An Analytical Approach to Solving Motor Vibration P

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An Analytical Approach to Solving Motor Vibration Problems

Copyright material IEEE

Paper No. PCIC-99-20

Mark M. Hodowanec

Member

Industrial Products Division

Siemens Energy & Automation, Inc.

4620 Forest Ave.

Norwood, OH 45212

William R. Finley

Senior Member

Large Motors & Pumps

Siemens Energy & Automation, Inc.

4620 Forest Ave.

Norwood, OH 45212

Warren G. Holter

Industrial Products Division

Siemens Energy & Automation, Inc.

4620 Forest Ave.

Norwood, OH 45212

Abstract: Vibration problems in induction motors can be

extremely frustrating and may lead to greatly reduced

reliability. It is imperative, in all operations and manufacturing

processes that down time is avoided or minimized. If a

problem does occur the source of the problem is quickly

identified and corrected. With proper knowledge and

diagnostic procedures, it is normally possible to quickly

pinpoint the cause of the vibration. All too often erroneous

conclusions are reached as a consequence of not

understanding the root cause of the vibration. This may result

in trying to fix an incorrectly diagnosed problem, spending a

significant amount of time and money in the process. By

utilizing the proper data collection and analysis techniques,

the true source of the vibration can be discovered. This

includes, but is not limited to:

Electrical imbalance

Mechanical unbalance – motor, coupling, or driven equipment

Mechanical effects – looseness, rubbing, bearings, etc.

External effects - base, driven equipment, misalignment, etc.

Resonance, critical speeds, reed critical etc.

Once the electrical and mechanical interactions in a motor are

understood, and the influence external components have on

the apparent motor vibration, identification of the offending

component is usually straightforward. This paper provides an

analytical approach for expeditiously understanding and

solving these types of problems.

Index Terms: Induction Motors, Troubleshooting Vibrations,

Cause of Vibration.

most critical concern. To solve a vibration problem one must

differentiate between cause and effect. For this to happen,

one must first understand the root cause of the vibration. In

other words: where does the force come from? Is the

vibratory force the cause of the high levels of vibration or is

there a resonance that amplifies the vibratory response.

Perhaps the support structure is just not stiff enough to

minimize the displacement. In this paper the various sources

of electrical and mechanical forces will be explained.

Additionally, how the motor reacts or transmits this force and

how this force can be amplified or minimized will be explained

as well. When a vibration problem occurs it is important that

one use a good systematic, analytical approach in resolving

the problem. This includes performing the proper diagnostic

tests. The process starts by listing all the possible causes for

the particular identified frequency of vibration and any

variations under different operating conditions. Then eliminate

the incorrect causes one by one until all that remains is the

true source of the problem, and now this can be efficiently

eliminated.

II. SOURCES OF VIBRATION

There are many electrical and mechanical forces present in

induction motors that can cause vibrations. Additionally,

interaction of these various forces make identification of the

root cause elusive. In subsequent sections, the major

mechanisms are discussed. For a more comprehensive list of

electrically and mechanically induced vibrations Table I should

be referenced.

I. INTRODUCTION

Much has been written about vibration over the years. This

includes many papers and books on vibration in general and a

number of papers on vibration in induction motors in

particular. This is an ongoing subject, continually extended by

advances in analytical and diagnostic tools and methods. For

this reason, and because this is an important and complex

subject, it is worthwhile periodically to both present any new

knowledge and experience as well as to review prior

knowledge and concepts.

Vibration problems can occur at anytime in the installation or

operation of a motor. When they occur it is normally critical

that one reacts quickly to solve the problem. If not solved

quickly, one could either expect long term damage to the

motor or immediate failure, which would result in immediate

loss of production. The loss of production is oftentimes the

Page 1 of 16

FIG. 1. Stator and Rotor

Twice Line Frequency Vibration:

There are many different forces and interactions as a result of

the power source and the interactions between the stator and

rotor as seen in Fig. 1. The power source is a sinusoidal

voltage that varies from positive to negative peak voltage in

each cycle. Many different problems either electrical or

mechanical in nature can cause vibration at the same or

similar frequencies. One must look closely to differentiate

between the true sources of vibration.

A power supply produces an electromagnetic attracting force

between the stator and rotor which is at a maximum when the

magnetizing current flowing in the stator is at a maximum

either positive or negative at that instant in time. As a result

there will be 2 peak forces during each cycle of the voltage or

current wave reducing to zero at the point in time when the

current and fundamental flux wave pass through zero as

demonstrated in Fig. 2. This will result in a frequency of

vibration equal to 2 times the frequency of the power source

(twice line frequency vibration). This particular vibration is

extremely sensitive to the motor's foot flatness, frame and

base stiffness and how consistent the air gap is between the

stator and rotor, around the stator bore. It is also influenced

by the eccentricity of the rotor.

vibration which is created by an unbalanced magnetic pull due

to air gap dissymmetry and does not change with load.

On 2 pole motors, the twice line frequency vibration level will

appear to modulate over time due to it’s close relationship

with 2 times rotational vibration. Problems in a motor such as

a rub, loose parts, a bent shaft extension or elliptical bearing

journals can cause vibration at 2 times rotational frequency.

Due to it’s closeness in frequency to twice line frequency

vibration the two levels will add when they are in phase and

subtract when they are out of phase and then add again when

they return to being in phase. This modulation will repeat at a

frequency of 2 times the slip on 2 pole motors. Even at no-load, twice rotation vibration on 2 pole motors will vary from

7200 cpm (120Hz) due to slip. Since there is some slip on

Induction motors, although small at no load, it may take 5 to

15 minutes to slip one rotation. For those of you not familiar

with the term slip, there is a rotating field around the stator

that the rotor is trying to stay in phase with, but the rotor will

fall behind the stator field a certain number of revolutions per

minute depending upon the load. The greater the load the

greater the slip. Slip is typically 1% of rated speed at full load,

and decreases to near 0 slip at no-load. Since vibration levels

are not constant, to measure vibration, many times it is

necessary to perform what is referred to as a modulation test.

In a modulation vibration test the motor is allowed to run for a

period of typically 10 or 15 minutes, and vibration is recorded

Flux - Flux Around a Stator on a 2 Pole Motorcontinuously to allow the maximum and minimum to be

established.

Elliptical Stator due to Fundamental Flux:

0180360

As can be seen in Fig. 3, for 2-pole motors the

electromechanical force will attempt to deflect the stator into

an elliptical shape. The primary resistance to movement is the

Force - Force Between a Stator & Rotor on a 2 Pole Motorstrength of the core back iron and the stiffness of the housing

around the stator core, which is restraining the core's

movement. On 4 pole motors the distance between the nodes

is only 45 mechanical degrees, ½ that seen on 2 pole motors,

0180360thereby making the 4 pole stator core much stiffer to

movement resulting in much lower twice line frequency

vibration. Calculations on a typical 1000 HP two pole motor at

Fig. 2. One Period Flux Wave & Magnetic Force Wave

60 Hz show 120 Hz vibration at the stator core OD of about

Some people are inaccurately under the premise that twice

.12 inches per second, peak, while values for a four pole

line frequency vibration varies with load. This misconception

motor of the same size are only about .02 to .03 inches per

comes from the belief that twice line frequency vibration

second, one sixth to one quarter of this value. This twice line

excitation is due to a magnetic field generated by the current

frequency vibration is transmitted through the motor frame to

in the stator coil which varies with load and creates a

the bearing brackets where it is reduced somewhat in

magnetic force which varies with the load current squared. In

amplitude.

reality the ampere-turns of the stator and rotor tend to balance

one another except for the excitation ampere-turns. To

explain this to those not familiar with motor electrical theory,

the excitation ampere-turns are created by the motor no load

current. This establishes the magnetic field in the motor

necessary to generate a back EMF approximately equal to the

applied voltage. As load is applied to the motor, both stator

and rotor currents increase together and balance one another,

therefore, there are no significant changes in flux. This

means that the basic magnetic forces are independent of load

current and are nearly the same at no load or full load.

Therefore the main component of twice line frequency

Fig. 3. Electromechanical Force on 2 & 4 Pole Motors

Page 2 of 16

Non Symmetrical Air-gap:

Twice line frequency vibration levels can significantly increase

when the air gap is not symmetrical between the stator and

rotor as shown in Fig. 4.

One Times Rotation Vibration - Electrical

Eccentric Rotor:

An eccentric rotor, which means the rotor core OD is not

concentric with the bearing journals, creates a point of

minimum air gap which rotates with the rotor at one times

rotational frequency. Associated with this there will be a net

balanced magnetic force acting at the point of minimum air

gap, since the force acting at the minimum gap is greater than

the force at the maximum gap, as illustrated in Figure 5. This

net unbalance force will rotate at rotational frequency, with the

minimum air gap, causing vibration at one time rotational

frequency.

The flux causing the magnetic force is the fundamental flux

wave, which rotates around the stator at the synchronous

speed of the motor. The rotor attempts to keep up with the

rotating flux wave of the stator, but the rotor slips behind the

stator field as needed to create the necessary torque for the

load. When the high point of the rotor (point of minimum air

gap) aligns with the high point (maximum) of the stator flux,

the force will be a maximum, and then it will decrease,

Fig. 4. Unsymmetrical Air Gap Around Rotor

becoming small under a point of minimum flux. Thus, an

This particular condition will result in the force being greater in

unbalance force is created which rotates at rotational speed

the direction of the smaller air gap. That is, an unbalanced

and changes in magnitude with slip. The end result is a one

times rotational speed vibration, which modulates in amplitude

magnetic pull will exist in the direction of the minimum air gap.

with slip. This condition occurs at no load or full load. At no

2load, the frequency approaches synchronous speed and could

Force ≈ B/d

have a modulation period of 5 to 15 minutes. At full load the

Where B= Flux density

frequency of modulation in CPM will equal the slip in rpm

And d= distance across air gap

times the number of poles. The slip is equal to the

Of interest here, not only is the stator pulled in one direction,

synchronous speed minus the full load speed, typically 1% of

but also the rotor is pulled in the opposite direction, to the side

rated rpm. For example, a 2-pole motor with a full load speed

that has the minimum air gap. This causes higher shaft

of 3564 rpm at 60 Hz will have a slip of 3600-3564 = 36 cycles

vibration, which is more detrimental to bearing life. Note that

per minute (1% slip) and will result in a modulation frequency

in Fig. 4 the rotor OD is concentric with the axis of rotation

of 2*36 = 72 cycles per minute.

thereby causing the force to remain a maximum in the

direction of minimum air gap.

One Times Line Frequency Vibration:

Although not nearly as prevalent as twice line frequency

vibration, one times line frequency vibration can exist.

Unbalanced magnetic pull may result in vibration at line

frequency (one times line frequency) as well as the usual

twice line frequency vibration. If the rotor or stator moves

from side to side, the point of minimum air gap may move

from one side of the motor to the other. When the frequency

of this motion corresponds to the frequency of the traveling

flux wave, the unbalanced magnetic pull will shift from side to

side with the point of minimum gap, resulting in vibration at

line frequency. This line frequency vibration is normally very

small or non-existent, but if the stator or rotor system has a

Fig. 5. Eccentric Rotor

resonance at, or near, line frequency, the vibration may be

large.

Broken Rotor Bar:

If a broken rotor bar or open braze joint exists, no current will

flow in the rotor bar as shown in Fig. 6. As a result the field in

Page 3 of 16

the rotor around that particular bar will not exist. Therefore the

force applied to that side of the rotor would be different from

that on the other side of the rotor again creating an

unbalanced magnetic force that rotates at one times rotational

speed and modulates at a frequency equal to slip frequency

times the number of poles.

requirements normally do not require that these frequencies

be included in overall vibration.

Fig. 6. Rotor with Broken Rotor Bar

If one of the rotor bars has a different resistivity a similar

phenomenon (as in the case of a broken rotor bar) can exist.

It should be noted that this is one of the few conditions that

can not be seen at no-load. But there is an additional

phenomenon associated with this condition that can be seen

at no load after the motor is heated to full load temperature by

any method that creates rotor current. These methods would

include, coupled full load test, dual frequency heat run,

multiple accelerations or heating by locking rotor and applying

voltage. In addition, broken rotor bars or a variation in bar

resistivity will cause a variation in heating around the rotor.

This in turn can bow the rotor, creating an eccentric rotor,

causing basic rotor unbalance and a greater unbalanced

magnetic pull, thereby creating a high one times and some

minimal twice line frequency vibration.

Rotor Bar Passing Frequency Vibration:

High frequency, load-related magnetic vibration at or near

rotor slot passing frequency is generated in the motor stator

when current is induced into the rotor bars under load. The

magnitude of this vibration varies with load, increasing as load

increases. The electrical current in the bars creates a

magnetic field around the bars that applies an attracting force

to the stator teeth. These radial and tangential forces which

are applied to the stator teeth, as seen in Fig. 7, create

vibration of the stator core and teeth.

This source of vibration is at a frequency which is much

greater than frequencies normally measured during normal

vibration tests. Due to the extremely high frequencies, even

very low displacements can cause high velocities if the

frequency range under test is opened up to include these

frequencies. Though these levels and frequencies can be

picked up on the motor frame and bearing housings,

significant levels of vibration at these higher frequencies will

not be seen between shaft and bearing housing where they

could be damaging. For this reason vibration specification

Fig. 7. Magnetic Field around Rotor Bar and Resulting Force

on Stator Teeth

Since vibration at rotor bar passing frequency occurs at a high

frequency, the vibration velocity level may be significant, but

the effect on motor reliability is insignificant. Considering the

stress that results in the motor as a consequence of the

vibration makes this determination. For example, suppose a

two pole motor exhibiting a vibration at 2800 Hz due to rotor

bar passing frequency plus a 120 Hz side band:

Velocity, (IPS) 0.1 0.5

Displacement (mils) 0.011 .057

Stress in Stator Core Iron 30 psi 150 psi

Stress in Stator Tooth Iron 50 psi 250 psi

The typical fatigue strength of the core iron is 35,000 psi.

Similar low stress levels can be calculated for all parts of the

motor (including the stator windings). In addition, the typical

minimum oil film thickness ranges from 1.0 mils to 1.5 mils.

Since only a small displacement such as .011 to .057 mils as

mentioned above could be seen, this vibration will not have an

adverse affect on bearing performance.

The rotor slot and side band frequencies are in the frequency

range normally related to noise rather than vibration

performance, and are taken into account in noise predictions

during motor design. In fact, these force components are the

principal sources of high frequency noise in electrical

machines, which has been for some time subject to noise

regulations and limits. Experience has shown that where

noise has been within normal or even high ranges, there has

been no associated structural damage. The significance of

these high frequency vibrations is distorted by taking

measurements in velocity and then applying limits based on

experience with lower frequency vibration.

Load Related Magnetic Force Frequencies and Mode Shapes

The frequencies of the load related magnetic forces applied to

the stator teeth and core equal the passing frequency of the

Page 4 of 16

rotor bars plus side bands at + or – 2f, 4f, 6f and 8f Hz, where

f is the line frequency. A magnetic force is generated at the

passing frequency of the rotor slot (FQR), which is motor

speed in revolution per second times the number of rotor slots

as shown in (3).

FQR = RPM*Nr / 60, Hz (3)

where

Nr = number of rotor slots

For the typical two pole 3570 rpm motor with 45 rotor slots in

the example above, FQR = 2680 Hz.

The side bands are created when the amplitude of this force is

modulated at two times the frequency of the power source.

On a 60 Hz system the 120 Hz modulation produces the side

bands, giving excitation frequencies of FQR, FQR + 120, FQR

– 120, FQR + 240, FQR – 240 Hz, etc.

The forces applied to the stator teeth are not evenly

distributed to every tooth at any instant in time; they are

applied with different magnitudes at different teeth, depending

upon the relative rotor- and stator-tooth location. This results

in force waves over the stator circumference. The mode

shape of these magnetic force waves is a result of the

difference between the number of rotor and stator slots as

shown in (4).

(4) M = (Ns – Nr) +/-KP

Where

Ns = number of stator slots

Nr = number of rotor slots

P = number of poles

K = all integers 0, 1, 2, 3, etc.

Mode Shapes and Natural Frequencies of Core Vibration:

Under the applied magnetic forces the stator core is set into

vibration in the same manner that a ring of steel would

respond if struck. Depending upon the modal pattern and

frequencies of the exciting force, as described above, the

stator would vibrate in one or more of its flexural modes m of

vibration, as shown in Figure 8. Each of the mode shapes

has its associated natural frequency. The core may be

somewhat influenced by the stator frame in actuality, but in

analysis the frame is usually neglected, both due to

complexity and because the effect on higher frequency modes

is minimal.

To understand the resonant frequency of the core at a given

mode of vibration, the core can be represented as a beam,

which is simply supported on both ends and flexes between

the ends due to forces applied on the beam. The length of the

beam is equal to the circumferential length of the mean

diameter of the stator core for one-half the mode wave length

(see Fig. 9) [8].

ΠDs

L=2MIf the resonant frequency of the core is close to the forcing

frequency, a high level of vibration will result. The lower

modes of vibration may produce resonant frequencies that are

close to the primary forcing frequencies.

Fig. 8.

Mode Shapes

Fig.9. a) Fourth Mode of Vibration

b) Linear Representation of Core

for one-half Wavelength of Force

Page 5 of 16

Fig. 10. Stator Tooth Forces

The frequency of stator tooth resonance is also a concern.

The tangential forces applied to the teeth can excite a

resonant condition in the tooth. The tooth is a cantilever

beam supported at the root by the core. The resonant

frequency of the cantilever beam is a function of the beam

length and width. A longer and narrower beam will produce a

lower resonant frequency.

The force applied to each tooth produces displacement of the

tooth and the core. The displacement will have a greater

amplification the closer the forcing frequency is to the

resonant frequency of the core or tooth (5):

1 (5)

AmplificationFactor=1−(ff0)2

Where

f

is the line frequency and

f0 is the natural frequency.

This vibration is sometimes incorrectly associated with loose

rotor bars, but there are reasons why loose rotor bars won’t

create rotor slot passing frequency vibration.

First, on most larger motors the centrifugal forces are so great

that the only time there could possibly be rotor bar movement

is while the rotor is accelerating. This in itself could be a

serious problem since the number one cause of rotor bar to

end connector failure is rotor bar movement as a result of

multiple restarts of a high inertia load. But, the only increase in

vibration at speed due to loose rotor bars would be due to a

shift in the rotor cage causing a one times rotational

mechanical unbalance.

Secondly, looking at any one rotor bar, the bar itself is never

subject to a force at the rotor slot passing. The bars are

rotating at rotational speed. There is an alternating field in the

rotor, which has a frequency close to 0 cycles per minute at,

no-load, then increases to a frequency equal to the slip

frequency times the number of poles at full load. On a 2 pole

motor typically 2 (poles) times 36 Rpm (typical slip) or 72

cycles per minute. To make this easier to understand consider

one point or bar on the rotor of a 2 pole motor, and that this

point is rotating at 3564 Rpms. There is a field around this

bar at a very low frequency. It is applying a force to the stator

at varying magnitudes depending on the level of flux in the

rotor at that instant in time. This flux pulsates each time it

passes by a stator slot. Note that the force that the rotor sees

is at the stator slot passing frequency and is modulating at

twice the slip. This will produce vibration of the rotor bars at

the stator slot passing frequency plus and minus side band

frequencies in multiples of the (slip) x (poles).

One Times Rotation Vibration - Unbalance

Motor Unbalance:

Balancing is required on all types of rotating machinery,

including motors, to obtain a smooth running machine. This is

performed in the factory in a balance machine at a level of

precision determined by the motor speed, size, and vibration

requirements. The highest precision is required for two pole

motors. Two pole and large four pole motors should be

balanced at their operating speed in the balance machine.

The assembled motors are then run in test to confirm that

vibration requirements are met in operation.

Although they do not usually concern the user directly, a few

salient factors affecting factory balance will be discussed

here. These mainly apply to two pole motors.

Most medium to large motors are used for constant speed

applications, although there has been a recent increase in the

number and size used for variable speed applications on

adjustable speed drives. Constant speed motors need only

be precision balanced at one speed, their operating speed.

Variable speed applications require that good rotor balance be

maintained throughout the operating speed range, which

typically may be from 40% to 100% of synchronous speed.

Rotor balance involves the entire rotor structure which is

made up of a multitude of parts, including the shaft, rotor

laminations, end heads, rotor bars, end connectors, retaining

rings (where required) and fans. These many items must be

controlled in design and manufacture to achieve stable

precision balance.

Fundamental requirements for precision balance on any

machine are:

•

Parts must be precision manufactured for close

concentricities and minimal unbalance individually.

•

Looseness of parts, which can result in shifting during

operation, causing a change in balance, must be avoided

or minimized.

•

Balance correction weights should be added at or near

the points of unbalance.

For motors, rotor punchings must be precision manufactured

with close concentricities of all features and have a shrink fit

on the shaft that is maintained at all operating speeds and

temperatures. The punchings must be stacked square with

the bore, uniformly pressed, and clamped in position when

shrunk on the shaft to prevent movement with speed change.

When end connectors require retaining rings, the rings are of

Page 6 of 16

high strength material designed with proper interference fit.

Rotor bars are shimmed and/or swaged so they are tight in

the slots. There are other methods to assure tight rotor bars,

such as heating the core and chilling the bars, but these

methods are not common. End connectors should be

induction brazed symmetrically to the bars, which helps

eliminate variations in balance due to thermal change. The

shaft and assembled rotor are precision machined and ground

to concentricities well within .001 inch. The rotor is

prebalanced without fans, then the fans are assembled and

final balanced on the rotor. The fans are individually balanced

before assembly on the rotor. For motors with a heavy

external fan, two plane balance of the fan may be required.

Constant speed applications are usually satisfied with either a

stiff shaft design, for smaller machines, or a flexible shaft

design for larger motors. A “stiff shaft” design is one that

operates below its first lateral critical speed, while a “flexible

shaft” design operates above the first lateral critical speed

[12]. When the rotor is precision designed and manufactured

as described above, a two plane balance making weight

corrections at the rotor ends, will usually suffice even for

flexible rotors. Occasionally, however, a flexible rotor may

require a three plane balance to limit vibration as the machine

passes through its critical speed during runup or coastdown.

This is accomplished by also making weight corrections at the

rotor center plane as well as at the two ends.

Adjustable speed applications require a stiff shaft to prevent

major balance changes with speed due to shaft deflection,

such as may occur with a flexible shaft. In addition, however,

the many other factors affecting balance in this complex

structure, discussed above, must also be controlled to

maintain good balance at varying speeds. In particular, any

bar looseness will result in excessive change in balance with

speed. This is prevented by rotor bar shimming and

sometimes swaging as noted above. Shims around bars,

such as used here allow the bars to be driven tightly into the

slots without concern for having the laminations shear pieces

of the bar off, causing bars to be loose. This design also

prevents the bars from becoming loose over time in the field

due to a similar phenomenon, which may occur during heating

and cooling where the bars may not expand and contract at

the same rate as the core.

During balancing and no load testing in the shop, the shaft

extension keyway is completely filled with a crowned and

contoured half key held in place by a machined sleeve to

avoid any unbalance from this source. Load testing is carried

out with the motor mounted on a massive, rigid base,

accurately aligned to a dynamometer and coupled to the dyne

with a precision balanced coupling and proper key.

Thermal Unbalance:

Thermal unbalance is a special form of unbalance. It is

caused by uneven rotor heating, or uneven bending due to

rotor heating. The proper solution is to determine the reason

for uneven heating affecting shaft straightness, and fix the

rotor. Before such major rework is performed, the severity of

the thermal situation needs to be ascertained. All rotors will

have some change in vibration in transitioning from a cold

state to a hot one. API 541, 3rd edition allows 0.6 mils change

in shaft vibration (at rotational frequency, 1X), and, 0.05

inches per second change in housing vibration. However, if

the application is one of continuous duty, and, vibration levels

are not excessive during startup (i.e. motor cold), it is

permissible to allow more change cold to hot without any

damage to the motor. In these situations if the lowest

vibration levels are desired at operating conditions, a hot trim

balancing procedure can be performed. To perform this

procedure, run the motor until all conditions thermally

stabilize, and quickly perform a trim balance. If necessary,

run the motor again after the initial trial weights have been

installed and let the motor thermally stabilize before taking

additional vibration measurements for final weight correction

Coupling Unbalance:

The coupling unbalance limit given in API 671 of 40W/N,

when applied to a typical 1000 HP 3600 rpm 2 pole motor for

example, gives a value equal to about one-third of the motor

unbalance limit for one end.

Analysis shows this would be about the correct value to have

minimal effect on motor vibration. Comparing this to AGMA

coupling unbalance limits commonly used in the industry, it is

comparable to a Class 11 balance which requires a balanced

coupling. It is considerably better than a Class 9 balance (by

a factor of 3) which is not a balanced coupling. AGMA Class

9 balance couplings are sometimes used for 2 pole motors,

but do not meet API 671 and can give vibration problems with

precision motors.

Use of a proper key and a balanced coupling leaves the

machine alignment and mounting and the driven equipment

balance as the remaining major factor in system vibration.

Oversize Coupling:

One consideration in coupling selection is coupling size. The

coupling should be large enough to handle the application,

including the required service factor, but should not be

exceptionally large. Potential results of oversize couplings

are:

•

Increased motor vibration due to increased coupling

unbalance and/or a change in the critical speed or rotor

response due to increased weight. This is particularly

true for flexible shaft machines.

•

A greatly oversize coupling can result in greatly severe

shaft bending, excessive vibration, and, heavy rubbing of

seals, ultimately resulting in catastrophic shaft failure.

The predominant vibration frequency as a consequence of an

oversized coupling would be at one times rotation, just like an

unbalance condition. The concept of ‘bigger is better’ does

not hold true here!

Driven Machine Unbalance:

Under normal circumstances, the unbalance of the driven

machine should not significantly affect the motor vibration.

However, if the unbalance is severe, or if a rigid coupling is

Page 7 of 16

being used, then the unbalance of the driven machine may be

transmitted to the motor.

Maintaining Balance in the Field:

When a finely balanced high speed motor is installed in the

field, its balance must be maintained when the motor is mated

to the remainder of the system. In addition to using a

balanced coupling, the proper key must be used.

One way to achieve a proper key is to have the shaft keyway

completely filled, with a full key through the hub of the

coupling and the entire key outside the coupling crowned to

match the shaft diameter. A second approach is to use a

rectangular key of just the right length so that the part

extending beyond the coupling hub toward the motor just

replaced the unbalance of the extended open keyway. This

length can be calculated if the coupling hub length and

keyway dimensions are known.

An improper key can result in a significant system unbalance,

which can cause the vibration to be above acceptable limits.

For example, calculations for a typical 1000 HP, 2 pole 3600

rpm motor show that an error in key length of .125 inches will

give an unbalance of .7 oz.-in. This is about equal to the

residual unbalance limit for each end of the rotor of 4W/N

given in API 541 for motors, and exceeds by a factor of 3 the

residual unbalance tolerance of a typical one-half coupling of

40W/N given in API 671 for couplings.

A problem occasionally arises in the field when a flexible shaft

machine with a high speed balance is sent to a service shop

for repair. If the rotor is rebalanced in a slow speed balance

machine at the service shop, then this usually results in

unbalance at operating speed, and the machine will run rough

when tested or reinstalled. The solution, of course, is to not

rebalance unless absolutely required by the nature of the

repair. If rebalance is absolutely required, than it should be

done at the operating speed of the rotor, otherwise, a trim

balance may need to be performed after the motor is

reassembled.

Forcing Frequency Response Vibration

Weak Motor Base:

If the motor is sitting on a fabricated steel base, such as a

slide base, then the possibility exists that the vibration which

is measured at the motor is greatly influenced by a base

which itself is vibrating. Ideally the base should be stiff

enough to meet the “Massive Foundation” criteria defined by

API 541 [1]. Essentially, this requires that support vibration

near the motor feet to be less than 30% of the vibration

measured at the motor bearing. To test for a weak base,

measure and plot horizontal vibration at ground level, at

bottom, middle, and top of the base, and at the motor bearing.

Plotted, this information would look like Fig. 11, for a motor

sitting on a weak base. In this particular example, had the

motor been on a rigid base, the vibration at the bearing would

have been closer to .25 mils rather than the measured 2.50

mils.

Fig. 11. Plot of Vibration (in mils)

Vs. Base/Motor Position

A weak motor base usually results in high 1x vibration, usually

in the horizontal direction as shown in Fig. 11. However, it

may also result in high 2X (twice rotational frequency) or 2f

(twice line frequency) vibration, which also is a common

vibration frequency in motors. To determine the nature and

source of this high 2x vibration requires vibration

measurements be made at the motor feet in both the vertical

and horizontal direction, taking phase as well as amplitude to

determine a mode shape. The “rocking mode” of the motor

observed in a particular case is illustrated in Fig. 12. The

horizontal component

δHV due to the rocking adds to the

inherent

δHM of the motor alone to give a high total at the

bearing housing, as shown by the equivalency below.

δH =

δHM +

δHV

where:

δH

= Actual motor horizontal vibration

measured in the field

δHM

= Horizontal vibration of motor alone

measured on a massive base in shop

δHV

=

DVB, calculated horizontal vibration

E component due to

δVB

, measured vertical

vibration at each motor foot in the field.

The recommended repair for the weak motor base illustrated

is that the support posts be tied together and heavily stiffened

with the intent to meet the criteria for a “massive foundation.”

Even where resonance of the base is not a factor, heavy

stiffening of a light support structure can greatly reduce

vibration.

Page 8 of 16

reed critical data. This includes the reed critical that the

motor alone would have if it were mounted on a rigid, seismic

mass. In addition the motor manufacturer supplies the

following information to aid in determining the system

resonant frequency with the motor mounted on the user’s

base: Machine weight, center of gravity location, and static

deflection. Bases found in typical installations are not as stiff,

and correspondingly, the reed critical frequency will be

lowered. If the reed critical drops into a frequency at which

there is a forcing function present (most commonly the

operational speed), the reed critical frequency will have to be

changed. Usually, this is not difficult to do, and is most

commonly accomplished by either changing the stiffness of

the base, or by changing the weight of the base/motor.

Where the reed critical drops below the operational speed to

about 40% to 50% of running speed, this can result in

subharmonic vibration at the system resonant speed in motors

with sleeve guide bearings. This could be due to either oil

whip effects or inadequate guide bearing oil film.

WR = rotor weight

WS = stator weight (motor weight – WR)

Reed Critical Base Issues:

KR = rotor shaft and bearing stiffness (lbs./in.)

KS = motor frame stiffness (lbs./in., considering

A vertical motor’s reed critical frequency is a function of its

bending, shear deflection, and flange bending).

mass, distribution of mass, and base geometry. The reed

critical should not be confused with the motor rotor’s lateral

critical speed. However, in large vertical motors, the rotor

Fig. 13. Structural Representation of Vertical motor for Reed

Critical Frequency Calculation Including Rotor Shaft

lateral critical speed may be a determining factor in the reed

Flexibility

critical frequency, particularly of the motor alone. The effect

of the rotor may be determined by considering it as a separate

mass and including rotor shaft flexibility in the reed frequency

Resonant Base:

calculation. That is, consider the motor as a two mass, two

degrees of freedom system as shown in Figure 13, rather than

If the motor’s operating speed (or any other frequency at

a single degree of freedom system as described in NEMA MG

which a forcing function is present) coincides with the base

1-20.55. Figure 13 shows that the motor structure (a) is

resonant frequency, great amplification in the vibration

basically a two mass system which can be progressively

amplitude will occur. The only solution to this problem is to

simplified, first to a beam-mass structural schematic (b), then

change the resonant frequency of the base. Usually, this is

not difficult to do, and is most commonly accomplished by

to an equivalent two mass, two spring system (c).

either changing the stiffness of the base, or by changing the

Where the lateral critical speed of the rotor is less than the

weight of the base/motor.

reed frequency calculated as a single degree of freedom

system, the true reed frequency will be lower than calculated.

Bearing Related Vibration:

It will be approximately equal to the rotor lateral critical speed.

However, when mounted on a flexible base in the field, the

Bearing related vibrations are common to all types of rotating

rotor shaft effect will be less and a single degree of freedom

equipment, including motors, and in themselves encompass

calculation is usually adequate. Just as in the case of a

extensive fields of technology. They will be dealt with briefly

lateral critical, if the motor’s operating speed (or any other

here.

frequency at which a forcing function is present) coincides

Sleeve bearing machines may occasionally experience “Oil

with the reed critical, great amplification in the vibration

amplitude will occur. Motor manufacturers routinely issue

Whirl” vibration, which occurs at a frequency of approximately

Fig. 12. Rocking Mode due to Weak Base

Page 9 of 16

45% of running speed. This may be quite large, particularly if

there is a critical speed at or just below 45% of running speed,

which is referred to as an “oil whip” condition. Other than

basic bearing design considerations which will not be dealt

with here, a common cause is high oil viscosity due to low oil

temperature in flood lubricated motors operating in cold

ambient conditions. Similar subharmonic vibration, but low in

amplitude, may occur in ring lubricated bearings, probably due

to marginal lubrication. Other causes of vibration are journal

out of roundness or bearing misalignment.

Anti-friction bearings have four identifiable rotational defect

frequencies for which formulas for calculation or tabulations of

values are given in the literature. These defect frequencies

are for the inner race, outer race, ball (or roller) spin, and cage

fundamental train. Much research has proven that no

absolute answer can be given to allowable amplitudes at

bearing defect frequencies. Therefore, the most important

thing to look for indicating significant bearing wear is the

presence of a number of bearing defect frequency harmonics,

particularly if they are surrounded by sidebands independent

of amplitude [14]. Tracking of vibration should be carried out

starting at installation, observing these indicators to predict

remaining bearing life.

discrete frequencies of the vibration. To do so on an overall

vibration measurement, complete knowledge of the entire

spectral data is required (i.e. amplitude for each frequency

band, for all the lines of resolution).

100DisplacementVibration

Amplitude1010.10.01VelocityAcceleration0.001110100Frequency100010000Fig. 14. Comparison of vibration amplitudes

Expressed in acceleration, velocity,

and displacement

III. IDENTIFICATION OF CAUSE OF VIBRATION

Today, the most common units are displacement for shaft

vibration measurement, and velocity for housing vibration

PROBLEM

measurement. The use of these units is further reflected in

Now that the causes of vibration are understood it is time to

most current standards such as API and NEMA.

establish a systematic approach to solve any problem that

Direction of Measurement:

may arise.

Measurements should be made in three planes (vertical,

Vibration Data Gathering/Analysis:

horizontal, and axial) on both bearing housings, as shown in

Many of the details of rotor dynamics, vibration data

Fig. 15.

gathering, and analysis have not been presented in detail in

this paper. For additional information references [1] and [2]

can be reviewed.

Now one must keep in mind that all of the electrical sources of

vibration and the mechanical sources of vibration are not

necessarily at the same phase angle or exactly the same

frequency. To make matters worse, the electrical vibration

may modulate, and when superimposed on the mechanically

induced vibration may result in an overall vibration signature

that is unsteady in amplitude and phase. Through proper data

collection, testing, and analysis, it is possible to identify the

root cause of the vibration.

Vibration Units:

Fig. 15. Vibration Measurement Positions

Vibration can be measured in units of displacement (peak to

peak, mils), units of velocity (zero to peak, inches per

Shaft Vibration vs. Housing Vibration:

second), or units of acceleration (zero to peak, g’s).

Acceleration emphasizes high frequencies, displacement

The determination of obtaining shaft vibration data vs. housing

emphasizes low frequencies, and velocity gives equal

vibration data is dependent upon the type of problem being

emphasis to all frequencies. This relationship is better

experienced. Oftentimes it is advantageous to have both

illustrated in Fig. 14. In this figure the vibration level is

shaft and housing vibration data. If the problem originates in

constant at .08 inches per second throughout the entire

the rotor (unbalance or oil whirl for instance), then shaft

frequency range, with corresponding vibration levels shown in

vibration data is preferable. If the problem originates in the

acceleration (in g’s) and displacement (in mils). It is possible

housings or motor frame (twice line frequency vibration for

to convert from one unit of measurement to another at

instance), then housing vibration data is preferable. Housing

Page 10 of 16

vibration is generally obtained with magnetically mounted

accelerometers. Shaft vibration can be obtained one of two

ways: shaft stick or proximity probe. There is an important

distinction between the two methods of obtaining shaft

vibration data: the proximity probe will give vibration

information of the shaft relative to the housings, whereas

measurements obtained with a shaft stick yield vibration

information with an absolute (i.e. inertial) reference. Housing

vibration data is always obtained in terms of an absolute

reference. If the motor has proximity probes then they should

be used. If it does not, then proximity probes may be carefully

set up with magnetic mounts. In this case it is important to

have the tip of the proximity probe on a ground, uninterrupted

surface. Even with this precaution taken, the electrical runout

will be higher than in a motor specifically manufactured for

use with proximity probes.

Modulation vs. Snapshot:

A snapshot refers to obtaining spectral vibration data at an

instant in time. Details of amplitude vs. frequency is readily

available in this format. A modulation refers to collecting

vibration data for a period of time (typically ten or fifteen

minutes), so that the variation in vibration as a function of time

can be analyzed. Typically, the following frequencies are

tracked when taking a modulation: 1/2X, 1X, 2X, and 1ƒ, 2ƒ,

and overall vibration levels (i.e. unfiltered), where X

corresponds to rotational frequency and

f,

line fequency.

Additionally, the phase information should be tracked when

taking the modulation, especially for the one times rotational

frequency. This will make the identification and subsequent

correction of various vibration problems possible.

It is sometimes desired to separate twice line frequency and

twice rotational frequency vibration. Different methods are

required to do this at no load and full load. Under full load the

difference in frequency is large enough so that the separate

components can each be measured directly with most

vibration analyzers. However, at no load, the frequencies are

so close together that this can not be done, even using the

zoom mode on a high resolution analyzer, so that an indirect

method is required. This can be accomplished by measuring

the 2 x RPM value at reduced voltage (25%) where the 2 x

line component is negligible, and then subtracting this from

the peak 2 x component in the modulation test which is the

sum of 2 x line and 2 x RPM components. This is usually only

possible at a motor manufacturer’s facility or at a motor

service shop.

Troubleshooting Procedure:

If a vibration problem occurs there are various tests that

should be performed. But first, the following maintenance

items should be checked.

Maintenance Items

Check for loose bolts – mounting or other loose parts

Keep motor clear of dirt or debris

Check for proper cooling and inlet temperatures or

obstructions such as rags, lint or other enclosures

Check Bearing and Stator Temperatures

Lubricate as recommended

Check proper oil levels

Check vibration periodically and record

The affected frequencies and other vibration characteristics

are listed in Table I.

•

Are all bolts tight? Has soft foot been eliminated?

•

Is hot alignment good? If it’s not possible to verify hot

alignment, has cold alignment been verified (with

appropriate thermal compensation for cold to hot)?

•

Is any part, box top cover, piping vibrating excessively

(i.e. are any parts attached to motor in resonance)?

•

Is the foundation or frame the motor is mounted to

vibrating more than 25% of motor vibration (i.e. is the

motor base weak or resonant).

•

Is there any looseness of any parts on motor or shaft?

•

Integrity of fans and couplings – have any fan blades

eroded/broken off, are any coupling bolts loose/missing,

is coupling lubrication satisfactory?

If all of the above items check out satisfactorily, and vibration

remains high, a thorough vibration analysis shall be required.

Essentially, there are only two steps in diagnosing a problem:

•

Obtain vibration data – not always clear cut because of

noise, sidebands, combination of signals, modulation, etc.

•

Determine what conditions increase, decrease, or have

no effect on vibration through different test conditions to

help isolate root cause.

Ideally, vibration measurements should be obtained with the

motor operating under the following conditions:

•

Loaded, Coupled, Full Voltage, All Conditions Stabilized

(i.e. normal operating conditions):