Vibration analysis of lathe structrure due to gear defect using fem 02

Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005

M-Tech Thesis P.E.S.C.E., Mandya

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CHAPTER 1

I�TRODUCTIO�

1.1 GE�ERAL I�TRODUCTIO�

Machine condition monitoring (MCM) involves the continuous analysis of

operational equipment and the identification of problems before component breakage or

machine failure.

One of the main challenging problems of present day machine tools is the

development of machine tools with high vibration proof qualities. Vibration ranks among the

most destructive forces in the machine tools. Vibration influences the operation, performance

and life expectancy of the machine tools. Deterioration in the machine running conditions

always produces a corresponding increase in the vibration level. By monitoring vibration

level it is possible to obtain information about the machine condition. Excessive vibration in

the rotating machineries is the major cause of premature bearing failure and can lead to

disastrous machinery breakdown. The end result is a costly unscheduled plant shutdown.

Vibration can be caused by a variety of factors. This includes unbalance-rotating

elements, misalignment of bearings, looseness of parts and resonance from machineries.

However, the most common cause of machine vibration is unbalance. It is the most damaging

one and informs most about the machines condition. Hence there is a need to have a

predictive maintenance program for rotating machineries. The objective is to detect a change

in the vibration levels over a period of time and to act on that information which results in

increased productivity, improved product quality etc.

Most of the basic information required for the diagnosis of vibration problems is

provided by the frequency analysis of the vibration. The major characteristic, which must be

identified in the investigation of a vibration problem, is the frequency at which vibration is

occurring and for this purpose frequency domain analysis of the vibration present is

considered. Useful information can also be obtained by time domain analysis wherein the

recording and the study of the vibration is analyzed which varies with time.

Lathe is one of the most versatile and complex machine tool used in manufacturing

industries for producing cylindrical work pieces. The quality of the finished products



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depends mainly on the stability and rigidity of different machine components of a lathe. The

resulting markings on the finished work piece are related to the amplitude and frequency

content of the vibration present. A bearing is the most common critical component in a lathe.

Proper performance and functioning of bearings has always been a major concern in

rotating machinery. The shaft in the gearbox rotates at various speeds by combination of the

different meshing gears and hence the gear loads and the bearing loads vary leading to

innumerable computations. Thus the spindle bearings and the gearbox are found to be the

critical elements of the lathe on which condition monitoring has to be concentrated.

The Finite Element Analysis has become the most popular choice of practicing

engineers to solve the real life problems of vibration, stress and heat flow analysis of

machine tools. General-purpose finite element software’s provide the necessary tools to

perform such analysis for a wide variety of problems without compromising accuracy. The

finite element model of a lathe was developed by using finite element package A9SYS 7.1.The

lathe model was made up of elastic shell elements SHELL 63, structural mass element MASS

21, beam elements BEAM 188 and spring elements MATRIX 27. The finite element software

A9SYS 7.1 provides the necessary tools to perform modeling as well as analysis.

The objective of the present work deals with the study of the unbalance forces

generated by the various machine elements like spindle, chuck, pulley shafts, spindle shafts,

gear shafts and the effect of gear mesh frequencies. The effect of these unbalance forces on

the machine structure was analyzed by frequency domain and time domain approach.

Transient dynamic analysis was also carried to study the effect of defect present in the gear.

The experimentation will be carried out on the lathe by using the instrument Machine

Condition Tester T 30 that was compatible with the computer. Vibration velocities were

measured on the bearing housing by placing vibration transducer on the critical points for

the different spindle speeds. The experimental data obtained from Machine Condition Tester

T 30 were used to analyze the condition of the machine elements and also the effects of the

vibration level on the structure.



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1.2 OBJECTIVE OF THE WORK

The objective of the present work was to conduct theoretical and experimental

analysis to monitor the machine elements in the lathe.

� Finite Element Modeling and analysis

I Modeling of a lathe structure by using elements like elastic shell elements SHELL

63, structural mass element MASS 21, beam elements BEAM 188 and spring

elements MATRIX 27.

II To carry out the Modal analysis of a lathe structure. Determine mode shapes of

the structure, and its corresponding natural frequencies.

III To carry out the Harmonic Response Analysis by using both the frequency domain

and time domain for the various unbalance forces present on the rotating

machineries.

IV To carry out the Transient response analysis and to know the response of the

structure for the induced defect in gear.

� Experimental Method

I Measurement of RMS vibration velocity from the Gear box of an

E9TERPRISE 1330 lathe for different spindle speeds by using MACHI9E

CO9DITIO9 TESTER T 30 equipment.

1.3 ORGA�IZATIO� OF THE THESIS

The thesis has been organized in the following manner:

� Chapter 2 deals with the brief literature survey carried out related to the present

work, Introduction to condition monitoring, types of condition monitoring,

advantages of condition monitoring, vibration monitoring and an characteristics of

gear defects.

� Chapter 3 deals with the finite element method and analysis, steps involved in doing

finite element analysis, finite element modeling and analysis procedures.

� Chapter 4 will discuss about the experimental procedure, specification of enterprise

lathe 1330, machine condition tester T30 vibration measurement procedure.

� Chapter 5 deals with the results and discussion of both the experimental and

theoretical analysis.

� Chapter 6 explains the conclusion of the project work and scope for further

improvement.



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CHAPTER 2

LITERATURE SURVEY

2.1 REVIEW OF PAPERS

Several researches have been done in the field related to condition monitoring.

Condition monitoring is applied as a technique to improve productivity, efficiency and

reliability of the machine tool and its operations. Following are the papers related to the

field of condition monitoring of gearboxes.

Dr. Ramachandra A. et.al [1] have discussed about the vibration analysis of

machines and various types and methods of condition monitoring. They also dealt with

various methods of condition monitoring of ball and roller bearings and presented some case

studies wherein the SPM was useful in finding the condition of the bearing thereby saving the

cost, work of replacement and loss of production.

Grzegorz Litak and Michael I. Friswell [2] gave the information about Dynamics of a

Gear System with Faults in Meshing Stiffness. Gearbox dynamics is characterized by a

periodically changing stiffness. In real gear systems, a backlash also exist that can lead to a

loss in contact between the teeth. Due to this loss of contact the gear has piecewise linear

stiffness characteristics, and the gears can vibrate regularly and chaotically. In this paper

we examine the effect of tooth shape imperfections and defects. Using standard methods for

nonlinear systems we examine the dynamics of gear systems with various faults in meshing

stiffness.

J. Antoni Randall [3] in the paper titled “Differential Diagnosis of Gear and Bearing

faults” discusses the vibration-based diagnosis of rolling element bearings in the presence of

strong interfering gear signals from the gearboxes. A strong emphasis is placed on how to

distinguish between gear and bearing faults where the two signals may interact through the

analysis of their vibration signals. The key idea consists in recognizing gear signals as

purely periodic, whereas bearing signals experience some randomness. This is demonstrated

by introducing a comprehensive model for the vibration generating process of bearing faults

and the distributed faults.



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W. J. Wang and P. D. Mc Fadden [4] describe the decomposition of gear motion and

the related dynamic measurements for the condition monitoring and fault diagnosis of

gearboxes. In the case of gearbox monitoring, the teeth of the gears are the components to

be monitored. The important signal generated in a gearbox is the meshing vibration, which

propagates through all kinds of media and via all possible routes. The vibration signal

measured carries the information describing the condition of the gears. In gear condition

monitoring, a kinematics analysis can be performed by applying the various static and

dynamic loads on the gear. Any change in the condition such as wear, a fatigue crack will

cause some change in the motion of the gear. It is known that the tooth meshing vibration of

the gears is caused by the motion errors. The motion errors of the gear in quantified by

several motion error functions, which may be taken as indicators of the condition of the gear.

The motion error signal is separated according to fundamental frequencies into the harmonic

error and the residual error, which are used to quantify the gear condition. Analysis of the

time domain average of a gearbox casing vibration signal enables early detection of gear

damage.

Zeping Wei [5] discuses about Current methods of calculating gear contact stresses

use Hertz’s equations, which were originally derived for contact between two cylinders. To

enable the investigation of contact problems with FEM, the stiffness relationship between the

two contact areas is usually established through a spring placed between the two contacting

areas. This can be achieved by inserting a contact element placed in between the two areas

where contact occurs. The results of the two dimensional FEM analyses from A9SYS are

presented. These stresses were compared with the theoretical values. Both results agree very

well. This indicates that the FEM model is accurate.

Paula J. Dempsey and James J. Zakrajsek of 9ASA [6] discuses about Minimizing

Load Effects on 9A4 Gear Vibration Diagnostic Parameter and expressed formulation and

fluctuation load during destructive pitting. A change to the calculation of 9A4 is required to

minimize the effect of a fluctuating load on 9A4. This change, 9A4 reset, is made when the

load increases or decreases by a given percentage. For this application, a 10 percent load

change was used. For 9A4 reset, when the load changes by 10 percent, the denominator

resets to the square of the variance of the same reading, and a new average variance is

calculated starting with the reading measured when the load changed. Each time the load

changes by 10 percent, the first reading in the average variance resets to the first reading



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when the load changed. For the purpose of this paper, damage is defined as destructive

pitting if the depth is greater than 1/64 inches and the diameter is less than 1/16 inches.

Paula J. A [7] of 9ASA Discussed about Comparison of Vibration and Oil Debris

Gear Damage Detection Methods Applied to Pitting Damage, Two vibration diagnostic

parameters were used in this analysis, FM4 and 9A4. FM4 was developed to detect changes

in the vibration pattern resulting from damage on a limited number of teeth. Initial pitting for

the purpose of this paper is defined as pits less than 1/64 inch in diameter with a depth less

than 1/64 inches. At the completion of the test, the gears were inspected for damage

Tadashi and Kazuhide [8] discussed about Gear Whine Analysis with Virtual Power

Train Meshing transmission error (TE) is well known as a contributing factor of gear whine,

but system- level prediction of transmission error and quantitative analysis of dynamic

meshing vibromotive force have not been analyzed adequately until now. This paper

describes the use of a computer- aided-engineering (CAE) model for the analysis of the

dynamic gear meshing behavior and for the prediction of dynamic transmission error from

the input torque of the system. This paper also describes the analysis of a dynamic

vibromotive force at a bearing location where vibration is transmitted to the vehicle body.

The gear whine critical frequency can be predicted with the proposed method at an early

stage of passenger-car development when no prototype is available.

J.J. Zakrajsek and D.P. Townsend [9] discussed about Transmission Diagnostic. A

number of previously published and newly developed methods to specifically detect damage

on gear teeth were applied to vibration data from the spur gear, spiral bevel gear, and face

gear fatigue tests. The primary purpose was to verify the various methods with naturally

occurring faults and to determine their relative performance. Of the various techniques

investigated, only methods FM4, 9A4, and 9B4 responded to gear damage on a relatively

consistent basis over the various gear types and failure modes.

Timothy S Irwin [10] gave discussions on Gearbox Spectral Components and

Monitoring Methods; gave information’s about Five Fundamental Gear Frequencies,

Additional Component Frequencies, Fundamental Frequency Analysis, Transducer Selection

and Monitoring



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2.2 I�TRODUCTIO� TO CO�DITIO� MO�ITORI�G

Condition monitoring is applied as a technique for improving productivity, efficiency

and reliability of the machine components. It is the recent development in the field of

maintenance engineering. It involves monitoring the health of the machinery through

measurement by using parameters such as vibration, shock pulse, speed, temperature,

pressure etc.

Condition monitoring systems are becoming increasingly necessary in improving the

efficiency of the manufacturing system. The main demand made of these monitoring systems

is the detection of bearing failure, estimation of the bearing wear and wear rate. Unless

condition-monitoring technology is implemented in all its aspects no fruitful results or

economics can be achieved. Condition monitoring plays a vital role in ensuring the

availability of plant machinery. With the proper skills and equipment, plant maintenance

technicians not only detect problems before they result in a major machine malfunction or

breakdown, but they also perform root cause failure analysis to prevent problems from

recurring.

Condition monitoring has emerged as a new discipline and is considered as a

powerful technique in Modern Maintenance Management. This success has been possible

due to the tremendous development and contribution made by Instrumentation, Electronic

and Computer Specialists all over the world. Machine failures are now more openly

discussed and solutions sought. [12]

Condition Monitoring has developed both as a Science and Management with regard

to techniques, Computer assistance, Cost benefit and other utilitarian considerations. In the

country, there is already a large-scale awareness in most of the Educational Institutions,

R&D Laboratories and Industrial Sectors. Unless Condition Monitoring methodology is

implemented in all its aspects, no fruitful results or economics can be achieved. Condition

Monitoring is taken to mean the use of advanced technologies in order to determine

equipment condition, and potentially predict failure. Condition Monitoring is most

frequently used as a Predictive or Condition-Based Maintenance technique.

The business need that will drive sustainable change in condition monitoring is Asset

Effectiveness – the need to extract maximum profits from the minimum investment in plant



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and equipment. We achieve this through the use of Condition Monitoring technologies in the

following five ways:

• By improving Equipment Reliability through the effective prediction (and then

avoidance) of equipment failures.

• By minimizing downtime through the integrated planning and scheduling of repairs

indicated by Condition Monitoring techniques.

• By maximizing component life by avoiding the conditions that reduce equipment

life (for example, by ensuring ongoing precision alignment, minimal lubricant

contamination etc.)

• By utilizing Condition Monitoring techniques to maximize equipment performance

and throughput.

• By minimizing Condition Monitoring costs.

The main function of condition monitoring is to provide the knowledge of machine

condition and of its rate of change, which is essential to the operation of this method. The

knowledge may be obtained by selecting a suitable parameter such as vibration for

measuring deterioration and reading its value at intervals. In recent years improved

diagnostic techniques have become available and the condition of plant and machinery can

be monitored with sufficient accuracy and consistency to enable condition monitoring to be

widely used in the industry.

Condition Monitoring involves the measurement or checking of all vital primary and

secondary parameters or signals given out by the machine during its operation. Pressure,

temperature flow rate etc. are primary parameters whereas vibration, noise, corrosion, wear

etc. are secondary parameters. [12]

Condition Monitoring is appropriate in situations where failure mechanisms are

predominantly time dependent and where breakdown from such mechanisms are fairly

frequent over the plant lifetime. These time dependent mechanisms include corrosion,

erosion, wear, and fatigue and solids deposition causing excessive dynamic problems. A

condition-monitoring program should be evaluated for its reliability and techno economic

benefits before implementation in a system.



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Before moving on to the practical establishment of a condition monitoring

programme, it might be well to keep in mind the basic simplicity of the steps involved.

1. Detection: A periodic vibration check, using a hand-held meter takes only a few

seconds per machine. The check points should be clearly marked on each machine by

a small metal disc, machine indent or painted circle, so that the pick-up measures at

the same spot each time.

2. Analysis: Where periodic checks show an increase in the vibration reading a portable

analyser is used to pinpoint the trouble.

2. Correction: As the problems have been discovered at an early stage, correction –

including in-place balancing – can be scheduled for a convenient time.

2.3 TECH�IQUES OF CO�DITIO� MO�ITORI�G

There are many techniques available to monitor the health of the machinery. In spite

of the large amount of techniques available, there are few techniques of condition monitoring

and these are explained below: [13]

1. Visual Monitoring: It involves inspection and recording of surface appearance.

Inspection can be done by means of visual testing aids such as magnifying lenses,

microscopes, photographs, boroscopes, fiber optic scanners, surface imprinting etc.

Inference is made from overall appearance and properties such as color, shape and

texture.

2. Vibration Monitoring: Vibration analysis can give useful quantitative idea about the

condition of the equipment. This essentially uses vibration pick-up and frequency

analyzers. The existence of a problem can be detected from overall vibration levels.

Problems can also be diagnosed from frequency content, wave shape, and direction

of major component and phase analysis of the vibration signals.

3. Wear Debris Monitoring: This method works on the principle that the working

surfaces of a machine are washed by means of lubricating oil, and any damage to

them should be detectable from particles of wear debris in the oil. The amount of

wear particles in the lubricating oil gives information about the problem existence.



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Analysis of the size, shape, density and material composition of wear particles helps

to pin point the problem.

4. Performance Trend Monitoring: It involves checking the performance of a machine

or component to see whether it is behaving correctly. By monitoring the trend in the

performance characteristics such as temperature, pressure, efficiency etc., we will be

able to assess the condition of the equipment. This may for example involves the

monitoring the performance of a bearing by measuring its temperature to see whether

it is carrying out its function of transmitting load.

5. Corrosion Monitoring: Some of methods used for CM are i) Corrosion Coupons ii)

Measurement of polarization resistance, which is inversely proportional to rate of

corrosion, iii) Electrical resistance method, which makes use of the fact that change

in area due to material loss changes resistance.

6. Sound Monitoring: The noise given out from equipment contains useful diagnostic

data for condition assessment. Experienced personnel can make intuitive evaluation

by directly listening to the sound. Quantifiable diagnostics can be obtained form

sound signatures and data processing.

7. �on-Destructive Testing: This involves Radiography, ultrasonic flaw detection,

acoustic emission technique, Dye-penetrant tests, magnetic particle test etc. Suitable

technique is to be selected depending upon the type of defect and nature of data to be

obtained.

2.4 VIBRATIO� MO�ITORI�G

Vibration monitoring is one of the successful techniques of predicting the health of

the machine structures. Vibration monitoring is the process in which the machine

components are regularly checked and the condition i.e., whether it is healthy or faulty, is

checked on the basis of vibration signals got from the machine components. Vibration

analysis can give useful quantitative idea about the condition of the equipment. This

essentially uses vibration pick-up and frequency analyzers. The existence of a problem can

be detected from overall vibration levels. Problems can also be diagnosed from frequency



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content, wave shape and direction of major component and phase analysis of the vibration

signals.

As a part of vibration monitoring, vibration signature analysis is based on the

following factors.

� As there is no perfect machine all machines tends to vibrate.

� When mechanical trouble develops, the vibration level increases.

� Mechanical trouble causes vibration in different ways.

Therefore a periodic vibration check reveals whether the troubles are present or not.

Vibration signature analysis reveals which part of the machine is defective and hence

vibration monitoring is proved to be one of the most reliable condition monitoring technique

to check the machine condition. Application of vibration monitoring includes spindle

bearings, couplings, shafts, turbines, compressor and gearboxes. Vibration signature

analysis uses the transducers to pickup the signals from the machine structure and the picked

up signals are monitored.

2.5 CAUSES OF VIBRATIO�

The vibration analysis provides a complete machine diagnostic system and is not

limited to only a certain number of faults. During the vibration of rotating machinery, many

defects will be observed. The most common problems, which produce vibration, are

mentioned below:

1) Misalignment 11) Gear wear 2) Imbalance 12) Gear defects 3) Mechanical looseness 13) Gearwheel backlash 4) Critical speed excitation 14) Bearing defects 5) Coupling lock-up 15) Tilting pad wear 6) Uneven loading of a machine 16) Blade/vane defects 7) Shaft rubbing 17) Blade fouling 8) Cracked shaft 18) Blade rubbing 9) Rotor instability 19) Steam leaks 10) Electric motor defects 20) Compressor surge



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2.6 CHARACTERISTICS OF VIBRATIO�

A lot can be learnt about the machine conditions & mechanical problems by noting

its vibration characteristics. The vibration characteristics are as follows. [14]

� Vibration displacement

� Vibration velocity

� Vibration acceleration

� Vibration frequency

� Phase

2.6.1 Vibration Displacement

The total distance traveled by the vibrating part from one extreme limit of travel to

the other extreme limit of travel is referred to as the “peak to peak” displacement; it is

normally expressed in terms of microns. Vibration amplitude i.e., the displacement is an

indicator use to determine how good or bad the operation of a machine is. The greater the

amplitude, more severe the vibration. Although displacement readings are not widely

recommended for determining overall machinery condition, under the condition of dynamic

stress, displacement may be the better indicator of severity. Therefore, it is recommended to

measure the displacement in those machines, which are subjected to low frequency vibration

(below 600 CPM), where stress failure is of significant importance.

2.6.2 Vibration Velocity

The velocity of the motion is constantly changing throughout the cycle. The highest or

peak velocity is selected for the measurement. Vibration velocity is normally expressed in

terms of mm/sec. It provides the best overall indication of machine condition & is a direct

measure of vibration severity & appears to be function of displacement, which is significant

at medium frequencies (600 to 60000 CPM), where parts are subjected to fatigue.

2.6.3 Vibration Acceleration

The velocity of the part approaches zero at the extreme limits of travel each time the

parts come to stop at the limits of travel. It must accelerate to pickup speed as it travels

towards the other extreme limit. Therefore vibration acceleration is another important

characteristic of vibration. Vibration acceleration measurements are closely related to the



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vibratory force being applied to the machine & relatively large forces can occur at high

frequencies. Therefore generally vibration acceleration measurements are recommended for

vibration frequencies above 60000 CPM.

2.6.4 Vibration Frequency

The number of cycles for a given interval of time is the frequency. It is more useful in

identifying the cause of vibration. Frequency is normally expressed in hertz. Knowledge of

frequency allows use to identify which is at the fault & what the problem is. The forces,

which accuse vibration, are generated through rotary motion of the machine parts. Therefore

these forces change in magnitude & direction as the rotating parts changes its position with

respect to the rest of machine. As a result the vibration produced will have frequency

dependent upon the rotating speed of the part, which has the trouble.

2.6.5 Vibration Phase

Phase is defined as the position of vibrating part at given instant with references to a

fixed point or another vibrating part. In practical sense, phase measurement offers a

continent way to compare one vibratory motion with another or to determine how one part is

vibrating relative to another. Phase readings are normally expressed in degrees.

2.7 CRITERIA FOR ASSESSME�T OF VIBRATIO�

SEVERITY I� ROTATI�G MACHI�ES International standards on the vibration severity classify all machines into four categories.

Table 2.2 lists the classification of machines as per the international standards ISO 2372.

Table 2.1 Classifications of Machines as per the International Standards.

Class/group Description

I Individual parts of engines and machines integrally connected with the

complete machine in its normal operating conditions e.g.: electric motors up

to 15KW

II Medium sized machines Eg: Electric motors up to 15-75 KW

III Large prime movers and other large machines with rotating masses on rigid

and heavy foundations, which are relatively stiff in the direction of

measurement.

IV Large prime movers and other large machines with rotating masses on

foundations, which are soft in the direction of measurement.



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For each of these categories, the various levels of RMS vibration velocities are

divided into four relative quality bands, ranging from good through satisfactory and poor to

bad and it is given in the Table 2.3 given below. The particular range selected by the user is

based upon a number of parameters like.

� Type and size of the machines.

� Type and service expected.

� Mounting system.

� Effect of machinery vibration on the surrounding environment.

The vibration level measured on the bearing housing is compared with the vibration

standards based on ISO 2372 as shown in the Table 2.3 below [16]. It gives condition bands

for four classes of machines.

Table 2.2 Ranges of Vibration Severity as per ISO2372

Range of RMS

Vibration Severity in

mm/sec

Examples of quality judgment for separate classes of machines

Small

Machines

Class – I

Medium

Machines

Class-II

Large

Machines

Class-III

Turbo

Machines

Class-IV

0.29

0.45

0.71

1.12

1.80

2.80

4.50

7.10

11.20

18.00

28.00

45.00

A

A

B

C

A

B

C

A

B

C

B

C

D

D

D

D

A – Good B – Satisfactory C – Poor D – Bad



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2.8 VIBRATIO� FREQUE�CY A�ALYSIS

Vibration, and associated frequency, analysis has become a very popular monitoring

technique due to the myriad of information that it can provide about the condition of

machinery and structures. Vibration/frequency analysis of machinery has been extensively

documented for successfully, and at times automatically, detecting faults Furthermore,

vibration analysis is very effective for monitoring of undesirable high vibration levels or

foundation looseness, which affect machine health and lead to structural fatigue problems.

Methods for monitoring vibrations involve the measurement of three different

parameters, although they are all based on the same vibration. These include: Displacement,

Velocity, or Acceleration. Measurements of acceleration tend to accentuate higher frequency

vibrations, while displacement measurements emphasize the lower frequencies (this may be

understood by double-differentiating the displacement relation of a vibration). Consequently,

a variety of electrical and magnetic-based sensors have been developed to measure these

parameters (i.e., electrical strain gauges, eddy current proximity probes, piezoelectric

transducers, etc.) Each technique has a limited frequency range of measurement and is

therefore ideally suited for specific applications.

9ot only is frequency information important for the detection of the incipient faults,

but it also enables the cause of the fault to be diagnosed. A frequency analysis reveals the

frequencies at which the significant level changes have occurred and these can usually be

correlated with a particular mechanical phenomenon: rotation speed of the shaft (unbalance

and misalignment), gear meshing frequency, resonances, critical shaft frequency etc. A

vibration trouble shooting chart shown in Table 2.3 gives the nature of the faults, its

direction and the frequency with which it appears. [17]



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Table 2.3 Vibration Trouble-Shooting Chart

�ature of

fault

Frequency of dominant

vibration (Hz or rpm/60)

Direction Remarks

Rotating

members out

of balance

1 x rpm Radial A common cause of excess

vibration in machinery.

Misalignment

and bent shaft

Usually 1 x rpm Often 2 x

rpm. Sometimes 3 and 4 x

rpm

Radial

and axial

A common fault.

Damaged

rolling

element

bearings (ball,

rotor, etc.)

Impact rates for the

individual bearing

component. Also vibrations

at high frequencies (2 to 60

Hz) often related to radial

resonance in bearings

Radial

and axial

Uneven vibration levels, often

with shocks.

Journal

bearings loose

in housing

Sub-harmonics of shaft rpm

exactly ½ or 1/3 x rpm

Primarily

radial

Looseness may only develop at

operating speed and temperature

(e.g. turbo machines).

Oil film whirl

or whip in

journal

bearings

Slightly less than half shaft

speed (42% to 48%)

Primarily

radial

Applicable to high-speed (e.g.,

turbo machines).

Hysteresis

whirl

Shaft critical speed Primarily

radial

Vibrations excited when passing

through critical shaft maintained

at higher shaft speeds. Can

sometimes be checking tightness

of rotor components.

Damaged or

worn gears

Tooth meshing frequencies

(shaft rpm x number of

teeth) and harmonics

Radial

and axial

Sidebands around tooth meshing

frequencies indication (e.g.,

eccentricity) at frequency

corresponding to spacing.

9ormally only detectable with

very narrow-basis and cepstrum.

Mechanical

looseness

2 x rpm Also sub and interharmonics, as

for loose journal.

Faulty belt

drive

1, 2, 3 and 4 x rpm of belt Radial The precise problem can usually

be identified virtual help of a

stroboscope.

Unbalanced

reciprocating

forces and

couples

1 x rpm and/or multiples

for higher order unbalance

Primarily

radial

Electrically

induced

vibrations

1 x rpm or 1 or 2 times

synchronous frequency

Radial

and axial

Should disappear when turning

off the power.



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2.9 MODES OF GEAR FAILURES

From one point of view, causes of gear failure may include a design error, an

application error, or a manufacturing error. Design errors include such factors as improper

gear geometry as well as the wrong materials, quality levels, lubrication systems, or other

specifications. Application errors can be caused by a number of problems, including

mounting and installation, vibration, cooling, lubrication, and maintenance. Manufacturing

errors may show up in the field as errors in machining or heat-treating. AGMA recognizes

four main modes of gear failure, plus a fifth that covers everything else. They are wear,

surface fatigue, plastic flow, breakage, and associated gear failures (Fig 2.1).

2.9.1 WEAR FAILURES

� Moderate wear (Fig 2.1) shows up as a contact pattern in which metal

removal occurs from both the addendum and dedendum tooth surfaces, and

the operating pitch line remains as a continuous line. This may be caused by

lubricant contamination but is often unavoidable due to limitations of

lubricant viscosity, gear speed, and temperature. It may occur normally

throughout the design life of a gear set, particularly when gears operate near

boundary lubrication conditions. Increasing oil film thickness, either by

cooling the lubricant, using a higher viscosity lubricant or operating at higher

speeds, can sometimes reduce normal wear. Replacing a splash-fed

lubrication system with a filtered positive-spray system may improve

lubrication by removing particles and delivering a more consistent supply of

oil to the working surfaces. Further solutions include reducing the gear

loading and changing the gear geometry, materials, or hardness.

� Extreme wear (Fig 2.1) may appear as the same kind of contact pattern and

pitch line visibility that occur with moderate wear, but the progression rate is

much faster. Here, a considerable amount of material may be removed

uniformly from the gear tooth surfaces, and the pitch line may show signs of

pitting. Extreme wear will cause failure to occur before the design life of the

gear set is reached. It may cause enough damage to the tooth profile that the

resulting high dynamic loads will further accelerate the wear. Causes of



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extreme wear include a lubricating film too thin for the tooth load, fine

abrasive particles in the lubrication system, and severe vibratory loads. Shaft

seals and air-vent filters, properly installed and maintained, may help reduce

wear. Other solutions include oil cooling, higher viscosity lubricants, higher

speeds, reduced loads, and possibly reduced vibratory loads if the application

permits.

� Abrasive wear (Fig 2.1) shows up as a lapped surface, with radial scratches

or grooves on the tooth contact surfaces. When this occurs shortly after

startup of a new installation or on any open gearing, particles in the

lubricating system are generally the causes. These may include metal

particles from the gears and bearings, weld spatter, scale, rust, and sand, dirt,

or other environmental contaminants. Fig. 2 shows severe abrasion. Careful

cleaning of the gearbox and lubrication system before use can minimize

abrasive wear. With a circulating lubrication system, adding a filter or using

a finer replacement filter will help reduce this type of wear. Regular oil

changes will help for splash-lubricated drives, and higher viscosity oil also

may help protect either type of system with a thicker oil film that will keep the

finer particles from scratching.

� Corrosive wear (Fig 2.1) is visible as surface deterioration, caused by the

chemical action of active ingredients in the lubricant. These may include acid,

moisture, foreign materials, and extreme-pressure additives. During

operation, the oil breaks down and allows corrosive elements present in the

oil to attack the gear contact surfaces. This action may affect the grain

boundaries and cause fine, evenly distributed pitting. Checking the oil for

breakdown and changing it at regular intervals can help minimize corrosive

wear. Lubricants with high antiscuff, antiwear additive content must be

observed even more carefully because they are chemically active. Gear units

that are exposed to salt water, liquid chemicals, or other foreign materials

should be sealed from their environment.



19

2.9.2 SURFACE FATIGUE FAILURE

Surface fatigue can be noticed by the removal of metal and the formation of cavities.

These may be small or large and may grow or remain small. It occurs when the gear

material fails after repeated stresses that are beyond the endurance limits of the metal. Here

are the main types of surface fatigue, their causes, and cures.

� Pitting (Fig 2.1) failures depend on surface contact stress and the number of stress

cycles. Initial pitting, with areas of small pits from 0.015 in. to 0.030 in. in diameter,

occurs in localized parts of the gear teeth that are over-stressed. It is sometimes

called corrective pitting because it tends to redistribute the load by progressively

removing high contact spots, and often stops once the load has been redistributed.

Continued operation may polish or burnish the pitted surface and improve its

appearance. Pitting can be monitored by periodically putting some bluing on the

affected area, then applying some cellophane tape to lift the pattern and put it in a

notebook. Comparing the impressions over time will tell whether the pitting has

stopped. While accurate manufacturing control of involute profiles is the best method

of preventing pitting, a careful break-in at reduced loads and speeds once the unit is

installed also will help minimize pitting by improving gear tooth contact.

� Destructive pitting (Fig 2.1) appears as much larger pits than initial pitting, often in

the dedendum section of the gear teeth. These larger craters usually are caused by

more severe overload conditions that cannot be relieved by initial pitting. As stress

cycles build up, pitting will continue until the tooth profile is destroyed. To correct

the cause of destructive pitting, the load on the surface of the gear needs to be

reduced below the material’s endurance limit, or the material hardness needs to be

increased to raise the endurance limit to where pitting will not occur.

� Spalling (Fig 2.1) resembles destructive pitting, except that the pits may be larger,

quite shallow, and irregularly shaped. The edges of the pits break away rapidly,

forming large, irregular voids that may join together. Spalling is caused by

excessively high contact stress levels. Remedies include reducing contact stress on the

gear surface or hardening the material to increase its surface strength.



20

Both Spalling and destructive pitting are indications that the gears do not have sufficient

surface capacity and should probably be redesigned if possible.

� Micro pitting (Fig 2.1) is a type of contact fatigue that appears as frosting or gray

staining under thin film conditions. The surface acquires an etch-like finish, with a

pattern that sometimes follows the slightly higher ridges left by cutter marks or other

surface irregularities. It usually shows up first on the dedendum section of the driving

gear, although it may begin on the addendum section as well. When viewed under

magnification, the surface is seen as a field of very fine micro pits under 0.0001 in.

deep. Causes include high surface loads and heat generation, which thins the

lubrication film and leads to marginal lubrication. Improving the surface finish is an

effective remedy, through either manufacturing techniques such as hard honing and

grinding or a careful break-in cycle. These techniques help lower heat generation by

improving conformity of tooth contact and equalizing load distribution. Reducing the

lubricant temperature and surface loading will also minimize frosting. Sometimes,

frosted areas that appear initially will slowly be polished away during subsequent

operation if loads and temperatures are not excessive.

� Case crushing (Fig 2.1) occurs in heavily loaded case hardened gears, including

those that are carburized, nitrided, or induction hardened. It is a subsurface fatigue

failure that occurs on material where the case is substantially harder than the core,

when surface contact stress at high cycle levels exceeds the material’s endurance

limit. Case crushing may appear similar to pitting, if some damage occurs on

contacting surfaces. However, it often occurs as longitudinal cracks on the surface of

only one or two teeth, and long pieces of the tooth surface may break away. The case

material may appear to have chipped away from the core in large flakes. Case

crushing occurs when cracks form because stresses in the subsurface area exceed the

strength of the core material. High residual stresses may contribute to this effect. The

cracks move toward the case-to-core boundary and then to the gear surface, where

they may eventually cause large pieces of material to fall off. To prevent case

crushing, it may be necessary to increase the depth of the case hardening and



21

possibly the hardness of the core material. Changes in the material, heat treatment

process, or the design itself may be necessary

2.9.3 PLASTIC FLOW FAILURE

Plastic flow is a surface deformation that occurs when high contact stresses combine

with the rolling and sliding action of the meshing gear teeth to cause cold working of the

tooth surfaces. Although usually associated with softer materials, it also can occur in heavily

loaded case hardened and through-hardened gears. Plastic flow generally takes one of three

distinct forms.

� Cold flow, rolling, and peening (Fig 2.1) can be identified through evidence of

metal flow in the surface and subsurface material. The surface material may have

been worked over the tips and ends of the gear teeth, resulting in a finned

appearance. Tips of the gear teeth may be heavily rounded over, and a matching

depression may appear on the tooth surface. Cold flow occurs under heavy loads and

high contact stresses, as the rolling and peening action of the meshing gear teeth

cold-works the surface and subsurface material, pushing or pulling it in the direction

of sliding. Continued operation during this deterioration increases dynamic loading

and results in a dented, battered appearance on the surface, much as if it had been hit

with a ball peen hammer. To eliminate the problem it is necessary to reduce contact

stress and increase hardness of the contacting surface and subsurface materials.

Increasing the accuracy of both tooth spacing and profiles will help reduce dynamic

loads, and any mounting deflections or helix angle errors should also be corrected.

� Rippling (Fig 2.1) is a regular, wave-like formation that occurs at right angles to the

direction of motion and has a fish scale appearance. It is most common on hardened

gear surfaces and is generally considered a surface failure only when it has

progressed to an advanced stage. It usually occurs in slow speed operation with an

inadequate oil film thickness. High contact stresses during repeated cycles may then

roll and knead the surface, causing it to ripple. Rippling can be prevented by case

hardening the tooth surface, reducing the contact stress, increasing oil viscosity, and

using an extreme-pressure oil additive



22

� Ridging (Fig 2.1) is a definite series of peaks and valleys that occur across the tooth

surface in the direction of sliding. It occurs when high contact compressive stresses

and low sliding velocities cause plastic flow of the surface and subsurface material. It

is frequently found on heavily loaded worm gear drives, as well as on hypoid pinion

and gear drives. Remedies for ridging include reducing contact stress, increasing

material hardness, and using more viscous lubricating oil with extreme-pressure

additives.

2.9.4 BREAKAGE FAILURE

Breakage is the fracture of a whole tooth or substantial part of a tooth. Common causes

include overload and cyclic stressing of the gear tooth material beyond its endurance limit.

� Bending fatigue breakage (Fig 2.1) starts with a crack in the root section and

progresses until the tooth or part of it breaks off. It can be recognized by a fatigue

“eye” or focal point of the break. The break area itself usually shows signs of fretting

corrosion and smooth “beach marks” that resemble patterns in the sand on a beach.

A small area will probably have a rough, jagged look where the last portion of the

tooth broke away. Most such failures result from excessive tooth loads, which cause

repeated root stresses that eventually exceed the endurance limits of the material.

Stress risers, such as notches in the root fillet, hob tears, inclusions, small heat

treating cracks or grinding burns, may aggravate this condition. To remedy this

condition, root fillets can be polished and shot-peened. Material should be properly

heat-treated to minimize residual stresses. If redesign is necessary, use a full-fillet

radius tooth, which is less prone to breakage and has greater capacity than a tooth

with too small a fillet radius.

� Overload breakage (Fig 2.1) appears as a stringy, fibrous break that has been

rapidly pulled or torn apart. In harder materials, the break will have a finer stringy

appearance. The eye and beach markings found in fatigue breakage will be missing.

This type of breakage is caused by an overload that exceeds the tensile strength of the

gear material. Typical overloads that lead to such breakage include a bearing



23

seizure, failure of driven equipment, foreign material passing through the gear mesh,

or a sudden misalignment. Since the failure is usually the result of some

unpredictable occurrence, it is difficult or impossible to prevent. If possible overloads

are anticipated, torque-limiting couplings may provide some protection.

� Random fracture (Fig 2.1) can occur in areas such as the top or the end of a tooth,

rather than the usual root fillet section. These failures are typically caused by stress

concentrations from such things as minute grinding cracks, foreign materials in the

gear mesh, or improper heat-treating. Little can be done to prevent random fracture,

except at the design and manufacturing stages. However, maintaining cleanliness of

the lubricant can help prevent one cause

2.9.5 ASSOCIATED GEAR FAILURES

Associated gear failures usually are caused by improper processing, environmental

conditions, or possibly by accidents. To minimize many of these failures, any gear that is

repaired and heat-treated should be checked by magnetic particle inspection before being

put back into service to be sure no cracks have developed. Whenever repairs are made to any

gearing, at the very least, a dye penetrant inspection should be performed to check for

cracks.

� Quenching cracks (Fig 2.1) may appear across the top land of a tooth, in the fillet

area, or randomly at the tooth ends, although they may not become visible until after

they have been used for a short time. They are caused by improper quenching or

uneven cooling during heat treatment, which causes excessive internal stresses.

Prevention of quenching cracks calls for a thorough review of heat-treating

procedures, as well as an inspection of the equipment used.

� Grinding cracks (Fig 2.1) usually show up as a definite pattern, either as a series of

short cracks that are parallel to each other or with the appearance of chicken wire

mesh. Usually, they are between 0.003 in. and 0.005 in. deep, with the parallel type

being deeper than the chicken wire pattern. Causes include improper heat treatment

or a metallurgical structure that is prone to cracking. To prevent this cracking, the



24

grinding procedure should be reviewed. Feeds and speeds may have to be reduced to

lower the heat developed during grinding. The metallurgy of the gear material also

should be examined to choose an alloy and heat treatment that will not tend to crack

during grinding.

� Rim and web failures (Fig 2.1) tend to start between two teeth and propagate

through the rim and into the web. These failures are common on highly loaded thin

rim and web sections. Causes include stress risers from holes in the web as well as

from web vibrations. Remedies include increasing rim or web thickness, depending

on failure mode, and eliminating stress risers such as grinding marks, tool marks,

and sharp fillets. Rim and web failures also may be caused by vibrations, which can

be minimized by damping or by redesign to change the natural frequencies of the

gear.

� Electric current damage (Fig 2.1) shows up as tiny pits occurring in a well-defined

pattern that is distributed uniformly along the gear surfaces. They can be further

identified by their smooth, molten appearance and lack of any fibrous appearance.

This damage results from electric current passing through two lightly contacting

surfaces, either from arc welding or from electric equipment such as motors or

electrically actuated clutches. The remedy is to insulate the electrical equipment or

relocate the grounding wires properly. Welders and maintenance workers should be

made aware of proper grounding procedures.



25

Moderate wear Abrasive wear Corrosive wear

Scoring Pitting Destructive pitting

Spalling Micropitting Micropitting magnified

Case Crushing Rippling Ridging

Quenching cracks Grinding cracks Rim and web failures

Electric current damage

Fig 2.1 Modes of gear failures



26

2.10 TOOTH LOAD VS TIME DISTRIBUTIO� I� GEAR

MESHI�G

Fig: 2.2 Tooth load VS time distribution (a) for low speed, (b) for medium speed, (c) for

high speed

The Fig. 2.2 shows the tooth Vs load distribution during gear meshing [23]. During low

speed the Dynamic load transmitted will be systematic and during medium the load varies

and similarly the load varies violently during high speed. This effect is due to the reduction

of time gap between two successive teeth. The gap can range from 2e-12

for high speed and

2e-6

to low speed. This gives load to transmit irrespective to its plot and gives more effective

tooth load to excite.

2.11 BA�D OF CO�TACT GEAR MESHI�G

Gear fails by pitting and wear as well as by tooth breakage [22]. Frequently gear will

wear to the point where they begin to run rough. Then the increased dynamic load plus the

stress concentration affects of the worn tooth surface cause the teeth ultimately to fail by

breakage. Figure shows the kinds of stresses that are present in the region of the contact. In

the canter of the band there is a point of maximum compressive stress, directly underneath

this point there is a maximum subsurface shear stress. The depth to the point of maximum

shear stress is a little less than one-third the width of the band of contact. The gear toot



27

surfaces move across each other with a combination of rolling and sliding motion. The

sliding motion plus the coefficient of friction tend to cause additional surface stresses and

just behind the band of contact there is a narrow region of tensile stress. A bit of metal on the

surface of a gear tooth goes through a cycle of compression and tension each time a mating

gear tooth passes over it.

Fig �o: 2.3 Gear meshing band of contact.

2.12 GEAR POWER TRA�SMISSIO� SYSTEM According to AGMA standard Test charts the distribution of Gear Transmission

Power will be uniform. During any defect the power fluctuate and the effect of defect will be

suppressed by fluctuating of power. This means the transmission of power does not vary

during running conditions in defective cases but fluctuate to overcome the defect.

The transmission loss during any disturbance like pitting in Gear will lead to

addition of fluctuate power to compromise the defect. [6] [7]

The amount of additional power will be constant 2% to 10% of full power per each

Gear pair that is 1-1 contact for destructive pitting. This addition is to overcome the defect

and transmit the corresponding power to the system.



28

2.13 FORMATIO� OF GEAR DESTRUCTIVE PITTI�G

The formation of Destructive pitting is as shown in the Fig 2.4. Here, a considerable

amount of material may be removed uniformly from the gear tooth surfaces, and the pitch

line may show signs of pitting at constant rate. Pitting failures depend on surface contact

stress and the number of stress cycles. Initial pitting, with areas of small pits from 0.4 mm. to

0.4 mm in diameter, occurs in localized parts of the gear teeth that are over-stressed.

Destructive pitting appears as much larger pits than initial pitting of 1.5mm in diameter,

often in the dedendum section of the gear teeth. These larger craters usually are caused by

more severe overload conditions that cannot be relieved by initial pitting. As stress cycles

build up, pitting will continue until the tooth profile is destroyed. To correct the cause of

destructive pitting, the load on the surface of the gear needs to be reduced below the

material’s endurance limit, or the material hardness needs to be increased to raise the

endurance limit to where pitting will not occur.

Fig �o: 2.4 Formation of pitting in Gear



29

CHAPTER 3

FI�ITE ELEME�T METHOD

3.1 I�TRODUCTIO�

Finite Element Method is a numerical procedure for solving physical problems in the

fields of mechanics, fluid dynamics, thermodynamics etc. Finite element method is

particularly useful for solving problems that do not have satisfactory analytical procedures.

The analytical procedures maybe difficult because of complicated geometry of the body that

cannot be modeled numerically. The finite element method solves the problems by

discretizing the body into small elements of known geometry, whose solution can be found

easily. The method generates a set of algebraic equations that can be solved numerically.

With the advent of fast processing computers, these procedures have become even simpler,

faster and effective. [18]

The finite element method is a numerical method, which can be implemented to solve

many problems. The method was used for the accurate solution of complex engineering

problem. It was first developed in 1956 for the analysis of aircraft structural problems.

Thereafter within a decade, the potential of the method for the solution of different types of

applied sciences and engineering problems were recognized. Over the years, the finite

element technique has been so well established that today it is considered to be one of the

best methods for solving a wide variety of practical problems efficiently.

The FEM originated as a method of stress analysis. Today FEM is used to analyze

problems of heat transfer, fluid flow lubrication, electric and magnetic fields and many

others. Thus it has become a powerful tool for the numerical solution of a wide range of

engineering problems with the advances in computer technologies and CAD systems,

complex problems can be modelled with relative ease, several alternative configurations can

be tried out on a computer before the first prototype is built. In this method of analysis, a

complex region defining a continuum is discretized into simple geometric shapes called finite

elements. The material properties and the governing relations are considered over these

elements and expressed in terms of unknown values at element corner. An assembly process,



30

duly considering the loading and constraints, results in a set of equations gives us the

approximate behavior of the continuum.

3.2 FI�ITE ELEME�T A�ALYSIS

Finite Element Analysis is a way to simulate loading conditions on a design and

determine the design’s response to those conditions. The design is modeled using discrete

building blocks called elements. Each element has exact equations that describe how it

responds to a certain load. The “sum” of the response of all elements in the model gives the

total response of the design. The elements have a finite number of unknowns, hence the name

finite elements. [19]

The finite element analysis is needed to reduce the amount of prototype testing.

Computer simulation allows multiple “what-if” scenarios to be tested quickly and effectively.

To simulate designs that is not suitable for prototype testing. Example: Surgical implants,

such as an artificial knee. Finite element analysis results in Cost savings; Time savings

reduce time to market and create more reliable, better-quality designs.

3.3 E�GI�EERI�G APPLICATIO�S OF FEM

In particular the FEM can be systematically programmed to accommodate complex

and difficult problems such as non-homogeneous materials, non-linear stress strain

behaviour, and complicated boundary conditions. This FEM is applied to wide range of

boundary value problems in engineering. In boundary value problems, a solution is sought in

the region of the body, while on the boundaries or edges of the region, values of dependent

variables or their derivatives are prescribed.

There are three major types of boundary value problems.

• Equilibrium or steady state problems.

• Eigen value problems.

• Propagation or transient problems.

In an equilibrium problem, we need to find the steady state displacements or stress

distribution if it is in solid mechanics problems, temperature or heat flux distribution if it is a

heat transfer problem and pressure or velocity distribution if it is a fluid mechanics problem.



31

In Eigen value problems, time will not appear explicitly. They may be considered as

extensions of equilibrium problems in which critical values of certain parameters are to be

determined in addition to the corresponding steady state configurations. In this problems we

have to find the natural frequencies or buckling loads and mode shapes if it is a solid

mechanics or structural problem, stability of laminar flows if it is a fluid mechanics problem

and resonance characteristics, if it is an electric circuit problem. The propagation or

transient problems are time dependent problems. This type of problem arises, for example,

whenever we are interested in finding the response of a body under time varying loads, in the

area of solid mechanics and under sudden heating or cooling in the field of heat transfer.

3.4 STEPS I�VOLVED I� THE FI�ITE ELEME�T

A�ALYSIS

In general, a finite element solution may be broken into the following three stages. This is

a general guideline that can be used for setting up any finite element analysis.

1. Preprocessing: Defining the problem; The major steps in preprocessing are

given below:

� Define key points/lines/areas/volumes

� Define element types and material/geometric properties

� Mesh lines/areas/volumes as required

The amount of detail required will depend on the dimensionality of the analysis (i.e.

1D, 2D, axi-symmetric, 3D).

2. Solution: Assigning loads, constraints and solving; Here we specify the loads

(point or pressure), constraints (translational and rotational) and finally solve the

resulting set of equations.

3. Post processing: Further processing and viewing of the results; In this stage

one may wish to see:

� Lists of nodal displacements

� Element forces and moments

� Deflection plots

� Stress contour diagrams



32

3.5 A�SYS 7.1

A9SYS is a general-purpose finite element modeling package for numerically solving

a wide variety of mechanical problems. These problems include: static/dynamic structural

analysis (both linear and non-linear), heat transfer and fluid problems, as well as acoustic

and electro-magnetic problems. The A9SYS 7.1 Family of Products continues A9SYS, Inc.'s

commitment to provide the highest quality engineering tools to help all of your design and

analysis needs. This release of the products contains all of the capabilities from previous

releases, plus many new features to enhance your productivity. [19]

A9SYS enables to perform the following tasks.

� Creating of computer models or structures, products, components, or systems.

� Apply operating loads or other design performance conditions.

� Study physical response, such as stress levels, temperature distributions.

� Optimize a design early in the development process to reduced production costs.

� Do prototype testing in environment where it otherwise would be undesirable or

impossible.

3.6 A�ALYSIS PATTER�S

Structural analysis is probably the most common application of the finite element

method. The term structural (or structure) implies not only civil engineering structures such

as bridges and buildings, but also naval, aeronautical, and mechanical structures such as

ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as

pistons, machine parts, and tools.

The four types of structural analyses available in the A9SYS family of products are

explained below. The primary unknowns (nodal degrees of freedom) calculated in a

structural analysis are displacements. Other quantities, such as strains, stresses, and

reaction forces, are then derived from the nodal displacements.

Static Analysis: Used to determine displacements, stresses, etc. under static loading

conditions.

Modal Analysis: Used to calculate the natural frequencies and mode shapes of a structure.

Different mode extraction methods are available.



33

Harmonic Analysis: Used to determine the response of a structure to harmonically time-

varying loads.

Transient Dynamic Analysis: Used to determine the response of a structure to arbitrarily

time-varying loads.

3.7 ELEME�T TYPES

There are mainly three types of elements, which could be used in FEA based on the

shape of the structure. They are O9E, TWO and THREE dimension elements. An exhaustive

element library is available with all FEM packages, which could be used to select the

suitable type of element. [19]

Depending on the application, one-dimensional elements can be classified as bar and

beam elements. Bar elements is one, which can take only axial tension and compression

loads. Beam elements are one, which can withstand bending loads along with axial tension

and compression loads. Similarly, under two-dimensional elements, commonly used elements

are membrane, plate and shear elements. Membrane elements can take only in-plane loads

and plate elements can take in plane and also bending loads. The shear element can

withstand pure shear loads. So, one has to be familiar with the element library of a

particular FEA package and accordingly should choose the right kind of element depending

on the application and shape of the structure.

The elements used for modeling the lathe structure are elastic shell elements SHELL

63, structural mass element MASS 21, beam elements BEAM 188 and spring elements

MATRIX 27.

3.8 ELEME�T LIBRARY

The A9SYS element library consists of more than hundred different element types. An

element type is identified by a name and a unique identifying number. The different elements

used during the modeling of a lathe structure are elastic shell elements SHELL 63, structural

mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. The

description of the above elements is given below. [19]



34

3.8.1 SHELL 63

SHELL 63 has both bending and membrane capabilities. Both in-plane and normal loads are

permitted. The element has six degrees of freedom at each node: translations in the nodal x,

y, and z directions and rotations about the nodal x, y, and z-axes.

The element is defined by four nodes, four thicknesses, elastic foundation stiffness, and the

orthotropic material properties. The element x-axis may be rotated by an angle THETA (in

degrees).

A summary of the element input is given as follows

Element 9ame : SHELL 63

9odes : I, J, K, L

Degrees of Freedom : UX, UY, UZ, ROTX, ROTY, ROTZ

Real constants : TK (I), TK (J), TK (K), TK (L), EFS, THETA

�o. �ame Description

1 TK(I) Shell thickness at node I

2 TK(J) Shell thickness at node J

3 TK(K) Shell thickness at node K

4 TK(L) Shell thickness at node L

5 EFS Elastic foundation stiffness

6 THETA Element X-axis rotation

3.8.2 MATRIX 27

MATRIX 27 represents an arbitrary element whose geometry is undefined but whose elastic

kinematic response can be specified by stiffness, damping, or mass coefficients. The matrix is

assumed to relate two nodes, each with six degrees of freedom per node: translations in the

nodal x, y, and z directions and rotations about the nodal x, y, and z-axes

The element is defined by two nodes and the matrix coefficients. The stiffness, damping,

or mass matrix constants are input as real constants. All matrices generated by this element

are 12 by 12. The degrees of freedom are ordered as UX, UY, UZ, ROTX, ROTY, ROTZ for

node I followed by the same for node J. If one node is not used, simply let all rows and

columns relating to that node default to zero.

The element input summary is as given below.



35

Element 9ame : MATRIX 27

9odes : I, J


Real Constants : Constants C 1 through C 78 defines the upper triangular

portion of the matrix. Constants C 79 through C 144 define the lower triangular portion of

the matrix.

3.8.3 BEAM 188

BEAM 188 is suitable for analyzing slender to moderately stubby/thick beam

structures. BEAM 188 is a linear (2-node) beam element in 3-D. BEAM 188 has six degrees

of freedom at each node. BEAM 188 is defined by nodes I and J in the global coordinate

system. 9ode K is always required to define the orientation of the element.


Element 9ame : BEAM 188

9odes : I, J, K


Material Properties : EX, PRXY, DE9S, GXY, GYZ, GXZ, DAMP

3.8.4 MASS 21

MASS 21 is a point element having up to six degrees of freedom: translations in the

nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The mass element

is defined by a single node.


Element 9ame : MASS 21

9odes : I


Real Constants : MASSX, MASSY, MASSZ, IXX, IYY, IZZ



36

3.9 DEVELOPI�G FEM MODEL OF A LATHE

The development of the lathe structure is considered to be the complex method by

using classical approaches. Hence a suitable approach has to be considered and the finite

element modeling is the one that gives the representation of the geometrical model in terms of

finite number of elements and nodes, which are the building blocks of the structure. The lathe

model was divided into a number of elements, so that the behavior of the different elements can

be studied under the action of loads transmitted from the adjacent elements.

The finite element model of a Lathe was developed by using A9SYS 7.1. The model

was described as given below. A finite element model of a lathe structure is as shown in the Fig.

3.1. The lathe model was made up of elastic shell elements SHELL 63, structural mass element

MASS 21, beam elements BEAM 188 and spring elements MATRIX 27.

In a model, left leg, right leg, carriage, tool post, bed walls are modeled by elastic

shell element SHELL 63, which has six degrees of freedom at each node. It has both bending

and membrane capabilities. The spindle shafts front and rear bearing was modeled by using

MATRIX 27, which was represented by stiffness and damping values. The spindle shaft was

modeled by using BEAM 188 element.

The material data along with their properties is listed in the Table 3.1 below. Table

3.2 gives the lists of parts and element names. The finite element of the lathe structure has

totally 2050 elements and 1869 nodes.

The various unbalance elements of the lathe structure considered for the analysis was

shown in Fig. 3.2 and the headstock assembly of the lathe showing the unbalance elements was

shown in Fig. 3.3.

Table 3.1: Material Data used in Modeling

Material

Model �O:

Material

�ame

Modulus of

Elasticity

Kgf/mm2

Poissons

Ratio

Density

Kgf/mm3

1 Cast iron 9700 0.27 7.9e-9

2 Steel 21000 0.3 7.8e-10



37

Table 3.2: Details of the parts with their Element �ame

Sl. �o. Part �ame Element �ame

1 Tail stock SHELL63

2 Head stock SHELL63

3 Right leg SHELL63

4 Bed walls SHELL63

5 Feed gear box SHELL63

6 Head stock SHELL63

7 Carriage SHELL63

8 Spindle bearing front horizontal MATRIX27

9 Spindle bearing front vertical MATRIX27

10 Spindle bearing rear horizontal MATRIX27

11 Spindle bearing rear horizontal MATRIX27

12 Spindle shaft BEAM188

Fig. 3.1: Finite Element Model of a lathe



38

Fig. 3.2: Unbalance Components of a Lathe

Fig. 3.3: Head Stock Assembly of a Lathe



39

3.10 A�ALYSIS PROCEDURE

The analysis of Lathe is done in three forms first the Modal Analysis second the Harmonic

Analysis and lastly Transient Analysis with assumed Defect in Gear. The three types are

mentioned below.

3.10.1 MODAL A�ALYSIS After the modeling of lathe structure, first step is to carryout modal analysis. It is

used to calculate the natural frequencies and mode shapes of a structure. The natural

frequencies and mode shapes are important parameter in the design of a structure for

dynamic loading condition; mode shapes can be defined as the amplitude of displacements of

all the mass points during the vibration of the structure at natural frequencies. Modal

analysis results obtained can be used for the dynamic analysis such as harmonic response

analysis, transient response analysis or a spectrum analysis. Mode extraction is used for this

purpose. Block Lanczos extraction method is employed. [19] The analysis was carried out in

the absence of damping and load. The number of modes to compute is ten to know the

behavior of the structure completely at the natural frequencies.

3.10.2 HARMO�IC RESPO�SE A�ALYSIS Harmonic response analysis was used to determine the response of the structure to

harmonically time varying loads. The idea is to calculate the structures response at several

frequencies and to obtain a graph of vibration velocity with frequency. Due to the presence

of the rotating members in the structure, there exist unbalance forces, which vary

harmonically with time. These unbalance forces given by the various elements in the

structure is calculated and applied on the structure at their location and the response is

observed at their corresponding operating frequencies.

The unbalance forces are calculated as follows.

The weight of the various elements is obtained by multiplying area, length and

density. Unbalance centrifugal force is given by

m * r * ωωωω2

-------------- 3.1

Where m = mass of the element -9

r = Eccentricity mm



40

ω = Angular velocity rad/s

According to Indian Standard, the balanced quality grade for machine tool spindle is

G 6.3 mm/s. i.e., V = 6.3 mm/s [20]

Speed of the spindle = 1200 rpm

Frequency = 9/60 = 20 Hz

Eccentricity r = V/ω ------------- 3.2

∴ = 6.3 * 1000

40* π

= 50.134 µ

Bearing clearance = 8 µ (In spite of preloading) [21]

Total Eccentricity = (50.134 + 8) µ

= 58.134 µ

= 0.05814 mm

The unbalance forces from the different rotating members in the lathe structure were

considered and calculated as follows:

Chuck Unbalance Force

Weight of the chuck = 10 kg

Unbalance Force = m * r * ω2

= 10/9810 * 0.05814 * (40π) 2

= 9.31821 9

Spindle Unbalance Force

Weight of the spindle = πr2L * Density

= π [(352 – 20

2) + (32.5

2 – 20

2)] * 225 * 7.8 * 10

– 6

= 8.166 kg

Unbalance force = m * r * ω2

= 8.166 * 0.05814 * (40π) 2

9810



41

= 7.494 9

Gear Shaft Unbalance Force

Speed of the gear = 800 rpm

= 800/60

= 16.67 Hz

Maximum permissible deflection of the shaft

= 2 * 10– 4

* length of the shaft [20]

= 2 * 10– 4

* 450

= 0.09 mm

∴Weight of the shaft = π* 202

* 450 * 7.8 * 10– 6

= 43.26 9

Angular velocity ω = 2π9/60

= 2 * π* 800

60

= 83.77 rad/s

∴Unbalance force = 4.41 * 0.09 * (83.77) 2

9810

= 2.7850 9

There were three gears present on the shaft. From the specification of the lathe

structure the module of three gears are 2.75 mm, 2 mm and 2 mm respectively. The

unbalance forces due to these gears are as follows.

Radial clearance of the bearings = 15 µ

Permissible deflection of the gears = 10 * Module [21]

Mass of gear 1 = 19.62 9



42

Permissible deflection = 10 * 2.75

= 27.5 µ

Mass of gear 2 = 3.5 kg

Deflection = 10 * 2

= 20 µ

Mass of gear 2 = 29.43 9

Deflection = 10 * 2

= 20 µ

∴Total deflection of gear 1 = 27.5 + 15 = 42.5 µ = 0.0425 mm

Total deflection of gear 2 = 20 + 15 = 35 µ = 0.035 mm

Total deflection of gear 3 = 20 + 15 = 35 µ = 0.035 mm

Unbalance force due to gear 1 = m * r * ω2

= 2/9810 * 0.425 * (83.77) 2

= 0.5964 9


= 3.5/9810 * 0.035 * (83.77) 2

= 0.8593 9


= 3.0/9810 * 0.035 * (83.77) 2

= 0.7357 9

Pulley Shaft Unbalance Force

Speed of the pulley = 760 rpm

Angular velocity ω = 2π9/60

= 2 * π* 760

60

= 79.59 rad/s



43

Due to Weight of the pulley:

Outside diameter = 206 mm

Inside diameter = 132.35 mm

Length = 80 mm

∴Weight = π[(206/2) 2

– (132.35/2) 2] * 80 * 8 * 10

– 6

= 122.82 9

Deflection of pulley = 0.478 mm

∴Unbalance force due to pulley

= 12.52/9810 * 0.478 * (79.59) 2

= 37.92 9

Due to the Weight of the Pulley Shaft:

Weight of the pulley shaft = π * 20 2

* 400 * 7.8 * 10– 6

= 3.92 kg

Deflection of pulley shaft = 0.15 mm

∴ Unbalance force = 3.92/9810 * 0.15 * (79.59) 2

= 3.7278 9

Due to Gear on the Pulley:

Gear is present at the center of the pulley shaft

Deflection of the gear = 0.109 mm

Mass of the gear = 29.43 9

Radial clearance of the bearing = 0.015 mm

Total Deflection = 0.109 + 0.015 = 0.124 mm

∴Unbalance force due to gear on the pulley

= 3/9810 * 0.124 * (79.59) 2

= 2.3544 9

In the rotating machineries, it was also observed that the gear meshing frequencies

also contribute towards getting the response of the structure. These unbalance forces from

the gears are occurred at their corresponding gear meshing frequencies. The unbalance

force obtained is the tangential load Ft acting on the gear. Calculation of the unbalance

forces Ft on the meshing gears present on different shafts are as follows.



44

Unbalance gear-meshing force on Pulley Shaft

Speed of the pulley = 760 rpm

Gear meshing frequency = 9umber of teeth on the gear * speed of the shaft [21]

= 42 * 760/60 = 532 Hz

For non-cutting conditions Idle power = 0.3 KW from the wattmeter.

Tangential load of meshing gear Ft = 2 Mt/d --------------- (3.3)

Where Mt = 975000P/9

= 975000 * 0.3/760

Mt = 3775.57 9-mm

Diameter of the gear d = 84mm

∴ Unbalance tangential force Ft = 89.8939 9

Similarly gear-meshing forces due to gear shaft and spindle shaft has been calculated. The

summary of the unbalance forces and their corresponding frequencies were given in the

Table 3.3.

Table 3.3 Unbalance Forces and their Corresponding Frequencies

Sl. �o. Component Unbalance

force �

Frequency of

occurrence Hz

1 Chuck 9.182 20

2 Spindle 7.494 20

3 Gear shaft 2.785 13.33

4 Gear 1 on the gear shaft 0.596 13.33



7 Weight of the pulley 37.92 12.67

8 Gear on the pulley 2.354 12.67

9 Weight of the pulley shaft 3.727 12.67

10 Meshing gears on the gear shafts 67.19

43.47

533.33

11 Meshing gear on the pulley shaft 89.89 532

12 Meshing gear on the spindle shaft 28.98 600

The unbalance forces calculated above were applied at their corresponding

locations. Frequency range of 0-600 Hz was selected to know the response of these forces.

The responses in the form of vibration velocity were taken at front and rear bearings along

both the horizontal and vertical directions.



45

3.10.3 TRA�SIE�T RESPO�SE A�ALYSIS Transient response analysis was a technique used to determine the dynamic response

of a structure under the action of any general time-dependent loads. The variation of loads

can be represented in terms of vibration velocity with respect to time [22]. A defect assumed

as Destructive pitting and the effect of this defect on the vibration level was studied.

Transient dynamic analysis is carried out to determine the response of structure subjected to

time varying loads. The variation of loads can be represented in terms of amplitude versus

time. The pitting defect that is assumed is present in all teeth of the driven gear, which is

meshing with the driver gear in main spindle of the machine tool. The unwanted disturbing

forces are generated due to meshing of good gear with pitted Gear teeth. The nature of

contact of two mating pair is shown in the below figure 3.4 using band of contact as the point

of contact. This gives sufficient details about the effect and load distribution with respect to

time. The figure 3.5 shows the corresponding load transmitted Vs time for the given pitting

defect for any speed only the time varies according to the standard time calculations.

Fig �o: 3.4 Band of Contact during Pitting



46

Fig. 3.5 Load Transmitted Vs Time Graph during Pitting

Once both the gear starts to rotate, the concept of movement of band of contact is

addendum to dedendum in driven gear and dedendum to addendum in driver gear. When

meshing starts during pitting the band of contact starts from normal position to pitting

leading to zero contact. When the contact starts again the force required to over come is

high leading to fluctuation power utilization of driving motor. The figure 3.4 and 3.5 shows

how band of contact is establish during pitting and transmission of load versus time is

established.

In figure 3.5 the graph shows normal ideal power running at 0.3 KW of main Ideal

Power. This Power shoots up to 2% of Full power only when it starts to retard from its zero

contact position. This effect is due to slight backlash effect or in other words jerking of

driver gear to retard itself to its original position. The amount of fluctuation load is

calculated as 2% of Full Power per pair of Gear Teeth in meshing.

The time taken by the pinion for one revolution is 20 sec at 1200rpm. As each tooth of

gear meshes with defected tooth of pinion, it produces a triangular pulse. Thus, for one

revolution of driven gear 30 pulses were generated.



47

�ormal ideal torque and Disturbing force calculations for 1200 rpm:

Speed of the spindle, 9 = 1200RPM

Idle Power, P = 0.3 KW

Ideal Torque=2385.69 9-mm

Ideal Load=2 * Ideal torque/D

Diameter of the Driven Gear, D = 82.5mm

Ideal load = 57.83 �

Due to defect 4% of Full power is taken as Additional Power

Speed of the spindle, 9 = 1200rpm

Additional Power = 0.045 KW

Additional Torque = 36.491 9-mm

Additional Load = 2* Additional Torque/D

Diameter of the Driven Gear, D = 82.5mm

Additional Load = 8.67 �

Disturbing Load = Ideal Load + Additional Load = 57.83 + 8.67

Disturbing Load = 66.50 �

Similarly the analysis has been carried for different spindle speeds and results are

calculations and tabulated below.

Table 3.4 list of disturbing force at different speed

Sl. �o Spindle speed,

Rpm

Idle Load

�

Disturbing Load

�

1 1200 57.83 66.50

2 775 89.53 102.95

3 500 138.75 159.57

4 315 220.25 253.33

5 140 495.75 567.56

These results are applied to the graph shown in figure below and the time steps or

increments are noted and the effect is studied in transient analysis.



48

CHAPTER 4

EXPERIME�TAL A�ALYSIS

4.1 EXPERIME�TAL SETUP

Experiments were carried out on the enterprise 1330 precision lathe. This lathe has

eight spindle speeds ranging from 54 to 1200 RPM. The specification of the lathe is given in

Table 4.1. Fig. 4.1 shows the enterprise 1330 precision lathe.

Table 4.1: Specification of Enterprise –1330

1 Center height 175 mm

2 Swing over Bed 350 mm

3 Swing over Cross slide 200 mm

4 Swing in Gap 520 mm

5 Width of gap in front of Face plate 130 mm

6 Spindle nose 4”-D1 Cam lock

7 Morse Taper in spindle sleeve MT 3

8 Spindle Bore 41 mm

9 Power of Motor (Main motor) 2.25 K.W. (3 H.P)

10 Range of spindle speed (8 9os.) 54- 1200 RPM

11 Cross slide travel 210 mm

12 Compound slide travel 100 mm

13 Tai Tail -stock Quill travel 140 mm

14 Capacity of Sq. Tool Post 20 x 20 mm Shank

15 Longitudinal feed range (36 9os.) 0.045 – 0.676 mm/rev

16 Metric Thread range (11 9os.) 0.5 – 6.0 mm

17 Inch Thread Range (36 9os.) 4 – 60 T.P.I

18 Lead Screw Pitch (1” diameter) 4 T.P.I / 6 mm pitch



49

Fig. 4.1 Enterprise 1330 Precision Lathe



50

4.2 MACHI�E CO�DITIO� TESTER T 30

Machine Condition Tester is the instrument used to carry out the experiment. It has

gained application in industries as a practical bearing-monitoring tool, providing relevant

information on bearing condition. The Machine Condition Tester is based on high frequency

acceleration signal referred as shock pulse. Machine Condition Tester is the instrument used

to monitor rolling element bearings and detect wear and damage at an early age. Planned

replacements will help to reduce downtime and prevent bearing failures. A ring surface of a

bearing always has certain roughness even when they are new, which causes low acoustic

emission. During the usage, cracks and pits appear due to which small particles of metal

comes off and these are circulated within the bearing. As the fault area pass into caution

zone, they cause small knocks, which are transmitted into bearing housing as a discontinuous

knocks. More severe the crack, stronger will be the knock and pulses. These pulses will have

high frequency range. Table 4.2 shows the specification of Machine Condition Tester T 30.

Fig 4.3 shows the Machine Condition Tester T 30.

Fig. 4.2: Machine Condition Tester T 30.

Machine Condition Tester T 30 is available in three different versions: [21]

� BASIC

� LOGGER

� EXPERT



51

“Basic” measures vibration severity, shock pulses and temperature. It has no data

logging functions. Measuring results are recorded manually. “Logger” measures the same

quantities. In connection with the SPM software it gets its measuring instructions from a

computer and uploads measuring results via cable to the computer. “Expert” has all the

logger features. In addition, it uses the EVAM method for vibration spectrum analysis.

Machine condition Tester combines the functions of a shock pulse meter, vibration meter,

and tachometer. It requires few input data and allows an instant interpretation of machine

condition by supplying,

• Direct indication of machine vibration and bearing condition in terms of good -

reduced –bad

• Digital display of shock values and vibration severity.

With the Machine Condition Tester T 30, it is possible to monitor all significant aspects of

mechanical machine condition during a single inspection round like the mechanical

condition of the rolling element bearings and the general machine condition due to the effect

of structural looseness and imbalance on machine vibration. The machine condition tester T

30 is based on two different methods for condition monitoring. Each method is tailored to

supply the most accurate and useful information on the machine condition.

Table 4.2: Specification of Machine Condition Tester T 30

1 Measuring range, SPM - 9 to 99 dBsv

2 Resolution, SPM 1 dBsv

3 Measuring range, VIB 0.2 – 99.9 mm/sec RMS

4 Resolution, VIB 0.1 mm/sec

5 Accuracy, VIB ± (0.1 mm/sec + 2% of reading)

6 Measuring range, TAC 10 to 19,999 rpm optical

7 Measuring distance Max. 0.6 m (2 ft.)

8 Resolution, TAC 1 rpm

9 Accuracy, TAC ± (1 rev. + 0.1 % of reading)

10 Temperature range 0o to 50

o C

11 Power 6 x 1.5 V LR6 cells

12 Size, T 30 255 x 105 x 60 mm

13 Weight, T 30 0.85 kg

14 Display Liquid crystal



52

4.3 MEASURI�G PARAMETERS

Vibration ranks among the most destructive forces in the machine tools. Vibration

influences the operation, performance and life expectancy of the machine tools. The

vibratory signatures measured will be of a greater value in knowing the machine condition.

Since lathe is a complex system, it is not possible to monitor all the parameters. The

parameters selected for measurement are vibration velocity. Vibration velocity is the

parameter to evaluate the severity of the vibration of the lathe measured in RMS value. In

driving spindle, the most frequent failure is due to spindle bearings.

4.4 MEASUREME�T LOCATIO� The proper selection of the measurement location is important and care should be

taken to select the measurement location and direction of measurement to ensure that the

most effective data is obtained. The measurement locations generally selected are the

bearing housing of a lathe because it is through these housing that the force of vibration of

the rotating elements are transmitted. The measurements are made on the front and rear side

of the bearing housing in the horizontal and vertical directions respectively. When the

dominant mechanical defect in a machine is unbalance, vibration transducers which are

mounted on each bearing housing in horizontal direction will be adequate to detect such

imbalance. If the defect in the machine is misalignment, to insure its presence, measurements

in both horizontal and vertical directions are needed.

4.5 EXPERIME�TAL PROCEDURE

4.5.1 VIBRATIO� VELOCITY MEASUREME�T

For measuring vibration velocity Machine Condition Tester T 30 was used. It

measures vibration severity in the range of 0.2 to 99.9 mm/s. To measure the vibration one

end of the vibration transducer was connected to the input marked VIB of T 30 instrument

and the other end of the cable was connected to the vibration transducer and switch on the T

30 to the VIB mode. The same measuring points were selected for measuring the vibration.

Machine class number is set to class I according to ISO 2372 recommendations since the

power of the motor was 2.25 KW [16]. To measure the vibration velocity, transducer with the

magnetic base was placed at the front and rear bearing housings along horizontal and

vertical directions respectively. The readings were taken for different spindle speeds. After



53

taking the readings, the data was transferred back to the computer for the further analysis.

Table 4.5 shows the experimental values for different spindle speeds at the front and rear

bearing

Table 4.3: vibration velocity at different spindle speeds

Sl. �o. Spindle speed

(rpm)

Vibration velocity at Front

Bearing mm/s

Vibration velocity at

Rear Bearing mm/s

Horizontal Vertical Horizontal Vertical

1 140 0.21 0.10 0.12 0.10

2 315 0.24 0.13 0.16 0.11

3 500 0.29 0.17 0.19 0.16

4 775 0.35 0.19 0.20 0.18

5 1200 0.39 0.22 0.23 0.21



54

CHAPTER 5

RESULTS A�D DISCUSSIO�

5.1 MODAL A�ALYSIS

Modal analysis was carried out to obtain the natural frequencies and its mode shapes. The

natural frequencies and mode shapes were important parameters in the design of a structure

for dynamic loading conditions. The first ten mode shapes were computed. The Fig. 5.1

shows the first mode shape of the lathe structure. When modal analysis is performed on a

lathe, it reveals the possible resonant conditions and these resonant conditions with their

frequencies of occurrence and their description are given in the Table 5.1. Mode shapes are

defined by the amplitude of displacements of all the mass points during the vibration of the

structure at natural frequencies. From the Fig. 5.1 it was observed that the rocking of the

bed was occurring in the X- direction during the first mode shape of resonant frequency

57.199 Hz. Similarly the five different mode shapes were shown in the Fig. 5.2 to Fig. 5.5.

Modal analysis was used as a starting point for a harmonic response analysis. The results

obtained were used in the harmonic response analysis.

Table 5.1: Mode Shapes and Its �atural Frequencies

Mode shapes �atural frequencies in Hz Description

1 57.199 Rocking of the bed in X- direction

2 71.388 Bending of the carriage.

3 83.861 Bending of the right and left leg.

4 88.477 Twisting of the right leg

5 119.29 Twisting of the bed.

6 151.67 Torsion movement of the carriage.

7 152.96 Deformation in the right leg.

8 169.55 Torsion movement of the left leg

9 179.29 Deformation in the left leg.

10 199.62 Higher mode deformation in the left leg.



55

Fig. 5.1: First Mode Shape of a Lathe Structure

Fig. 5.2: Second Mode Shape of a Lathe Structure



56

Fig. 5.3: Third Mode Shape of a Lathe Structure

Fig. 5.4: Fourth Mode Shape of a Lathe Structure



57

Fig. 5.5: Fifth Mode Shape of a Lathe Structure

5.2 HARMO�IC RESPO�SE A�ALYSIS

After the modal analysis, next step is to carry out harmonic response analysis.

Harmonic response analysis was used to determine the response of the lathe structure to the

unbalance forces. Fig 5.6 to Fig 5.17 shows the response of the structure in terms of

vibration velocity in the frequency domain measured at the front and rear bearing housing

along horizontal and vertical directions respectively. Fig.5.6 shows the vibration velocity at

front bearing along horizontal and vertical direction. The effect of unbalance forces from the

chuck and the spindle are as shown in the Fig.5.6 and gives the information about the

vibration level during the operation. The value of vibration velocities by the chuck and the

spindle at their operating frequency of 20 Hz were observed. Also, as it is seen from the Fig.

5.6 the resonance was occurring at the first natural frequency i.e. at 57.199 Hz. Fig.5.7

shows the vibration velocity at the rear bearing. Similarly Fig. 5.8 to Fig. 5.17 shows the

vibration velocities from the different elements at front and rear bearing.



58

Fig. 5.6: Vibration Velocity due to Chuck and Spindle at Front Bearing

Fig. 5.7: Vibration Velocity due to Chuck and Spindle at Rear Bearing



59

Fig. 5.8: Vibration Velocity due to Gears at Front Bearing

Fig. 5.9: Vibration Velocity due to Gears at Rear Bearing



60

Fig. 5.10: Vibration Velocity due to Pulleys at Front Bearing

Fig. 5.11: Vibration Velocity due to Pulleys at Rear Bearing



61

Fig. 5.12: Vibration Velocity due to Pulley Shaft at Front Bearing

Fig. 5.13: Vibration Velocity due to Pulley Shaft at Rear Bearing



62

Fig. 5.14: Vibration Velocity due to Gear Shaft at Front Bearing

Fig. 5.15: Vibration Velocity due to Gear Shaft at Rear Bearing



63

Fig. 5.16: Vibration Velocity due to Spindle Shaft at Front Bearing

Fig. 5.17: Vibration Velocity due to Spindle Shaft at Rear Bearing



64

Further, the vibration levels in the frequency domain are transformed to vibration

levels in time domain. This is to obtain the RMS value of the vibration velocity of various

signals, which are at different frequencies. For this Fast Fourier Transformation analysis

technique was used to convert the vibration velocity from the frequency domain to time

domain. Fig.5.18 to Fig.5.21 shows the vibration velocities due to different elements

measured in the time domain. Fig. 5.18 shows the vibration velocity in time domain

measured at front bearing along horizontal direction. It is the result of harmonic analysis in

frequency domain converted to time domain. The figure depicts the effect of unbalance forces

of individual elements on the machine tool. The combined effect of these unbalance forces is

shown as RMS velocity having the value of 0.36477 mm/s. Fig. 5.19 shows the vibration

velocity in time domain measured at front bearing along vertical direction. The RMS

vibration velocity for the front bearing along vertical direction was 0.1957 mm/s. Similarly;

the RMS vibration velocities in horizontal and vertical direction for rear bearing are 0.1791

mm/s and 0.239 mm/s respectively as shown in the Fig. 5.20 and Fig. 5.21.

Fig. 5.18: Vibration Velocity in Time Domain at Front Bearing along Horizontal

Direction



65

Fig. 5.19: Vibration Velocity in Time Domain at Front Bearing along Vertical Direction

Fig. 5.20: Vibration Velocity in Time Domain at Rear Bearing along Horizontal

Direction



66

Fig. 5.21: Vibration Velocity in Time Domain at Rear Bearing along Vertical Direction

5.3 TRA�SIE�T RESPO�SE A�ALYSIS

The vibration velocities obtained from an induced defect on the driven gear is as

shown respectively to horizontal and vertical directions to location front and rear bearing.

The additional power added is 2% of full power in order to over come the defect. [6]

Fig. 5.22 shows vibration velocity for 1200 rpm at front and rear location for

horizontal and vertical direction. The values obtained are 0.016 mm/s in horizontal and

0.0011 mm/s in vertical direction at front bearing and 0.020 mm/s in horizontal and 0.00085

mm/s in vertical direction at rear bearing.

From Fig 5.22 to Fig 5.26 the vibration velocity at front and rear location in

horizontal and vertical direction are shown for 775 rpm, 500 rpm, 315 rpm, and 140 rpm

respectively.

Also from the graphs it was observed that vibration velocity increases due to

reduction of speed. This is due to increases in force of the impact between Gear elements and

the time gap reduces between each Gear meshing and the Forced Vibration gets time to

propagate as discussed in 2.10.



67

Fig. 5.22: Vibration Velocity for a Gear Defect along Horizontal and vertical Directions

at two bearing points at 1200 rpm





68







69



Table 5.2 Vibration Velocities for Different Speed at two Bearing Locations

Speed in rpm Velocity in X-

direction at

Bearing1

(mm/sec)

Velocity in X-

direction at

Bearing 2

(mm/sec)

Velocity in Y-

direction at

Bearing 1

(mm/sec)

Velocity in Y-

direction at

Bearing 2

(mm/sec)

1200 0.016 0.020 0.0011 0.00085

775 0.028 0.032 0.0025 0.0014

500 0.048 0.056 0.010 0.005

315 0.10 0.085 0.018 0.012

140 0.30 0.32 0.014 0.0085



70

To discuss about Transient Analysis of Lathe structure due to Gear defect the Vibration

velocity of each must be studied as cases according to the sped limits.

Case 1 for 1200 rpm [Fig 5.22] the vibration velocity is 0.016 in horizontal and

0.0011 in vertical direction at bearing point 1. Vibration velocity is 0.020 in horizontal and

0.00085 in vertical directions at bearing point 2. Here disturbing force is 66.50 9 and the

time for forced vibration to propagate will be roughly of order 2e-12

. This time gap between

successive gear impacts will not permit forced vibration to propagate and hence the

vibration velocity will be less.

Case 2 for 775 rpm [Fig 5.23] the vibration velocity is 0.028 in horizontal and

0.0025 in vertical direction at bearing point 1. Vibration velocity is 0.032 in horizontal and

0.00014 in vertical directions at bearing point 2. Here disturbing force is 102.95 9 and the

time for forced vibration to propagate will be roughly of order 2e-10

this time gap between

successive gear impacts will not be able to propagate same as 1200 rpm and hence the

vibration velocity is slightly more than 1200 rpm due to load difference.

Case 3 for 500 rpm [Fig 5.24] the vibration velocity is 0.048 in horizontal and 0.010

in vertical direction at bearing point 1. Vibration velocity is 0.056 in horizontal and 0.005 in

vertical directions at bearing point 2. Here disturbing force is 159.57 9 and the time for

forced vibration to propagate will be roughly of order 2e-09

.This time gap between

successive gear impacts starts forced vibration to propagate. This is minimum value where

the vibration velocity starts to increase.


in vertical direction at bearing point 1. Vibration velocity is 0.085 in horizontal and 0.012 in

vertical directions at bearing point 2. Here disturbing force is 253.33 9 and the time for


.This time gap between

successive gear impacts is high and forced vibration gets time to propagate. This is the value

where the vibration velocity shows uniform motion as discussed in Article 2.8 Page 27.


in vertical direction at bearing point 1. Vibration velocity is 0.032 in horizontal and 0.0085

in vertical directions at bearing point 2. Here disturbing force is 567.56 9 and the time for


.This time gap between successive

gear impacts is very high and forced vibration gets enough time to impact and propagate.



71

In 1400 rpm the vibration velocity shows uniform motion but the values are in higher

order due to high load.

The vibration velocity is distributed in horizontal direction more than in vertical

direction because Lathe structure is stiffer in vertical direction in any speed variation it

shows the same trend. [24]

From the Table 5.2 it can be concluded that the vibration velocity at rear bearing was

more compared to the vibration velocity at front bearing. The reason for this is, defective

Gear is located near front Bearing and rest of the Spindle Shaft is over hanging and

supported by rear bearing. This generates lot of disturbance to rear bearing.

It can be observed that as speed increases vibration velocity reduces and when speed

decreases the vibration velocity increases. The graph obtained, that is from Fig 2.2 to Fig

2.6, shows the same trend which is discussed in the 2.10.

5.4 VIBRATIO� VELOCITY A�ALYSIS The vibration velocity in RMS value was measured at front and rear bearing housing

shown in Table 4.3.

The vibration velocity measured for different spindle speeds were plotted as shown in

Fig. 5.27 for front bearing and Fig. 5.28 for the rear bearing. It was observed that the

vibration velocity increases with the increase in the spindle speed.

Also the vibration velocity measured in the horizontal direction was more compared

with the vertical direction because the lathe structure is stiffer in the vertical direction.

The vibration velocity along horizontal direction was found to be 0.39 mm/s front

bearing and 0.23mm/s rear bearing which is well within the vibration severity chart

recommended by ISO 2372 for machine class I.



72

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 200 400 600 800 1000 1200

Spindle speed in rpm

Vibration velocity mm/s

horizontal

vertical

Fig. 5.27: Variation of Vibration Velocity at Front bearing for different Spindle Speeds

0

0.05

0.1

0.15

0.2

0.25

0.3

0 200 400 600 800 1000 1200

Spindle speed in rpm

Vibration velocity mm/s

horizontal

vertical

Fig. 5.28: Variation of Vibration Velocity at Rear bearing for different Spindle Speeds



73

From the Fig 5.18 it was observed that the RMS vibration velocity was found to be

0.36477 mm/s and the experimental value measured at front bearing housing at 1200 rpm

along horizontal direction was 0.39 mm/s. It was observed that the theoretical value obtained

was nearer to the experimental value.

The difference may be due to the wearing and ageing of the lathe structure. From the

Fig 5.19, RMS vibration velocity is 0.1957 mm/s and the corresponding experimental value

measured at front bearing housing at 1200 rpm along vertical direction is 0.22 mm/s and

was nearer to the experimental value. Hence, the Harmonic Response Analysis was found to

be the reliable methods to confirm the effect of unbalance forces causing undesirable

vibrations on the machine tool structure.

The Table 5.3 below shows the vibration velocity at front and rear bearings obtained

by Harmonic, Transient and Experimental method along horizontal and vertical directions

respectively.

Table 5.3 Comparison of Vibration Velocity of Different Analysis

Location Theoretical

Horizontal vibration

mm/s

Experimental

Analysis

Horizontal

vibration

mm/s

Theoretical

Vertical vibration

mm/s

Experimental

Analysis

Vertical

vibration

mm/s Harmonic

Analysis

Transient

Analysis

with Gear

Defect

Harmonic

Analysis

Transient

Analysis

with Gear

Defect

front

bearing

0.36477 0.016 0.39 0.1957 0.0011 0.22

rear

bearing

0.1791 0.020 0.23 0.239 0.00085 0.21

In transient dynamic analysis, the value of vibration velocity of front bearing at 1200 rpm

was found to be 0.016 mm/s in horizontal and 0.0011 mm/s in vertical direction. At rear

bearing the vibration velocity was found to be 0.020 mm/s and 0.00085 mm/s in horizontal

and vertical direction respectively. This may be due to the assumptions made that; all the

other machine components of lathe machine tool except driven gear in gear system are in

good condition.



74

5.5 SUMMARY OF THE PRESE�T WORK

The objective of the project was to analyze the lathe structure numerically. For this it

was required to make the lathe structure. Finite element software A9SYS 7.1 was used to

develop the lathe structure. Modal analysis was carried to determine the natural frequencies

and its mode shapes. Harmonic response analysis was done to study the behavior of the

structure for the unbalanced forces developed by rotating masses in the structure. Transient

analysis was carried to study the vibration analysis by inducing defects on the Gear.

Experiments were carried on enterprise 1330 lathe by using Machine Condition

Tester T 30 to measure the vibration velocity at different spindle speeds. The vibration

signals were measured on the front and rear bearing housings along horizontal and vertical

directions. The experimental results obtained were used to analyze the condition of the

bearings and also to study the level of vibration on the lathe. Finally theoretical results

obtained by harmonic response analysis were compared with the experimental results.



75

CHAPTER 6

CO�CLUSIO�

6.1 CO�CLUSIO�

Condition monitoring is applied as a technique for improving productivity, efficiency

and reliability of the machine components. It involves monitoring the health of the machine

tool. Several condition-monitoring techniques are available to study the health of the

machine tool. Among the various techniques, vibration monitoring is one of the successful

techniques of predicting the health of the machine structures.

In the present work, lathe structure was analyzed both theoretically and

experimentally. For the theoretical analysis, finite element software A9SYS 7.1 was used.

Finite Element Analysis has become the powerful tool for the structural analysis of the lathe.

The lathe model was developed by using the elements such as elastic SHELL 63, BEAM 188,

MATRIX 27 and MASS 21 to determine the static and dynamic characteristics of the

structure. Modal analysis was carried out to determine the natural frequencies and the mode

shapes. From the modal analysis it was observed that the first natural frequency was

occurring at 57.199 Hz. But the operating frequency of the lathe is 20 Hz which is well below

the possible resonance condition to occur.

Harmonic response analysis was carried out to determine the response of the

structure due to unbalance forces. It was observed that the vibration velocity measured at

front bearing along horizontal direction is found to be 0.36477 mm/s and along vertical

direction 0.197 mm/s, for 1200 rpm. The experimental data obtained from Machine

Condition Tester T 30 at front bearing was 0.39 mm/s along horizontal direction and 0.22

mm/s along vertical direction for 1200 rpm. It was observed that the vibration velocity

measured along the horizontal direction was more compared with the vertical direction

because the lathe structure may be stiffer in the vertical direction.

The RMS vibration velocity from the harmonic response analysis in time domain was

compared with the experimental values. From the comparison it was observed that the

theoretical value was in close agreement with the experimental value. Hence the Harmonic

Response Analysis was found to be the reliable method to confirm the effect of unbalance

forces on the machine tool structure.



76

In Transient dynamic analysis, the value of vibration velocity of front bearing at 1200

rpm was found to be 0.016 mm/s in horizontal and 0.0011 mm/s in vertical direction. At rear

bearing the vibration velocity was found to be 0.020 mm/s and 0.00085 mm/s in horizontal

and vertical direction respectively. This may be due to the assumptions made that; all the

other machine components of lathe machine tool except driven gear in gear system are in

good condition.

Form the Transient analysis, the vibration velocity decreases due to increase in speed

when gear defect is considered. This is due to decrease in impact load on the gear teeth and

decrease in time for the propagation of the forced vibration signals. In total the Transient

dynamic analysis was helpful to find out the effects of gear defects on lathe structure.

6.2 SCOPE FOR FUTURE WORK

� The present work was done by considering vibration velocity as the

parameters. The work can be extended by considering the other parameters

like temperature, acoustic emission signals and wear debris.

� The work can be extended by considering the cutting conditions for the

different combinations of tool and work material. The harmonic response

analysis can be carried out by considering various spindle speeds.

� The work can be extended by considering the different types of pitting

dimensions and location of pitting.



77

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