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

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 A SYS 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
A SYS 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
E TERPRISE 1330 lathe for different spindle speeds by using MACHI E
CO DITIO 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 A SYS 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
Load Effects on

ASA [6] discuses about Minimizing

A4 Gear Vibration Diagnostic Parameter and expressed formulation and

fluctuation load during destructive pitting. A change to the calculation of A4 is required to
minimize the effect of a fluctuating load on A4. This change, A4 reset, is made when the
load increases or decreases by a given percentage. For this application, a 10 percent load
change was used. For

A4 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

ASA 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 A4. 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,

A4, and

B4 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
2) Imbalance
3) Mechanical looseness
4) Critical speed excitation
5) Coupling lock-up
6) Uneven loading of a machine
7) Shaft rubbing
8) Cracked shaft
9) Rotor instability
10) Electric motor defects

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11) Gear wear
12) Gear defects
13) Gearwheel backlash
14) Bearing defects
15) Tilting pad wear
16) Blade/vane defects
17) Blade fouling
18) Blade rubbing
19) Steam leaks
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
I

II
III

IV
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Description
Individual parts of engines and machines integrally connected with the
complete machine in its normal operating conditions e.g.: electric motors up
to 15KW
Medium sized machines Eg: Electric motors up to 15-75 KW
Large prime movers and other large machines with rotating masses on rigid
and heavy foundations, which are relatively stiff in the direction of
measurement.
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
0.29

Examples of quality judgment for separate classes of machines
Small
Medium
Large
Turbo
Machines
Machines
Machines
Machines
Class – I
Class-II
Class-III
Class-IV
A

0.45

A

0.71

B

1.12

A

C

B

A
B

1.80

B

2.80
4.50

C

7.10
11.20

C
D

C

18.00

D

28.00

D

D

45.00

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.
ot 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
Frequency of dominant
fault
vibration (Hz or rpm/60)
Rotating
1 x rpm
members out
of balance
Misalignment Usually 1 x rpm Often 2 x
and bent shaft rpm. Sometimes 3 and 4 x
rpm
Damaged
Impact
rates
for
the
rolling
individual
bearing
component. Also vibrations
element
bearings (ball, at high frequencies (2 to 60
Hz) often related to radial
rotor, etc.)
resonance in bearings
Journal
Sub-harmonics of shaft rpm
bearings loose exactly ½ or 1/3 x rpm
in housing
Oil film whirl Slightly less than half shaft
or whip in speed (42% to 48%)
journal
bearings
Hysteresis
Shaft critical speed
whirl

Direction
Radial

A common cause of excess
vibration in machinery.

Radial
and axial

A common fault.

Radial
and axial

Uneven vibration levels, often
with shocks.

Primarily
radial

Looseness may only develop at
operating speed and temperature
(e.g. turbo machines).
Applicable to high-speed (e.g.,
turbo machines).

Primarily
radial

Primarily
radial

Damaged or Tooth meshing frequencies Radial
worn gears
(shaft rpm x number of and axial
teeth) and harmonics

Mechanical
2 x rpm
looseness
Faulty
belt 1, 2, 3 and 4 x rpm of belt
drive
Unbalanced
reciprocating
forces
and
couples
Electrically
induced
vibrations

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Remarks

Radial

Vibrations excited when passing
through critical shaft maintained
at higher shaft speeds. Can
sometimes be checking tightness
of rotor components.
Sidebands around tooth meshing
frequencies indication (e.g.,
eccentricity)
at
frequency
corresponding
to
spacing.
ormally only detectable with
very narrow-basis and cepstrum.
Also sub and interharmonics, as
for loose journal.
The precise problem can usually
be identified virtual help of a
stroboscope.

1 x rpm and/or multiples Primarily
for higher order unbalance radial

1 x rpm or 1 or 2 times Radial
synchronous frequency
and axial

16

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.

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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.
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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

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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
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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
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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
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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.

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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
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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
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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.

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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

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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,

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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.
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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
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3.5 A SYS 7.1
A SYS 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 A SYS 7.1 Family of Products continues A SYS, 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]

A SYS 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 A SYS 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.
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Harmonic Analysis: Used to determine the response of a structure to harmonically timevarying 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 O E, 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 A SYS 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]

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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 ame

:
:

odes

SHELL 63
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.
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Element ame

:

MATRIX 27

:

odes

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

Element ame

:
:

odes

BEAM 188
I, J, K



Material Properties

EX, PRXY, DE S, 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 ame
odes

:

MASS 21

:

I



Real Constants

MASSX, MASSY, MASSZ, IXX, IYY, IZZ

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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 A SYS 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

Poissons

Density

Elasticity

Ratio

Kgf/mm3

Kgf/mm2
1

Cast iron
2

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9700

0.27

7.9e-9

Steel

21000

0.3

7.8e-10

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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

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Fig. 3.2: Unbalance Components of a Lathe

Fig. 3.3: Head Stock Assembly of a Lathe

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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 * ω2
Where

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

m = mass of the element r = Eccentricity mm

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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 = /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

Spindle Unbalance Force
Weight of the spindle = πr2L * Density
= π [(352 – 202) + (32.52 – 202)] * 225 * 7.8 * 10– 6
= 8.166 kg
Unbalance force

= m * r * ω2
= 8.166 * 0.05814 * (40π) 2
9810

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= 7.494
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
= π* 202 * 450 * 7.8 * 10– 6

∴Weight of the shaft

= 43.26
Angular velocity ω

= 2π /60
= 2 * π* 800
60
= 83.77 rad/s

∴Unbalance force

= 4.41 * 0.09 * (83.77) 2
9810
= 2.7850

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

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= 10 * 2.75
= 27.5 µ

Mass of gear 2

= 3.5 kg

Deflection

= 10 * 2
= 20 µ

Mass of gear 2

= 29.43

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


= m * r * ω2
= 3.5/9810 * 0.035 * (83.77) 2
= 0.8593


= m * r * ω2
= 3.0/9810 * 0.035 * (83.77) 2
= 0.7357

Pulley Shaft Unbalance Force
Speed of the pulley = 760 rpm
Angular velocity ω

= 2π /60
= 2 * π* 760
60
= 79.59 rad/s

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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

Deflection of pulley

= 0.478 mm

∴Unbalance force due to pulley
= 12.52/9810 * 0.478 * (79.59) 2
= 37.92
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

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

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
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.
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Unbalance gear-meshing force on Pulley Shaft
Speed of the pulley

= 760 rpm

Gear meshing frequency = umber 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
Where

Ft = 2 Mt/d

--------------- (3.3)

Mt = 975000P/
= 975000 * 0.3/760
Mt = 3775.57 -mm

Diameter of the gear d = 84mm
∴ Unbalance tangential force Ft = 89.8939
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

1
2
3
4
5
6
7
8
9
10

Chuck
Spindle
Gear shaft
Gear 1 on the gear shaft
Weight of the pulley
Gear on the pulley
Weight of the pulley shaft
Meshing gears on the gear shafts

11
12

Meshing gear on the pulley shaft
Meshing gear on the spindle shaft

Unbalance
force
9.182
7.494
2.785
0.596
0.859
0.735
37.92
2.354
3.727
67.19
43.47
89.89
28.98

Frequency
of
occurrence Hz
20
20
13.33
13.33
13.33
13.33
12.67
12.67
12.67
533.33
532
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.

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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

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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.
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ormal ideal torque and Disturbing force calculations for 1200 rpm:
Speed of the spindle,
Idle Power,

= 1200RPM
P = 0.3 KW
Ideal Torque=2385.69 -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,

= 1200rpm

Additional Power = 0.045 KW
Additional Torque = 36.491 -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.

Sl. o
1
2
3
4
5

Table 3.4 list of disturbing force at different speed
Spindle speed,
Idle Load
Disturbing Load
Rpm
1200
57.83
66.50
775
89.53
102.95
500
138.75
159.57
315
220.25
253.33
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.
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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 os.)

54- 1200 RPM

11

Cross slide travel

210 mm

12

Compound slide travel

100 mm

13

Tai Tail -stock Quill travel

14

Capacity of Sq. Tool Post

20 x 20 mm Shank

15

Longitudinal feed range (36 os.)

0.045 – 0.676 mm/rev

16

Metric Thread range (11 os.)

0.5 – 6.0 mm

17

Inch Thread Range (36 os.)

4 – 60 T.P.I

18

Lead Screw Pitch (1” diameter)

4 T.P.I / 6 mm pitch

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Fig. 4.1 Enterprise 1330 Precision Lathe

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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
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“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
2
3
4
5
6
7
8
9
10
11
12
13
14

Measuring range, SPM
Resolution, SPM
Measuring range, VIB
Resolution, VIB
Accuracy, VIB
Measuring range, TAC
Measuring distance
Resolution, TAC
Accuracy, TAC
Temperature range
Power
Size, T 30
Weight, T 30
Display

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- 9 to 99 dBsv
1 dBsv
0.2 – 99.9 mm/sec RMS
0.1 mm/sec
± (0.1 mm/sec + 2% of reading)
10 to 19,999 rpm optical
Max. 0.6 m (2 ft.)
1 rpm
± (1 rev. + 0.1 % of reading)
0o to 50o C
6 x 1.5 V LR6 cells
255 x 105 x 60 mm
0.85 kg
Liquid crystal

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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
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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

Vibration velocity at Front

Vibration velocity at

(rpm)

Bearing mm/s

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

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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.

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Fig. 5.1: First Mode Shape of a Lathe Structure

Fig. 5.2: Second Mode Shape of a Lathe Structure

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Fig. 5.3: Third Mode Shape of a Lathe Structure

Fig. 5.4: Fourth Mode Shape of a Lathe Structure

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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.

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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

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Fig. 5.8: Vibration Velocity due to Gears at Front Bearing

Fig. 5.9: Vibration Velocity due to Gears at Rear Bearing
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Fig. 5.10: Vibration Velocity due to Pulleys at Front Bearing

Fig. 5.11: Vibration Velocity due to Pulleys at Rear Bearing
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Fig. 5.12: Vibration Velocity due to Pulley Shaft at Front Bearing

Fig. 5.13: Vibration Velocity due to Pulley Shaft at Rear Bearing

M-Tech Thesis

61

P.E.S.C.E., Mandya


2004 /2005

Fig. 5.14: Vibration Velocity due to Gear Shaft at Front Bearing

Fig. 5.15: Vibration Velocity due to Gear Shaft at Rear Bearing

M-Tech Thesis

62

P.E.S.C.E., Mandya


2004 /2005

Fig. 5.16: Vibration Velocity due to Spindle Shaft at Front Bearing

Fig. 5.17: Vibration Velocity due to Spindle Shaft at Rear Bearing

M-Tech Thesis

63

P.E.S.C.E., Mandya


2004 /2005

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

M-Tech Thesis

64

P.E.S.C.E., Mandya


2004 /2005

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
M-Tech Thesis

65

P.E.S.C.E., Mandya

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

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

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