Vibration

CONTENTS

SL. TOPIC PAGE

NO. NO.

1. INTRODUCTION 1

2. FUNDAMANTALS OF VIBRATION 2

3. SOURCES OF VIBRATION 20

4. VIBRATION MEASUREMENT 44

5. VIBRATION ANALYSIS 66

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1. INTRODUCTION

Everyone in the course of our daily life encounters the phenomenon of vl 'bration.

The effect of vibration is not only physically unpleasant but may also weaken the

structure. It must therefore be regarded as a most undesirable condition, which must be

eliminated for both comfort and safety.

On the contrary, the vibration is often useful and may be essential in some

application. Occasionally, for example vibration can be used to unmix things; as in

sieves and other sorting devices, for conveying grain from one place to another, concrete

will flow far -more readily into the furthermost recesses when it is poured into shuttering

if it is suitably vibrated. Also vibration has got application in medical practice. For

instance, it is used to massage away patients unwanted bulges and for removal of kidney

stones.

Large sums of money are spent nowadays on the study of various forms of

vibration. The subject of vibration has acquired considerable importance, with the

increasing pace of industrial and technological developments in the world over there has

been a phenomenal increase in the speed and power of industrial machines. All devices

which have mass and elasticity are capable of vibrating, however, rigid, they might seem.

Whether it is desired to use vibration as a tool for failure and maintenance

prediction or for using vibration control measure to avoid discomfort and failure, it is

necessary to have a proper understanding of the subject. -This course material is

concerned with fundamentals of vibration, sources of vibration, measurement of vibration

and vibration analysis of rotating machines.

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2. FUNDAMENTALS OF VIBRATION

2.0 INTRODUCTION

The study of vibration is concerned w' ith oscillatory motions of bodies and the

forces associated with them. All bodies possessing mass and elasticity are capable of

vibration. Thus most engineering machines and structures experience vibration to some

degree. The effects of vibration depend on the magnitude , frequency and duration of the

vibration. Also, some times the vibration of a system emits lot of noise, which is harmful

from human point of view.



2.1 WHAT IS VIBRATION

Vibration is defined as the resp onse of an elastic system to a dynamic disturbance.

There are two general classes of vibrations - free and forced. Free vibration takes

place when a system oscillates under the action of forces inherent in the system itself, and

when external impressed forces are absent. The system under free vibration will vibrate

at one or more of its natural frequency, which is a property of dynamic system

determined by its mass and stiffness distribution.

Vibration that takes place under the excitation of external forces is called forced

vibration.

The simplest way to show vibration is to follow the motion of a weight suspended

at the end of a spring as shown in figure 2. I. This is typical of all machines since, they

too have weight and spring-like quality namely elasticity.

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Until a force is applied to the weight to cause it to move, we have no vibration.

By applying an upward force, the weight would move upward, compressing the spring.

If we release the weight, it would drop below its neutral position to some bottom limit of

travel, where the spring would stop the weight. The weight would travel upward through

the neutra position to tie top limit of motion, and then back again through the neutral

position. This is vibration! This motion will dampen with time unless force is applied

again.



2.2 CHARACTERSTICS OF VIBRATION

A lot can be learned about a machine's condition and mechanical problems by

simply not'mg its vibration characteristics. Refem'ng to the weight suspended on a

spring, we can study the detailed,characteristics of vibration by plotting the movement of

the weight against time. This plot is shown in figure 2.2.

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The simplest form of vibration motion is simple harmonic motion. The motion of

the weight from its neutral position, to the top limit of travel back through the neutral

position to the bottom limit of travel, and its return to the neutral position, represents one

cycle of motion. This one cycle of motion has all the characteristics needed to measure

the vibration. Continued motion of the weight will simply be repeating these

characteristics. When the instantaneous displacement of the mass is plotted against time,

the motion takes sinusoidal form as shown in figure.

Fig: 2.2 CHARACTERSICS OF VIBRATION

As vibrations are movements of the machines around a rest point, they may be

quantified in terms of' displacement, velocity or acceleration. These characteristics of

vibration are measured to determine.the amount of severity of the vibration. The

displacement, velocity or acceleration of a vibration is often 17eferred to as the

'amplitude' of the vibration.



In terms of the operation of the machine, the vibration amplitude is the indicator

used to determine how bad or good the operation of the machine may be. The greater the

amplitude, the more severe the vibration.

2.2.1 DISPLACEMENT (PEAK TO PEAK)

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'. In

Metric units, the peak-to-peak vibration displacement is usually expressed in microns,

where one micron equals one-thousandth of a millimeter (0.001-mm). Peak-to-peak

vibration displacement is sometimes expressed in mils, where 1 mil equals one

thousandth of an inch (0.001 inch).

2.2.2 VELOCITY (PEAK)

Since the vibrating weight shown in the figure.2.2 is moving, it miist be moving at

some speed- However, the speed of the weight is constantly changing. At the top limit of

the motion the speed is zero since the weight must come to a stop before it can go in the

opposite direction. The speed or velocity is greatest as the weight passes through the

neutral position. The velocity of the motion is definitely a characteristic of the vibration

but since it is constantly changing throughout the cycle, the highest or 'peak' velocity is

selected for measurement. In Metric units, vibration velocity is expressed in millimeters

per second peak. Vibration velocity is expressed in terms of inches per second peak for

English or imperial units.

2.2.3 VELOCITY (RMS)

The ISO in its work to establish internationally acceptable- units for measurement

of machinery vibration decided to adopt VELOCITY (RMS) (root mean square) as the

standard unit of measurement. This was decided in an

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attempt to derive criteria, which would determine an effective value for the varying

function of velocity. It should be noted that IRD Mechanalysis instruments may be

calibrated to read in -terms of VELOCITY (PEAK) or VELOCITY (RMS).

2.2.4 ACCELERATION

In discussing vibration velocity, we pointed out tfiat the velocity of the part

approaches zero at the extreme limits of travel. Of course, each time that the part comes



to a stop at the limit of travel, it must 'accelerate' to pick-up speed as it travels towards the

other extreme limit of travel. Vibration acceleration is another important characteristic of

vibration. Technically, acceleration is the rate of change of velocity.

Referring to the motion plot, figure 2.2, the acceleration of the part is maximum at

the extreme limit of travel where the velocity is zero point 'A'. As the velocity of the part

increases, the acceleration decreases. At point 'B', (the neutral position) the velocity is

maximum and the acceleration is zero. As the part passes through the neutral point, it

must now 'decelerate' as it approaches the other extreme limit of travel. At point 'C',

acceleration is at peak.

Vibration acceleration is normally expressed in "g's" peak, where one is the

acceleration produced by the force of gravity at the surface of the C2 earth. By

international agreement, the value of 980.665 cm/se equals 386.087 C2

C2 inches/se also equals 32.1739 feet/se has been chosen as the standard acceleration due

to gravity.

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2.3 CONVERSION OF AMPLITUDES The displacement, velocity and acceleration of a vibration are directly related. If

the peak-to-peak displacement and frequency of a vibration are known, the velocity of

vibration can be found as follows: -

V Peak = 52.3D ( F / 1000 ) X 0.001

Where: -

V Peak = vibration velocity (mm/sec) peak

D = vibration displacement (microns) peak to peak

F = vibration frequency (CPM

Further to the above when it is required to calculate vibration acceleration, the

following formula can be used. -

G (Peak ) = 5.6 D ( F / 1000 )2 X.0001

Where: -

G (Peak ) = Vibration acceleration

D = Vibration displacement (microns) (peak-to -peak)

F = Vibration frequency (CPM)



It is sometimes necessary to convert Metric measurement to Imperial, or the

converse. To convert velocity or displacement measurement from Metric to Imperial: -

Velocity (mm/sec) Velocity (inches/sec) = 25.4

Displacement (microns) Displacement (mils) = 25.4

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From Imperial to Metric: -

Velocity (mm/sec) = Velocity (inches/sec) X 25.4

Displacement (microns) = Displacement (mils) X 25.4

2.4 DISPLACEMENT, VELOCITY OR ACCELERATION WHICH SHOULD

WE USE?

Since the amplitude of vibration can be measured in terms of displacement, velocity

or acceleration, the obvious question is 'Which parameter should we use?

Vibration amplitude readings taken for checking overall machinery condition

indicate the severity of the vibration. But which is the best indicator of vibration

severity: displacement, velocity or acceleration? To answer this question, consider what

happens when a wire or piece of sheet metal is bent repeatedly back and forth.

Eventually, this repeated bending causes the metal to fai'i by fatigue in the area of the

bend. This is similar in many respects to the way a machine or machine component fail

from the repeated cycles of flexing caused by excessive vibration. Of course, the time

required to fail the wire or sheet metal can be reduced by: -

1 . Increasing the amount of the bend (displacement). The further the metal is

bent each time, the more likely it is to fail.

2. By, increasing the rate of bending (frequency). Obviously, the more times

per minute the metal is flexed, the quicker it will fail.

Thus the severity of this bending action is a function of both how far the

metal is bent (displacement) and how fast the metal is bent (frequency). Vibration

severity then appears to be a function of displacement and frequency.

PAGE 9



However, since vibration velocity is also a function of displacement and frequency

it is reasonable to conclude that a measure of vibration velocity is a direct measure of

vibration severity. Through experience we have found this to be basically true.

Vibration velocity provides the best overall indicator of machinery condition.

Displacement and acceleration readings are sometimes used to measure vibration

severity. However, when displacement or acceleration is used, it is also necessary to

know the frequency of the vibration. Charts like those shown in figure.2.3 and figure. 2.4

are often used to cross-reference the displacement or acceleration with frequency to

determine the level of severity. Note from figure 2.3 that a displacement of 25 microns

occurring at a frequency of 1200 CPM is in the 'GOOD' range, however, the same

displacement of 25 microns at a frequency of 20,000 CPM is in the 'VERY ROUGH'

range. Note also, that the diagonal lines dividing the zones of severity are constant

velocity lines. in other words, a velocity of 12.7 mms per second peak is in the 'ROUGH'

range regardless of the frequency of the vibration. Referring to the chart, figure 2.4, we

can note that an acceleration of 1.0 g at a frequency of 100,000 CPM is in the 'GOOD'

region of the chart; however, 1.0 g at a frequency of 18,000 CPM is in the 'SLIGHTLY

ROUGH' region.

So the real significance of the characteristics of vibration lies in the fact that they

are used to detect and describe the unwanted motion of a machine. Each of the

characteristics of vibration tells us something significant about the vibration. Therefore,

the characteristics might be considered to be symptoms used to diagnose inefficient

operation or impending trouble in a machine.



2.5 VIBRATION FREQUENCY

Frequency is the number of complete cycle in unit time. From the figure 2.2, the

amount of time required to complete one cycle of vibration is the period of vibra@on. If

a period of one second is required to complete one cycle of vibration, then during one

minute the cycle will be repeated 50 times or 50 cycles per minute (CPM). The measure

of the number of cycle for a given interval of time is the frequency of vibration and

usually expressed in cycles per second or Hertz (CPS or Hz) or cycles per minute (CPM).

2.6 VIBRATION PHASE Phase is defined as the position of a vibrating part at a given instant with reference

to a fixed part or another vibrating part. By measuring the phase we can

Ø Compare one vibration with another

Ø Determine how one part is vibrating relative to another part

Phase readings are normally expressed in degrees (00 to 3600) where one

complete cycle of vibration equeals 3600.

Phase angle of vibrations, like amplitude and frequency, is a useful parameter, for

analysis of vibrations. Measurement of phase and its analysis can help in the diagnosis of

a machinery problem.

Figure 2.5 shows the phase diagram of a vibrating object relative to a fixed

reference, which corresponds to the equilibrium position. The phase diagram gives the

phase angle @2, @3.......... corresponding to any position 2,3 ........... etc., as shown, as

measured from a datum.. Figure.2.6 shows the displacement time diagrams, A and B, of

two vibrating par't-s or objects.

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Fig: 2.6 PHASE DIFFRERANCE BETWEEN TWO VIBRATING PARTS

The two reach their peaks or zero values, at different instants. The time difference,

being td, phase angle between the two vibrating objects is td X 3600, since the time

period corresponds to a full cycle or a phase of 360'.

In the case of a rotor, the phase angle gives the location of the rotor at any instant

e.g. it defines the location of the heavy spot of the rotor at each measurement point

relative to a fixed point and is useful for balancing.



The phase may be measured with a stroboscope, as shown in figure 2.7. This is

shown for a rotor rotating at same speed. If the frequency of flash of the stroboscope

equals the running speed, any mark on the rotor appears stationary and the reading

against a fixed reference scale would give the phase difference.

2.7 VIBRATION SEVERITY

Since vibration amplitude (displacement, velocity or acceleration) is a measure of

the severity of the trouble in a machine, the next question may be; 'how much vibration is

too much?' To answer this question, it is important to keep in mind that our objective

should be to use vibration checks to detect trouble in its early stages for scheduled

correction. The goal is not to find out how much vibration a machine will stand before

failure, but to get a fair, warning of impending trouble so it can be eliminated before

failure.

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Absolute vibration tolerance or limits for any given machine are not possi 'ble.

That is, it is impossible to select a vibration limit which, if exceeded, wi ill result in

immediate machinery failure. The development of mechanical failure is just far

too,complex for such limits to exist. However, it would be impossible to effectivel utilise

vibration as an indicator of machinery condition y unless some guidelines are available



and the years of experience of those familiar with machinery and machinery vibration

have provided some realistic guidelines.

The vibration velocity provides a direct measure of machinery condition for the,

intermediate vibration frequencies (600 to 60,000 CPM). The velocity values in figure

2.3 and figure, 2.4 are offered as a guide for overall unaltered velocity readings. When

vibration amplitude is measured in displacement or acceleration, the charts in figure 2.3

and figure 2.4 may be used as guides in selecting acceptable levels of machinery

vibration. Displacement and acceleration measurements applied to these charts should be

filtered readings only.

The guidelines offered in the above figures apply io machinery such as motors,

fans, blowers, pumps and general rotating machinery where vibration does not directly

influence the quality of a finished product. Amplitude readings should be those taken on

the bearings or structure of the machine.

Of course, the vibration tolerances suggested in these references will not be

applicable to all machines. For example, some machines such as hammer mills or rock

and coal crushers will inherently have high levels of vibration. Therefore, the values

selected using these guides should be used,' only so long as experience, maintenance

records and history proves them to be valid.

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For machines such as gr' ders and other precision machine tools where vibration

can affect the quality of a finished product, refer the 'Guide to Vibration Tolerance For

Machine Tools' provided in Table 2.1. Applying vibration tolerances to machine tools is

rather easy because they can be based on the machine's ability to produce a certain size or

finish tolerance. The values shown in the table are the result of years of experience with

vibration analysis of machine tools, and represent the vibration levels for which

satisfactory parts have been produced. Of course, these values may vary depending on

specific size and finish tolerances required. A comparison of the normal pattern of

vibration on the machine and the quality of finish, and size control required would reveal

what level of vibration is acceptable. The first time the quality of finish or size control

deteriorates, an unacceptable vibration level would be indicated. The initial values

selected from Table 2.1 can then be modified to the new, more realistic ones.



Another severity standard which is coming into increasing use is ISO 2372 (BS

4675) as given in Table 2.2. This standard differs somewhat to the general severity

standards referred to as it seeks to establish classifications of various types of machinery.

Annexure-A, which follows the standard, describes the machines covered in the

classification. To use ISO 2372 it is first necessary to classify the machine. Next reading

across the chart can correlate the severity of the machine condition. The severity of the

machine condition is indicated by the letter A 5 B, C or D.

Making the decision to correct a condition of vibration is often a very difficult one

indeed, especially when it involves downtime of critical machinery. Therefore, when

establishing acceptable levels of machinery vibration, e erience and factors such as

safety, labour costs downtime costs

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and the importance of a machine's operation to. the company's profits must be considered.

Table-2.1

TENTATIVE GUIDE TO VIBATION TOLERANCES FOR MACHINE TOOLS

TYPE OF MACHINE Displacement of vibration as read

with pickup on spindle bearing

housing in the direction of cut.

§ Grinders ___ Tolerance Range

Thread Grinder 0.25 to 1.5 microns

Profile of Contour Grinder 0.76 to 2.0 microns

Cylindrical Grinder 0.76 to 2.5 microns

Surface Grinder (vertical reading) 0.76 to 5.0 microns

Gardner or Besly Type 1.3 to 5.0 microns

Centreless 1.0 to 2.5 microns

§ Boring Machine 1.5 to 2.5 microns

§ Lathes 5.0 to 25.Omicrons

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Table 2.2

ROLERANCES BASED ON B.s. 4675 : 1976

(ISO 2372) 'A BASIS FOR COMPARATIVE EVALUATION OF VIBRATION IN MACHINERY'

Velocity (mm/ s) RMS

Velocity (mm/s) Peak

Velocity Ins/Sec Peak

Class I M/C

Small

Class II M/C

Medium

Class III M/C

Large

Class IV M/C

Turboo (1) (2) (3)

0.28 0.40 0.016 0.45 0.64 0.025 A 0.71 1.00 0.039 ------ A 1.12 1.58 0.062 B ------ A 1.80 2.54 0.100 ------ B ------ A 2.80 3.96 1.160 C ------ B ------ 4.50 6.37 0.250 ------ C ------ B 7.10 10.00 0.390 D ------ C ------

11.20 15.80 0.620 D ------ C 18.00 25.40 1.000 D ------ 28.00 39.60 1.560 D 45.00 63.70 2.500

A= Good B = Acceptable C = Still Acceptable D = Not Acceptable

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ANNEXURE-A

CLASSIFICATION EXAMPLES FROM BS 4675 (ISO 2372)

(For guidance purposes only)

In order to show how the recommended method of classification may be applied,

examples of specific classes of machines are given below. It should be emphasised,

however, that they are simply examples and it is recognised that other classifications are

possible and may be substituted in accordance with the circumstances concerned. As and

when circumstances permit, recommendations for acceptable levels of vibration severity

for particular types of machines will be prepared. At present experience suggests that the

following classes are appropriate for most applications

CLASS I

Individual parts of engines and machines integrally connected with the complete machine

in its normal operating condition. (Electrical motors of up to kw are typi@al examples of

machines in this category).

CLASS II



Medium sized machines. (Typically electrical motors with 15 to 75 kw output)

without special foundations, rigidly mounted engines or machines (upto 300 kw) on

special foundations.

CLASS III

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

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

measurement.

CLASS IV

Large prime movers and other large machines with rotating masses mounte( on

foundations which are relatively soft in the direction-of,vibration measurement (for

example turbo-generator sets, especially those with lightweight sub-structures).

PAGE 20

3. SOURCES OF VIBTRATION 3.0 INTRODUCTION

3.0 INTRODUCTION

In a machine, vibration is a result of minor faults that are the natural consequences

of manufacturing and material limitations. Common causes of vibration are as follows.

3.1. UNBALANCE:

This is a major contributor to vibration in rotating machinery. It is caused by

unequal distribution of mass in a rotating part. Points of unbalance produce additional

forces in the radial direction and the machine bearings restrain these forces resulting in

vibration. The unbalance can be static or dynamic as shown in figure 3. 1.

In either case the frequency of vibration equals the rotational frequency (IxRPM).

Amplitudes of vibrations are excessive in the radial directions. Phase measurement by a

stroboscope shows a single steady reference mark.

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In the case of overhung rotors, vibrations in axial direction are also encountered due

to unbalance, in addition to those in radial directions. Vibrations at all bearings, in such a

case, would all be in phase.

Sometimes, reasons other than unbalance may also result in vibrations at rotational

frequency. In such cases, the unbalance as a possible cause should be confirmed by the

difference in phase between vibrations in the two radial directions - horizontal and

vertical. If the phase is 900,the cause of vibrations is unbalance. Defects like eccentric

pulleys may also cause vibrations at the frequency of rotational speed. In such a case, the

phase difference between vibrations, in the two directions, may not be 90' due to the

effect of reaction forces of the belt.

3.2 MISALIGNMENT

Like unbalance, misalignment is another common problem. Inspite of self-

aligning bearings and flexible couplings, it is difficult to align the shafts and their

bearings so that no force exists which will cause vibration. There are three possible types

of coupling misalignment as shown in figure 3.2

§ ·Angular the center line of the two shafts meet at an angle

§ Offset the shaft center lines are parallel but di 'laced from one another

§ A combination of angular and offset misalignment.

Misalignment, even with flexible, couplings, results in two forces, axial and radial,

which result in axial and radial vibrations. This is true even when the misalignment is

within the limits of flexibility of the coupling. The Magnitude of the forces and therefore

the amount of vibration generated will increase with increased misalignment. The

significant characteristic of

PAGE 22

vibration due to misalignment is that it will be in both the radial and axial directions.



Normally, the vibration frequency is lx RPM; however, when the misaligmnent is

severe, second order (2xRPM) and sometimes third order (3x RPM) vibration frequencies

may appear.

There can be a misalignment' not involving a coupling. The misalignment of a

bearing with its shaft is one example.

In the case of a misaligned sleeve type bearing, no vibration will result unless

there is also unbalance. In such a case radial vibration as well as an axial vibration will

be present due to the reaction of the misaligned bearing to the force caused by the

unbalance. If the real cause of this vibration is unbalance, then both the axial and radial

readings will be reduced when the part is balanced.

When an anti-friction bearing is misaligned with a shaft, then axial vibration will

exist even When the part is balanced. We have to install the bearing properly to

eliminate the vibration.

The misalignment of sheaves and sprockets used in V-belt drives and chain drives

results in high axial vibration. The angular and offset

PAGE 23

misalignment conditions result in destructive vibration and leading to accelerated wear of

sheaves, sprockets, chains and drive belts.

A bent shaft acts very much like angular misalignment, so its vibration.

characteristics are included with misalignment. We can suspect misalignment or a bent

shaft whenever the amplitude of axial vibration is greater than one-half of the highest

radial (horizontal or vertical).

2.3 MECHANICAL LOOSENESS

The causes of mechanical looseness could be loose mounting bolts, excessive

bearing clearance or a crack in' the structure of bearing pedestal.

For the vibration characteristic of mechanical looseness to occur, it needs some

other exciting force to cause it, say, unbalance or misalignment. But, when the looseness

is excessive, just - a small amount of unbalance or misalignment will result in large

vibrations. So, looseness simply allows more vibration to occur than would otherwise

appear. This does mean that if we can eliminate the unbalance or misaligmnent forces,

we can reduce the vibration, but it needs an extremely fine level of balance or alignment,

which may be impractical. So, removing the looseness is more practical.



Mechanical looseness leads to a heavy beating action and these cause a vibration at

a frequency of twice the rotating speed (2xRPM) and higher, orders of the loose' part.

The highest amplitude of vibration occurs at 2xRPM of the equipment.

The nature of mechanical looseness and the reason for the characteristic vibration at

2xRPM can be explained as follows in figure 3.3.

PAGE 24

Fig: 3.3 MECHANICAL LOOSENESS

There are two applied forces for each revolution of the shaft. One is applied by

the rotating unbalance, the other when the bearing drops against the pedestal. Therefore,

the vibration frequency is 2xRPM. We can view this with an oscilloscope attached to the

vibration analyzer.

Also there will be some clearances inherent in every' machine, and it is normal

that some vibration will occur at a frequency of 2xRPM whenever some unbalance or

misalignment is present.

Generally, we should suspect mechanical looseness to be the problem whenever

the seventy of vibration at 2xRPM is more than one half the severity of vibration at

rotating speed (lxRPM). Moreover, if we have great difficulty in eliminating the

vibration by balancing or realignment, we should verify whether there is any looseness.

3.4 BAD BELT DRIVES

V-belt drives are popular'for power transmission because of their capacity to

absorb shock and vibration. They are also quiet in operation when compared to chain or

gear drives. But, for machine tools where very low levels

PAGE 25



of vibration must be maintained, they can be the source of vibration beyond limits. Such

problems are of two types.

• Belt reaction to other disturbing forces in the equipment

• Vibration due to actual belt problems.

When we see the whip and flutter of V-belts (the flexible strands between the

pulleys), we conclude that they are the source of vibration. Because of the ease with

which the belts could be changed and because the vibration of belt is readily visible than

other parts, belt replacement often happens to be the immediate solution. But

remember excessive unbalanced eccentric pulleys, is misalignment or mechanical

looseness, all these may result in belt vibration. The belt may be just an indicator of other

disturbances in the equipment. Hence, before replacing drive belts, make an analysis to

pinpoint the root causes.. Looking at the frequency of the vibration we can do this.

If the belt is reacting to other disturbing forces in the machine, the frequency of

belt vibration will most probably be the same as the disturbing frequency. When we

are using the strobe light of the analyser, that part of the machine, which is actually

generating the disturbing forces, will appear to stand still. For multi belt drives all belts

should have equal tension. If not, the slack belts may cause excessive vibration even for

very minor condition. Additional problems are belt slippage and rapid belt and pulley

wear. Vibration from actual belt defects will be at 1,2,3 & 4 times belt RPM. The

articular p frequency found would depend on the nature of the belt problem as well as

the number of pulleys and idlers over which the belt must pass.

To summarise, the vibration due to belt drives can -be reduced by the following

methodes.

PAGE 26

§ Make sure belts are in good physical condition

§ Check whether the number and size of belts meet the load

requirements

§ Use matched set of belts in multi-belt installations to get equal tension

§ Verify whether the pulleys and sheaves are round and accurately aligned with one

another

§ Check for wear of pulley grooves. Too much wear will allow the belt to ride in

the bottom of the groove, causing slippage and poor efficiency.



§ Verify whether the belts are properly installed and adjusted to proper tension as

recommended by the manufacturer.

§ Keep other disturbing forces in the machine to a minimum.

3.5 ECCENTRICITY

Eccentricity means that the shaft (rotating) centerline is not the same as the rotor

(,geometric) centerline. It is not out-of-roundness or ovality. Eccentricity is a common

source of unbalance and results in more weight on one side of the rotating centerline than

on the other side. As an example, when the bore of the inner race is not concentric with

the inner race geometric centerline in an anti-friction bearing, an apparent unbalance in

the part mounted on the bearing will be introduced. If we balance the rotor, the forces

causing the vibration will be compensated and the vibration will disappear. That is why

balancing a rotor in its own bearing is recommended. Different sources of eccentricity

are, shown in figure 3.4.

PAGE 27



Fi2: 3.4 SOURCES OF ECCENTRICITY

Though eccentricity can be corrected by routine balancing techniques, eccentricity

can also result in reaction forces, which may not be corrected by simple balancing. In

eccentric gear, the largest vibration will occur in the direction on a line through the

centers of the two gears, at a frequency equal to I XRPM of the eccentric gear. It is not

unbalance, though it will look like it.

Eccentricity of the V-belt sheaves will result in reaction forces similar to the

eccentric gear. Here, the largest vibration will occur in the direction of belt tension at a

frequency equal to lx RPM of the eccentric sheaves. Again, the vibration looks like

unbalance, but cannot be corrected by applying a balance correction.

PAGE 28

Eccentric fan, blower, pump and compressor rotors may also create forces, which

result in vibration. Here, the forces are unequal aerodynamic and hydraulic forces

against the rotor. These forces will be the greatest on the high side of the rotor, so will

resemble unbalance. For this equipment, there is no positive test for eccentricity except

that we can try to balance. If we get no results. verify if the impeller is concentric with

the shaft journals.

3.6 FAULTY ANTI-FRICTION BEARINGS

Rolling element bearings find many uses in today's machinery. They can be found

in motors, slow-speed rollers, gas turbines, pumps, and many other machines. Some of

the reasons for using the rolling element bearings are: low starting friction, low operating

friction, ability to support loads at low speed (even zero), lower sensitivity to lubrication

(compared to fluid film bearings so a simpler lubrication system can often be used) and

the ability to support both radial and axial loads in the same bearing.

Rolling element bearings have very little damping, so whenever a machine with.

rolling element bearings traverses a balance resonance, large vibration can result. Also,

compared to fluid film bearings, which generally have a long life, rolling element

bearings have a limited fatigue life due to the repeated stresses involved in their normal

use.

Rolling element bearings, regardless of type (ball, cylindrical, spherical, tapered, or

needle) consist of an inner and. outer race separated by the rolling elements, which are

usually held in a cage. Mechanical flaws may develop on any of these components.



Using the basic geometry of a bearing, the fundamental frequencies generated by these

flaws can be determined.

PAGE 29

The frequency of vibration caused by anti-friction is usually several times the

rotating speed of the part, but it is unlikely to be an even multiple of shaft RPM. So, if

we observe the rotating shaft with the strobe light, we may not see a stationary image (as.

it would for vibration caused by unbalance, misalignment or gears', which occur at even

multiples of shaft RPM) and also observe an unsteady frequency meter.

Take the case of a bearing having a flat spot on only one ball. As the ball rolls, the

flaw will intermittently come into contact with the bearing inner and outer races and will

result in vibration at 1, and possibly, 2-times ball rolling frequency. Because the rolling

frequency of the ball will be several times the RPM of the shaft, the resulting vibration

will be high compared to rotating speed frequency. The amplitude of the vibration will

depend on the extent of the bearing fault. In addition to the vibration occurring at or

multiples of ball rolling frequency, these momentary impacts may excite vibration at

natural frequency.

Every object has its own unique natural frequency. A flaw on a rotating element

of a bearing will produce the intermittent impacting type of force, which will cause the

various parts (inner and outer races, shaft, and bearing housing) to vibrate at their

respective natural frequencies. Normally, these will be high compared to the RPM of the

machine. Hence, these vibration frequencies measured from a faulty bearing will also be

high. Also, it is that these will be exact multiples of shaft RPM, Thus, the frequency of

unlikely bearing vibration will probably not be a direct multiple of shaft RPM. Finally,

there are many parts, hence many simultaneous vibration frequencies to varymg degrees,

which cause the frequency meter to be unsteady or moving.

PAGE 30

3.7 DEFECTIVE SLEEVE BEARINGS

High levels of vibration or noise in sleeve bearings generally result from excessive

bearing clearance (caused by wiping), looseness (babbitt loose in the housing), or

lubrication problems. A sleeve bearing with excessive clearance may allow a relatively

minor unbalance, misalignment or some other vibratory force to result in mechanical

looseness or pounding. Here the bearing is not the actual cause; it simply allows more



vibration to occur than in the case where the bearing clearances were correct. A bearing,

which has been wiped, can often be detected by comparing the horizontal and vertical

amplitudes of vibration. Machines, which are securely mounted to a rigid foundation or

structure, will normally reveal slightly higher amplitude of vibration in the horizontal

direction. In several instances where the amplitude of vibration in the vertical direction

appeared usually high compared to the horizontal, a wiped bearing was found to be the

cause.

Oil whirl is another problem associated with sleeve-type bearings. This' vibration

occurs only on machines equipped with pressure-lubricated sleeve bearings and operating

at relatively high speed - normally above the second critical speed of the rotor. Oil whirl

vibration is often quite severe, but is easily recognized because the frequency is slightly

less (5% to 8%) than one-half the RPM of the shaft.

Under normal o eration, the shaft of the machine will rise up the side of p the

bearing slightly, depending on the shaft RPM, rotor weight and oil pressure. The shaft

operating at an eccentric position from the bearing center draws oil into a wedge to

produce a pressurized load-carrying film. If the eccentricity of the shaft within the

bearing is momentarily increased from its equilibrium position (say, as a result of a

sudden surge, an external shock load or other'

PAGE 31

transient condition), additional oil will immediately be pumped into fill the space vacated

by the shaft, thus increasing the oil film may drive the shaft into am pressure. This

additional force developed by the oil film may drive the shaft into a whirling path around

the bearing. . If the damping within the system is sufficient, the shaft will return to its

normal position in the bearing; otherwise, the shaft will continue in a whirling path.

Improper bearing design is normally attributed to the problem of oil whirl,

however, excessive bearing wear, an increase in lubrication oil pressure or a change in

oill viscosity are other possible causes. A temporary correction can some times be made

by changing the temperature (viscosity) of the lubricant. Increasing the loading on the

bearing by introducing a slight unbalance or misaligmnent is also some -crimes effective.

Scrapping the sides. of the bearing or grooving the bearing surface to disrupt the lubricant

wedge are also successful in some cases.



There are several special sleeve-beanng configurations to reduce the possibility of

oil whirl. The axial-groove bearing is normally limited to smaller bearing applications

such as those used in light gas turbines and turbo-chargers. The three-lobed bearing

provides improved bearing stability against oil whirl. The three individual bearing

surfaces generate pressurized oil films that act to center the shaft, Axial grooves are

sometimes included at the intersection of the lobe segments to increase whirl resistance.

The tilting pad bearing is a common choice on larger high-speed industrial,

machinery. In a manner similar to the lobed-bearing, each segment or pad develops a

pressurized oil wedge, which tends to center the shaft in the bearing. - The tilting feature

allows each pad to follow the shaft, improving system damping and overall stability.

PAGE 32

Sometimes, a normal machine may exhibit oil whirl vibration. This may occur

when an external source transmits vibration to the machine through the foundation or

piping. If th is background vibration occurs at just the right frequency (ie. the probable

oil whirl frequency of the machine) oil whirl will likely occur-. This condition is referred

to as externally excited whirl.

In a similar manner, a normally stable machine may be excited into oil whirl by -a

foundation --or piping which is vibrating in resonance at a frequency equal to the

probable oil whirl frequency. The resonant vibration of the piping or foundation may be

the result of pulsation or flow turbulence. Oil whirl resulting from this condition is called

resonant whirl.

Whenever the vibration characteristic of oil whirl is found, we must carry out a

complete vibration survey, of the installation including background sources, foundation

and related piping to determine the true cause.

Another problem encountered on machines equipped with sleeve bearings is called

ffiction whirl or hysteresis whirl. It is similar to oil whirl except that'the vibration will

occur on rotors operating above their first critical speed and the frequency of the

vibration will always be the critical speed frequency of the rotor. For example, if a rotor

operates at 3000 RPM and the first rotor critical speed is 2000 RPM. As is obvious, this

vibration may not have the characteristic frequency of slightly less than 1/2 RPM

associated with oil whirl. However, for machines operating above or near their second



critical speed, the frequency of hysteresis whirl may coincide with that of oil whirl

resulting in an extremely severe vibration problem.

In hysteresis or ffiction whirl, a rotor which, operates above critical speed will

tend to deflect or bow in a direction opposite the unbalance heavy spot. As

PAGE 33

a result, the internal friction damping (hysteresis damping) of the rotor, which normally

works to restrict deflection,. will be out of phase and this damping force will act to

further deflect the rotor. This condition is normally kept in check by the damping

provided by the bearings. However, if stationary damping is low,, compared to the

internal dampin of the rotor, trouble is likely to occur.

The usual solution. for hysteresis whirl is to increase stationary damping of the

bearings and structure. We can change to a tilting pad bearing or other special bearing

design. Sometimes, it can be solved by reduc'mg rotor damping for example, by

replacing a gear-type coupling with a frictionless coupling such as a flexible disk

coupling.

Improper lubrication can also cause vibration in a sleeve bearing. If the bearing

lacks lubrication or if the wrong lubricant is used, the result may be excessive ffiction

between the rotating shaft and stationary bearing. This friction serves to excite vibration

of the bearing and other related parts of the machine in a manner similar to the vibration

we can generate by simply moistening our finger and rubbing it over a pane of glass.

This vibration is called dry whip, is generally of high frequency and produces the

distinctive squeal as for a dry bearing. The vibration frequencies generated are not likel y

to occur at direct multiplies of-shaft RPM. Therefore, they will give no definite image

under the strobe light and the vibration is similar to that caused by a faulty anti-ffiction

bearing. Whenever vibration characteristic of dry whip is encountered, conduct an

inspection of the lubricant, lubrication system and bearing clearances. This condition has

been found on bearings with excessive and insufficient clearance.

PAGE 34

3.8 GEAR PROBLEMS

Common problems, which cause vibration in gear, are excessive gear wear, gear

tooth inaccuracies, faulty lubrication and dirt or foreign material trapped in the gear teeth.

Misaligmnent or a bent shaft can also be at fault. This is easy to identify because the



vibration normally occurs at a frequency equal to gear meshing frequency (the number of

gear teeth x the RPM of the faulty gear). In complex gear arrangements where several

meshing frequencies are possible, we have to examine the drawing of the gear box to

determine the RPM and number of teeth on the various gears to identify which gear or

gears are most likely at fault.

However, if the axial vibration occurring at motor RPM frequency is relatively

high on the gearbox and motor, misalignment may be the source of trouble. In this case,

this misalignment condition should be corrected first; this may also eliminate the high

frequency gear vibration.

Sometimes, vibration at a frequency and equal to gear meshing frequency may be

produced; for example, if a gear has only one broken or deformed tooth, a vibration at lx

gear RPM may result. Viewing the vibration waveform on an oscilloscope connected to

the analyzer will enable to differentiate this problem from unbalance because of the

spike-like signal caused by a faulty gear tooth. If more than one tooth is deformed, a

vibration frequency equal to the number of deformed teeth x gear RPM may result.

An eccentrically mounted gear will also cause vibration at 1 x gear RPM, similar

to unbalance. Where eccentricity is the problem, any attempt to balance in-situ will not

be fruitful. Eccentricity, unbalance ind bent shafts have also caused gear vibration at sub-

multiple frequencies of actual gear meshing frequency.

PAGE 35

The vibration amplitude and frequency from gears may also be erratic sometimes.

This occurs with gears, which are operating under a very light load alcondition where the

load may randomly shift back and forth from one gear to another. The impacts, which

occur as the load is shifted, will excite the natural to frequencies of the gears, bearings

and associated machine components. However, we can detect this gear vibration readily

at two or more points on the machine and, thus we can distinguish from the bearing

vibration which is predominate at the point of the faulty bearing. Because of the

characteristic high frequency, gear vibration is also a common source of objectionable

noise. For this reason, if we correct gear faults and other disturbances to reduce

excessive gear vibration, noise level also will be reduced.

3.9 ELECTRICAL PROBLEMS



Vibration of rotating electrical machinery can be mechanical or electrical in origin.

We have already seen mechanical problems. Electrical problems normally consist of

unequal magnetic forces acting on the rotor or stator. These y unequal magnetic forces

may be due to

• Rotor not round

• Eccentric armature journals

• Rotor and stator misaligned (rotor not centered in the sta,tor)

• Elliptical stator bore

• Broken bar

• Open or shorted windings

The frequency of vibration will be lxRPM, and will appear similar to unbalance.

An easy way to identify this source of vibration is to observe the change of vibration

amplitude; the instant electrical power is disconnected from the unit. Make this check

with the analyzer filter on the out position. If the

PAGE 36

vibration disappears the instant power is shut off; the vibration is likely due to electrical

problems. If so, conventional, electrical testing procedures can be carried out to. pinpoint

the true cause of the problem. If it decreases only gradually after power is removed, the

problem is probably mechanical in nature.

Electrical problems with induction motors often cause swinging or pulsating

amplitude in nature. The blasting noise and vibration is caused by the slip frequency,

characteristic of this type. Slip frequency = motor RPM synchronous frequency of the

rotating magnetic field. The synchronous frequency is always equal to or an exact sub

multiple of the AC. line frequency Therefore, if the motor has both electrical and

mechanical problems such as unbalance, there will actually be two different vibration

frequencies present. Since these two are close, their amplitudes will alternately add

together and then subtract at a rate equal to the difference between their frequencies. The

result will be a noticeable with steady beat as well as the corresponding swing of the

amplitude meter.

If the amplitude of this pulsating vibration is excessive, we must correct it. If we

observe the amplitude meter, the instant the power is shut off, we can decide whether it is

mechanical or electrical cause. The pulsation may not be detrimental to the performance



of the machine, but a pulsating noise is more noticeable than a steady one and affects the

personnel psychologically.

Electric motors have inherent vibration due to torque pulses. These torque pulses

are generated as the motor's rotating magnetic field energizes the poles in the stator. The

frequency of vibration resulting from torque pulses will be 2 times the AC line frequency

powering the motor. Thus, if AC line frequency is 50 Hz (50 cycles per second) or 3000

CPM, torque pulse frequency will be 6000 CPM. This is rarely troublesome except

where

PAGE 37

extremely low vibration levels are required, or if the torque pulses should behappen to

excite a resonant condition in the machine or structure. If resonance is excited, this can

also result in excessive noise.

In eccentric motor armature though the armature itself may be balanced or in

terms of rotor weight distribution, a lxRPM force is generated between the armature and

stator because of varying magnetic attraction between the eccentric armature and motor

poles. Increased load increases the magnetic field strength and results in increased

vibration.

To check this, measure the vibration, with the motor operating under power. Then, turn

the power off and observe what happens to the amplitude of vibration. If the amplitude

decreases gradually as the motor coasts down, the problem is likely unbalance.

On the other hand, if the vibration amplitude disappears the instant power is turned

off, the problem is electrical and possibly due to armature eccentricity. Other electrical

problems causing vibration are shorted windings, broken rotor bars, or a rotor, which is

not properly centered in the stator. A visual inspection using standard motor testing

procedures will reveal the nature of the electrical problem.

3.10 RESONANCE

We already know that every object and every part of a machine has natural frequency. If

we strike a bell, it vibrates at its own natural frequency. This continued vibration, called

free vibration, will eventually diminish because of inherent damping In addition to free

vibration, there are forced vibrations where the frequency depends on the frequency of

the driving force applied to the machine or structure. For example, the driving force of

rotor unbalance



may cause the forced vibration of a motor. In such case, the frequency of this forced

vibration is determined by the speed (RPM) of the motor.

To confirm whether or not a part is vibrating in resonance, we can apply the bump

test. . With the machine shut down, simply bump the machine or structure with a force

sufficient to cause it to vibrate. Since an object 'will undergo free vibration at its natural

frequency when bumped or struck, the frequency of free vibration generated in this way

will be indicated on the analyzer's frequency meter. The analyzer's filter must be in the

out position for this test. If the vibration diminishes very quickly, it may be necessary to

bump the machine several times in succession m order to sustain free vibration long

enough to register on the frequency meter.

We can also record the amplitude and phase of vibration versus the rotating speed

of the machine. We can use FFr analysis or make@ a similar plot by operating the

machine at a number of selected speeds and plotting the amplitude and phase of vibration

for each speed. If resonant conditions do exist, they will be clearly identified by a

characteristic peak vibration and by a large phase shift (around 180').

There are several ways to correct a resonance problem. We can change the

frequency of the exciting force so that it no longer coincides with the natural frequency of

the machine or structure. Either increasing or decreasing the RPM of the machine can do

this. If the exciting frequency cannot be changed, change the natural frequency - by

increasing or decreasing the stiffness or mass of the, object.

PAGE 39

3.11 AERODYNAMIC AND HYDRAULIC FORCES

Machine which handle fluids will have vibration and noise due to the reaction of

the vanes or blades on the irnpeller striking the fluid. This type of vibration is common

on pumps, fans and blowers. The frequency will be equal to the number of vanes or

blades on the impeller times the RPM of the machine.

Aerodynamic and hydraulic vibrations are rarely troublesome unless they excite

some part of the machine, piping or ductwork to vibrate at resonance. When we

encounter this type of vibration, carry out the tests for resonance to determine which part

of the machine is causing the problem. If no resonance condition can be found, the

problem may be due to improper design of the machine or related piping or du'ctwork.



Obstructions in the path of the gas or liquid. or sharp 90' turns in the direction of flow

may cause this vibration.

Cavitation, recirculation and flow turbulence is other problems that have similar

vibration characteristics. Vibration and noise resulting from these problems will be

random in nature Unlike steady state vibration from unbalance or misalignment, random

vibration and noise has no discreet frequency and / or amplitude characteristics. For

example, the vibration and noise caused by cavitation in a pump may cover a rather broad

frequency range where individual amplitudes and frequencies are constantly changing.

Cavitation normally occurs when a pump is operating with excess capacity or low

suction pressure. Since the pump is starved, the fluid coming into the pump will literally

be pulled apart in attempt to fill the void, which exists. This creates highly unstable

pockets or cavities of nearly perfect vacuum, which collapse or implode very quickly.

Because of their impactive nature,these implosions serve to excite the local natural

frequencies of the pump housing, impeller and other related parts. Since these

implosions may

PAGE 40

occur at random intervals at various locations within the pump or piping, the resulting

vibration and noise will also be random in amplitude and frequency.

In some cases, where the fluid undergoes a substantial pressure drop at a valve, in

the pump or at changes in piping diameter, dissolved gases may be released or the liquid

may boil. This is also called cavitation and has the same random vibration amplitude and

frequency characteristics.

Re-circulation normally occurs when a pump is operating at low capacity or high

suction pressure. In other words, restricting the capacity of the pump causes the excess

fluid to return from the discharge to the impeller. This reverse flow and the mixing of

fluids moving in opposite directions results in random noise and vibration similar to

cavitation.

Flow turbulence is the result of resistance to the normal flow of liquid, or gas.

This resistance may be caused' by obstructions, sharp turns or simply surface friction

between the fluid and the duct or piping. Another cause of flow turbulence is the mixing

of high velocity and low velocity fluids. A good example of this is the et engine where



high velocity exhaust gases are mixed with the outside air. Only minor engine vibration

is created, since this mixing takes place outside the engine.

Some random noise and vibration from flow turbulence may be inherent in the

normal operations of fans, blowers, pumps, compressors and gas turbines. Where these

are excessive, an inspection of the system together with, noise or vibration readings taken

along the machine and related piping and ductwork will usually pinpoint the problem.

Sometimes you may have to redesign, say, the fan duct work - changing the sharp right

angle turn to two 45' sections together with turning vanes.

PAGE 41

3.12 RECIPROCATING FORCES

Reciprocating compressors, piston pumps, gasoline and diesel engines will have

vibrations because of the reciprocating motion inherent in the design and operation of the

machine. These are the result of inertia of the reciprocating parts plus the varying

pressures on the pistons, which cause torque variations.

Vibration and noise analysis of reciprocating machines are complex because of the

many frequencies found, such as, those at 1 and 2 times RPM; however, frequencies

at.higher orders are also common depending on the number of pistons and their

relationship to one another. A six cylinder 4-cycle engine may have three power

impulses for each revolution of the crankshaft, which will result in a vibration at 3xRPM.

An 8-cylinder engine with four Ises per revolutio power impu will show a vibration at

4xRPM.

The higher order frequencies found on reciprocating machines are inherent in the

machine and will rarely be a cause for concern unless they excite a resonant condition in

the machine or structure.

The problems with reciprocating machines can be either mechanical or operational

problems. The mechanical problems include unbalance, misalignment, bent shafts,

looseness and faulty bearings. Operational problems include blow-by, leaking or sticking

valves, and injector or ignition problems. Often, both will be nearly the same. So, it is

sometimes difficult to pinpoint the exact problem without further evaluation of analysis

data.



There are several possible ways. For example, an operational problem such as

faulty ignition will normally be accompanied by a significant decrease in the efficiency

of the machine as well as excessive vibration. A mechanical

PAGE 42

problem like unbalance may show little or no change in overall efficiency. In addition,.

operational problems tend to increase unequal reciprocating forces and, thus may show a

much greater increase in vibration in a direction parallel to the reciprocating motion but

only a small increase in vibration in the direction perpendicular to this motion.

Mechanical problems such as unbalance or misalignment will normally show a

substantial increase in two or more directions.

3.13 RUBBING

Rubbing between the stationary and rotating parts of a machine may cause the

vibration to have a frequency at twice rotating speed, in addition to the rotating speed

frequency. If the rubbing is continuous, no particular vibration characteristics are likely.

However, a very high frequency of vibration and noise may be present due to friction

exciting natural frequencies of the system.

Rubbing in the seals of a steam turbine or a similar large machine will cause

changes in amplitude and phase from one run to the next when no changes have been

made to the system. For example, a steam turbine running at 3000 RPM may have a

steady amplitude and phase of vibration at rotating speed frequency. However, reducing

the speed to, say 1500 RPM and then increasing the speed again to 3000 RPM will often

produce a new amplitude and or phase of vibration. This seems to indicate that the point

at which rubbing occurs changes from one run to the next. Of course this condition must

be corrected before balancing could be carried out.

Rubbing is usually the result of a bent shaft, broken or damaged parts, or distortion

of the system that will usually be revealed by other vibration characteristics.

PAGE 43

3.14 BEAT VIBRATION

A noticeable beat or pulsation may be the result of a single exciting force, which is

continuously changing in amplitude or frequency. However, more often a pulsating

vibration and noise results from the interaction of two or more steady-state-sources of

unequal frequency,



The pulsating noise and vibration often associated with induction type electric

motors is one example of beat. One force occurs at electrical frequency and another at

the slightly lower rotational frequency. We have referred to this slip frequency

characteristic earlier.

Pulsating noise and vibration can also occur where two or more individual

machines are involved. Consider two machines mounted side-by-side on the same

structure with one machine operating at 1500 RPM and the other at 1400 RPM. If the

vibration or noise amplitudes are significant at these two frequencies, their interaction

will result in a noticeable beat. The two forces alternately and continuously coming in-

phase and then out of phase with one another produce the beat or pulsation. When the

two are in phase, their amplitudes will add together to give a maximum resultant

vibration or noise amplitude and when the two forces are out of phase, their amplitudes

subtract or cancel one another to give the minimum overall amplitude. The beat

frequency will be equal to the difference between the two exiting force frequencies. For

the example above, the beat will occur at 1500 CPM - 1400 CPM @ 100 CPM.

Sometimes, a beating will occur at a frequency equal to the sum of the two exciting force

frequencies for our example, 1500 CPM-+ 1400 CPM = 2900 CPM. The higher beat

frequency is usually less noticeable than the low frequency beat except perhaps where a

resonant frequency of the machine or structure is being excited.

PAGE 44

4. VIBRATION MEASUREMENT 4.0 INTRODUCTION

Vibration motion is usually desired to be recorded against time. This is done by a

measurement system, which is functionally similar to that for any other physical variable,

as in figure.4.1

Physical

Variable

Output

Fig.4.1 FUNCTIONAL ELEMENTS OF A MEASURING INSTRUMENT

The three essential functional elements are 1. Transducer element 2. Signal

conditioning element and 3. Display or recording element.

Transducer Element

Signal conditioning Element

Display or Recording Element



The transducer element converts the variable to be measured, in a usableform e.g.

vibratory signal is converted to an electrical signal, by an electromechanical transducer.

The signal conditioning elements include amplifiers or filters or differentiators,

integrators etc. and convert the signal so that it is recorded or displayed, according to the

requirements.

For measurement of motion or vibration of an object, there are basically two types

of transducers.

1 Fixed reference types as shown in figure 4.2 where the motion of the moving

object is measured relative to a fixed datum (earth).

2 Seismic type transducer is shown in figure 4.3. These are used in practical

situations where a fixed datum is not available. For

PAGE 45

example, for measurement of vibrations in a moving vehicle, a bridge or of a machine

located in. an industrial environment where the disturbance due to surrounding equipment

results in no availability of the fixed datum. In such cases, the seismic transducer has to

be attached to the vibrating object. Inside the transducer is a mass mounted on a spring

and damper and the relative motion of the mass Z relative to the frame of the instrument,

is a measure of the unknown vibration "x", the relation depending on the frequency of

vibration.



4.1 VIBRATION TRANSDUCERS

A transducer or pickup is a device which converts vibratory or shock motion into an

optical or a mechanical or more commonly an electrical signals that is proportional to a

parameter. of the motion. Of course one of the most widely used vibration sensors is the

human fingertip. When accessibility and temperature allow, this is often the first sensor

to be applied in diagnosing machine vibration.

The following factors are usually borne in mind while making a choice of a

vibration transducer

* Whether a seismic or a fixed reference type of transducer is required

in the situation under consideration.

* Whether the magnitude of motion is very sm all (microns), medium (mm) or

large (cm).

* Frequency range over which vibrations are likely to be encountered and over

which the transducer is expected to have a linear frequency response.

* Whether the output of the transducer is desired to be proportional to

displacement, velocity or acceleration.

* Whether the transducer is to be of contact type or proximity type.

* Whether the transducer is of self - generating type or an external supply is

required.

PAGE 47

* The type of associated circuit and its complexity, which would also determine

its cost.

There are several types of transducers available for measurement of vl 'bration a

few commonly used is discussed below.

4.1.1 ELECTRODYNAMIC TYPE

This is a fixed reference transducer has its magnet fixed and the core with a

number of coils is attached to the vibrating object. The reverse is also possible and the

core may be fixed and the magnet attached to the vibrating object. Relative motion

induces an electrical voltage in the coil, proportional to the velocity of the vibrating

object. Integrating and differentiating circuits are needed if displacement and



acceleration respectively, are desired. This is a self generating and contact type of

transducer, which is shown in figure 4.4.

PAGE 48

4.1.2 PHOTOELECTRIC DISPLACEMENT GAUGES Another useful displacement measuring device may be constructed by using a

light source and a photoelectric cell. A photocell is, essentially a current generating

device for which the amount of current generated is proportional to the amount of light

falling on it. Hence, if the light falling on the cell can. )e made proportional to the

displacement, the photocell becomes a displacement transducer. A schematic sketch is

shown in figure 4.5a.



The photo tube consists of a cathode coated with a material (such as lithium)

which emits electrons when struck by light. If this electron emitter is connected in circuit

as shown in figure4.5b, the emitted electrons flow to the anode. and through the load

resistance (RL).

The potential across the load (EL) is proportional to the current (or electron) flow

(EL= IRL) and hence to the light falling on the photo cathode. Since the current from a

photocell is very small, a photo multiplier tube is usually used.

4.1.3 LINEAR VARIABLE DIFFERENTIAL TRANSFORMER

LVDT (Linear Variable Differential Transducer) is of contact type, whose core is

attached to the vibrating object and the coils are f xed. There is a

PAGE 50

primary coil ((P3,), supplied with AC, carrier supply (Fig.4.6). The two secondary coils

are connected in series opposition so that the output is zero when the core is in the,

middle. Vibratory motion'; increases the inductance of one coil and decreases that of the

other, producing and output which varies fairly linearly with displacement over a wide

range..

4.1.4 HAND VIBROGRAPH

The hand vibrograph is a mass-spring type of mechanical device, which measures

vibration displacement and produces a hard copy record of the displacement. The

instrument is held so that a sensing tip touches the vibrating body. The displacement of

this body is imparted to the tip, which is attached to a writing stylus through a system of



levers. A strip of recording paper is moved under the stylus at constant speed producing

a plot of instantaneous tip position vs time. It is shown in figure 4.7.

PAGE 51

The high frequency response is limited by the inertia of the mechanical lever

system. Typical, limits are: Maximum frequency response - 250 cps, Low frequency

limit 5 cps, maximum displacement 0.125 inches and resolution

0.0002

4.1.5 EDDY CURRENT PROBES

Eddy current probes are primarily used to detect vibration in rotating machines, to

monitor shaft axial position or thrust wear and to measure relative expansion between

rotor and casing of a machine. It is also a proximity probe.

The probe uses the eddy current principle to measure the distance from the coil (on

the tip of the probe) to the surface of the shaft. This is accomplished by the generation of

a small radio frequency in the proximitor (driver). The RF signal escapes into the area

surrounding the probe tip. When no conductive material is within range of the signal,

virtually all of the power released to the surrounding area is returned to the probe tip. As

a conductive surface approaches the tip, the RF sets up small eddy currents on this

surface. This eddy current creates a power loss in the RF signal and is measurable. The

nearer the target material, the greater the eddy current loss. The losses of an eddy current

system appear as a parabolic curve when measurements are made at various gap

distances. Therefore, it is necessary that the probe have a linear voltage output as a



function of gap. This is normally provided in the proximitor by internal compensation.

The output of the proximitor is a d.c. voltage which varies as the gap distance varies, thus

providing the average gap distance from the probe tip to the target surface plus vibration

excursion level in both frequency and, amplitude of observed motion

PAGE 52

An inherent feature of eddy current measurement is that it is not disturbed by non-

conductive material in the gap between the probe and its observed surface, so that oil,

steam, gases and so forth, do not adversely affect the measurement. Special probes are

available for high vacuum, high pressure and high temperatures. Other models are

designed for use in water and saturated steam and some models for gaseous/liquid

oxygen.

The proximitor signal output voltage, when used to observe a rotating body such as

a turbine shaft, gear shaft or coupling indicates the vibration amplitude and frequency on

the same plane as the probe (vertical probe/vertical plane etc.) When two probes are

mounted in an XY configuration (vertical and horizontal or otherwise 900 angularly

separated) at the same lateral location, the total shaft relative radial motion is observed.

The output of the transducer system, as a varying d.c. voltage can be displayed on an

oscilloscope to pictorially represent the exact shaft motion with respect to probe

mounting, this is very useful for malftmction diagnosis.

The following things are to be noted while using an eddy current probe.

1. It is important to, know the material of the shaft, as the surface electrical

resistance will be factor in determining the amount of energy transferred and

thus the distance between the probe tip and target.

2. The probe must be positioned so that no metal is near to the tip other than the

'target' metal surface. The mounting hole should be chamfered or counter

bored, if necessary

3. The original distance between probe tip and target must be known.

PAGE 53

Depending upon the use, standard probes are available in ranges of 5 mils to 50

mils having sensitivities from 200 mV/mil (8 mV/micron) to 100 mV/mil (4mV/micron).

Standard probes are usable at temperature up to 200'F or 350'F. The frequency response

is from DC to 5 KHz. The eddy current probe is susceptible to changes in shaft surface



e.g. mechanical run out, electrical run out (residual magnetic field), shaft finish, and

coatings of different conductivity. Submerence in water can be troublesome unless well

seated in ceramic.

4.1.6 CAPACITANCE PROBE

The capacitive transducer is a contact free displacement sensitive pick up. It finds

application where mechanical motion must be detected without loading the test specimen.

The capacitive transducer consists of a gold plated electrode, which is shielded by

the housing to prevent stray capacitance from influencing the measurements. The target

surface or shaft forms the other plate of the probe and the air in the gap is the dielectric

material. When the capacitive transducer is mounted with the plane of the electrode

parallel to and at a suitable distance from the test. specimen, an air gap capacitor is

formed which is charged by the polarization voltage of the preamplifier with a high

frequency excitation. Variations in the gap between the fixed plate to test specimen due

to vibrations vary the capacitance, which changes the excitation signal. The read out

circuitry transforms this to a DC voltage proportional to instantaneous gap. A schematic

diagram of an AC carrier system, for use with this type of transducer is shown in figure

4.8.

PAGE 54

4.1.7 VELOCITY TRANSDUCER

The electrodynamics principal is used in the velocity type seismic transducer. The

output voltage of the pickup is proportional to the relative velocity between the coil and



the magnetic flux lines being cut by the coil. The open circuit voltage 'e' generated in the

coil is

E = -BI (10-8) volts

Where:

B - flux density, .in gausses

1 - total length of the conductor in the magnetic field, in cms

(relative velocity between the coil and magnetic field, in cm/sec).

The velocity pickup unit contains a permanent magnet that is an integral part of

the case, and an inertial mass that has a coil of wire wound around it. The mass is

suspended and free to move along a specified axis (figure4.7) when the machine casing

vibrates above the natural frequency of the pickup, the inertial mass (with the coil)

remains stationary and, the permanent magnet moves in and out corresponding t(?

machine casmg.

PAGE 55

Fig: 4.7 A VELOCITY PICK UP

The sensitivity of the pickup is quite large and can be measured directly on a high

impedance voltmeter. The sensor can be supported with a magnet, bolted to the bearing,

held with epoxy or dental cement. If the mounhng, is not proper sever . ..a. se resonant

signals can come due to mounting and not from the machine where one is interested to

take measurements. Regardless of position the transverse sensitivity is practically zero.

The pickup is stable upto 30 g's and can be used upto 5000 F. It is accurate upto 600 cps.



4.1.8 MAGNETIC TRANSDUCER

The magnetic transducer is a variable reluctance device, which is used as a velocity

sensitive vibration pickup. The moving part may be either the tested structure itself, if

this is ferro-magnetic or one of the high permeability discs supplied which is glued onto

the vibrating structure in front of the electromagnet.

The transducer is used where changes in mechanical motion have to be detected

without contact or added mass and where absolute amplitude measurements are not

necessary. It should be noted that the transducer is also sensitive to motion of non-ferro

magnetic conducting materials (parts made of aluminium,' copper etc.) due to formation

of eddy currents.

A typical magnetic transducer consists of a cylindrical ticonal permanent magnet on

which a Teflon base coil is wound. The winding with 8000 turns of polyester insulated

wire combines high sensitivity with low internal impedance. Coil and magnet are

electrically isolated from the housing, which is made of nickel-plated ')rass. The coaxial

output terminal is gold-plat to ensure a good contact.

A transducer has a sensitivity of 15 mv/@sec with a high permeability disc glued to

non-magnetic surface at a distance of 2mm from the transducer face. The sensitivity in

front of a large iron plate is around 37 my/@sec. The frequency response is upto 2000

Hz.

4.1.9 OPTICAL PICK-UP

An optical pickup is a transducer intended to be used as a temporary tachorneter

temporary keyphasor assembly line parts counting etc. It consists

PAGE 57

of an infrared light source, a photo-transistor, sensitive to the infrared source, a pickup

housin , and connecting cable and is shown in figure 4.8.



Fig 4.8 OPTICAL PICK UP INSTAL.ATION

It is designed to detect the passage of an object by optical means. The transducer

is a combined infrared light source and pickup device, which is built into a common

housing. The light source (light emitting diode), when excited, operates in the infrared

region which is not visible to the eye. Its emissions,

PAGE 58

transmitted within the pickup housing via fibre-optics, exit the pickup housing and are

reflected back with the passage of a reflective target. The reflected infrared light is

focused by the pickup lens onto the base of an infrared serxsitive phototr

increased conduction. ansistor driving it into The change in current through the ~o

transistor is detected by the signal conditioner circuit of the optical driver/power supply.

Passage of the reflective tape causes the output voltage to return to its previous level

producing the pulse trailing edge.

The optical pickup is designed to detect very small targets at close distances (at 0.

1 inches) or large targets at distance upto 4.00 inches away. The points which need to be

considered for use of an optical probe are: 1) target to sensor gap, 2) type of object -

narrow or large 3) contrast between totget and non-target surfaces 4) clean pick-up tip 5)

no mechanical interference of the bracket or clamping system used with nearby

equipment.

4.1.10 PIEZO-ELECTRIC ACCELEROMETERS



Certain solid state materials respond electrically to mechanical force. These

materials can be classified into two types: 1) self-generating type 2) passive circuit type.

Piezo-electric materials are of self-generating type and they produce an electrical charge

proportional to stress. Piezo-resistive materials are of passive type and has an electrical

resistance, which depends upon, applied force.

The basic, construction of a piezoelectric accelerometer is shown i n figures 4.9.

The active spring. element consists a number of piezoelectric discs. on which a mass

rests. The mass is preloaded by a spring and the whole assembly is sealed in a metal

housing with a thick base. For frequencies far

PAGE 59

Below the resonance frequency of mass and spring, the displacement is directly

proportional to the acceleration of the base.



4.2 SIGNAL CONDITIONING ELEMENTS

The second element in the measurement system is signal-conditioning elements.

The signal conditioning elements modify the output of transducers, so that it can be

displayed, according to the requirement. These elements include.

* Amplifiers, for amplifying the output of the transducer

* Compensating elements for improving the frequency response.

* Differentiating or integrating elements for the output to be proportional to the

desired input.

* Filters, for filtering out unwanted signals.

* Analog to digital converters for converting the analog output of the transducer

to digital forms.

4.3 DISPLAY AND RECORDING ELEMENTS

These form the final stage of measurement system and may be of analog or digital

types, depending on whether the display /recording is of continuous or discrete type

respectively.

Cathode Ray Oscilloscope (CRO) shown in figure 4.10 is widely used in practice,

for display of voltage signals as a function of time and also for phase and other

measurements. The electrons released from the cathode are controlled in vertical and

horizontal directions by voltage applied to the corresponding plates. CRO's may be

single or double beam types, with signals displayed against time by adjusting the time

base frequency.

PAGE 61



4.5 ABSOLUTE MOTION MEASUREMENT

For several types of rotating machinery, it is sometimes necessary to measure the

rotor absolute dynamic motion for the evaluation of their overall mechanical integrity.

Here by absolute motion, we mean the motion relative to free space or to a fixed point in

space. Two types of transducers are used for measuring shaft absolute motion - the shaft

rider and the dual probe.

4.5.1 SHAFT RIDER

The shaft rider consists of a rod assembly which extends through the bearing

housing (not necessarily always) and literally rides on the shaft via a spring-loaded

mechanism (figure 4.1 1). The top of the rod is directly attached to a seismic transducer,

usually a velocity pickup but sometimes an accelerometer. Through its spring-loaded

mechanism , the rod attempts to follow the motion of the shaft. The attached seismic

transducer produces a signal representing shaft absolute motion.

PAGE 62

The shaft rider was originally introduced as an enhancement to seismic bearing

housing measurement transducer for making shaft vibration measurements on large fluid

film bearing equipped with stern turbine generator sets. Due to its inherent design, the

shaft rider assembly is subject to wear. The shaft end of the rod must have constant

lubrication of the proper amount, too little lubrication will cause a dry rub and resulting

chatter, too much lubrication will cause insufficient direct contact with the shaft. Under

extreme cases, improper shaft rider contact may even dwnage the shaft surface.

FIG : 4.11 ABSOLUTE SHFT MOTION MEASUREMENT



The lower and frequency response of the system is limited by the characteristic of

the seismic transducer and the upper frequency limit is primarily a function of the spring

loaded mechanism to allow the rod to faithfully follow the shaft motion. The practical

lower limit and upper limit are 10 Hz and 100 Hz respectively. With these frequency

limits, the shaft rider cannot measure the shaft bow (thermal and/or mechanical) at

machine slow roll speeds and vibration amplitudes corresponding to more than two times

shaft rotative speed for common machines (3000 or 3600 rpm)

4.5.2 DUAL PROBE

The dual probe is a combination of two transducers - an eddy current proximity

probe and a velocity probe. The proximity probe is used alone for making measurements

on machine types with small bearing housing motion and is a good indication of the shaft

dynamic motion. However, for machines with significant amplitudes of both.shaft and

housing vibration, the proximity probe is installed- in conjunction with a seismic

transducer on the bearing housin Both transducers measure in the same axis and have the

same reference,' the bearing housing.

The basic functions of the dual probe assembly and interconnected components

are shown in figure 4.1 1. Here the relative motion of the shaft is considered to be in

phase with the case motion. The proximity probe measures shaft motion displacement

relative to its mounted location, e.g. the machine case or bearing housing. The velocity

seismic probe produces a case bearing housing velocity signal. The velocity signal is

integrated to displacement and the amplitude and phase are corrected for lower

frequencies. Then, the relative probe and seismic displacement signals are summed

vectorially to produce a measurement of the, shaft absolute motion.



Fig: 4.11 DUAL PROBE FUNCTIONAL DIAGROM

The dual probe assembly provides the following information

1 . Shaft absolute dynamic motion

2. Shaft dynamic motion relative to the bearing housing, including slow roll

data

3 Bearing housing absolute motion

4. Shaft average radial position within the bearing clearance ( relative to the

bearing center)

Shaft riders directly contact the shaft causing wear between shaft rider tip and the

shaft. It must be located in a lubricated area which usually means going through ;i

bearing. The shaft rider is susceptible to oil whip' and has poor frequency response (good

from 10 to 120 Hz). Due to moving parts and direct contact, sticking, slip bounce, and

chatter can occur which may give erroneous readings. These factors make it difficult to

calibrate a shaft rider system.

PAGE 65

Proximity sensors do not contact the shaft surface at all, but obtain a reading about

0.050 inch from the surface by transmitting and receiving a magnetic filed and getting its

measurements from the field intensity which is 'proportional to gap distance. ' There are

no moving parts (except the seismic sensor for absolute measurement) providing

excellent reliability and no wear. Accuracy and sensitivity are good upto 5 KHz.

PAGE 66



5. VIBRATION ANALYSIS 5.0 INTRODUCTION

Vibrations are motions of components or machinery parts, which is very small and

perform oscillations quite fast. Such phenomenon is called dynamic motion. The

measurement of dynamic phenomena is not so easy. This measurement is made possible

by converting the mechanical parameter into electrical voltage with the help of

transducers with good linearity. The electrical voltages generated by the transducers are

called signals.' These signals can be measured easily and calibration is made possible to

determine the value of mechanical parameter from the electrical voltages. With help of

these signals two important basic purpose are served viz.

* Precise measurement of the level or measurement of the parameter with high

resolufion.

* Measurement of rapidity i.e. frequency of oscillation.

The purpose of signal analysis is to measure frequency contained in it. This has

become possible because of advancement in electronic instrumentation.

5.1 SIGNAL ANALYSIS

There are several sources of forced excitations acting on the rotor, bearing etc.,

during operation of the rotating machinery. The dynwnic forces are defined by means of

their frequency, amplitude and phase. The machine produces response of these forces

depending on its dynamic characteristics. This response (i.e. time domain measurement);

is generally measured by transducers such as accelerometers, velocity pickups etc. The

most convenient

PAGE 67

location of measuring the response signals is the bearing caps. The signals (i.e.

acceleration or velocity signals) may have several frequency components. In general,

signal analysis performed by a spectrum analyser indicates the manner in which, signal

energy is distributed as a function of frequency. This technique is extremely important

because frequency characteristics of vibration signals are generally more revealing than

the domain characteristics. Typical time domain signal and its frequency domain

spectrum are shown,in Fig.5. I. The spectrum analysis of the response signals forms the

basis of signature analysis.



Fig: 5.1 THE TIME DIDMINE AND FREQUENCY DOMINE SPECTRUM

Signature analysis is a technique based on analyzed frequency spectrum of

vibration signals collected !tom the operating machine to determine the i) condition of the

machine and ii) to diagnose the.cause of the fault.

PAGE 68

5.1.1. CONDITION OF THE MACHINE

This is primarily to monitor the health of the machine. To assess the condition of

the machine a better approach is to know the vibration signature of the machine when it is

healthy. This healthy machine vibration signature is taken as a base line. During

operation t',ie condition of the machine deteriorates. This results in vibration signature

deviation from the base line signatures. It is required to compare the vibration signatures

over a period of time of machine operation with the established base line signature. A

skilled engineer can then easily realize when maintenance is required in order to avoid

catastrophic failure. This is a successful technique and if applied properly can save lakhs

of rupees.

5.1.2 FAULT DIAGNOSIS

The nature of fault can be directly related to the distribution of energy of the

vibration signal among various harmonics of frequency. The vibration of rotating

machinery contain synchronous (i.e. lx) frequency (i.e. frequency of rotation) and its



higher harmonics (such as 2x, 3x etc.) and sub~harmonics (suph as 0.5 x). Table5.1

gives the cause of vibration and their @equency relations.

5.2 VIBRATION ANALYSIS SYSTEM

The various functional elements of vibration analysis s@tem are shown in figure

5.2. A portable vibration meter with a transducer is widely used to get the RMS value of

the signal. The charge amplifier has high impedance at its input and low impedance at its

output. The integrators are used in case the output reading is required to be proportional

to velocity or displacement. The voltage signal is then applied to a detector for giving

RMS value, which squares. averages and find out the square root of the voltage signal

which is

PAGE 69

indicated as the RMS value of the signal. The RMS value of the signal, especially of the

velocity signal, gives a useful indication about the health or condition of a machine.

VOLTAGE

SIGNAL

Fig: 5.2 RMS VALUE OF SIGNAL AS SEEN ON VIBROMETER

5.2.1 FREQUENCY ANALYSIS

In vibration analysis, it is more convenient to work in the frequency domain rather

than in the time domain. Often , the time domain signal gives too much information in an

unintelligible form. Conversion of the signal to the frequency domain makes the

interpretation of data contained by it much simpler. This has led to the idea of frequency

analysis, where the amplitude against time signals is converted to one of amplitude

against frequency. It has become one of the most important toojs in vibration

measurement, The object of frequency analysis is to break down a complex signal into its

components at

The role of frequency analysis is to provide useful information or data about a

machine from its vibration signals. These signals representing the machine's vibratory

ACCELERO METER

CHAARGE AAMPLIFIER

INTEGRATORS

SQUARING AVERAGING SQUARE ROOT

VIBRATION METER



motion are complex in nature and are composed of many frequencies at different

amplitudes related to the forces being generated by

PAGE 70

various components of the machine. Since the design characteristics of the machine

permit us to calculate forcing frequencies associated with the machine at various speeds,

processmg in the frequency domain gives us convenient relationships to use in the

interpretation of the data.

Filters are used in measurements of frequency spectrum components. They have

the ability to exclude all frequencies 1 other than those in a limited range around their

"centre frequency".

There are two basic types of filters used for the frequency analysis: the constant

bandwidth type filter, where the filter is a constant absolute bandwidth and the constant

percentage bandwidth filter where the filter bandwidth is a constant percentage of the

tuned centre frequency.

Constant bandwidth analysis gives better frequency resolution at high frequencies

and when plotted on a linear frequency scale is particularly valuable for sorting out

harmonic, patterns etc.

Constant percentage bandwidth analysis tends to match the natural response of

mechanical systems to forced vibrations, and allows a wide frequency range to be plotted

on a compact chart.

Two special classes of constant percentage bandwidth filters octave and third octave

are widely used. The octave filters have a bandwidth such that the upper limiting

frequency of the pass band is always twice the lower limiting frequency, resulting in a

band@idth of 70.7%. Third octave filters are obtained by dividing each octave band into

three geometrically equal sub-sections. The percentage of bandwidth of third octave

filter is 23. 1 %. Commercially available frequency analysis has percentage band width as

low as 3% or still lower in the case of more sophisticated instruments.

PAGE 71

5.2.2 HOW FREQUENCY ANALYSIS IS DONE:

Frequency analysis of vibration signals will involve the basic functions of

filtering, detecting, and displaying of the data (figure 3.4).



SIGNAL IN

Fig: 3.4 METHOD FOR FREQUENCY ANALYSIS

These functions may be accomplished using analog techniques, digital techniques,

or a combination of the two. Digital techniques offer many advantages including

decreased processing time required, ease of performing various operations, high

resolution and good repeatability. The type of filtering used classifies the processing

systems.

Many signal processing techniques and methods are conducive to machinery vibration

analysis. Although most signals will be stationary and periodic in nature, many of the

techniques are applicable to non-stationary signals as well. Primarily, most processing

for machinery vibration analysis work is based on the Fourier Analysis concept or the

representation of a complex waveform in tenns of its various frequency components.

Such processing will permit one to analyze the vibration amplitudes (displacement,

velocity, and acceleration) at specific frequencies. This concept and its many variations

have given us frequency analysis methods, which are utilized extensively in today's

machinery vibration analysis work.

5.3 PROCEDURE FOR SOLVING VIBRATION PROBLEMS

Experience leads to the conclusion that the major task in solving, machine

vibration problems is to identify the specific problem or cause of vibration.

PAGE 72

Once this has been done, the solution of the problem is often straightforward. Of

course, there are some cases of inherently poor machine design, where there is no

practical way to correct the problem, short of replacing the equipment. The only

approach to this situation is to obtain a clear definition of the problem (or machine

deficiency) and how this causes the vibration. Operating conditions must then be

adjusted to accommodate the limitations of the machine, one can often safely "live with

the proble@', having done this.

5.3.1 DATA TO DEFINE THE PROBLEMS.

FILTER DETECTOR RECORDER



The first step towards defining the problem is to marshal the evidence. that

indicates the presence of a problem. Presumably the problem came into being only

recently, what were the attendant circumstances, and what coincident changes occurred in

monitored operating variables. Some of these data which should be gathered and studied

are listed below:

a) Charts from recording vibration monitors, or plots of daily or periodic log-

sheet readings of such monitor and any evidence, which indicates whether

the vibration increased gradually or suddenly.

b) A "profile" sketch of vibration readings, indicating the amplitudes at all

monitored locations, or at all points where readings were taken with

portable instruments.

c) Recent history of bearing and oil temperatures, and condition of the oil

supply and scavenging system.

d) Statements,from operating personnel about changes in audible noise level

or character.

e) History of deliberate changes in the process (i.e., load, rotational speed,

process fluid flow rate, pressure and temperatures) for the period

immediately before and after the problem first arose.

PAGE 73

f) History of dependent performance parameters over the swne period,

indicating deterioration of process performance.

5.3.2 LONG TERM HISTORY OF THE MACHINE:

Next, one should review the earlier history of the individual machine, from both

operating and maintenance aspects. It include the following.

a. Were there difficulties during installation or initial start-up? What was the

nature of these difficulties? Could they be reappearing to cause the present

problem and were they ever really solved at the beginning of operation?

b. Is there a history of previous failures? Were these of consistent nature, or

randomly different?

c. How long has the machine run since the last outage or failure?

d. Has the performance of the machine varied over a long-term cycle?



e. What components have been repaired, replaced, and which components are

known to be in worn or damaged condition.

f. Has there been heavy construction activity or vehicle traffic in the immediate

area, which,might have affected foundation or alignment?

g. Is a vibration signature analysis available, which was taken when the machine

was known to be in good condition and running well?

h. Are the results of a critical speed and unbalance response analysis avai

lable'for the rotor-bearing system.

Close scrutiny of the data arrayed above can some times identify a problble cause

for vibration, or at least offer guidance for further investigation.

As an example, consider the actual case of a steam turbine driving a compressor

supply' ing process air. The unit had been operating satisfactorily for over 1 5 years. For

some unknown reason the vibration amplitude increase to the

PAGE 74

point where an oil pressure gage connection failed, causing a fire and requiring shut

down. The turbine was overhauled, the rotor rebalanced, the bearings replaced, the unit

was put back on line, and still vibrated excessively. Vibration signature data taken at

constant running speed revealed no apparent cause, only the fact that the rotor appeared

to be out of balance. This was disputed by the fact that it had just returned from overhaul

and rebalancing.

The problem was finally identified when process operations allowed the unit to be

taken off line again, vibrations data were then recor ded over the complete speed range,

from start up to just under trip speed. A tracking filter plot mode from the data clearly

defined a critical speed within the operating stage.

It also cwne to light that the throughput of the process had been reduced at the

time the vibration started, due to reduced capacity of downstrewn equipment. This had

required the compressor and turbine to operate at a lower . During the previous 15 years

period, the turbine had been running above this critical, basically a low vibration

condition. The new, lower operating speed coincided with the critical, where vibration

wnplitude was much more sensitive to small amounts of rotor unbalance.

Once this problem had been identified, compensating measure was put into effect.

There were economic arguments against modifying the turbine to shift the critical speed.



Therefore, more stringent balancing procedures and tolerances were instituted to

eliminate dynamic unbalance and reduce bending moments due to residual unbalance in

the turbine disk. Also, the operating speed was shifted as much as the process would

allow.

PAGE 75

The point of this example is that a review of recent operating changes, together

with some knowledge of the critical speed, would have allowed almost immediate

identification of this problem.

5.3.3 FIELD MEASUREMENT ANALYSIS PROCEDURES:

If the problem has manifested itself through vibration while the machine is still

operating, rather than by structural failure, the lower frequency components of vibration

will probably tell the story. If the problem centers more on performance deterioration or

change in audible noise, the higher frequency components may prove more informative.

Portable vibration meters with tunable band pass filters are frequently adequate, to

narrow down the range of possible cause. If the predominant amplitude occurs at sub-

rotational frequency, for instance, bearing instability should immediately be suspected. If

rotational frequency dominates, then some form of unbalance response problem is

probably involved. Amplitude and frequency measurements should be made on the

bearing caps'. If proximityprobe monitors are installed, the raw data signal should either

be observed on an oscilloscope or put through a band pass filter to identify the major

frequency.

If rotational frequency is the dominant component, further measurements with the

portable meter may help to identify the problem. Determine the end-toend phase

relationship at the two bearings. This can be done if the meter has a strobe light

(normally used for balancing) or with proximity probes by using an oscilloscope.

The tracking filter plot is one of the most informative types of test data This can be

obtained by tape-recording signals from shaft proximity probes or bearing cap vibration

sensors while the machine is run through its entire specs



range. Transient tests of this nature will often reveal loose rotor parts, shifting balance

conditions, instabilities and other faults. It is strongly recommended that provision be

made for this type of test.

If the problem includes larger vibration amplitudes on the bearing caps, inadequate

stiffness of the pedestals or foundation may be contributing. It may help define the

problem if the deflection mode shape or profile of the pedestal structure is developed.

This can be done by measuring vibration amplitudes with a portable meter at several

locations on the structure at constant speed.

In some instances, it may be helpful to experimentally determine natural

frequencies of the rotor and pedestal supports by impact ringing or "bang" tests.

Finally, a broad band signature analysis may reveal defective conditions,, which

cause or contribute to the problem.

Table 5.1 presents a list of typical operating faults, possible causes, and corrective

actions, which might be taken.



Table 5.1

MAACHINERY VIBRATION DIAGNOSTIC GUIDE

Probable source Disturbing

Frequency Dominant Plane Phase Angle Relationship Amplitude

1 2 3 4 5 UNBALANCE :

1. Mass imbalance 1x rotor speed Radial (Axial is higher on overhung rotors)

Force in phase (90o)

Steady

2. Bent Shft 1xrpm(2x rpm if bent at the coupling)

Axial 180o out of phase axially

Steady

3. Eccentric motor rotor

1x rpm, 1x and 2x line frequency

Radial N/A Steady

MISALIGNMENT 1. Parallel 1x,2x rpm Radial Radial - 180o

out of phase

2. Angular 1x,2x rpm Axial Axials - 180o out of phase

3. Both parallel and angular

1x,2x rpm Radial and axial Both radial and axial will be 180o out of phase

Steady

ELECTRICALLY INDUCED

1. All electrically caused problems can be isolated, i.e. eliminated by cutting the current to motor

2x slip frequency sidebands around 1x rpm, 1x and 2x line frequency

Radial N/A Steady

2. Loose stator laminaations

2x line frequency and high frequency (60KCPM) sidebands of 2x line frequency

Radial N/A High, steady

3. Broken rotor bar running speed with 2x slip frequency sidebands

Radial N/A Steady

4. Unbalanced coil or phase resistance

2x line frequency Radial N/A Low, steady

5. Stator problems (heating, shorts)

2x line frequency Radial (can also cause axial)

N/A Steady

6. Loose iron 2x line frequency Radial N/A High, steady



DEFECTIVE BEARINGS

1. Anti friction Early stages - 30 - 60KCPM depending on size and speed Late stages - high 1x & multiple harmonics

Radial, except higher axiaal on thrust bearing

N/A Increase as bearing degrades, may disappear just before failure

2. Sleeve Early stages -sub - harmonics (may only be noticeable on shaft)

Radial Shaft proximity probe orbits will indicate shaft position & dynamic charges

Increases as bearing degrades.

MECHANICAL LOOSENESS

1. Bearings, pedestals, etc. (non-rotating)

1x,2x and 3x predominant may be upto 10x at lower amplitude

Radial Varies with type of looseness

Steady

2. Impellers, etc. (rotating)

1x predominant, but may have harmonics upto 10x at low levels

Radial Will vary from start-up to start-up

Steady while running, but will vary from start up to start-up.

OPERATION (process related)

1. Blade/vane pass No. of blades/vane x rpm

Radial predominant in the direction of discharge piping

N/A Fluctuating

2. Cavitation or starvation

Random broadband Radial N/A Fluctuating



DRIVE BELTS 1. Mis-matched, worn or stretched- also applies to adjustable sheave applications.

Many multiples of belt frequency but 2x belt frequency usually dominant

Radial, especially high in the with belts

N/A May be unsteady and beating if a belt frequency is close to driver or driven speed

2. Eccentric and/or unbalanced sheaves

1x shaft speed Radial In-phase Steady

3. Drive belt or sheave misalignment

1x driver shaft Axial In-phase Steady

4. Drive belt resonance belt resonance with no relationship to rotational speeds

Radial N/A May be unsteady

RESONANCE Requires forcing funciton tom excite its natural frequencies

Axial or radial A center hung rotor resonance will display 180o out of phase bearing relationships. A component within a structure will disphay phase relationships dependent upon the bending mode excited.

Steady, but baseline energy functuations depend on force and damping

INSTABILITY 1) Oil whirl 40 to 46 percent of

running speed Radial N/A Steady

2) Oil whip Sun-rotational and equal to shaft resonance.

Radial N/A Steady

3) Rotor rub 50 percent of running speed and half harmonics

Radial N/A Steady



GEARS

1) Transmission error (poorly finished tooth face)

Gear mesh frequency (gear rpm x no. of teeth) and harmonics

Radial for spur gears, axial for helical or herringbone gears

N/A Depends on loadign, speed and total transmission error.

2) Pitch line run out, mass unbalanec, misalignment or faulty tooth

1x rpm and gear mesh frequency with +,- gear rpm side bands

Radial for spur gears, axial for helical or herringbone gears

N/A 1x rpm and mech. Frequency side bands depend on fault severity.



Vibration

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