Shock Absorb

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Mechanical Systemsand

Signal ProcessingMechanical Systems and Signal Processing 20 (2006) 373–388

0888-3270/$ -

doi:10.1016/j.

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Simulation and experimental validation of vehicle dynamiccharacteristics for displacement-sensitive shock absorber

using fluid-flow modelling

Choon-Tae Leea, Byung-Young Moonb,�

aDepartment of Mechanical and Intelligent Systems Engineering, Busan National University, 30 Changjeon-dong,

Keumjeong-ku, Busan 609-735, Republic of KoreabDepartment of Aerospace Engineering, Busan National University, 30 Changjeon-dong,

Keumjeong-ku, Busan 609-735, Republic of Korea

Received 23 February 2004; received in revised form 27 August 2004; accepted 27 September 2004

Available online 11 November 2004

Abstract

In this study, a new mathematical dynamic model of shock absorber is proposed to predict the dynamiccharacteristics of an automotive system. The performance of shock absorber is directly related to the carbehaviours and performance, both for handling and ride comfort. Damping characteristics of automotivecan be analysed by considering the performance of displacement-sensitive shock absorber (DSSA) for theride comfort. The proposed model of the DSSA is considered as two modes of damping force (i.e. soft andhard) according to the position of piston. For the simulation validation of vehicle-dynamic characteristics,the DSSA is mathematically modelled by considering the fluid flow in chamber and valve in accordancewith the hard, transient and soft zone. And the vehicle dynamic characteristic of the DSSA is analysedusing quarter car model. To show the effectiveness of the proposed damper, the analysed results of dampingcharacteristics were compared with the experimental results, which showed similar behaviour with thecorresponding experimental one. The simulation results of frequency response are compared with the onesof passive shock absorber. From the simulation results of the DSSA, it can be concluded that the ridecomfort of the DSSA increased at the low-amplitude road condition and the driving safety was increasedpartially at the high-amplitude road condition. The results reported herein will provide a better

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ress: [email protected] (B.-Y. Moon).

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C.-T. Lee, B.-Y. Moon / Mechanical Systems and Signal Processing 20 (2006) 373–388374

understanding of the shock absorber. Moreover, it is believed that those properties of the results can beutilised in the dynamic design of the automotive system.r 2004 Elsevier Ltd. All rights reserved.

Keywords: Shock absorber; Damping force; Quarter car model; Vehicle vibration; Ride comfort; Displacement

sensitive; Body valve

1. Introduction

Shock absorber is an important part of automotive which has an effect on ride characteristicssuch as ride comfort and driving safety. There are several kinds of automotive shock damperssuch as position-sensitive damping, acceleration-sensitive damping, and continuous dampingcontrol. Displacement-sensitive shock absorber (DSSA), which is also called stroke-dependentshock absorber, and has a similar structure compared with conventional passive shock absorber.Nevertheless, the DSSA has additional flow passages such as displacement-sensitive orifice at thecylinder wall. The DSSA has two modes of damping force according to piston stroke.When piston stroke is in the range of displacement-sensitive orifice, the leakage occurs through

this orifice. In this range, the damping force become low compared with the passive shockabsorber. On the other hand, when the piston stroke is out of range of displacement-sensitiveorifice, leakage through the orifice is blocked. In this range, the damping force becomes highbecause of leakage block. Such a DSSA improves ride comfort on the paved road drivingconditions because of low damping force caused by small piston stroke. Also, the driving safety isimproved when the vehicle is driving on rough roads or bumper roads because of high dampingforce caused by large piston stroke and high-vibration amplitude. Accordingly, the DSSA cankeep ride comfort and driving safety as well.There have been several studies about shock absorber. At first, Lang [1] proposed simple

mathematical model of passive shock absorber. After that many studies have been carried out toanalyse the performance of shock absorber [2]. Cherng et al. [3] reported the effect of noise ofshock absorber using acoustic index method. Koenraad [4] proposed a mathematical model of themono-tube-type gas-charged shock absorber. Herr et al. [5] proposed a mathematical model oftwin tube-type shock absorber. Simms et al. [6] investigated the influence of damper properties onluxury vehicle dynamic behaviour through the simulation and test. Liu et al. [7] reported thecharacteristics of non-linear dynamic response for the twin-tube hydraulic shock absorber byusing a software programme. Nevertheless, there have been few studies carried out on the DSSA.Recently, there has been a study reported on the DSSA [8]. In those studies [9], the transientcharacteristics of displacement-sensitive orifice were not considered and the performance of thevehicle with the DSSA was not verified. In general, those studies are insufficient to understand thedynamic characteristics of DSSA completely to judge the handling and ride comfort ofautomotive.Therefore, in this study a new mathematical and simulation model of the DSSA is proposed

and analysed, which considered the transient range of displacement-sensitive orifice of the DSSA.And the vehicle dynamic characteristics of the proposed model are evaluated in the time andfrequency domain using quarter car-simulation model. The results of the dynamic characteristics

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C.-T. Lee, B.-Y. Moon / Mechanical Systems and Signal Processing 20 (2006) 373–388 375

and the performance of the DSSA are compared with the passive shock absorber to prove theeffectiveness.

2. Method of analysis of shock absorber

2.1. Mathematical modelling of DSSA

Fig. 1 illustrates the configuration of a typical twin-tube-type passive shock absorber of anautomotive system. Basically the shock absorber consists of a piston, which moves up and downalong fluid-filled cylinder. The cylinder is fastened to the axle or wheel suspension, and the pistonis connected via the piston rod to the frame of the vehicle.As the piston is forced to move with respect to the cylinder, a pressure differential is developed

across the piston causing the fluid to flow through orifices and valves in the piston. The portion ofthe cylinder above the piston is known as the rebound chamber, and the portion of the cylinderbelow the piston is known as the compression chamber, and the volume which surrounds thecylinder is known as the reservoir chamber. The reservoir chamber is partially filled with fluid andpartially filled with a gas phase, normally air. The fluid flow between the compression andreservoir chambers passes through the body valve assembly at the bottom of the compressionchamber. Fig. 2 shows the configurations of the piston valve assembly and the body valveassembly and their part of the shock absorber. As can be observed in Fig. 2, the DSSA has anadditional flow passage in the cylinder wall of a typical passive shock absorber. And thesedisplacement-sensitive orifices can be divided into three zones such as the soft, transient andhard zone. Here, the transient zone has tapered scheme to avoid abrupt changes of damping force.Fig. 3 illustrates the analytic model of the DSSA, which describes a fluid-flow pattern according topiston movement.The fluid flows at the compression stroke can be divided into two flows such as Qr and Qc. The

first Qr is a flow which flows from the compression chamber to the rebound chamber through the

Fig. 1. Schematic diagram of typical twin-tube-type passive shock absorber of an automotive system.

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Fig. 2. Typical configuration and fluid flow pattern of DSSA: (a) fluid flow pattern of DSSA at compression and

rebound stroke and (b) cross-section of A–A.


piston valve (1) and the other Qc is a flow which flows from the compression chamber to thereservoir chamber through body valve (2), where the valve numbers are noted in Fig. 2(a). Theflow Qr, which flows through the piston valve, can be divided into three flows Qri, Qro and Qrd.The flow Qri flows through the bleed valve (4). The flow Qro flows through intake valve (6) and theflow Qrd flows through displacement-sensitive orifice (9) of piston valve, respectively. The flow Qc,which flows through body valve (2) at the compression stroke, can be divided into two flows Qci

and Qcf. The flow Qci flows through the bleed valve and the flow Qcf flows through a blow-offvalve.On the contrary, at the rebound stroke the fluid flows can be divided into two flows Q�r and Q�c :

The first Q�r is a flow which flows from the rebound chamber to the compression chamber throughpiston valve (1) and the other one Q�c is a flow which flows from the reservoir chamber to thecompression chamber through body valve (2).The flow Q�c ; which flows through body valve (2), can be divided into two flows Qci and Qco.

The flow Qci flows through the bleed valve and the flow Qco flows through suction valve (7). Also,the flow Q�r ; which flows through piston valve (1), can be divided into three flows Qri, Qrf and Qrd.

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Fig. 3. Schematic diagram of fluid flow and pressure at compression and rebound stroke.


The flow Qri flows through bleed valve (4), the flow Qrf flows through blow off valve (5) and theflow Qrd flows through the displacement-sensitive orifice, respectively.

2.2. Flow continuity equations at the compression and rebound chamber

The flow continuity equation of the compression chamber at the rebound stroke, as described inFig. 3, can be expressed as follows:

�Vc

K�@Pc

@t¼ �Ap _xþ ðQ

�r þQ�c Þ: (1)

The flow continuity equation of the compression chamber at the compression stroke can beexpressed as follows:

�Vc

K�@Pc

@t¼ Ap _x� ðQr þQcÞ; (2)

where K is a bulk modulus of elasticity of working fluid, Vc is a volume of compression chamber,Pc is a pressure of compression chamber, Ap is an area of piston and _x is a velocity of piston.

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Similar way, the flow continuity equation of the rebound chamber at the rebound stroke can beexpressed as follows:

�Vr

K�@Pr

@t¼ ðAp � ArodÞ _x�Q�r : (3)

The flow continuity equation of the rebound chamber at the compression stroke can beexpressed as follows:

�Vr

K�@Pr

@t¼ ðAp � ArodÞ _xþQr; (4)

where Vr is a volume of rebound chamber, Pr is a pressure of rebound chamber and Arod an areaof piston rod.

2.3. Flow equations at the compression stroke and rebound stroke

The flow rate of the piston valve Qr which flows between the rebound and compressionchambers at the compression stroke can be expressed as follows:

Qr ¼ Qri þQro þQrd : (5)

Here, each flow rates can be obtained as follows:

Qri ¼ CdApb

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

rðPc � Pd1Þ

s¼ CdAd1


rðPd1 � PrÞ

s; (6)

Qro ¼ CdAd2


rðPc � Pd2Þ

s¼ Qim

ðPd2 � PicrÞ

ðPim � PicrÞ: (7)

Here, when Pd2oPicr; Qro becomes zero.

Qrd ¼ CdAdsðxÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

rðPc � PrÞ

s; (8)

AdsðxÞ ¼

wf hz2ðxþ z1Þ þ hg ðz1oxpðz1 þ z2ÞÞ;

wh ð�z1oxpz1Þ;

wf� hz2ðx� z1Þ þ hg ð�ðz1 þ z2Þoxp� z1Þ;

8><>: (9)

where Cd is a coefficient of discharge and Apb is a bleed valve (4) orifice area of piston valve (1).Ad1 and Ad2 are areas of piston valve (1) port restriction (3), Pd1 and Pd2 are pressures at pistonvalve (1) port restriction (3), Qim is a maximum flow rate of the intake valve (6), Picr is a crackingpressure of intake valve (6), Pim is a pressure of intake valve (6) at the maximum flow rate Qim andAds is an area of the displacement-sensitive orifice.The flow rate Qrd becomes zero when the displacement of the piston detaches from

displacement-sensitive orifice, and the flow rate of the body valve Qc, which flows between the

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reservoir and compression chambers. At the compression, stroke can be expressed as follows:

Qc ¼ CdAa3


rðPc � Pa3Þ

s¼ Qci þQcf : (10)

Each flow rates of Eq. (10) can be obtained as follows:

Qci ¼ CdAbb


rðPa3 � PaÞ

s; (11)

Qcf ¼ Qbm

ðPa3 � PbcrÞ

ðPbm � PbcrÞ: (12)

Here, when Pa3oPbcr; Qcf becomes zero. Abb is a bleed valve orifice area of body valve (2), Ad3 is aport restriction area (8) of body valve (2), Pa3 is a pressure at the port restriction of body valve (2),Pa is a pressure of reservoir chamber, Qbm is a maximum flow rate of the blow-off valve at thebody valve, Pbcr is a cracking pressure of the blow-off valve at the body valve and Pbm is apressure of the blow-off valve at the maximum flow rate at the body valve.The flow rate of the piston valve Q�r ; which flows between rebound and compression chambers

at the rebound stroke can be expressed as follows:

Q�r ¼ Qri þQrf þQrd ; (13)

Qri ¼ CdApb


rðPd1 � PcÞ

s; (14)

Qrf ¼ Qpm

ðPd1 � PpcrÞ

ðPpm � PpcrÞ: (15)

Here, when Pd1oPpcr; Qrf becomes zero.

Qrd ¼ CdAdsðxÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

rðPr � PcÞ

s; (16)

where Qpm is a maximum flow rate of blow-off valve (5) at the piston valve, Ppcr is a crackingpressure of the blow-off valve at the piston valve and Ppm is a pressure of the blow-off valve at themaximum flow rate of the piston valve. Qrd becomes zero when the displacement of the pistondetaches from the displacement-sensitive zone. And the flow rate of body valve Qc

*, which flowsbetween the reservoir and compression chambers at the rebound stroke can be expressed asfollows:

Q�c ¼ Qci þQco; (17)

Qci ¼ CdAbb


rðPa � Pd3Þ

s¼ CdAd3


rðPd3 � PcÞ

s; (18)

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Qco ¼ CdAd4


rðPa � Pd4Þ

s¼ Qsm

ðPd4 � PscrÞ

ðPsm � PscrÞ: (19)

Here, when Pd4oPscr; Qcf becomes zero, where Ad4 is a port restriction (8) area of the bodyvalve. Pd4 is a pressure at the body valve port restriction (8), Qsm is a maximum flow rate ofsuction valve (7). Pscr is a cracking pressure of the suction valve and Psm a pressure at themaximum flow rate of the suction valve.

2.4. Flow analysis at the reservoir chamber

Because the piston rod passes through the rebound chamber, and is connected to the reboundside of the piston, the area of the rebound side is less than the area of the compression side of thepiston. Accordingly, as the piston moves, the combined volume of the compression and reboundchambers changes by an amount equivalent to the inserted, or withdrawn piston rod volume. Theamount of fluid equivalent to the inserted, or withdrawn piston rod volume must be transferredto, or from, the reservoir chamber which normally surrounds the cylinder. Air pressure of thereservoir chamber can be expressed as an ideal gas equation as follows:

PaVa ¼ maRT ; (20)

where Pa is an air pressure of the reservoir chamber, Va is an air volume of reservoir chamber, ma

is an air mass of reservoir chamber, R is a gas constant and T is the temperature of air in thereservoir chamber.Generally, the mass of air is assumed constant because the chamber is sealed, and the

temperature T of the reservoir chamber in assumed constant to simplify the analysis. Accordingly,the air of the reservoir chamber can be expressed as an ideal gas equation as follows:

PaVa ¼ const: (21)

The time variation of air volume Va of reservoir chamber can be expressed as follows:

VaðtÞ ¼ Va0 �

ZQc dt; (22)

where Va0 is an initial air volume of the reservoir chamber. Therefore, the air pressure variation ofthe reservoir chamber can be obtained from Eqs. (20) and (22) as follows:

Pa ¼maRT

Va0

RQc dt

: (23)

2.5. Damping force of shock absorber

The damping force of shock absorber is determined by the forces acting on the both sides of thepiston. And the friction forces are another factor that determines damping force. Nevertheless, inthis study, the friction forces are ignored to simplify the analysis. Fig. 4 shows free body diagramof the piston considering the damping force.

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Fig. 4. Free body diagram of the piston.


By considering the forces acting on the piston, the damping force can be obtained as follows:

Fdamping ¼ PrAr � PcAp � F friction; (24)

Ar ¼ Ap � Arod; (25)

where Fdamping is a damping force. Ffriction is the friction force, that is acting on piston rod.

3. Results of the dynamic analysis and discussion

Numerical calculation results of vehicle system are obtained under the road excitation.Dynamic characteristics of the response are observed by the proposed method.

3.1. Analytical results of DSSA

As an analysis model, a shock absorber system, which is shown in Fig. 2, is considered. Fig. 5shows simulation results of damping force versus stroke for the excitation velocity of 0.1, 0.3, 0.6and 1.2m/s, respectively. The damping force changes from soft mode to hard mode due to thedisplacement-sensitive characteristics around the stroke of 720mm, as shown in Fig. 5.Especially, the damping force changes smoothly around the transient zone. It illustrates well thefunction of transient zone which prevents abrupt changes of the damping force.To verify the reliability of simulation results of the proposed method, experimental results of

shock absorber study are presented in Fig. 6 [8]. As can be observed in Fig. 6, the experimentalresult shows very similar tendency with the result of this study.

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-40 -20 0 20 40

-1200

-800

-400

0

400

800

1200

1600

2000

2400transient zonetransient zone

hard zone hard zonesoft zone

1.2 [m/sec]

0.6 [m/sec]

0.3 [m/sec]

0.1 [m/sec]

dam

ping

for

ce [

N]

stroke [mm]

Fig. 5. Analytical result of DSSA in stroke-damping force.

Fig. 6. Experimental result of DSSA in stroke-damping force.


3.2. Analysis results of the quarter car model

In this study, quarter car model adopted to analyse dynamic behaviour, including the DSSA inthe vehicle, as shown in Fig. 7. Here, a tire model is assumed to have both characteristics of springand damping. And a relative displacement of the shock absorber is calculated from the absolutedisplacement of the body and suspension to embody the displacement-sensitive characteristics ofthe shock absorber.The main physical properties of quarter car simulation model are listed in Table 1.

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Fig. 7. Quarter car model including DSSA.

Table 1

Properties of quarter car model

Parameter Value

Sprung mass, M 250kg

Un-sprung mass, m 50 kg

Shock absorber spring constant, K 18N/mm

Shock absorber damping coefficient, C 1273–1697N/m/s

Tire spring constant, k 270.8N/mm

Tire damping coefficient, c1 0.1N/m/s


To analyse the dynamic characteristics of the DSSA, four kinds of damping modes are selectedand the corresponding results are compared with each other, as listed in Table 2. The DSSA hastwo kinds of damping modes according to the piston stroke, such as soft and hard mode. Here,the mid-mode has an intermediate characteristic of the soft and hard mode. Thereby, the mid-mode is estimated as a typical passive shock absorber in this paper.

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3.3. Results of frequency characteristics analysis

In general, driving characteristics of the vehicle are affected by sprung mass verticalacceleration, dynamic wheel force and suspension deflection. The vertical acceleration of thesprung mass means the magnitude of vibration transmitted to sprung mass, which is directlyrelated to the ride comfort. The dynamic wheel force affects on the holding force characteristics

Table 2

Definition of damping modes

Mode Damping coefficient (N/m/s) Damping ratio z

Soft mode 1273 0.3

Mid-mode 1485 0.35

Hard mode 1697 0.4

Displacement-sensitive mode 1273–1697 0.3–0.4

-0.030 2 4 6 8 0 2 4 6 8 1010

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

inp

ut

dis

pla

cem

ent

[m]

time [s] time [s]

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

der

ivat

ive

of

inp

ut

[m/s

]

1 10 100

10-9

10-10

10-11

10-12

10-13

10-14

10-15

10-16

10-17

Frequency (Hz)

PS

D o

f in

pu

t [m

2 /Hz]

(c)

(a) (b)

Fig. 8. Input characteristics of quarter car model of DSSA: (a) input excitation signal, (b) derivative of input excitation

and (c) PSD of input.

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between the tire and road, which is related to the driving stability. And the suspension deflection isrelated to the rattle space of the suspension system, which is necessary to operate suspensionsystem properly. Accordingly, it becomes a constraint condition at the initial stage of thesuspension system design.To analyse the frequency characteristics of the DSSA in a quarter car model, the input

excitation signal is applied as described in Fig. 8. A sinusoidal sweep function from 0 to 30Hz wasapplied according to the road input condition. In each frequency range, the maximum velocity is0.3m/s. The velocity characteristics of input signal is shown in Fig. 8(b). As shown in figure, themaximum velocity of input signal is a constant of the value 0.3m/s. Also, the power spectrumdensity (PSD) of input signal is illustrated in Fig. 8(c), which stands for the random process of theroad condition.Fig. 9(a) shows the sprung mass acceleration response of the displacement-sensitive mode using

the DSSA in time domain against the input signal stated in Fig. 8. Also, Fig. 9(b) shows the PSD

-3

0 2 4 6 8 10

-2

-1

0

1

2

3

4

spru

ng m

ass

acce

lera

tion

[m/s

2 ]

time [s]

10-5

10-6

10-7

hard mode

soft mode

mid modesoft modehard modedisp.sensitive mode

Frequency (Hz)

PS

D o

f spr

ung

mas

s ac

cele

ratio

n [(

m/s

2 )2 /Hz]

1 10

(a)

(b)

Fig. 9. Sprung mass acceleration response of displacement-sensitive mode: (a) time response of sprung mass

acceleration and (b) PSD of sprung mass acceleration response.

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of sprung mass acceleration response for the four damping modes, which is described in Table 2.As shown in Fig. 9, the response characteristic of the DSSA shows a similar one with the passiveshock absorber around the resonance frequency range of sprung mass. However, at the resonancefrequency of un-sprung mass, which means low-amplitude condition of input, the DSSA showssoft damping characteristics. Therefore, it can be said that the ride comfort characteristics ofDSSA was improved compared with the ones of passive shock absorber.Fig. 10(a) shows the analysis result of suspension deflection of the displacement-sensitive mode

using the DSSA in the time domain. Fig. 10(b) shows the analysis results of suspension deflectionin the PSD for the four damping modes in the frequency domain. As shown in Fig. 10, theresponse characteristic of the DSSA seems similar to the ones of passive shock absorber aroundthe resonance frequency range of sprung mass. However, at the resonance frequency of un-sprungmass, the DSSA shows soft damping characteristics.Fig. 11 (a) shows the analysis result of dynamic wheel force in the displacement-sensitive mode

using the DSSA in the time domain. Fig. 11 (a) shows response results of dynamic wheel force inthe PSD for the four damping modes in the frequency domain. As illustrated in Fig. 11, aroundthe resonance frequency of sprung mass, which means high-amplitude condition of input, the

-0.06

-0.04

-0.02

0.00

0.02

0.04

susp

ensi

on d

efle

ctio

n [m

]

time [s]

10-8

10-9

10-10

10-11

10-12

hard mode

hard modedisp. sensitive & soft mode

mid mode

soft mode mid modesoft modehard modedisp.sensitive mode

Frequency (Hz)

PS

D o

f sus

pens

ion

defle

ctio

n [m

2 /Hz]

0 2 4 6 8 10

1 10

(a)

(b)

Fig. 10. Suspension deflection of displacement-sensitive mode: (a) time response of suspension acceleration and (b)

PSD of suspension deflection.

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1000

0 2 4 6 8 10

2000

3000

4000

5000

6000

7000

dyna

mic

whe

el fo

rce

[N]

time [s]

101

100

10-1

10-2

hard mode

soft mode &disp. sensitive mode disp. sensitive mode

soft mode mid mode

hard mode

Frequency (Hz)

PS

D o

f dyn

amic

whe

el fo

rce

[N2 /H

z]

1 10

(a)

(b)

Fig. 11. Response of dynamic wheel force in displacement-sensitive mode: (a) response of dynamic wheel force and (b)

response of dynamic wheel force in PSD.


DSSA shows slightly improved characteristics of driving safety compared with the ones of thepassive shock absorber.This paper has a validation of a mathematical model for a sensitive shock damper. As a result,

the proposed DSSA has an engineering knowledge as follows. From the sprung mass accelerationresponse analysis, the response characteristic of the DSSA showed soft damping characteristics,which stands for the improvement of ride comfort characteristics of the DSSA compared with theones of passive shock absorber on the paved road driving conditions. From the analysis result ofsuspension deflection, the response characteristic of DSSA showed soft damping characteristics,which stands for the improvement of ride comfort characteristics of the DSSA. From the analysisresult of dynamic wheel force, the response characteristic of the DSSA showed improvedcharacteristics of driving safety compared in a high-amplitude condition. Those improved

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characteristics of ride comfort and driving safety will contribute to the design of a shock absorber.And the geometry of the displacement-sensitive orifice will be defined in a further study.

4. Conclusions

In this study, a new mathematical dynamic model of the DSSA is proposed. The fluid rate andthe damping force of a shock absorber of an automotive system was theoretically formulated. Theanalysis results of the proposed mathematical dynamic model of the DSSA showed similar resultsof the corresponding experimental study. It is shown that the damping force could be efficientlycalculated according to the excitation. And the vehicle dynamic characteristic of the DSSA isanalysed using quarter car model. Several damping properties of the automotive shock absorberthat are of interest in vehicle vibration applications are reviewed in accordance with the ridecomfort problem. The simulation results of frequency response are compared with the ones ofpassive shock absorber. From the analysis results of the DSSA, the ride comfort of the DSSAincreased. The results reported herein will provide a better understanding of the shock absorber.Moreover, it is believed that those properties of the results can be utilised in the dynamic design ofthe automotive system.

Acknowledgements

This work was supported by Grant No: R08-2003-000-11075-0 from the basic ResearchProgram of the Korea Science Engineering Foundation and the authors wish to thank for thissupport.

References

[1] L.H. Harvey, A study of the characteristics of automotive hydraulic dampers at high stroking frequencies, Ph.D.

Thesis, Department of Mechanical Engineering, University of Michigan, USA, December 1977.

[2] S.W. Duym, R. Stiens, G.V. Baron, K.G. Reybrouck, Physical modeling of the hysteretic behavior of automotive

shock absorbers, Society of Automotive Engineers 970101 (1997) 125–137.

[3] J.G. Cherng, T. Ge, J. Pipis, R. Gazala, Characterization of air-borne noise of shock absorber by using acoustics

index method, in: Proceedings of the 1999 SAE International Congress and Exposition, 1999-01-1838.

[4] K. Reybrouck, A nonlinear parametric model of an automotive shock absorber, Society of Automotive Engineers

940869 (1994) 79–86.

[5] F. Herr, T. Malin, J. Lane, S. Roth, A shock absorber model using CFD analysis and easy 5, in: Proceedings of the

1999 SAE International Congress and Exposition, 1999-01-1322.

[6] A. Simms, D. Crolla, The influence of damper properties on vehicle dynamic behavior, Society of Automotive

Engineers 2002-01-0319 (2002) 79–86.

[7] Y. Liu, J. Zhang, F. Yu, H. Li, Test and simulation of nonlinear dynamic response for the twin-tube hydraulic

shock absorber, Society of Automotive Engineers 2002-01-0320 (2002) 91–98.

[8] J. Park, Dongwoo Joo, Youngho Kim, A study on the stroke sensitive shock absorber, Journal of Korean Society of

Precision Engineering 14 (1997) 11–16.

[9] B.Y. Moon, B.S. Kong, Statistical seismic response analysis and reliability design of nonlinear structure system,

Journal of Sound and Vibration 258 (2002) 269–285.

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Shock Absorb