*

-0.56

**

-0.74

*

-0.50

**

-0.74

*

-0.50

**

-0.67

*

-0.01


(with Wh)

-0.67

*

-0.50

**

-0.65 -0.45

*

-0.65 -0.45

*

-0.9

***

-0.08


Wd than the vertical components with Wk instead of the weighting functionWh for hand-arm transmitted vibrations (Fig. A.1 in Appendix A). Addi-tionally, spectrally weighted parameters, which are determined in the narrowfrequency bands around the prominent 2nd motor order (∆B3), correlatesignificantly with the subjective ratings, rP = −0.74∗ and rD = −0.50∗∗

(Fig. 4.15). Thence the energy at low frequencies is also important forthe subjective assessments. The correlation coefficients between all calcu-lated unweighted and weighted parameters and the assessments are listedfor different frequency ranges in Tab. 4.5.

The spectrally weighted and unweighted parameters in the higher frequencyranges (∆B4 and ∆B5) correlate with the subjective ratings for petrol carsbut does not for diesel cars. However, the significant correlation coefficientfor the unweighted vibration total value aV for petrol cars is affected byobjective values of just one car which implies very high energy componentsat higher frequencies. Additionally, the small number of data pairs has tobe considered. Therefore, just the weighted parameters in broad and narrowfrequency regions are probably adequate parameters for the description ofthe quality of steering-wheel vibrations for petrol cars.

Small class cars

Each small class car was rated by two testers, thence nP = 42 and nD = 44objective and subjective data are utilizable for the following analysis. Thejudgement of the two testers are similar which is confirmed with statisticaltests. This contradicts the judgements of these two testers for the quality of


V [au]

subj

. Rat

ing

[cu]

rP= −0.44**

nP=42

rD= −0.062

nD=44

↑


↑

bette

r



V [au]

rP= −0.44**

nP=42

rD= −0.068

nD=44


DieselPetrol

Fig. 4.16: Relation between the spectrally unweighted and weighted (with Wh)vibration total values a′V , aV in the frequency band: ∆B1, respectively, and thesubjective ratings of the steering-wheel vibrations for small class cars.


seat vibrations. The relation between the spectrally unweighted / weightedparameter (with the spectral weighting function Wh for hand-arm vibrations)and the subjective assessments for steering-wheel vibrations are shown inFig. 4.16. The objective parameters are calculated from the accelerationsof the whole frequency range (∆B1).

The clouds of data for diesel cars testify that there is no correlation betweenthe subjective ratings and the spectrally unweighted vibration total value,rD = −0.06. It is not possible to improve the correlation coefficient for dieselcars by using a psychophysically motivated spectrally weighted parameterwith weighting function Wh, rD = −0.07 or Wk and Wd, rD = −0.08.In contrast to that the correlation coefficient between the ratings and theunweighted vibration total values is statistically significant for petrol cars,rP = −0.44∗∗. But the diagram of the data (Fig. 4.16) shows that thesignificant correlation coefficient is caused by data of just one car (in threedifferent conditions, n= 3) which has very high accelerations for steering-wheel around 75 au. Therefore it is doubtful if the calculated parametersfor steering-wheel vibrations really yield a good description of the subjectivejudgements for petrol cars because no significant correlations are given if

Tab. 4.6: Correlation coefficients rP and rD between the subjective assessmentsand the objective parameters - spectrally weighted (with hand-arm and whole-body vibration weighting functions Wh, Wd and Wk) and unweighted vibrationtotal value a′V and aV - for steering-wheel vibrations of the small class cars.




rP rD rP rD rP rD rP rD


-0.44

**

-0.06 -0.44

**

-0.07 -0.43

**

-0.07 -0.42

**

-0.03


(with Wd andWk)

-0.40

**

-0.08 -0.40

**

-0.08 -0.40

**

-0.08 -0.06 -0.04


(with Wh)

-0.44

**

-0.07 -0.43

**

-0.07 -0.42

**

-0.07 -0.40

**

-0.01


a statistical test is conducted without the three data pairs (around 75 au).An application of the spectrally weighted vibration total values instead ofthe unweighted parameters deliver similar results (Fig. 4.16).

The correlation coefficients between the spectrally unweighted and weightedparameters in various broadband and narrow band frequency ranges andthe subjective ratings are summarized in Tab. 4.6. The results show twogeneral tendencies: firstly the correlation coefficients are almost unchangedif the objective parameters are calculated in different narrow frequency bandsinstead of the whole spectra (∆B1) and secondly the usage of spectralweighting functions for the determination of the objective parameters doesnot have any influence on the correlations with the subjective ratings. Anadditional correlation analysis of the relation between the subjective andobjective data for petrol and diesel cars, separated after each subjectivetesters, verifies the previous assumptions.

There are no significant correlations between the presented spectrally un-weighted and weighted parameters and the judgements for diesel cars. Fur-thermore, the relations for the petrol cars are affected by data pairs ofjust one car with very high accelerations. Therefore the relation betweenthe calculated objective parameters and the subjective ratings is doubtful.These findings are supported by the supposition that professional subjectivetesters, who are familiar with the car type and know the series variance, areneeded for the evaluation of the ’subjective discomfort’ caused by vibrationsin vehicles. The description of the subjective assessments of the seat vibra-tions in the same car class with objective parameters verify the hypothesis(Chapter 4.4.1).

4.5 Discussion

The quality of seat and steering-wheel vibrations are judged by one or twoprofessional testers for different classes of cars (small, middle and liftedmiddle class) in three different conditions in idle running. All used carshave 4-cylinder engines. Each car class was analyzed separately. Vibrationsignals are picked up at four different position on and at the driver seat, aswell as at one position for steering-wheel simultaneously with the subjectiveratings of the testers. The objectives are to identify parameters for seat andsteering-wheel vibrations which correlate significantly with the subjectiveratings and consequently describe the subjective vibration discomfort causedby vibrations.

The results can be summarized as follows: horizontal vibrations are equallyimportant for the subjective comfort ratings of the seat vibrations as the

4.5. Discussion 133

vertical vibrations (z-axis) for the investigated cars. In particular, if thevibration components in all three directions (x/y/z-axes) have nearly thesame magnitudes, especially around the 2nd motor order. This findingverifies results from the literature (Bellmann et al., 2000b). That is thereason why a psychophysically motivated spectral weighting after the ISO2631-1/2 or VDI 2057-2 does not give as high correlation coefficients asspectrally unweighted parameters a′V with the subjective ratings. Further-more, the vibration energy in the low frequency region between the 1st and2nd motor order, especially around the prominent 2nd motor order, con-tributes to the quality assessments of the seat and steering-wheel vibrationssignificantly. The energy in higher frequency bands does not correlate withthe subjective ratings for seat vibrations. Additionally, the energy of theprominent 6th order correlate significantly with the subjective assessmentsfor the steering-wheel vibrations sometimes. The optimal measuring posi-tion for seat vibrations depends on the car class and used car seat but notalways from the engine-type.

Moreover, the vibration total value aV , calculated with the weighted steering-wheel vibration signals (with Wh or Wd and Wk), yields in any case andfor nearly all classes higher (diesel cars) or similar (petrol cars) correlationcoefficients between the objective parameter and the subjective comfort as-sessments than the unweighted vibration total value a′V . Seat and steering-wheel vibration parameters, which take into account accelerations of allthree (x/y/z) directions, deliver higher correlation coefficients with the sub-jective assessments than parameters which include accelerations from justone direction (e.g., z-acceleration az or awz).

A separate analysis of petrol and diesel models improve the correlation coef-ficients. In this study objective parameters are calculated from the vibrationrecordings which just include spectral properties of the seat and steering-wheel vibrations. The different judgement behaviors of petrol and diesel cars- with nearly the same value of the objective parameter diesel cars obtainbetter subjective ratings than the petrol cars - are not exclusively explainedwith changes of the spectral parameters for the steering-wheel and seatvibrations.

The cars from the small class were a new production run so that the sub-jective ratings of the two testers for steering-wheel vibrations do not prob-ably correlate with the objective spectral parameters. Additionally, the twotesters show different judgements for seat vibrations. Therefore a hypothe-sis can be stated that professional testers are needed who are familiar andknow the series variance of the tested cars to receive constant and concur-rent subjective assessments of the seat and steering-wheel vibrations.

Chapter 5

Psychophysical measurementson the perception of verticalseat vibrations on a car seat

In Chapter 4 the subjective (dis-) ’comfort’ caused by the seat vibrationswere rated by subjective-testers in idle running cars. The used vibrationparameters in the last chapter showed that the subjective ratings are influ-enced by the level (acceleration) of the seat vibrations. In detail, the ratingdecreases with increasing vibration parameter. It would be very advanta-geous to know the properties of the vibration signals which are fundamentalfor detailed subjective quality assessments. Therefore basic psychophysi-cal measurements on the perception of vertical whole-body vibrations areconducted on a real car seat according to findings in basic experiments(Chapter 3) and for applications in cars (Chapter 4). The focus lies on twoaspects: first, which influence has the level of the seat vibrations and thesimultaneously heard booming noise on the subjective rating ? And second,is it possible to explain the slightly different judgement behaviors of differentsubjective-testers by using individual parameters like perception threshold,just noticeable differences in level, etc. for the perception of seat vibrationson a real car seat ?

It is just possible to investigate the influence of the level of the seat vibrationsand the booming noise on the subjective ratings of the seat vibrations ina laboratory because it is difficult or impossible to change systematicallythose parameters in a real car. Additionally, it is not really clear what kindof influence a cushioned seat has on basic experiments of the perceptionof whole-body vibrations. Therefore psychophysical measurements on the

5.1. Measurement set-up 135

perception of synthetically sinusoidal and real broadband (recorded in cars)seat vibration signals are conducted on a real car seat. Normally differenttypes of car seats must be used to investigate the influence of different seatproperties on the perception of vibration. In this study just one car seat isused which is the same seat type as in the measured cars (middle class) inChapter 4.4.1. First perception thresholds and just noticeable differences inlevel are repeated for synthetically sinusoidal signals on a real (cushioned)car seat according to Chapter 3 with subjects from the car industry (some ofthem are professional subjective-testers). Following, seat vibrations (whichare recorded in real cars) are varied in level to investigate the influenceof the level of the seat vibrations on the subjective ’comfort’ assessment.Additionally, the influence of the booming noise on the subjective ratings ofthe seat vibrations are investigated thereafter.

An excitation in just vertical direction is used in the following experimentsbecause the vertical component (especially around the 2nd motor order) isusually the prominent vibration component in idle running cars. Moreover,the human body is more sensitive to vibrations in the vertical directionthan in the horizontal plane for whole-body vibrations according to existingstandards (e.g., ISO 2631-2, 1989; VDI 2057-2, 1987). Finally, it is easierto control vertical vibrations than horizontal vibrations on a simulator inthe laboratory. The conducted psychophysical measurements are in detail:

Experiment 1 : Perception thresholds at 16 and 31.5 Hz

Experiment 2 : Just Noticeable Differences in Level (JNDL) at 31.5 Hz

Experiment 3 : Influence of the level on the seat vibration assessments

Experiment 4 : Influence of booming noise on the subjective seatvibration ratings

5.1 Measurement set-up

Experimental set-up

Whole-body vibrations are produced by using the Sound & Vibration Re-production System c© (see Chapter 2.2). This system is optimized for therealistic reproduction of recorded interior noise and vibrations of vehicles.Only the so-called ’vibration-pad’ – system which produces whole-body vi-brations in all three axes (Chapter 2.2) – is used for the production of verticalwhole-body vibrations for these measurements. On this system a real carseat is mounted, see Fig. 5.1. The audible components during the experi-

136 Chapter 5. Psychophysical measurements on a car seat

Fig. 5.1: Schematicview of the ’vibration-pad’which is used for the in-vestigation of human per-ception of vertical whole-body vibrations on a realcar seat.

ments are reproduced by closed headphones (HDA 200 from Sennheiser) ifnecessary. The experiments are conducted in a room with sound absorbingmaterials on the walls. In this room a background noise of L = 42 dB(A)was measured. It is possible to reduce the background noise to a level ofL = 31 dB(A) by wearing the closed headphones. With those headphonesthe reproduction of low frequency components of the booming noise with asubwoofer is not necessary.

The vibro-acoustic signals for the measurements are reproduced by an IBMcompatible computer with the aid of a SQLab II system from HEAD acous-tics and the software packages ArtemiS 3.01.100 or an AFC package forMatlab1. The control-diagram of the Sound & Vibration ReproductionSystem c© is figured in Fig. B.2. The parametric equalizers of the SonyTA-E 2000 ESD Digital Processing Control Pre-Amplifier are used to lin-earize the transfer-function of the vibration-pad for this experiment. Hencebroadband seat vibration signals can be reproduced in a frequency rangefrom 10 to 100 Hz, as well. A picture of the used measurement set-up isgiven in Fig. 5.2.

The vibration-pad is calibrated for each volunteer individually at the begin-ning and at the end of each measurement session. Signals for the calibrationare sinusoidal vertical vibrations with f = 16 and 31.5 Hz according to thedominance of the 1st and 2nd motor order in the recorded spectra (Chap-ter 4) and for the subjective ratings of the quality of seat vibration. Thereproduced whole-body vibrations are controlled at four different position atthe seat. The measuring positions are as follows (see Fig.5.1, too):

• Vibration acceleration a at the right back rail of the driver seat -referred to as position ’P1’- (PCB 356A15 accelerometer, triaxial).

1The AFC-package is developed at the University of Oldenburg, c©Stephan Ewert

5.1. Measurement set-up 137

Fig. 5.2: Picture ofthe measurement set-up(’vibration-pad’ includingcontrol sequence) for thepsychophysical measurementson a real car seat.

• Vibration acceleration a at the left front rail of the driver seat - referredto as position ’P2’- (PCB 356A15 accelerometer, triaxial).

• Vibration acceleration a on the driver seat - referred to as posi-tion ’P3’- (accelerometer cushion MMF KB103SV – sometimes calledSAE-pad –, triaxial).

• Vibration acceleration a at the floor of the vibration-pad between thefeet of the volunteers - referred to as position ’P4’ - (PCB 356A15accelerometer, triaxial).

The measuring positions P1 to P3 are specified for experiments on real carseats in a laboratory in ISO 10326-1 (1992), see Fig. A.3 in Appendix A.These positions are the same positions used during the test-sessions in areal car (see Chapter 4.2). The transduced vibrations on different positionsinto the human body are manageable and reproducible with the individualcalibration parameters. Thence each subject feels more or less the samevibrations on the vibration-pad and the experiments can be reproduced underconstant and repeatable conditions. Additionally, it is not only possible toproduce sinusoidal vibration signals but also broadband vibration signals inthe frequency range from 10 to 100 Hz in an adequate fashion.

Stimuli

For the first two experiments, perception thresholds and just noticeable leveldifferences are measured with sinusoidal vibration stimuli with frequenciesof 16 and 31.5 Hz. These frequencies are used because of the dominance ofthe 1st and 2nd motor order in the spectra of seat vibrations measured inidle running cars (Chapter 4.2). The exposure times of the vibration signalsare 1 s which are separated by a break of 500 ms. Hanning time-windowsare used with a duration of 10% of the stimulus duration for a soft closure


and break. All synthetic stimuli are produced by using an AFC-package c©

for Matlab. For the third and fourth experiment seat vibration signals arereproduced which are recorded in real cars from the middle class (see Chap-ter 4.1). The audible stimulus is a pink noise (30 < f < 10, 000 Hz) witha level of L = 66 dB(A) or real booming noise signals measured simul-taneously in cars in idle running condition with the vibration signals. Theexact measurement designs are summarized in the following subsections.

5.2 Subjects

All subjects are healthy volunteers (aged between 24 and 45 years) and aremembers of one company from the car industry. The number of subjectsvaries between 4 and 16 for the different experiments. The specific numbersof the participants are summarized in Tab. 5.1 for each experiment. Fourprofessional subjective-tester from the car industry with long term experienceparticipated consistently in all four experiments and they can be referred toas highly ’trained’ subjects. Two of the testers participated in the subjectivetesting-session of the subjective ’(dis-) comfort’ inside cars caused by seatand steering-wheel vibrations (Chapter 4). The other participants are un-trained subjects who are not familiar with the subjective testing-session inreal cars. Anthropometric data are measured, like body-size and weight,of each subjects. The Body Mass Index ’BMI’ (Kg/m2) and the Rohrer

Tab. 5.1: Number of subjects separated by the different experiments.

Experiment No. of subjects Gender

No. (No. of professional testers) (male / female)

Experiment 1 16 (4 Tester) 15 / 1




5.2. Subjects 139

Index ’RI’ (Kg/m3) are calculated from the measured data (after Eq. 3.1and Eq. 3.2; adapted from Garrow & Webster, 1985, see also Chapter 3.2).All personal (exogenous and endogenous) data are summarized in Tab. 5.2separated for the four subjective-testers and the other participants.

All experiments are conducted for seated subjects on a real car seat. Theposture of the subjects is normal and preferably comfortable on the seat:feet on the rigid floor of the vibration-pad and with an upstanding upperpart of the body which is leaning on the backrest (Fig 5.2). During themeasurements the posture is not controlled but the subjects had the ordernot to change their position during the experiments.

There are no significant differences in the mean and standard deviationsbetween the data of the four subjective-testers and the set of the othersubjects. These two groups can be separated into ’trained’ and ’untrained’subjects.

In the following experiments, the results of both subject groups (trained anduntrained) are regarded to investigate the differences between trained anduntrained subjects. Additionally, it is investigated whether the subjective-

Tab. 5.2: Anthropometric and other personal (exogenous and endogenous) dataof the subjects.

untrained subjects trained subjects (testers)

Parameter Mean Median Mean Median

age [a] 31.2 ± 7.2 30.0 35.3 ± 4.9 36.0

body-size [cm] 178.7 ± 7.3 180.0 178.8 ± 4.7 179.0

weight [Kg] 75.7 ± 10.6 77.6 79.0 ± 9.9 78.0

BMI [Kg/m2] 23.6 ± 2.5 23.5 24.7 ± 3.1 24.1

RI [Kg/m3] 13.2 ± 1.4 13.1 13.9 ± 1.8 13.7


testers are able to reflect the perception and the subjective judgement behav-ior of a large number of untrained subjects which are the potential customers(car drivers) for the car industry. The vibration parameters are representedas averaged rms-values after existing standards (ISO 2631-1 and VDI 2057-2). The vibration parameters in experiment 3 and 4 are given in arbitraryunits [au] like in Chapter 4.

5.3 Experiment 1: Perception thresholds

The perception thresholds are determined with an adaptive 3 - AFC 1 up- 2 down measuring method (70.7% point of the psychometric function,Chapter 1.2.1 and 3.3). The initial step-size is 8 dB and is halved aftereach upper reversal to an ending step-size of 1 dB (Chapter 1.2.2). Thetest-frequencies are 16 and 31.5 Hz according to the prominent 1st and2nd motor order of a 4-cylinder engine. The measurement is conducted intwo different conditions for each subject: the first condition is without anadditional audible stimulus (’quasi’ in silence with a background noise ofL = 31 dB(A), referred to as ’silent condition’) and the second conditionis with an additional acoustic stimulus2. A synthetic pink noise is usedbecause the frequency-characteristic of a real booming-noise is similar. Theresults for the condition ’silent condition’ is marked with opened symbolswhereas closed symbols signify the data for the condition ’with noise’ inthe next figures. 16 different subjects participated in these measurementswith one repetition for each condition per subject. Just one repetition ismade because the results of Chapter 3.5 show that there are no learningeffects or anything else. The order of the conditions, as well as the orderof the test-frequencies is randomized to prohibit order effects. The effectof an audible stimulus on the perception threshold can be investigated withthese measurements. Additionally, differences between the subjective-testers(circles) and the untrained subjects (squares) are analyzed. The mean ofthe last four reversals with the ending step-size of 1 dB characterizes themeasured perception threshold.

The measured vibrations on the seat surface include components in moreor less all three (x/y/z) directions although just a vertical excitation of thevibration-pad is used. This phenomenon is not unknown and is specific forcushioned seats (even car seats) because the seat is describable as a mass-spring system with more than one degree-of-freedom and with no linear

2acoustic stimulus: pink noise in a frequency range from 30 Hz to 10 kHz with a levelof L = 66 dB(A), referred to as ’with noise’


guides (reported frequently as single-input multiple output system in litera-ture, e.g., Griffin, 1990). The transmitted vibrations in the human body (atposition ’P3’) probably depend on the weight, body-size and posture of theseated subject. Therefore the vibration parameters for the description onthe perception of seat vibrations considers the vibrations in all directions onthe seat. In contradiction to this the accelerations which are reproduced onthe vibration-pad and are transduced into the human body by the feet is in-dependent of the anthropometric data of the seated subjects. Additionally,the accelerations transduced by the feet consist of just vertical components.The measured vibrations on the seat surfaced indicate components in allthree directions, as mentioned before. Therefore not only the vibrations inthe excitation axis (vertical, z-axis) are used for the description of the per-ception but also vibrations in the horizontal plane. Two parameters are usedfor description of the perception threshold according to existing standards(e.g., ISO 2631-2, 1989): the vibration total value referred to as aV,seat,which includes the vibrations transmitted by the seat, and the vibration to-tal value referred to as aV,seat−feet for vibrations transmitted by the seat(triaxial) and by the feet (just z-axis) into the body. The parameters arecalculated as follows, Eq. 5.1 and 5.2:

aV,seat = (k2xa2

x + k2ya2

y + k2za2

z)12 (5.1)

aV,seat−feet = (k2xa2

x + k2ya2

y + k2za2

z + k2z,feeta

2z,feet)

12 (5.2)

with

aj = the rms acceleration for seat vibrations in j = x, y or z axes

az,feet = the rms acceleration for feet vibrations in z-axis

kj = weighting-factors for three (j = x/y/z) directions of the seat

kz,feet = weighting-factors for z-directions of the feet

The weighting factors kj for seat vibrations in the three (x/y/z) directionsare kx = ky = kz = 1 and kz,feet = 0.4 for the transmitted vibrations bythe feet according to the recommendation for comfort and perception eval-uation in ISO 2631-1 and VDI 2057-2. The averaged perception thresholdsseparated for two groups – the four subjective-testers (trained subjects; cir-cles) and the untrained subjects (squares) – are given for both conditions inFig. 5.3. The results for the condition ’silent condition’ (opened) and ’withnoise’ (closed) are shifted in the frequency range for a better illustration.


16 31.576

78

80

82

84

86

88

90

92

vibration total value aV,seat

16 31.5

vibration total value aV,seat−feet

trained subjects (tester)untrained subjects

Fig. 5.3: Measured perception thresholds for vertical sinusoidal whole-body vibra-tions on a real car seat. The participants are separated into two subject groups:the four subjective-testers – trained subjects (circles) – and the untrained subjects(squares). On the left side the vibration total value aV,seat for vibrations whichare transmitted by the seat into the body and on the right side the vibration totalvalue aV,seat−feet are figured. The parameter aV,seat−feet considers vibrationswhich are transmitted by the seat and by the feet into the human body. Theresults for the condition ’without noise’ (opened) and ’with noise’ (closed) areshifted in the frequency range for a better illustration.

The perception thresholds for aV,seat−feet including the interindividual stan-dard deviations rise with increasing frequency from about 84 dB at 16 Hzto 87 dB at 31.5 Hz. In comparison to this finding the perception thresholdaV,seat is minimum 2 dB below aV,seat−feet at f = 16 Hz and decreasesslightly with increasing frequency. The reason for this is maybe a dampingeffect of the seat which depends on the frequency, among other things, butboth tendencies are not statistically significant (T-Test, p > 0.05). There-fore a nearly constant perception threshold at 16 and 31.5 Hz is measured.A correlation analysis points out that there are no significant differencesbetween the results of both subject groups (T-Test, p > 0.05). Hence theresults of the four subjective testers reflect the results of a large group ofuntrained subjects very well. An additional acoustic stimuli with a level of66 dB(A) does not influence the perception threshold (T-Test, p > 0.05).However, the interindividual standard deviation is about 3 dB for the ’silentcondition’ and increases slightly for the condition ’with noise’. Additionally,a statistical test shows that the measured perception thresholds are indepen-dent of the personal (exogenous and endogenous) data: body-size, weight,Rohrer Index (RI) and Body-Mass Index (BMI), as well as age. These re-sults verify findings from Baumann (2001b) who reports similar results basedon body-size and weight for experiments on the perception of whole-bodyvibrations on a real cushioned car seat.

5.4. Exp. 2: Just Noticeable Differences in Level (JNDL) 143

There are just a few data for the perception of vibrations on real seats inthe literature. Besides, each type of car seat (e.g., sport seat, comfortableseat, etc.) has different frequency-characteristics which probably influencethe perception thresholds, as mentioned before. Data from Baumann etal. (2001a) were measured with a similar seat and a similar masking noise(pink noise with L = 68 dB(A)) for 16 subjects (particularly trained anduntrained), see Fig. 5.4. These results are comparable with the perceptionthresholds of the four testers but they are nearly 1 dB below the results ofthe tester. This is probably affected by individual differences of the usedsubject groups and besides the differences are not statistically significant(T-Test, p > 0.05).

The results can be summarized as follows: The individual sensitivity (mea-sured perception thresholds) of the subjects on a real car seat are indepen-dent of exogenous and endogenous data like age, weight, body-size, RI andBMI, as well as frequencies of 16 and 31.5 Hz. Additionally, the results foruntrained subjects do not differ significantly from the results of the highlytrained subjective-tester. Moreover an additional ’masking’ noise (here pinknoise) with a level of L = 66 dB(A) has no influence on the perceptionthresholds. These findings are similar to results from Baumann et al. whoused a similar measurement set-up and nearly the same car seat.

5.4 Experiment 2: Just noticeable differencesin level

The difference thresholds for (’quasi’) vertical seat vibrations are measuredat 31.5 Hz - almost the prominent 2nd motor order for a 4-cylinder en-gine car - in the presence of an audible stimulus (pink noise with a levelof 66 dB(A)). The measuring method is again an adaptive 3 AFC 1 up -2 down method (Chapter 3.6). The reference stimulus is a sinusoidal ver-tical vibration at the position P1 and P2 with f = 31.5 Hz and a level ofLV ib = 100 dB (a = 0.1 m/s2). This level is in a level range which is ’notuncomfortable’ (after the ISO 2631-1 (1997), see Tab. 1.2). Additionally,this is a common acceleration level for cars in idle running conditions. Thereference level is very similar to the reference level of the JNDL measured ona rigid seat (Chapter 3.6.1). The test-vibrations have an inertial vibrationlevel of LV ib = 110 dB. The step-size is halved after each upper reversalfrom 4 to an ending step-size of 0.25 dB. The JNDLs are determined just inthe presence of an additional audible stimulus because some studies reportthat there are no effects of noise on the difference thresholds in level (e.g.,


16 31.576

78

80

82

84

86

88

90

92

vibration total value aV,seat

16 31.5

vibration total value aV,seat−feet

trained subjects (tester)Baumann et al, ‘01

Fig. 5.4: Perception thresholds from Fig. 5.3 in comparison to literature datafrom Baumann et al. (2001a). The data are a little bit shifted in the frequencyrange for a better illustration.

Baumann, 2001b) at similar noise level (L = 68 dB(A)). 15 male subjectsparticipated in this measurement with one repetition for each subject.

The relative just noticeable level differences for testers and untrained sub-

0.06

0.12

0.19

0.26

0.33

Rel

ativ

e di

ffere

nce

thre

shol

d, ∆

I/I

16 20, 25 31.5 40 50 63 80

0.5

1

1.5

2

2.5

Frequency [Hz]

JND

L [d

B]

trained subjects (testers)untrained subjects Baumann et al ‘01

Fig. 5.5: Just noticeable differences in level measured on a real car seat are plottedas a function of frequency (left y-axis) for trained (circles) and untrained subjects(squares). The right y-scale denotes the relative difference thresholds (∆I/I).Additionally, data from Baumann (2001b) in a frequency range from 16 to 80 Hzwith a similar measurement set-up are shown. The audible stimulus has a level of66 dB(A) for results of this study and 68 dB(A) for results of Baumann (2001b).

5.5. Exp. 3: Influence of level on seat vibration assessments 145

jects at 31.5 Hz are shown in Fig. 5.5. The difference thresholds are rangedat about 1.5 dB ± 0.5 dB or ∆I/I = 19% ± 5%. The averaged JNDL,as well as the intra- and interindividual standard deviations are a little bithigher for the untrained subjects than the ones for trained testers. But thedifferences between the results of the two subject groups are not statisticallysignificant (T-Test, p > 0.05). Similar results, which are also independentof frequency, are reported by Baumann (2001b) in a frequency range from16 to 80 Hz measured in presence of a similar audible stimulus (pink noisewith a level of 68 dB(A)). No significant differences (T-Test,p > 0.05) areobservable between the results of both studies.

The range of the measured difference thresholds in level on a real car seatare the range as the results measured on a rigid seat in Chapter 3.6.1. Theseat has probably no influence on the just noticeable differences in level atlow magnitudes and is almost a constant of about 1.5 dB even though thestimuli on a real cushioned car seat include components in all three axes.

5.5 Experiment 3: Influence of the level on theseat vibration assessments

The task of the participating subjects in this experiment is to give theirsubjective ’comfort’ ratings on the presented seat vibrations. The level of theseat vibration changes during the experiment. The task of this experimentdoes not differ from the ’normal’ measurement procedure for a subjectivetesting-session in a real car, except for the location (see Chapter 4). Thetarget of this experiment is to investigate the relation between the levelof the seat vibrations and the appendant subjective ’comfort’ assessmentwithout visual and acoustic components since results in Chapter 4 showthat there is an influence of the size of the calculated objective vibrationparameters on the subjective ratings. Hence the subjective rating decreaseswith increasing acceleration.

The seat vibrations are just the vertical components of the vibration signalsfrom a real petrol- and a real diesel-engine car (4-cylinder engine) from thesame car type (middle class). These two seat vibrations were judged by twoprofessional testers with subjective ratings which are in the middle range ofthe used scale in Chapter 4.4.1. The used two vibration signals were digitallychanged in level. Therefore seat vibration signals with seven different levelsfor petrol and for diesel cars are used for this experiment. The signals withthe highest level indicate a low quality and the ones with the lowest leveldenote a highly one. The level changes and limits are based on the results of


the regression analysis, see Fig. 4.5 and 4.6, as well. In contrast to the usedsignals in Chapter 4.4.1 the signals are changed in level but not in frequency(like different rpms). The duration of the vibration signals are 30 s.

The different vibration signals - separated into seven diesel and seven petrolcar vibrations - are presented in randomized level order to the subject. Thesubjects know that the felt seat vibrations are recorded in a petrol- or in adiesel-engine car during this experiment like in the normal testing-session3.The subjective ratings are given in terms of categorical units [cu] (Chap-ter 4.3) according to the ’(dis-) comfort’ of the felt seat vibrations. 14(1 female and 13 male) subjects participated in this measurement. Fourof these subjects are the subjective-testers who are familiar with the usedcategorical scale and the measurement procedure. The other subjects areuntrained and are not familiarized with the subjective rating scale. Thereforethe seat vibrations with the highest and the lowest levels are presented tothe 10 untrained subjects at the beginning of the experiment to give theman overview about the level range of the vibration signals which occur dur-ing the experiment. This experiment is repeated three times for each enginetype and for each subject. During the experiments the subjects do not hearan acoustic stimulus, except for the background noise in comparison to theassessment situation in a real car.

The untrained subjects were not able to give consistent answers (results)during the three repetitions which is confirmed in a statistical test. Seatvibrations with increasing level do not always obtain decreasing subjectiveassessments. That is the reason why the results do not show a high con-sistency. Additionally, some subjects transfer the presented seat vibrationsinto the given categorical scale. That means that the seat vibration withthe highest acceleration level is judged with the lowest categorical note andthe lowest acceleration obtains the highest note. This transformation effectis well known in psychoacoustic measurements and is reported frequently.The application of the scale from the untrained subjects is inconsistent withthe usage of the trained subjective testers who use just a limited range ofthe scale for their evaluations of the seat vibrations. The consistency coef-ficient of each subjective-testers is one. Furthermore, the four testers showsimilar judgement behaviors which is confirmed with a statistical correlationanalysis. Therefore the results of the four testers are used for the follow-ing analysis and the subjective assessments of the testers are summarized.It is just briefly noted that the two subjective-testers, who assisted in thetesting-session in the real cars, give similar subjective ratings for seat vibra-tions with the original acceleration level as in the real car even though they

3The subjective-testers are able to recognize the differences between different enginetypes.

5.5. Exp. 3: Influence of level on seat vibration assessments 147

Acceleration [arbitrary units]

Sub

ject

ive

Rat

ings

[cu]

↑

↓

2 categorical unit [cu]

→Regression PetrolrP = −0.86***

nP = 84

← Regression DieselrD

= −0.87***n

D = 84

↑

bette

r

PetrolDiesel

Fig. 5.6: Relation be-tween the presented seatvibration acceleration andthe appendant averagedsubjective ratings of thefour subjective-testers.Additionally, the re-gression curve whichis calculated from thesingle values of theexperiment is plotted.The acceleration and thesubjective ratings aregiven in arbitrary [au]and categorical units [cu],respectively.

do not know that the presented vibrations are the same as in the real testingsession (Chapter 4.4.1).

The results of all testers are classified into petrol and diesel cars includingthe three repetitions (np = nD = 84). A correlation analysis is conductedbetween the subjective assessments and the objective vibration accelera-tion afterwards. There is a relation between the subjective ratings andthe presented acceleration of the seat vibrations. The correlation coeffi-cients are highly significant for petrol rP = −0.86∗∗∗ and for diesel signalsrD = −0.87∗∗∗. The linear regression curve is calculated and is figuredas well as the summarized results (mean inclusive interindividual standarddeviation) in Fig. 5.6. The accelerations and the subjective ratings are givenin arbitrary and categorical units, respectively, like in Chapter 4.

The plotted results contain two main tendencies: first, there is an anti-proportionality between the acceleration of the seat vibrations and the sub-jective ratings whereas the interindividual standard deviations rise with in-creasing acceleration. The second tendency is that diesel-engine cars receivebetter subjective ratings than petrol-engine cars for the same objective accel-erations, see Fig. 5.6. The difference in the subjective assessments increaseslightly with increasing acceleration. Both findings are similar to resultsfrom subjective testing-sessions in real cars, except for the slopes of the re-gression curves (see Chapter 4.4.1). The different judgements for diesel andpetrol cars are not caused by parameters depending on frequency or level.

The interindividual standard deviation increases with rising acceleration, asmentioned before. In contrast to this the intraindividual standard deviations


for each subjective tester are very small and below one categorical unit.The question is: why do the subjective ratings from the testers slightly dif-fer with increasing acceleration ? Perhaps the interindividual differences areattributed to individual differences for the perception of vibrations. It is justbriefly noted that the real car seat vibrations imply a dominate 2nd motororder at about 31.5 Hz in the spectra. Furthermore, the energy at low fre-quencies around the second motor order is from decisive importance for thesubjective comfort assessments of the seat vibrations in this car class (Chap-ter 4.4.1). Therefore the pregenerated changes in the acceleration of seatvibrations are transformed into intraindividual just noticeable differences inlevel of the four testers at f = 31.5 Hz. The interindividual standard de-viation decreases perspicuously, especially for higher accelerations, by usingthe transformation from acceleration into difference threshold units in level(referred to as JNDLU). Additionally, a relation between the JNDLUs andthe categorical units can be calculated: An increase of the seat vibrationsof about 3.5 JNDLU for petrol cars and 4.8 JNDLU for diesel cars deliversa decreasing subjective rating of two categorical units. A correlation analy-sis between the perception thresholds and the individual judgement of thetesters delivers no significant correlation.

The findings of the regression analysis for this experiment and for the sub-jective testing-sessions in a real car are not really comparable to each othersince many measuring parameters like the presented acoustic stimuli and themeasurement environment are changed. But the tendencies of the regres-sion curves are very similar. Therefore the results of this experiment validatethe findings of the correlation analysis in Chapter 4 based on the influenceof level on the quality assessments. However, the level (acceleration) isjust one parameter which influences the subjective judgement behavior ofthe seat vibrations. Furthermore, the result shows the importance of theknowledge of basic psychophysical parameters like JNDLs. The individualdifferences in the judgement behavior can be particularly explained by thedifferences for JNDLs.

5.6 Experiment 4: Influence of interior soundon the subjective seat vibration ratings

Interior sound and vibrations in cars impair the subjective comfort. Hencethe subjective ratings of sound and vibration in a vehicle are an importanttool to assure defined quality standards. The dependence of the level ofthe seat vibrations on the subjective quality assessments is investigated inthe last section (Chapter 5.5). However, the level is just one parameter

5.6. Exp. 4: Influence of sound on seat vibration ratings 149

which probably has an influence on the evaluation of seat vibrations. It iswell known that the booming noise signals are highly correlated with therecorded vibration signals in cars which is confirmed with statistical testsfor the recorded signals of the used cars in Chapter 4. The reason forthis is that the whole passenger cabin (windows, floor, etc.) vibrate andtherefore emit audible sound. Another aspect is that the found regressioncurves of the last experiment and of the testing-sessions in a real car showsome differences between each other. Consequently, the assessments of seatvibrations are not probably independent from the interior sound and fromthe judgement of the booming noise. Therefore this experiment investigatesthe influence of the booming noise on the subjective ’comfort’ judgementsof the seat vibrations. The task of the subject is to change (increase ordecrease) the level of a presented seat vibrations until the adjusted seatvibrations are matched optimally (task 1) or not optimally (task 2 and 3)to the simultaneous presented interior sound of a car.

The used seat vibration signals are the same as the ones in the last experi-ment (petrol and diesel car from the middle class). The audible componentsin this measurement are the appropriate booming noise signals recordedsimultaneously with the seat vibrations in the (middle class) cars. Thebooming noise is presented to the subjects with the original level by head-phones (HDA 200 from Sennheiser). The level of the seat vibrations arechangeable with a logarithmic potentiometer by the participating subjects.The four testers participate in this experiment because the results of last ex-periment for untrained subjects, who are not familiar with the measurementprocedure, are biased and inconsistent.

Three different initial accelerations for seat vibrations are applied: (a) obvi-ously below the original acceleration (around the perception threshold) (b)around and (c) obviously above the original acceleration of the recordedvibrations. The task of the testers is to change the accelerations in sucha way that the felt seat vibrations match optimal with the heard boomingnoise (task 1). The second and third task is to increase or to decrease themagnitude of the vibrations until the force (perception) of the vibrations isjust too strong (task 2) or just too weak (task 3) for the simultaneouslyheard booming noise, see Fig. 5.7. This experiment is repeated three timesfor each inertial acceleration condition in randomized order. Additionally,the order of the tasks are randomized, too. Therefore nine adjusted acceler-ations for each engine type, for each tester and for each tasks are availablefor the following analysis. The duration for vibrations is 30 s. The subjectsknow if the presented ’vibro-acoustic’ signals are recorded in a petrol ordiesel car.

The averaged adjusted levels for task 1 are nearly the original accelerations


SP

L [d

B]

Acc

eler

atio

n[m

/s2 ]

Original level of the booming -noise

Original accelerationof the seat vibration

Perception threshold

Task 3: seat vibration is too weak for the booming -noise

Task 1: seat vibration is optimal matched to the booming -noise

Task 2: seat vibration is too strong for the booming -noise

Diff

erne

ce a

Diff

erne

ce b

Diff

erne

ce c

Test vibration

Acceleration of the test vibration is variable

SP

L [d

B]

Acc

eler

atio

n[m

/s2 ]

Original level of the booming -noise

Original accelerationof the seat vibration

Perception threshold

Task 3: seat vibration is too weak for the booming -noise

Task 1: seat vibration is optimal matched to the booming -noise

Task 2: seat vibration is too strong for the booming -noise

Diff

erne

ce a

Diff

erne

ce b

Diff

erne

ce c

Test vibration

Acceleration of the test vibration is variable

Fig. 5.7: Schematic view of the tasks for experiment 4. The test-vibrations (seatvibrations) are changeable in level by the subject in such a way that the test-vibrations are just too strong, just too weak for the booming noise or are matchedoptimal with the booming noise.

which are recorded in used cars (Chapter 4). This result exhibits the highrepeatability of the professional subjective-testers. Furthermore, a statisticaltest (T-Test) points out that there is no influence of the initial accelerationof the seat vibrations on the results of the three different tasks (p > 0.05).The acceleration differences for seat vibrations between the different tasksare calculated in a second analysis part. The judgement behaviors of the fourtesters are similar which is confirmed in a statistical test. Additionally, theinterindividual standard deviations for all four testers can be reduced if theacceleration differences are translated in terms of just noticeable differencesin level (JNDLU). The differences between the two extremes (tasks 2 and3: force (perception) of the vibrations is just too weak or just too strong forbooming noise, respectively) are about 3 JNDLs for the diesel and 3.5 JNDLsfor petrol cars.

It is not possible to transform the differences of task 2 and 3 according totask 1 in terms of categorical units like in subjective testing-session in realcars (Chapter 4 or in the last experiment, Chapter 5.5). But the findingsof this experiment support the influence of the booming noise on the as-sessments of the seat vibrations. If the booming noise is mismatched tothe felt vibration the ’comfort’ ratings are probably biased. In addition,the interindividual differences between the subjective testers can be reduced

5.7. Discussion 151

with respect to the individual perception of vibration. This finding showsthe importance of psychophysical parameters like JNDLs for the subjectiveevaluation of the quality of seat vibrations.

5.7 Discussion

The influences of, e.g., the acceleration level or acceleration the perceptionthresholds and the difference thresholds in level on the subjective qualityratings of seat vibrations on a real car seat are investigated in the laboratory.First, the perception thresholds are measured at 16 and 31.5 Hz on a real(cushioned) car seat according to the first and the prominent second motororder for a 4-cylinder engine in idle running cars. A real car seat is a single-input multiple-output system (see ,e.g., Griffin, 1990) for a just verticalexcitation (what is well known in the car industry). Therefore the vibrationsin all three (x/y/z) directions have to be comprised at all contact areasbetween the vibrating part (seat surface, backrest and floor) and the humanbody for the determination of adequate parameters for the description ofthe individual perception threshold on a real (cushioned) car seat. Thosemeasured data are statistically independent of frequency. Additionally, noinfluence of an additional audible stimulus with a level of L = 66 dB(A) onthe perception thresholds is observable which is confirmed in a statisticaltest. No significant differences were found between untrained and highlytrained subjects. Furthermore, these findings do not differ from data ofBaumann (2001b) which are determined with a similar measurement set-upon a similar car seat.

A level difference in the acceleration level of about 1.5 dB ± 0.4 dB isdetectable (JNDL) for seat vibrations on a real car seat in the range ofLV ib = 100 dB. Besides, no differences between untrained and trainedsubjects, as well as data from literature (Baumann, 2001b) exist. Theseresults are similar to difference thresholds which are determined on a rigidseat (Chapter 3.6 at a similar reference acceleration. It seems that the justnoticeable differences in level for a sinusoidal vertical excitation are nearlyindependent of the seat type and the contact areas between the human bodyand the seat for frequencies below 31.5 Hz. Additionally the vibrations onthe seat surface of a real car seat contribute components in nearly all threedirections (x/y/z-axes) instead of just vertical components on a rigid seatin Chapter 3.6.1. The individual sensitivity (measured perception thresholdsand the just noticeable differences) of the subjects on a real car seat areindependent of exogenous and endogenous data, like age, weight, body-size,RI and BMI, as well as frequencies of 16 and 31.5 Hz.


The last two experiments deal with broadband vibration signals and vibro-acoustic signals which are measured in a real petrol- and diesel-engine car.With these experiments the influence of the acceleration level and the boom-ing noise on the subjective assessments of seat vibrations are investigated.First, a real vertical vibration signal from a petrol-engine and from a diesel-engine car are changed in the acceleration level. The task of the participatingsubjects is to judge the quality of the felt seat vibrations. The same cat-egorical scale, like in Chapter 4, is used for the subjective assessments ofthe seat vibrations. The subjective ratings of the presented seat vibrationsdecrease with increasing acceleration for both engine types. The correlationcoefficients between the subjective assessments and the (objective) acceler-ations on and at the seat are statistically significant. However, diesel-enginecars get a better subjective rating than petrol-engine cars if the cars featurethe same objective acceleration level. This result is similar to findings oftesting-session in real cars (Chapter 4). A transformation of the accelerationdifferences of the presented seat vibrations in terms of the individual justnoticeable differences in level units (JNDL) for the four subjective-testerspoints out that an increase of the seat vibrations of 1.7 to 2 JNDL yields toa rise of the subjective rating of 1 categorical unit. For this reason the vibra-tions of two (seats or) cars must differ about more than 1 JNDL in order toobtain a different subjective rating according to the (dis-) comfort causedby the seat vibration. Moreover, this experiment is just practicable withprofessional testers who are familiarized with the subjective rating scale andare highly trained in judging seat vibrations of the used class of cars to getconsistent and repeatable results. The regression curves between the sub-jective ratings and the objective vibration parameter of this experiment andof the testing sessions in a real car (Chapter 4) are not comparable to eachother because too many measuring parameters are varying like excitationaxes, acoustic components and so on. But the results of both correlationanalysis show the same tendency.

In the last experiment the vibrations should be (active) changed by the sub-jects in order to receive (1) an optimal matching between the heard boomingnoise and the felt seat vibrations, (2) the vibrations are too strong or (3) thevibrations are too weak based on the heard booming noise. The subjectivetesters adjust the original seat vibrations for the task (1) in a laboratory.This finding shows the repeatability of the professional testers again. Addi-tionally, an increase or a decrease of about 1.5 individual JNDL delivers amismatching between the sound and vibration (task 2 and 3), respectively.Therefore the ’comfort’ assessments of the seat vibrations seem to dependon the heard booming noise, as well. The results of the last experimentand this one are not really comparable but the findings show a similar and

5.7. Discussion 153

more general tendency: The judgement of subjective-testers according to thequality of seat vibrations is nearly independent of the individual perceptionthreshold but depends significantly on the just noticeable level differencesof the felt seat vibrations. This means that the same number of individ-ual just noticeable differences in level for different subjective testers deliversthe same difference of the subjective ratings. Furthermore, the relationshipbetween heard sound and perceived vibration in a car is from decisive impor-tance for the acceptability and the subjective ratings of the seat vibrations.The relation between the results of this measurement and the findings ofreal testing-sessions (Chapter 4) and experiment in Chapter 5.5 could beinvestigated with a repetition of this measurement. But then the subjectivetester must give a subjective rating on the categorical scale according to thetask, as well.

Summary and conclusion

This thesis deals with three different aspects of the perception of whole-bodyvibrations for sitting subjects. First, basic experiments on the perception ofvertical sinusoidal vibrations are conducted on a rigid seat (Chapter 3) be-cause incomplete details exist in the literature or the data from the literatureshow considerable differences to the existing standards. The second aspectfocuses on an application from daily life traffic (Chapter 4) because the hu-man body is exposed to sound and vibrations everywhere, especially insidepassenger cabins in vehicles. In the third part of this thesis the perceptionof vibrations on a cushioned car seat is investigated (Chapter 5) because itis not possible to compare the results of the basic experiments (Chapter 3)with the applications inside a car (Chapter 4).

In Chapter 3 four basic experiments on the perception of vertical whole-bodyvibrations are conducted with new and reliable psychoacoustic measuringmethods to inhibit and to minimize the influence of measuring parameterson the results. The vibrations are produced by using the vibration-floor.This system was developed while performing the experiments of this the-sis. This system emits just low sound pressure, which is not audible forlow frequencies up to 50 Hz and around the auditory threshold for higherfrequencies, during the production of vibrations (Chapter 2.1). Therefore,the vibration-floor is suited to investigate the perception of vibrations in anearly silent environment.First, the psychometric functions are measured for 5 Hz with the method ofconstant stimuli for 14 subjects (Chapter 3.3). The duration of the stim-ulus is 2 s because there is an influence on the perception threshold for5 Hz if the duration is shorter (Chapter 3.4). The measured psychomet-ric functions show considerable differences for the perception of sinusoidalvertical vibrations between individuals. Additionally, a maximum likelihoodfit is made for the psychometric functions which shows a good consistencewith the measured data (Chapter 3.3). The logistical function of the av-eraged data of all subjects has a slope of 10.7 %/dB at the central point


L50 = 82.9 dB. There are no data in the literature found for measurementsof the psychometric function.

In the second experiment the perception thresholds of vertical whole-bodyvibrations are measured with an adaptive 3 - AFC 1 up - 2 down measuringmethod in a frequency range from 5 to 200 Hz (Chapter 3.5). But be-fore the perception thresholds are measured for a large number of subjectsthe influence of some measuring parameters, like stimulus duration andmeasuring method, on the threshold are investigated with some subjects(Chapter 3.4). For example, the stimulus duration of the vibration signalsis 2 s for vibrations below 16 Hz and 1 s for higher vibrations because theperception threshold decreases with rising exposure time (pre-experiment 1,Chapter 3.4.1). Furthermore, the perception thresholds are measured forfrequencies above 16 Hz in presence of an additional audible stimulus (pinknoise, L = 69 dB(A)) to prohibit an influence of the emitted sound from thevibration-floor, especially for 63 Hz (Chapter 3.4.2). – There is no influenceof an audible stimulus up to this level on the perception threshold (Meloni,1991; Baumann et al., 2001a). – The averaged curve increases from 5 to8 Hz with nearly 7 dB/octave and is constant up to 63 Hz at a level ofLV ib = 88 dB thereafter. For higher frequencies the perception thresholddecreases a bit to a level of about LV ib = 86 dB. This slightly increasingsensitivity and decreasing perception threshold for 125 and 200 Hz probablydepends on the bone conduction threshold because no additional audiblecues are measurable at the ear of the subjects via air conduction. However,a measurement of the perception threshold is difficult or maybe impossibleeven with masking audible noise, if bone conduction influences the percep-tion thresholds for higher frequencies. For future investigations basic puretone bone conduction threshold audiometry experiments should be made toinvestigate the influence of bone conduction on the perception of verticalwhole-body vibrations, especially for frequencies above 63 Hz. Additionally,the vibrations on the head and between the chair (seat surface) and thehuman body should also be measured. Just a few data are found in theliterature for bone conduction thresholds (e.g., Queller & Khanna, 1982;Khanna et al., 1976) which indicate a decreasing bone conduction thresh-old with increasing frequency up to some kHz. Furthermore, more data forthe seat-head-transmissibility (some clues are given in Chapter 3.4.2 and inAppendix C) are necessary at low magnitudes for higher frequencies (above25 Hz) to investigate if body resonances (modes) yield an additional (au-dible) cue during the perception threshold measurements. Most studies forthe seat-head-transmissibility report about results in the frequency rangefrom 1 to 20 Hz with high vibration magnitudes (≥ 1 m/s2) and with abroadband (shock) excitation (some are summarized in Griffin, 1990). But

156 Summary and conclusion

the human body is a highly non-linear system (which is reported frequentlyin the literature, e.g., Griffin, 1990; Mansfield & Griffin, 2000). Moreover,the influence of the posture and the contact areas between the vibratingsurface and the human body must be controlled because an influence ofthe vibrating contact area on the bone conduction thresholds is reported(Queller & Khanna, 1982). The lack of such data and the difficult mea-suring conditions are probably the reasons why no or only few data above63 Hz are available for the perception threshold in literature. These dataalso show a decreasing perception threshold for frequencies above 63 Hz.Another way to investigate a possible influence of bone conduction is to usehearing impaired subjects who have a loss of function of the inner ear. Thosesubjects could not detect any audible stimuli via air or bone conduction.

However, the interindividual standard deviations are large (about 5 dB) formeasurements of the perception threshold with vertical vibrations (Fig. 3.13,Chapter 3.5). The differences between individuals (interindividual standarddeviations) for the perception thresholds in this study are not explicablewith anthropometric exogenous variables like weight, body-size, Body-MassIndex (BMI) and Rohrer Index (RI) or endogenous variables like age andgender (Chapter 3.5). These findings verify results of different other stud-ies which are found in the literature (like Griffin & Whitham, 1978; Griffin,1982; Parsons & Griffin, 1982; Corbridge & Griffin, 1986; Griefahn & Brode,1997; Baumann, 2001b) for different aspects of the perception of verticalvibrations. Additionally, the seat pressure distributions of some participantsare measured at the contact between the seat and the human body witha special pressure distribution measurement cushion (Chapter 3.5, as well).Simple parameters like mean and maximum pressure p, pressure gradient(| 5 p|) and size of the contact area are calculated from these individ-ual pressure distributions. The calculated simple parameters are also notsuited to systematically explain the differences between humans. This find-ing also verifies results from Kruse (2001). However, the presented percep-tion threshold for vertical whole-body vibrations show no higher deviationsto some literature data (like McKay, 1972), except for low frequencies be-low 16 Hz. It is just briefly noted that the data at low frequencies are ofteninfluenced by visual or audible additional cues (described in Griffin, 1990, orFig. 3.13). Existing standards (e.g., ISO 2631-2, 1989; VDI 2057-2, 1987)for vertical vibrations show considerable deviations to the summarized litera-ture data. The standard curve rises with increasing frequency from 8 Hzupwards with constant 6 dB/octave Therefore the standard data overesti-mate or underestimate the vertical whole-body vibrations below or above50 Hz, respectively (Fig. 3.13). It is necessary to repeat the measurementsof the perception thresholds for vertical whole-body vibrations with many


healthy volunteers and with comparable measuring conditions at differentlaboratories to get repeatable and constant data for a revision of the stan-dard perception thresholds which are specified in existing standards.

In a third experiment the Just Noticeable Differences in Level (JNDL, Chap-ter 3.6.1) and in Frequency (JNDF, Chapter 3.6.2) are determined in a fre-quency range from 5 to 50 Hz and from 5 to 40 Hz for vertical vibrations,respectively. The difference thresholds for vertical whole-body vibrations areabout 1.5 dB. Additionally, the JNDLs show no significant frequency depen-dence. The intra- and interindividual standard deviations are about 0.4 dBand indicate a high repeatability of the JNDLs. This finding is very inter-esting because different mechano receptors in the skin are involved in thedetection of vibrations with different frequencies (Fig. 1.18). These recep-tors are specialized in detecting different objective properties of the stimuluslike magnitude, velocity and acceleration (Chapter 1.2.3). This is probablythe reason for the fine structure of the JNDL curves in Fig. 3.14. However,the differences (fine structure) of the JNDLs at different frequencies arestatistically not significant (T-Test, p < 0.01). There are not a lot of datain the literature published for a sinusoidal vibration excitation for JNDLsbut data from Morioka & Griffin show no significant deviations to results ofthis study. Additionally, data from Baumann (2001b) validate the findingseven though the JNDLs are measured on a cushioned car seat; but thereis a tendency observable that the JNDL decreases slightly with increasingacceleration level of the reference stimulus. These findings indicate that justa small number of noticeable level differences for vertical vibrations betweenthe perception and the ’pain’ threshold are detectable for humans. It isjust briefly noted that there are some parallels to the JNDLs for the hearingwhich also depend on the presented level and are almost independent offrequency over a large frequency range (Zwicker & Fastl, 1999).

Additionally, the Just Noticeable Differences in Frequency (JNDF) are mea-sured for a small number of participants. The measured data show thatthe humans are highly sensitive for frequency changes at 5 Hz. The JNDFis about 0.25 Hz at 5 Hz and increases linearly depending on frequencyup to 16.7 Hz at 40 Hz. The linear increase in proportion to frequency isabout 0.34 · f − 1.25 Hz which is just applicable for reference frequen-cies between 5 and 40 Hz. The differences between subjects are very large(Fig 3.16) in comparison to the very low intraindividual differences whichincrease slightly with the reference frequency. This measurement should berepeated for more subjects and for more frequencies between 5 and 40 Hzto verify these findings. It seems that humans are not trained to detectfrequency changes in a vibration signal. These results indicate that the fre-quency differentiation of the sense of touch for vibrations is not so distinct


than the frequency differentiation of the ear for acoustic stimuli (reportedin the psychoacoustic, e.g., in Zwicker & Fastl, 1999).

The last basic experiment is the determination of the (so-called) equal-vibration level contours (comparable to equal-loudness level contours) witha new psychophysical measuring method (adaptive 2 AFC interleaved 1 up- 1 down, Buus et al., 1997) in the frequency range from 5 to 80 Hz forvertical whole-body vibrations. This measuring method minimizes the influ-ences of the experimental procedure, e.g., the initial level dependence of thetest vibrations. Equal-vibration level contours are of interest for measuredvibrations in real situations like in buildings or transport facilities in dailylife where vibrations usually occur with broadband frequency characteristicsand with some components above the perception thresholds. The reasonfor the interest is that the inverted shapes of the curves could be used fora psychophysically motivated spectral weighting of a measured broadbandvibration signal and therefore deliver psychophysically motivated parameterswhich are better suited to describe and forecast the perception of broadbandvibrations. In this study the contours are measured close to the perceptionthreshold (reference stimulus: sinusoidal stimulus with fRef = 20 Hz andan acceleration level of LV ib = 100 dB). The curves show an increase de-pending on frequency from about 2.3 dB/octave from 6 to 63 Hz. Above63 Hz the slope of the equal-vibration level contour rises rapidly which indi-cates a decreasing sensitivity of the human body for higher frequencies. Thelow intraindividual standard deviations indicate a high repeatability of thesubjects but the interindividual standard deviation shows large differencesbetween individuals (Chapter 3.7). In existing standards for the perceptionof vibrations, (e.g., VDI 2057-2, 1987; ISO 2631-2, 1989), curves above theperception thresholds are specified for the horizontal plane (x/y-axes) andvertical direction (z-axis) to describe the sensation and perception of whole-body vibrations. These curves are the standardized perception thresholdsmultiplied with K-values (specified in existing standards, e.g., VDI 2057-1,see also Fig A.2 in Appendix A). The standard curves show considerabledifferences to the measured equal-vibration level contours. In the literaturesuch curves are sometimes denoted as equal-subjective vibration intensity(Shoenberger & Harris, 1971) or equivalent-comfort contours (e.g., sum-marized in Griffin, 1990) and they deviate from each other probably due tothe used measuring method and the used reference. Most of the measuredequivalent-comfort contours for vertical vibrations of seated subjects, whichare published by, e.g., Dupuis et al., 1972a-c; Griffin (1982); Donati et al.(1983); Corbridge & Griffin (1986), feature a rising curve for increasing fre-quency above 8 Hz with a slope of about 6 dB/octave and more. Thesecurves are often measured at high accelerations and show no considerable


differences to the specified curves in existing standards (e.g., VDI 2057-2).But there is a lack of data in the lower acceleration range and a discrepancybetween the findings of this thesis and the literature data, as well. Howarth& Griffin (1990) report similar tendencies but the data are measured with adifferent reference stimulus and measuring method: a narrow band (audible)noise as reference and a method of magnitude estimation was used. Thecontours obtained for magnitude estimations of 50 and 100 and 200 thatis why the data are not really comparable to each other; but both resultsshow nearly the same tendency even so different reference stimuli were used.Additionally, the shape (curve) of the measured equal-vibration level con-tours differs significantly from the measured perception threshold curve ofthis study even though the contours are measured close to the percep-tion threshold. The different shapes of both curves are not explicable withJNDLs which are independent of frequency. It is just briefly noted thatthis is contradicting findings in psychoacoustics where the equal-loudnesslevel contours, which are close to the auditory threshold, have a simi-lar shape as the threshold. The shape of the equal-loudness level con-tours changes depending on the presented level up to the ’pain’ thresh-old which becomes more flat. For future investigations it is necessaryto measure the equal-vibration level contours with a reference stimuluswhich has a fixed frequency and a varying magnitude from the percep-tion threshold to the ’pain’ curves. With such measurements the depen-dence of the equal-vibration level contours could be investigated. Ad-ditionally, these curves could be the basis of psychophysically motivatedspectral weighting functions which depend on acceleration level. Suchcurves are also of decisive importance for vibrations in the horizontal plane.These four basic experiments are just made with sinusoidal stimuli. Thenext step (for future experiments) is to repeat some experiments with nar-row band and broadband vibration stimuli. Additionally, the determinationof the critical bandwidth (Fletcher experiment) might help to understandthe perception of vibrations and could help to understand the different per-ception of sinusoidal and narrow band vibration signals. Furthermore, manybasic experiments with reliable measuring methods, which are well knownin the psychoacoustics, are missing for the description of the perception ofwhole-body vibrations.

An application of the perception of whole-body vibrations is given in thedaily life traffic where humans are usually exposed to broadband vibrations,especially in passenger cabins of vehicles. Therefore, the second and thirdparts of this thesis focus on the perception of vibrations on a real cushionedcar seat inside cars. Two main investigations are conducted: first, the qualityof seat and steering-wheel vibrations inside passenger cabins of vehicles are


judged by professional subjective-testers (Chapter 4). The objectives are toidentify objective parameters to get an objective method for the descriptionof the subjective (dis-) comfort caused by seat and steering-wheel vibra-tions. In the third part basic experiments for the perception of whole-bodyvibrations on a real (cushioned) cars seat are carried out, like perceptionthresholds and subjective ratings of (artificial) sinusoidal and (real) broad-band seat vibrations (Chapter 5). With these measurements, the gap ordiscrepancy between the findings in Chapter 3 (basic experiments with si-nusoidal vertical vibrations) and Chapter 4 (application inside a car withreal broadband multi-dimensional vibrations) should be clarified; addition-ally, the found objective parameters for the description of the quality of seatvibrations should be validated. Furthermore, the influence of psychophysi-cal parameters like just noticeable difference in level are investigated on thesubjective quality ratings of seat vibration.

Chapter 4 focuses on broadband vibration signals and exhibits an examplefor an application of the perception of vibrations in the passenger cabin ofvehicles in the car industry. The sound and the vibrations (seat and steering-wheel vibrations) have a decisive importance on the passenger comfort insidecars and the acceptability of a vehicle. It would be very advantageous toknow the properties of noise and vibration signals which are fundamental forthe subjective quality assessments. Therefore the target is to find (objective)signal parameters, which are calculated from multi-channel recordings of thesound and the vibrations inside passenger cabins of cars, in order to describeand forecast the (subjective) quality judgements. In detail: the quality ofseat and steering-wheel vibrations are judged by professional testers for dif-ferent classes of cars. The seat and steering-wheel vibrations as well assound are recorded inside cars of different classes (small, middle and uppermiddle class) in idle running conditions simultaneously with the subjectiveratings. These testing-sessions are a common way in the car industry forthe classification of the qualities of sound and vibrations. From the 19channel-recordings of the vibrations and the sound field inside the cabinobjective signal parameters for the seat and steering-wheel vibrations arecalculated which correlate significantly with the subjective ratings and con-sequently describe the subjective vibration comfort. Psychophysically moti-vated parameters (from existing standards, e.g., ISO 2631-1/2, ISO 5349-1/2, DIN 4051-1/2 and VDI 2057-1/2/3), as well as signal parameters fromthe car industry are considered for the classification of seat and steering-wheel vibrations. The subjective ratings of professional testers are correlatedwith the calculated parameters thereafter.

The results can be summarized as follows: it turns out that psychophysicallymotivated spectrally weighted vibration signal parameters as proposed in ISO


2631-2 (1989); ISO 5349-2 (2001); VDI 2057-2 (1987) deliver significantlyhigher correlation coefficients with the subjective assessments than spec-trally unweighted vibration parameters which are mostly used in the car in-dustry. This finding applies just for the steering-wheel vibrations. Spectrallyunweighted parameters for the seat vibrations, which are also band limited,show significant high correlation coefficients with the subjective ratings.The reason for this is that the horizontal vibrations are as important for thesubjective comfort ratings of the seat vibrations as the vertical vibrations(z-direction) for the investigated cars. But the standard spectral weightingfunction Wd (specified in VDI 2057-2, 1987; ISO 2631-1, 1997) attenuatesthe horizontal accelerations (x- and y-axes) more than the z- accelerationby using Wk. Additionally, the vibration energy in the low frequency regionbetween the 1st and 2nd motor order, especially around the 2nd motor or-der, contributes to the quality assessment of the seat and steering-wheelvibrations significantly (in 4-cylinder engine cars). Vibration total valuesfor the seat and the steering-wheel vibrations, which take into account ac-celerations of all three directions (x/y/z), deliver higher correlation coeffi-cients with subjective assessments than parameters which include only theaccelerations in z-direction. A correlation analysis separated in petrol anddiesel-engine models increases the correlation coefficients between the sub-jective and objective data significantly. The different judgement behaviorsin case of petrol and diesel cars with nearly the same value of the objectiveparameter (diesel cars get better subjective ratings than the petrol cars) arenot exclusively explained with changes of the spectral characteristics for thesteering-wheel and seat vibrations.

Both testers for small and middle class cars show almost similar judgementbehaviors for the steering-wheel vibrations and for the seat vibrations in themiddle class cars which is confirmed with statistical tests. Therefore thesubjective assessments are summarized together with the objective para-meters in the cases of the middle class vehicles. The small class cars werea new production run, therefore the subjective ratings of the two testers forthe steering-wheel vibrations do not probably correlate with the objectivespectral parameters. Additionally, the results for the seat vibrations of thesmall class cars show that the application of professional subjective-testerswho are highly trained and familiar with the specific car type are needed toget repeatable assessments for each tester, similar judgement behaviors fordifferent testers and to calculate objective parameters which correlate signifi-cantly with the subjective assessments. Furthermore, the optimal measuringposition of the seat vibrations depends on the car class and the used seatwith special seat rails. Therefore, an optimal measuring position cannot bespecified for all classes but for each class separately. For the verification of


these findings, a lot of cars should be used from each car class and should bejudged by a lot of subjective testers; especially for petrol cars of the uppermiddle class because the number of cars used in this study was very low.Additionally, the testing-sessions in the small class cars should be repeatedwith the same subjective-testers, who are highly trained now, to find out ifthe subjective ratings correlate significantly with the objective parametersthen.

The results from the correlation analysis between the objective vibrationparameters and the subjective ratings of professional testers show that itis necessary to specify psychophysically motivated spectral weighting func-tions, which are determined on the same seat as the used type of seat in thereal car. The measurement of the equal-vibration level contours for verticalexcitation (Chapter 3) indicates that the spectral weighting function Wk

shows considerable differences to the measured equal-vibration level con-tours. One way to get psychophysically motivated spectral weighting func-tions, which improve the description of (dis-) comfort, is to determine theequal-vibration level contours for the vertical (z-) and the horizontal (x/y-)axes from the perception threshold to the ’pain’ threshold with a fixed mea-suring method and with a fixed reference stimulus on the used real (cush-ioned) car seat. Additionally, measurements are needed for the equivalentperception of horizontal and vertical whole-body vibrations simultaneouslybecause the relative position of the spectral weighting function for the hor-izontal plane and for the vertical direction is of decisive importance for thesubjective ratings and for the psychophysically motivated spectral weightingfunctions. Moreover, some clues are reported in the literature about equiva-lent contours of vertical and horizontal vibrations (Griefahn & Brode, 1997).

In this study, a statistical test shows that if the weighting-factors kj for thethree directions (j = x/y/z) are changed so that kx and ky get higher valuesthan kz – this means that the vibrations in the horizontal plane give highercontributions to the vibration total value than the vertical components –the correlation coefficients between the calculated objective parameters andthe subjective ratings are nearly unchanged or increase significantly. Fur-thermore, such equal-vibration contours must be investigated not only withsinusoidal vibrations but also with frequency limited narrow band seat vibra-tions, as well. With such measurements it could be verified if there are anydifferences between the curves by using sinusoidal and narrow band vibra-tion signals. This verification is very important because the application inthe passenger cabin show that the vibration signals feature almost narrowband frequency limited character. This applies especially to low frequen-cies around prominent motor orders which are important for the subjective(dis-) comfort judgement of seat vibrations. In contrast to this the highly


significant correlation coefficients for the steering-wheel vibrations featurethat the spectrally weighted parameters describe the subjective rating ofsubjective-testers very well. Some laboratories reported about measure-ments of equal-vibration level contours which were determined with sinu-soidal rotational hand-arm vibrations (for example, Shayaa et al., 2001).These curves show no larger differences for the weighting functions as thestandard weighting curves in the ISO 5349-2. But the measurements ofequal-vibration level contours for hand-arm and especially for whole-bodyvibrations, which are found in the literature, are measured with differentmeasuring methods which probably bias the measured data. For a bettercomparability and for minimizing the influence of the measuring parameterson the result, an adaptive interleaved measurement should be used for futureinvestigations. Furthermore, a separate analysis of petrol- and diesel-modelsincreases the correlation coefficients significantly. The different judgementsfor the steering-wheel and seat vibrations of petrol and diesel models arenot exclusively explained with changes of the spectral parameters for thesteering-wheel and seat vibrations. In this study just frequency (spectral) de-pending parameters are used but it is not precluded that also time dependingparameters are needed for a full description of the subjective ratings for theseat and the steering-wheel vibrations, as well. Therefore multi-dimensionalor combined parameters, which include a combination of frequency and timedepending properties, are needed to get a full description of subjective carvibration quality assessments. Some clues for such an approach are pro-posed in different literature studies for the discomfort caused by a combinedexposure of sound and vibration from the aerospace section (for example,Dempsey et al., 1978). They suggest a parameter called DISC which isa combined parameter of the discomfort caused by sound and by vibrationseparately.

By the way, more knowledge and basic experiments on the perception ofvibrations on real cushioned seats like a car seat are important to find moreand better parameters for the description of the judgement behavior. It isnot possible to generalize the knowledge of the basic experiments (like inChapter 3) for the applications inside a car or on a (cushioned) car seatdue to many facts: on the one hand the vibrations inside a car are not onlyartificially sinusoidal but also broadband vibration signals and on the otherhand real car seats are cushioned and therefore the frequency-characteristicsof the seat and the characteristics of the subject, who sits on it, have maybean influence on the perception of vibrations. It would be very advantageousto know the properties of the vibration signals which are fundamental forthe subjective perception of vibration in detail to understand and to de-scribe the discrepancy between basic knowledge and special applications.


Therefore basic experiments, like perception thresholds and just noticeablelevel differences, are repeated on a real cushioned car seat in Chapter 5.Furthermore, experiment with broadband vibration signals are conducted,as well. With such experiments the influence of simple parameters, like thevibration level or an additional audible cue, on the quality judgements ofthe seat vibrations are investigated in the laboratory. For the description ofthe perception threshold on a real car seat a vibration parameter is neededwhich takes into account the vibrations in all three directions for all trans-duced vibrations, like the vibration total value. The reason for this is thata car seat is a single-input multiple-output system which features vibrationsin almost all three axes even though just an axial excitation is used. Theposition of the perception threshold significantly depends on the used seatthence considerable differences exist between the results on a rigid seat andon a real cushioned car seat (Chapter 3.5 and 5.3). In contrast to this, thejust noticeable differences in level (JNDL) seem to be independent of theused seat. Measurements on a rigid seat (Chapter 3.6.1) and on a car seat(Chapter 5.4) exhibit that level differences of about 1.5 dB are detectableat a reference level of about 100 dB. The JNDLs are also independent offrequency in a range from 5 to 80 Hz but there is a light dependence onthe level which is shown in the literature. This level dependence is compa-rable with results from the psychoacoustics, where the JNDLs show a lightlevel dependence, as well. Just a few data are found in the literature forthese measurements but they validate the findings of this study (Baumann,2001b; Morioka & Griffin, 2000). Additionally, there are no differences be-tween highly trained and untrained subjects.

Moreover, in another experiment the dependence of the level on the sub-jective ratings can be verified in the laboratory. The subjective ratingsof the subjective-testers decrease with increasing acceleration level of theseat vibrations. Furthermore, differences in the judgement behavior of theparticipants (subjective-testers) are for the petrol- and diesel-engine carsobservable like in the real car during a testing-session (Chapter 4.4.1 and5.5). The judgement behaviors show no considerable difference betweenthe testing-session in a real diesel car and in the laboratory. But there aresignificant differences for the petrol cars. The reason for this is probablyaffected due to differences in the spectra (frequency characteristics as wellas distribution of the vibrations in all three axes) of the used signals in thereal petrol car and in the laboratory. The interindividual differences betweenthe four testers could be explained by individual just noticeable differencesin level. A level difference of more than 1 JNDL but less than 2 JNDL leadsto a change in the subjective rating of the seat vibration of about 1 categor-ical unit for the diesel and petrol cars in the laboratory. These results show


that the level range for the seat vibrations, which are denoted with a goodor a poor subjective rating, is very small. Furthermore, the experiment ofthe dependence of booming noise on the subjective rating of the seat vibra-tions in Chapter 5 indicates, that different cues (like sound) influence thesubjective comfort and quality assessment according to vibrations.

The most existing standards, which take into account either the sound orthe vibration, are based on mono-sensorial inputs but the human body isusually exposed to multi-sensorial inputs (stimuli), especially vibro-acousticstimuli (sound and vibrations). These different cues could interact with orinfluence the perception of each other. Some clues are found in the literature(for example, Fleming & Griffin, 1975; Meloni, 1991; Howarth & Griffin,1990; Paulsen & Kastka, 1995; Bellmann, 1999). Therefore the interactionof sound and seat vibrations with narrow band and broadband vibrationsignals must be investigated in the future, as well. Finally, this study showsthat better standards are needed for improved designs that would increasecomfort and reduce the experienced annoyance from excessive vibrations.Additionally, not only knowledge about the perception of vibration in morethan one direction is missing but also data for the combined perceptionof sound and vibration. Moreover, knowledge about basic experiments onthe perception of vibration would help to understand the effects in specialapplications in practice, like the subjective (dis-) comfort caused by seat andsteering-wheel vibrations in cars, but it does not substitute measurementsin special locations like in the passenger cabin of a vehicle. Therefore it isnecessary to define multi-sensorial vibro-acoustic limits for special locationswith the specification of the relevant criterion stating with which probabilitya specified effect is prevented by the limit.

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Yeowart, N.S., Bryan, M.E. & Tempest, W ’The Monaural MAP Thresholdof Hearing at Frequencies from 15 to 100 c/s’, J. Sound Vib. Vol 6, No3,pp. 335-342, 1967

Yeowart, N.S. & Evans, M.J. ’Thresholds of audibility for very low-frequencypure tones’, J. Acoust. Soc. Am. 55, pp. 814-818, 1974

Zollner, M. & Zwicker, E. ’Elektroakustik’, Berlin: Springer-Verlag, 1993

Zwicker, E. ’Psychoakustik’, Berlin: Springer-Verlag, 1982

Zwicker, E. & Fastl, H. ’Psychoacoustics - Facts and Models’, Berlin:Springer-Verlag, 1999

Appendix A

Supplements for the vibrationstandards

ii Appendix A

Tab. A.1: Guide for the application of frequency-weighting curves for principalweightings defined in ISO 2631-1 (1997).

Frequency

weighting

Health Comfort Perception Motion

sick-

ness

Wk z-axis, seat

surface

z-axis, seat

surface z-axis,

standing verti-

cal recumbent

(except head)

x/y/z-axes, feet

(sitting)

z-axis, seat

surface z-axis,

standing

Wd x-axis, seat

surface y-axis,

seat surface

x-axis, seat

surface y-axis,

seat surface

x/y-axes, stand-

ing horizontal

recumbent

y/z-axes, seat

back

x-axis, seat

surface y-axis,

seat surface

x/y-axes,

standing

Wf vertical

Supplements for the vibration standards iii

0.016 0.063 0.25 1 2 4 8 16 31.5 63 125 250−90

−80

−70

−60

−50

−40

−30

−20

−10

0

10

Frequency [Hz]

Fre

quen

cy W

eigh

tings

[dB

]

Wk

Wd

Wf

Fig. A.1: Frequency weighting curves for principal weightings defined in VDI2057-2 (1987) and ISO 2631-1 (1997).

Acc

eler

atio

n Le

vel [

dB]

Frequency [Hz]1 10 100

60

70

80

90

100

110

120

130

140

x,y−axis base curve

10 100

z−axis base curve

10 100

combined−directioncriteria curve

0,1

0,2

0,4 0,8

1,6

3,15

6,3

12,5

25

50

KZ = 100 Kx = Ky = 100

50

25

12,5

6,3

3,15

1,6

0,8 0,4

0,2

0,1

KB = 100

50

25

12,5

6,3

3,15

1,6

0,8 0,4

0,2

0,1

Fig. A.2: Equivalent-comfort contours and multiplying factors after VDI 2057-2 (1987) for the description of vibrations with magnitudes above the standardperception threshold.

iv Appendix A

Fig. A.3: Positionof the accelerometers(triaxial) on theshaker-table (P), onthe seat surface (S)and at the backrest(B) of a real carseat defined in ISO10326-1 (1992).

Tab. A.2: Frequency weighting for x-,y- and z-axis whole-body vibration for cal-culating the Vibration Dose Value (VDV) defined in BS 6841 (1987a).

Frequency [Hz] z-axis x/y-axes Frequency [Hz] z-axis x/y-axes

0.5 0.4 1.0 8 1.0 0.250.63 0.4 1.0 10 1.0 0.20.8 0.4 1.0 12.5 1.0 0.161 0.4 1.0 16 1.0 0.125

1.25 0.4 1.0 20 0.8 0.1001.6 0.4 1.0 2.5 0.64 0.0802 0.4 1.0 31.5 0.5 0.064

2.5 0.5 0.8 40 0.4 0.0503.15 0.63 0.64 50 0.32 0.0404 0.8 0.5 63 0.25 0.0325 1.0 0.4 80 0.2 0.025

6.3 1.0 0.32

Supplements for the vibration standards v

Tab. A.3: Root-mean-square accelerations corresponding to estimated VibrationDose Values of 15 m/s1.75 defined in BS 6841 (1987a).

Frequency z-axis vibration x- and y-axis vibration

Hz 1 s 1 min 1 h 8 h 1 s 1 min 1 h 8 h

0.5 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

0.63 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

0.8 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

1 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

1.25 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

1.6 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

2 26.78 9.62 3.46 2.06 10.71 3.85 1.38 0.82

2.5 21.43 7.70 2.77 1.64 13.39 4.81 1.73 1.03

3.15 17.01 6.11 2.19 1.30 16.87 6.06 2.18 1.30

4 13.39 4.81 1.73 1.03 21.43 7.70 2.76 1.64

5 10.71 3.85 1.38 0.82 26.79 9.62 3.46 2.06

6.3 10.71 3.85 1.38 0.82 33.80 12.14 4.36 2.59

8 10.71 3.85 1.38 0.82 42.86 15.40 5.53 3.29

10 10.71 3.85 1.38 0.82 53.57 19.25 6.92 4.11

12.5 10.71 3.85 1.38 0.82 66.96 24.06 8.64 5.14

16 10.71 3.85 1.38 0.82 85.71 30.80 11.06 6.58

20 13.39 4.81 1.73 1.03 107.14 38.50 13.83 8.22

25 16.74 6.02 2.16 1.28 133.93 48.12 17.29 10.28

31.5 21.09 7.58 2.72 1.62 168.75 60.13 21.79 12.95

40 26.78 9.62 3.46 2.06 214.28 76.99 27.66 16.45

50 33.48 12.03 4.32 2.57 267.86 96.24 34.58 20.56

63 42.18 15.16 5.45 3.24 337.50 121.27 43.57 25.91

80 53.57 19.25 6.92 4.11 428.57 153.99 55.33 32.90

vi Appendix A

Tab. A.4: Ranges of multiplying factors to specify satisfactory magnitudes ofbuilding vibration with respect to human response. These factors have been ap-plied to the basic curves shown in Fig. 1.9 in Chapter 1.1.3 (adapted from ISO2631-2, 1989).

Place Time Continuousor inter-mittentvibration

Transient vibrationexcitation with sev-eral occurrences perday

Critical working areas(for example some

Day

hospital operating-theaters, some precisionlaboratories, etc.)

Night1 1

Day 2 to 4 30 to 90

ResidentialNight 1.4 1.4 to 20

Day

OfficeNight

4 60 to 128

Day

WorkshopNight

8 90 to 128

Appendix B

Supplements for the simulator

B.1 Vibration-Floor

Fig. B.1: Supplement for Fig. 2.10. Comparison of the acceleration levels onvarious points of the vibration-floor for 31.5, 63, 160 and 200 Hz.

viii Appendix B

B.2 Sound & Vibration Reproduction System

Optimization of the SVRS First of all, the simulator was iterative op-timized by changing of the filter coefficients and by using two professionaltester from the car industry. For the validation of the system a test wasmade with these two testers by using real ’vibro-acoustic’ recordings of thesteering-wheel and seat vibration, as well as the interior sound from fivedifferent vehicles. The professional testers judge the quality of the seat andsteering-wheel vibrations, as well as the booming noise simultaneously tothe recordings in the real cars. Those testing-sessions were repeated onthe ’Sound & Vibration Reproduction System c©’ in the laboratory severaltimes over a period of one year to investigate if the judgement behaviour ofthe tester change. The order of the signals was randomized in contrast tothe real assessment situation in these cars. The results of both testers arestatistically not significantly different from the assessments in the real ve-hicles. Additionally, both testers show almost similar judgement behaviourswhich is confirmed with statistical tests. Additionally the subjective ratingbehavior of both testers does not differ over a period of one year whichis confirmed with statistical tests. Therefore, it is possible to say that theused subjective testers give constant and repeatable results. Additionally,a facsimile reproduction of the vibro-acoustic recordings in different cars ispossible with the usage of the Sound & Vibration Reproduction System c©.

Tab. B.1: Physical properties of the PU-foam (Diepoelast 2.2 c© from PUR Ser-vice GmbH & Co. KG) which is used for the Sound & Vibration ReproductionSystem c©.

Basic quantity Value Unit Dynamic test

Density 200 Kg/m3 DIN 53420

stat. elasticity modulus 0.07 - 0.4 N/mm2 according to DIN 53513

stat. shearing modulus 0.08 N/mm2 according to DIN 53513

dyn. elasticity modulus 0.07 - 0.4 N/mm2 according to DIN 53513

dyn. shearing modulus 0.08 N/mm2 according to DIN 53513

breaking strenght 0.5 N/mm DIN 53455-6-4

mech. lost factor 0,23 — DIN 53513

workspace (force per area) 0 - 0.025 N/mm2

Supplements for the simulator ix

Tab. B.2: Features of the Sound and Vibration Reproduction System c©.

Features Vibration Sound

Frequency range 10 to 500 Hz 20 to 12 kHz

Dynamic 0,003 m/s2 to 3 m/s2 depends on the used

loudspeaker systems

Initiation direction x-, y- and z-axis, theoretical

all three rotational axis

Payload max. 250 Kg

Coupling elements via base plate and seat surface

Transformer Electro-dynamic Headphones, flexural

wave loudspeaker +

subwoofer

Special features removable, flexible seats

PC

D/A converter

(SQLab II Dic. 20 output -modul )

digital filter

(Sony TA -E 2000 ESD)

lowpass main amplifier(Yamaha P2100)

headphone pre-amplifier

Headphone

x

zz

yy

x

zz Steering - wheel

Subwoofer

VibrationpadVibration

Acoustics

Shaker

digital filter


main amplifier(Yamaha P2100)

main amplifier(Yamaha P2100)

digital filter


Fig. B.2: Control-diagram of the Sound & Vibration Reproduction System c©.

Appendix C

List of results

This section contains results of the experiments from Chapter 3 to 5 whichare not listed in the current chapters.

C.1 Experiments on the perception of vibration

The seat-to-head transmissibility is measured for two subjects (Chapter 3.4.2).The input signal is a sinusoidal (vertical) vibration with a frequency whichvaries in 1/3rd octave-steps from 5 to 100 Hz. The acceleration level ofthe input signal is constant LV ib = 95 dB. The reference position (input)is measured and controlled at the seat surface (area between the body andthe chair, position ’cushion’ in Fig.2.4) with an accelerometer cushion MMFKB103SV (triaxial). The output signal is measured at the right mastoid (ac-celeration level in all three directions). The just vertical vibrations at theseat surface (input) are transformed into vibrations in all three directions onthe mastoid. Therefore, with these two vibration signals the seat-to-headtransmissibility is calculated using the cross-spectral density methods withsquare root of the ratio of the output to the input power spectra usingEq. C.1 (e.g., described for a single-input multiple-output system in Griffin,1990).

H(f) =

[Goo(f)Gii(f)

] 12

(C.1)

List of Results xi

with

Goo(f) = Power spectrum of the output

Gii(f) = Power spectrum of the input

The results of the measured seat-to-head transmissibility of the two par-ticipating subjects is plotted in Fig. C.1. A magnitude of 0 dB indicatesthat the input and output magnitudes are equal. The curves for the twoparticipating subjects look similar. The magnitude of the ’transfer func-tions’ decrease with increasing frequency. At 5 Hz the magnitude is about6 dB. That means that the measured vibrations on the mastoid (output) arehigher than the transmitted vibrations from the seat surface to the humanbody (input). It is just briefly noted that some literature data are summa-rized in Griffin (1990) for the variations in the transmission of vertical seatvibrations to the head. These results show similar curves to the measureddata in Fig. C.1.

Tab. C.1: Correlation coefficients the individual sensitivity of the subjects - mea-sured perception thresholds at different frequencies - for vertical whole-body vi-brations and objective parameters which are calculated from the individual seatpressure contributions during the measurements.

Parameter pmean pmax contact size mean(| 5 p|) max(| 5 p|)

pmean 1.00* 0.66* -0.11 0.64* 0.47

pmax 0.66* 1.00* -0.18 0.50 0.80*

contact size -0.11 -0.18 1.00* -0.75* -0.45

mean(| 5 p |) 0.64* 0.50 -0.75* 1.00* 0.73*

max(| 5 p |) 0.47 0.80* -0.45 0.73* 1.00*

5 Hz -0.57 -0.28 -0.15 -0.34 -0.23

6.3 Hz -0.25 0.24 -0.63* 0.33 0.45

8 Hz 0.27 0.28 -0.30 0.35 0.43

10 Hz 0.22 0.23 0.26 -0.04 0.22

12.5 Hz -0.31 0.06 -0.61* 0.26 0.30

16 Hz 0.51 0.20 0.07 0.14 -0.04

31.5 Hz -0.17 -0.04 0.56 -0.26 0.03

63 Hz -0.11 -0.11 0.53 -0.31 -0.19

125 Hz 0.34 0.32 0.07 0.36 0.33

200 Hz 0.24 0.45 0.09 0.25 0.40

xii Appendix C

5 8 12.5 20 31.5 50 80 125−40

−30

−20

−10

0

10

Frequency [Hz]

Mag

nitu

de [d

B]

Subject 1Subject 2

Fig. C.1: Measured transfer function or seat-to-head transmissibility of two sub-jects between the vibrations which are transmitted from the buttock (position’cushion’ in Fig.2.4) into the human body (fundament) to the (right) mastoid ina frequency range from 5 to 100 Hz.

Tab. C.2: Correlation coefficients between the personal data of the subjects andthe individual sensitivity of the subjects - measured perception thresholds at dif-ferent frequencies - for vertical whole-body vibrations.

Parameter Gender Body-size Weight RI BMI Age

Gender 1.00* -0.52* -0.48 0.01 -0.23 -0.17

Body-size -0.52* 1.00* 0.73* -0.26 0.19 0.21

Weight -0.48 0.73* 1.00* 0.46 0.81* 0.43

RI 0.01 -0.26 0.46 1.00* 0.90* 0.38

BMI -0.23 0.19 0.81* 0.90* 1.00* 0.46

Age -0.17 0.21 0.43 0.38 0.46 1.00*

5 Hz 0.04 -0.08 -0.02 0.06 0.03 -0.18

6.3 Hz 0.24 -0.34 -0.39 -0.12 -0.27 -0.22

8 Hz 0.19 -0.31 -0.24 0.07 -0.07 -0.14

10 Hz 0.23 -0.06 0.06 0.18 0.15 -0.24

12.5 Hz 0.30 -0.27 -0.26 -0.01 -0.13 -0.27

16 Hz -0.10 -0.13 0.16 0.40 0.34 0.27

31.5 Hz -0.19 0.34 0.60* 0.46 0.60* 0.43

63 Hz -0.16 0.16 0.48 0.48 0.55* 0.67*

125 Hz -0.34 0.30 0.49* 0.36 0.48 0.71*

200 Hz 0.09 0.23 0.37 0.29 0.38 0.75

List of Figures

1.1 Electro-dynamic exciter, shaker . . . . . . . . . . . . . . . . 7

1.2 Frequency ranges of different vibrating systems . . . . . . . 9

1.3 Typical acceleration-frequency-characteristics of an electro-dynamic exciter . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Equivalent circuit of an electro-dynamic transducer and anequivalent mechanical circuit of an moving-element . . . . . 11

1.5 Model of a single degree-of-freedom damped self-oscillatingmass-spring system . . . . . . . . . . . . . . . . . . . . . . 12

1.6 The absolute and relative transmissibility for a viscous-dampedisolation system . . . . . . . . . . . . . . . . . . . . . . . . 14

1.7 Resonance curves for different fraction of critical damping ζof a constrained motion of an excited system . . . . . . . . 15

1.8 Basicentric axes of the human body . . . . . . . . . . . . . 20

1.9 Building vibration x/y- and z-axis base curve (perceptionthresholds) . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.10 Combined-direction criteria curves with various multiplyingfactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.11 Health guidance caution zones . . . . . . . . . . . . . . . . 27

1.12 Weber-quotient and Weber-law . . . . . . . . . . . . . . . . 29

1.13 Typical psychometric function for a psychophysical measure-ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.14 Schematic overview of an adaptive AFC 1 up - 2 down mea-suring method . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.15 Schematic view of an interleaved measuring method . . . . . 38

1.16 Absolute thresholds of RA-receptors and the appendant psy-chometric function . . . . . . . . . . . . . . . . . . . . . . . 41

xiv LIST OF FIGURES

1.17 Simple theoretical model of the resonance frequencies fR ofthe human body . . . . . . . . . . . . . . . . . . . . . . . . 43

1.18 Cross-section of skin showing the dermis and epidermis . . . 44

1.19 Characteristical spiking rate patterns of the four types sus-ceptible sensors . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1 Schematic views of the vibration-floor . . . . . . . . . . . . 48

2.2 Picture of the vibration-floor . . . . . . . . . . . . . . . . . 49

2.3 Control diagram of the vibration-floor . . . . . . . . . . . . 50

2.4 Measuring positions on the vibration-floor . . . . . . . . . . 51

2.5 Background vibrations on the vibration-floor . . . . . . . . . 51

2.6 Background noise in the laboratory . . . . . . . . . . . . . . 52

2.7 Vibrations on the vibration-floor in all three directions . . . . 54

2.8 Transfer function of the vibration-floor . . . . . . . . . . . . 55

2.9 Comparison of the vertical spectra on the vibration-floor . . 56

2.10 Comparison of the acceleration levels on various positions ofthe vibration floor for 8 and 16 Hz . . . . . . . . . . . . . . 57

2.11 Schematic view of the Sound & Vibration Reproduction System 58

2.12 Photo of the Sound & Vibration Reproduction System . . . 59

2.13 Another photo of the Sound & Vibration Reproduction System 60

2.14 Flexural wave loudspeaker in NXT c© technology . . . . . . . 60

3.1 Measurement set-up for basic experiments on the perceptionof vertical whole-body vibrations . . . . . . . . . . . . . . . 64

3.2 Measured and fitted psychometric functions for 14 subjects . 67

3.3 Perception thresholds for vertical sinusoidal whole-body vi-bration from the literature . . . . . . . . . . . . . . . . . . . 70

3.4 Comparison of results for the perception thresholds at 5, 12.5and 16 Hz with different stimulus durations . . . . . . . . . 71

3.5 Perception thresholds for 5, 12.5 and 16 Hz with differentstimulus durations . . . . . . . . . . . . . . . . . . . . . . . 72

3.6 Measured and fitted measured 70.7% point of the psycho-metric function . . . . . . . . . . . . . . . . . . . . . . . . 73

3.7 Perception thresholds from 16 to 200 Hz without a ’masking’sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

LIST OF FIGURES xv

3.8 Difference spectra between the emitted sound of the vibration-floor and the background noise . . . . . . . . . . . . . . . . 76

3.9 Comparison between perception thresholds measured withand without a ’masking’ audible noise . . . . . . . . . . . . 78

3.10 Interindividual differences of Fig. 3.9 . . . . . . . . . . . . . 79

3.11 Measured perception threshold (mean and median values) ina frequency range from 5 to 200 Hz . . . . . . . . . . . . . 81

3.12 Individual perception threshold in a frequency range from 5to 200 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.13 Same figure as Fig. 3.11 with data from literature . . . . . . 85

3.14 Just noticeable differences in level . . . . . . . . . . . . . . 88

3.15 The absolute difference thresholds (∆I) in level . . . . . . . 89

3.16 Individual just noticeable differences in frequency of six subjects 91

3.17 Measured just noticeable differences in frequency with re-gression curve . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.18 Equal-vibration level contours with different starting conditions 95

3.19 Intra- and interindividual differences of the measured equal-vibration level contours . . . . . . . . . . . . . . . . . . . . 96

3.20 Equal-vibration level contours with literature data . . . . . . 97

3.21 Measured perception threshold in comparison to equal-vibrationlevel contours . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.1 Measuring positions for seat and steering-wheel vibrations ina car . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.2 Typical averaged spectra for seat vibrations . . . . . . . . . 110

4.3 Illustration of a spectrally unweighted and weighted spectrafor seat vibrations . . . . . . . . . . . . . . . . . . . . . . . 111

4.4 Typical averaged spectra for steering-wheel vibrations . . . . 112

4.5 Middle class cars: Correlation between unweighted and weightedz-acceleration and subjective assessments of seat vibrations . 114

4.6 Same figure as in Fig. 4.5 for spectrally unweighted andweighted vibration total values . . . . . . . . . . . . . . . . 115

4.7 Same figure as in Fig. 4.6 in a narrow frequency band from10 to 35 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.8 Same figure as in Fig. 4.6 for spectrally unweighted andweighted vibration total values for upper middle class . . . . 119

xvi LIST OF FIGURES

4.9 Same figure as in Fig. 4.8 for spectrally unweighted andweighted vibration total values in a narrow frequency range. 120

4.10 Same figure as in Fig. 4.6 for spectrally unweighted andweighted vibration total values for small class . . . . . . . . 122

4.11 Same figure as in Fig. 4.10 for spectrally unweighted andweighted vibration total values in a narrow band frequencyrange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.12 Middle class cars: Correlations between unweighted and weightedvibration total values and subjective ratings for steering-wheel vibrations . . . . . . . . . . . . . . . . . . . . . . . . 125

4.13 Same figure as in Fig. 4.12 but the objective parameters arecalculated in the limited frequency range 20 to 35 Hz . . . . 126

4.14 Same figure as in Fig. 4.12 but for the upper class cars . . . 128

4.15 Same figure as Fig. 4.13 but for the upper class cars . . . . 129

4.16 Same figure as in Fig. 4.12 but for the small class cars . . . 130

5.1 Schematic view of the ’vibration-pad’ . . . . . . . . . . . . . 136

5.2 Measurement set-up for psychophysical measurements on areal car seat . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.3 Perception thresholds for vertical sinusoidal whole-body vi-brations on a real car seat . . . . . . . . . . . . . . . . . . . 142

5.4 Perception thresholds from Fig. 5.3 in comparison to litera-ture data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.5 Just noticeable differences in level on a real car seat . . . . . 144

5.6 Relation between the level of the seat vibration and the av-eraged appendant subjective rating . . . . . . . . . . . . . . 147

5.7 Schematic view of the tasks for experiment 4 . . . . . . . . 150

A.1 Frequency weighting curves for principal weightings . . . . . iii

A.2 Equivalent-comfort contours and multiplying factors . . . . . iii

A.3 Position of accelerometers on and at a real car seat after ISO10326-1 (1992). . . . . . . . . . . . . . . . . . . . . . . . . iv

B.1 Supplement for Fig. 2.10. . . . . . . . . . . . . . . . . . . . vii

B.2 Control-diagram of Sound & Vibration Reproduction System ix

C.1 Measured transfer function between buttock (seat surface)to the (right) mastoid . . . . . . . . . . . . . . . . . . . . . xii

List of Tables

1.1 Most relevant parameters for vibration time signals (adapted from

Meloni (1991). . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2 Approximate magnitudes of overall (rms) vibration total val-ues in public transport . . . . . . . . . . . . . . . . . . . . . 26

1.3 Response groupings for transformed up-down strategies . . . 36

1.4 Resonance frequencies fR of the human body with an im-pairment of health . . . . . . . . . . . . . . . . . . . . . . . 42

3.1 Anthropometric and other personal (exogenous and endoge-nous) data of the subjects for Chapter 3 . . . . . . . . . . . 65

4.1 Middle class car: Correlation coefficients between subjectiveand objective data for the driver seat vibrations . . . . . . . 117

4.2 Upper middle class car: Correlation coefficients between sub-jective and objective data for driver seat vibrations . . . . . 121

4.3 Small class car: Correlation coefficients between subjectiveand objective data for driver seat vibrations . . . . . . . . . 124

4.4 Middle class car: Correlation coefficients between subjectiveand objective data for steering-wheel vibrations . . . . . . . 128

4.5 Lifted middle class car: Correlation coefficients between sub-jective and objective data for steering-wheel vibrations . . . 129

4.6 Small class car: Correlation coefficients between subjectiveand objective data for steering-wheel vibrations . . . . . . . 131

5.1 Number of subjects separated by the different experiments . 138

5.2 Anthropometric and other personal (exogenous and endoge-nous) data of the subjects . . . . . . . . . . . . . . . . . . . 139

xviii LIST OF TABLES

A.1 Guide for the application of frequency-weighting curves forprincipal weighting . . . . . . . . . . . . . . . . . . . . . . ii

A.2 Frequency weighting for x-,y- and z-axis whole-body vibra-tion for calculating the VDV . . . . . . . . . . . . . . . . . iv

A.3 Root-mean-square accelerations corresponding to estimatedvibration dose values of 15 m/s1.75 . . . . . . . . . . . . . . v

A.4 Ranges of multiplying factors to specify satisfactory magni-tudes of building vibrations . . . . . . . . . . . . . . . . . . vi

B.1 Physical properties of the PU-foam which is used for theSound & Vibration Reproduction System c© . . . . . . . . . . viii

B.2 Features of the Sound and Vibration Reproduction System c© ix

C.1 Correlation coefficients between the personal data parameterswhich characterized the perception of whole-body vibrations. xi

C.2 Correlation coefficients between the personal data and themeasured perception thresholds . . . . . . . . . . . . . . . xii

Danksagung(Acknowledgement)

Herrn Prof. Dr. Volker Mellert danke ich fur die Ermoglichung und die freieGestaltung dieser Arbeit in der Arbeitsgruppe Akustik. Herrn Dr. ReinhardWeber danke ich fur die administrativen Arbeiten wahrend der Zusamme-narbeit mit der Volkswagen AG, sowie die zum Teil kontroversen Diskus-sionen wahrend des Projektes ohne die meine Arbeit nicht in dieser Formentstanden ware. Herrn Prof. Dr. Dr. Birger Kollmeier danke ich fur seineArbeit als Zweitgutachter.

Ein besonderer Dank gilt der Forschungsabteilung Akustik der VolkswagenAG in Wolfsburg fur die Ermoglichung des Forschungsprojektes ”Unter-suchung der Wirkung von Korperschall (Vibrationen) und Luftschall auf denKomfort im Fahrzeug” (Subjektives Zusammenwirken von akustischen undvibratorischen Signalen) und der uneingeschrankten Verwertung der Ergeb-nisse dieses Forschungsprojektes fur meine Dokotorarbeit (Kapitel 4 und 5).Insbesondere mochte ich mich bei Peter Hillebrand und Wolfgang Sollig vonder VW AG fur Ihre uneingeschrankte Kooperation in diesem Projekt be-danken. Auch wenn die Zusammenarbeit am Anfang nicht ganz reibungslosverlaufen ist, danke ich Euch fur die zahlreichen Diskussionen und Hilfestel-lungen bei den zahlreichen Messungen, die diese Arbeit erst moglich gemachthaben.

Ein großer Dank geht an Ingo Baumann und Roland Kruse aus ”meinemBuro”, die mir stets zur Seite standen (vor allem wahrend des VW Pro-jektes) und mich tatkraftig im Projekt mit Berechnungen von objektivenParametern, Kaffee und vielem mehr unterstutzt haben. Ich danke den Mit-arbeiter des Instituts fur technische und angewandte Physik GmbH (itap) furIhre Ratschlage und die uneingeschrankte Nutzung ihrer Gerate. Insbeson-dere danke ich Hermann Remmers fur die ausgiebigen Diskussionen geradebei technischen Fragen. Außerdem danke ich Ihm, dass er mir mit Rat und

Tat bei der Konstruktion und dem Bau der Simulatoren hilfreich zur Seitestand. Ein großer Dank geht auch an Gizem Nazim Forta, der mir nicht nurbei der Vermessung des ’Vibration-Floors’ geholfen hat, sondern mich auchbei den psychophysikalischen Messungen tatkrafig unterstutzt hat. Außer-dem bedanke ich mich bei Ihm fur sein unermudliches Korrektur-Lesen. Ichmochte mich auch bei der Arbeitsgruppe Akustik fur Tips und Anregungen,sowie zahlreichen Diskussionen bedanken.Ich danke Jorg Damaschke und Stephan Ewert fur die kreativen Denkanstoßein den gemeinsamen Stunden an der Uni und vor allen Dingen in der Freizeit.Ebenso gilt mein Dank all meinen zahlreichen Versuchspersonen, die stetsbereit waren sich den zum Teil nicht ganz angenehmen Ganzkorpervibrationenauszusetzen und dabei stets freundlich die Fragen beantworteten: ”Welchegespurte Vibration war starker ?” oder ”In welchem Intervall hast Du eineVibration gespurt ?”Bajo Meenen danke ich fur seinen technischen Support bei so vielen kleinenund großen Problemen.

Ich danke meine Eltern fur die uneingeschrankte Unterstutzung. Last butnot least, gilt mein besonderer Dank meiner Frau, Christine Bellmann, furihr unermudliches Korrektur-Lesen, was sicherlich nicht immer eine ein-fache Aufgabe war. Außerdem danke ich Ihr dafur, dass sie mich (in somacher kleinen Krise) uneingeschrankt unterstutzt hat wahrend der Entste-hung dieser Arbeit. Ferner konnte sie mich dazu bringen einige Dinge etwasruhiger und geordneter anzugehen.

Curriculum Vitae

Name : Michael A. Bellmann

Day of birth : 20th November 1972Place of birth : Brake (Unterweser), Germany

Nationality : German

School and professional career :

8/80-7/84 Elementary school: Eichendorff-Grundschule in Brake

8/84-7/85 Orientierungsstufe Nord in Brake

8/85-7/92 Secondary school: Gymnasium in Brake

04.06.92 Abitur (general qualification for university entrance)

6/92-9/93 Civil service at the Lebenshilfe e.V. in Brake (Schoolfor mentally disabled persons)

10/93-6/99 Student in Physics at the Carl von Ossietzky Universityin Oldenburg

22.06.99 Diploma in Physics

Since 7/99 Doctor thesis in the acoustics workgroup (departmentof physics) at the University of Oldenburg

Since 9/99 Research associate at the University of Oldenburg

Since 01/2001 Associated in the EU Graduate School ”Neuro-Sensorics”

06/99 - 03/02 Project with Volkswagen AG

Documents

Perception of Whole-Body Vibrations: From basic ... · PDF filePerception of Whole-Body Vibrations: From basic experiments to eﬀects of seat and steering-wheel vibrations on the