UNDERSTANDING THE VIBRATION FORCES
IN INDUCTION MOTORS
by
Michael J. Costello
President
Magnetic Products and Services, Incorporated
Houston Texas
was acceptable when he could stand a nickel on end on the bear­
ing housing.
There is no doubt that the induction motor has evolved con­
siderably over the past 20 years; however, this evolution was dic­
tated primarily from an electrical standpoint. Insulation mate­
rials were developed which allowed manufacturers to build
larger horsepower machines, and run them at progressively
higher and higher temperatures. As an aftermath of government
legal actions in the 1950s, the "White Sale" eliminated price fix­
ing between the manufacturers. This brought competition and
effectively lowered motor prices drastically. During the 1960s
and 1970s, material improvements and new manufacturing pro­
cedures resulted in significantly more efficient machines. Motor
base prices continued to drop and even now are lower than they
were 15 years ago. During this period, the mechanical aspect of
the motor became altered significantly. Motor frames were re­
duced in physical size, weight, and structural strength for a
given horsepower. However, they were still to contain the same
forces as their larger and more robust predecessors.
As a result of recent problems, the need for equipment relia­
bility, more knowledge in rotordynamics and more stringent
user specifications, motor manufacturers are presently being
forced to evaluate their product's mechanical performance.
Michael ]. Costello graduated from
New Jersey Institute of Technology in
1980 as an Electrical Engineer. Since
then, he has been employed by Nippes
Professional Associates and became Presi­
dent of its subsidiary, Magnetic Products
and Services, in July 1988. He has per­
formed electrical and substation design of
, power systems, and considerable analysis
\ of the performance of rotating electrical
machines up to 500 MW.
Mr. Costello has developed and implemented a Witness Accep­
tance Testing, Manufacturing Inspection and Project Specifica­
tions Program for clients, mostly in the petrochemical industry.
He is a member of the IEEE and is presently serving on the
Working Committee Pill for the revision of Standards on Test­
ing Induction Motors as well as the Induction Machinery Sub­
committee ofP E S . He is also a member of The Vibration Institute.
ABSTRACT
INDUCTION MOTOR OPERATING PRINCIPLES
Squirrel cage induction motors have been used extensively in
industry for over 50 years. While it appears that vibration prob­
lems are more pronounced nowadays, certain basic construction
features have always existed and have created considerable diffi­
culty from the initial stages of motor development. As induction
motor theory has never changed, the electromechanical forcing
functions have always existed and created vibration problems.
In fact, some of the most complete and best references on vibra­
tion in induction motors were written 30 to 40 years ago. It ap­
pears, however, that only recently has the induction motor been
critically reviewed by mechanical engineers and rotating
machinery specialists. Motors are now being treated for what
they are-extremely complex rotating machines having not only
the associated mechanical forces, but electromagnetic and elec­
tromechanical forces as well. The basic operating principles of
motors are discussed as well as the lateral vibration forcing func­
tions encountered when troubleshooting motor vibration prob­
lems. All motors described herein are squirrel cage, polyphase,
60Hz design.
To understand the operation of an induction motor, it is impor­
tant to become familiar with its major components. A cutaway
of a typical large motor is shown in Figure 1. A squirrel cage in­
duction motor consists of the following major components:
Stator- The stator consists of an electrical winding and a
cylindrical laminated steel core in which the winding coils are
inserted. After insertion, the coils are connected in a manner to
produce alternate pole polarity, the number of which dictates
the speed of the motor.
Rotor- The rotor is made up of a shaft, and a cylindrical
laminated steel core in which the rotor winding is inserted. In
a squirrel cage design, the rotor winding consists of nonmagne­
tic bars which are inserted through slots in the core. The bar
ends connect to end rings which short circuit the bars. The bars
and end rings together make up the rotor "squirrel cage."
Frame- The frame of the machine is either a fabricated or
cast structure in which the stator is inserted. This frame must
be strong enough to withstand mechanical and electromechani­
cal forces along with providing air passages employed to cool the
motor.
Enclosure- Various enclosures can be specified such as DP
(drip proof), WPI (weather protected I), WPII (weather pro­
tected II), TEWAC (totally enclosed, water-air-cooled), etc.
These enclosures are either integral vdth or are installed on top,
bottom, or sides of the frame.
The basic theory of the induction motor is actually very sim­
ple. As an alternating polyphase voltage is applied to the ends
of the stator windings, currents flowing in coil groups produce
a multipole alternating magnetic field which rotates around the
•
•
•
INTRODUCTION
•
The present trend in industry is towards long term reliability
on all major equipment. In order to accomplish this, more and
more motors are being outfitted for vibration and temperature
monitoring systems. \Vhile proximity probes have been in serv­
ice to measure vibration for over 20 years on turbines and com­
pressors, most motor manufacturers have not used them until
thl;l last five to seven years. It was only five years ago when a
manufacturer stated he knew a motor's mechanical performance
67
68
PROCEEDINGS O F THE NINETEENTH TURBOMACHINERY SYMPOSIUM
Figure 1. Cutaway of a Typical Large Squirrel Cage Induction
Motor Outlining the Various Major Components.
stator ID. The number of alternate polarity magnetic poles set
up by the winding connections dictate the speed of the rotating
magnetic field. The motor synchronous speed is as follows:
motor synchronous speed
120
X
==
frequency of applied voltage (Hz)
number of poles
Currents in the rotor cage are induced across the air gap of
the motor in a manner similar to those induced in the secondary
of a transformer. It is different from the transformer, however,
since the secondary or rotor winding rotates physically, trying
to gain synchronism with the stator winding rotating field [1].
The rotor cannot achieve synchronism because of torque or load
on its shaft. The amount of speed by which the rotor lags the
stator synchronous field is called "slip." The amount of slip and
motor current are higher as the motor torque load is increased.
As the field rotates around the stator, the reactionary tangential
force, which is a function of load torque, core loss, and friction
and windage losses, slips behind the stator magnetic field.
Under no load conditions, slip is low because torque needs only
to overcome the core and friction and windage losses; however,
a slight current is induced in the rotor cage. Because of this,
some slip is present even at no load, therefore, synchronous
speed can never be reached.
The torque to accelerate an inertial load to an operating
speed, will at any speed, be equal to the difference between the
motor torque developed and the load torque. The motor torque
is a function of the applied voltage during starting conditions,
and the load torque usually varies with speed. The rate of accel­
eration is proportional to this torque difference, and the motor
will hang up at a low speed value if the torque differential
reaches zero. This may also occur if the motor design is such that
its speed characteristic curve has parasitic torques or cusps.
MOTOR VIBRATION
Vibration analysis and rotordynamics has become a science in
itself, generally studied and reviewed by mechanical engineers
or rotating machinery specialists. It is not uncommon for tur­
bine and compressor rotors to successfully operate at speeds in
excess of 12,000 rpm. Therefore, most rotating machinery spe­
cialists cannot understand how motors, having maximurn speeds
of 3600 rpm, can exhibit vibration problems which are so dif­
ficult to diagnose. While motor speeds are relatively low com­
pared \\-ith turbomachinery, the dynamics associated with them
can be extremely complex due to additional forcing functions
present which are not found in a mechanical machine. Add to
this a rotor which is a laminated steel cylindrical core held axially
under compression and shrunk on a shaft, as well as a rotor cage
which is inherently "loose," and the difficulty of motor vibration
diagnostics increases dramatically.
It is true that two pole (3600 rpm) motors behave the worst
when discussing mechanical performance; however, lower
speed motors operate on the same principles. Electromagnetic
forcing functions are generated at all motor rotor speeds; how­
ever, they are more pronounced for two pole machines due to
the greater force between the magnetic poles [2]. In addition,
two pole motors have greater centrifugal forces and normally op­
erate much closer to the first critical speed.
Does the addition of electromagnetic forces really complicate
motor vibration diagnostics? Not in itself; however, when they
are combined with the mechanical forces seen on all rotating
machines, analysis becomes difficult. The fact that the elec­
tromagnetic forcing frequencies may be very close to running
speed, or its multiples, makes it easy to understand why
mechanical and electrical engineers alike have such difficulty in
motor vibration diagnostics.
To understand vibration in motors, the first thing to re­
member is that it is also a mechanical machine having all the
forcing functions as any rotating mechanical machine. The shaft
must be straight, the rotor must be balanced, bearings must be
adequate, etc. Electrically, various inherent electromagnetic
forces exist which cannot be eliminated. Problems \\-ill occur
when either the mechanical, electromagnetic, or elec­
tromechanical forces become excessive, which can occur due to
a number of reasons.
As this presentation is directed towards the mechanical en­
gineer, the purely mechanical dynamics of a rotating system will
not be discussed. The electromagnetic and electromechanical
aspects will be the point of concentration. Electromagnetic
forces are those which are purely magnetic, created by the rotat­
ing magnetic field. Electromechanical forces are those forces
most commonly generated as a result of an electromagnetic force
and a mechanical force, such as unbalance or a bent shaft, acting
in cooperation with one another. It can also result from an elec­
tromagnetic force and electrical dissymmetry (broken bars or
cracked end rings) also working in concert.
Electromagnetic Forces
The two main electromagnetic forces in an induction motor
occur at 60 Hz and 120 Hz. The frequency of the main air gap
magnetic flux wave is 60 Hz; however, it is actually a torsional
function on the rotor. Any dissymmetry in the magnetic circuit
\\-ill produce a lateral force whose frequency is at 60 Hz. This
component is generally very small and normally not a concern.
Inherent 120 Hz Force- The existence of a 120 Hz force can
result primarily from two sources. It is the result of the inherent
magnetic attraction between the rotor and stator acting on a sin­
gle point on the stator core each time it comes under the influ­
ence of a rotating magnetic field pole.
In one cycle of voltage, a magnetic field pole will pass this sta­
tionary point t\\-ice in one rotation of the magnetic field for two
69
UNDERSTANDING THE VIBRATION FORCES IN INDUCTION MOTORS
pole motors, fiJur times in one rotation of the magnetic field for
four pole motors, six times for six pole motors, etc. The speed
of rotation of the magnetic field pules is exactly 60 Hz for two
pole motors, exactly 30 Hz fin· four pole motors, and exactly 20
Hz h>r six pole motors. As a result, the fi·eqHency of the frJrce nf
attraction between the rotor and stator is 60 Hz times two f(n·
two pole motors, 30 Hz times four hn· kmr pole motors, and 20
Hz times six f<n· six pole motors. This 120 Hz force can, there­
fore, be defined as being a function of the speed of the rotating
magnetic field times th� nmnber of magnetic Held poles. Of
course, as the nurnber of poles dictate the speed of the rotating
magnetic field, this fin-ce as defined above, must always have a
fi·equency of 120 Hz and, thereliJre, is independent of the
number of magnetic Held poles.
\Vhile it is demonstrated prviously that an inherent 120 Hz
f(H-ce is present on all iuduction motors, the amplitude of this
f()!-ce is tvpically more pronounced on tvvo pole motors. This is
due to the much greater distance between the poles on a two
pole motor (180 degrees) as opposed to on slower speed
machines, 90 degrees h>r f<JUr pole motors, 60 degrees f(Jr six
pole motors, etc.
120 Hz jiJrce due to air gap dissymrnetry--The second source
fi>r 120Hz vibration f(Jrees, while not inherent in the motor, gener­
ally always exists due to a point of minimuu1 air gap being present
in the motor. Ideallv, the rotor should he perfectly concentric
with the stator hore. Practically, however, due to rnanuhtcturing
and assembly tolerances, this situation is impossihle to achieve.
Hopef1.tl.ly, the rnaximun1 deviation in the air gap will not he
greater than five percent fi·om the average (especially on higher
speed motors).
If it is assumed that the rotor is perfectly C'<lllC<:,ntric with the
stator, the net eff(-:ct of the magnetic Jlux f(nces in the air gap is
entirely balanced between rnagnetic field pole pairs (north and
south pole). If, however, a point of minimum air gap exists in
the motor, and a magndic pole lines up with this point, it creates
an area of rmLximum llllx density and theref(Jre the magnetic
f(,rces between the pole pairs are unbalanced. This unhalancc�
creates a magnc·tic pull J(Jrcc occurring each time a magnetic
field pole passes the poiut of maximum Hux densiiy. It can,
therefi,re, be staled that this 120Hz fi>rce due to air gap dissym­
metry is also defined as a hmclion of the speed of the rotating
magnetic field times the number of poles. As \Vas the case for
the inherent 120 Hz f(m:e, the frequency of the air gap dissym­
metry force is independent of the number of poles and occurs
at exactly 120 Hz [.3]. The generation of the 120 Hz fiJrce due to
air gap dissymmetry is demonstrated in Figure 2.
The electromagnetic forces discussed previously are depen­
dent entirely on voltage and the rotating magnetic flux wave.
This means that they exist whether the machine is running at
no load or fldl load. It is possible, however, that an increase in
temperature resulting from a full load run, can alter the air gap
mechanically, thereby increasing the air gap dissymmetry and
\Nith it the 120 Hz f(n-ces from the no load runs. It is f(H· this
reason that both a fi1ll load and no load test are valuable when
diagnosing motor vibration problerns.
Electromechanicall<orces
Electromechanical forces are present on all motors to some ex­
tent and are directly related to the motor slip speed. The forces
can be generated by a number of either electromagnetic or
mechanical dissymmetries, whieh creates an unbalance mag­
netic pull force with a fi·equency of modulation. The two most
common modulating unbalance magnetic pull forces occur at a
frequency of l) the number of poles times the slip speed, and 2 )
one times the slip speed.
To produce a force having a frequency of the number of poles
times the slip speed, a revolving point of minimum air gap must
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Figure 2. Generation u{ 120 Hz Electrom.agnetic Force Due lo
Air Gap Dissymrnetry.
be present in the machine. Due to the reasons discussed fi1r dec·
tromagnetic f(Jrces, this minimum air gap is present on all
machines; however, its deviation from the average is what deter­
mines the amplitude of the resulting modulating f(>rce. In addi­
tion, besides resulting from normal manufacturing, this can
result from mnch more severe problems sueh as a bent shaft,
broken rotor bars, excessive unbalance, etc. This revolving
point of minimum air gap will, as shown in Figure 3, comes
under the influence of maximum flux density (magnetic pole)
twice in one slip cycle for a two pole motor and four times in one
slip cycle fi:Jr a fonr pole machine. This produces an unbalanced
magnetic pull fiJrce modulating, pulsating, or heating at a fre­
quency of the number of poles times the slip speed [2].
Although not as prevalent, the second most common elec­
tromechanical forces has a frequency of one times the slip speed.
For this to occur, two dissymmetries must occur simultaneously
between the rotor and stator. An example would be of a rotor
which was not adequately centered radially in the stator and
vvhich also exhibits excessive unbalance. Assuming this example
is of a two pole motor, when a magnetic pole lines up with the
point of minimum air gap, the mechanical unbalance is 180 de­
grees from this point and therefore, the unbalance magnetic pull
\viii tend to "balance" the rotor [2]. The resulting force will,
therefore, be negligible during one half cycle of slip. During the
other half cycle, the magnetic pull will line up with the unba-
70
PROCEEDINGS OF THE NINETEENTH TURBOMACHINERY S Y MPOS IUM
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up with
not
raawlt,
or
A•
a
"Dahnoed"
uotad.
unbalanCie
"
�r
h
foc l eUpCiyola,
�!! � :::..
tb9
(II)
.
aagMtic
haly
•tfoCit
lO
Pin&Uy,
ravolutl<rfl•
of
fi,.ld,
polnt •u• U��e• up with
5101"
north
(II}.
oaad-Uu•
at
A•the
denuty
pola
(Ill),
oraat<HI
Uning
11ot
"eault.,
!:!!.,
�he
by
up with (R)
"""""11""
and
ar
"H"
Ae
h
a
tor l allp cycl•,
um..lenc:od
..11nat1c
auac:tlvely
o
....
pull
"batan.,<l<l"
notod.
: :::
h
tho
unbabnc.<l lll&'illl<1tlo
foroe
••
Figure 3. Demonstration of Electromechanical Force with a Fre­
quency of the Number of Poles T imes Slip Speed .
Figure 4. Demonstration of Electromechanical Force Having a
Frequency One Times the Slip Speed.
lance amplifying the unbalanced magnetic pull force. Therefore,
the resulting modulating force will occur once in one cycle of
slip. This situation is demonstrated in Figure 4.
While it is also possible for this to occur on slower speed
motors, a one times slip frequency force is much more difficult
to produce. As seen in Figure 4, for the four pole motor, a pro­
nounced force occurs when the unbalance force lines up with the
unbalanced magnetic pull force created by the point of
minimum air gap. In addition, a force is created each time the
unbalance force comes under the influence of a magnetic pole
except when the pole is 180 degrees from the point of minimum
air gap. This, in effect, also creates an unbalanced magnetic pull
force; but, it is not as great as when the unbalance lines up di­
rectly with the pole. Because of this, the unbalanced magnetic
pull force will have a tendency to modulate at one times slip fre­
quency. As this forcing function has yet to be seen on slower
speed machines, it should not be of a concern.
Either of the electromechanical forces previously described
above would be superimposed on any of the vibration compo­
nents whether it be the unfiltered or filtered values. The result
would be that particular vibration component modulating at ei­
ther one times slip speed or the number of poles times slip
speed. It is important to remember that a slip frequency related
unbalance magnetic pull force is always present; however, it
should not be excessive. The amplitude of modulation should
not be above 20 to 25 percent. If it is, a more severe dissym­
metry is present, most likely due to sloppy machining or exces­
sive tolerances during motor assembly. Critical problems such
as broken rotor bars, end ring cracks or bent shafts exhibit the
same modulation characteristics; therefore, all excessive mod­
ulation must be investigated.
A common misconception is that these unbalance magnetic
pull forces exist only when the machine is operating at full load
or close to full load. This is probably due to the fact that one can
hear an audible beat at full load while not hearing one at no load.
The unbalance magnetic pull force will not exist at no load if the
dissymmetry is load related such as a broken rotor bar or a ther­
mal bow; however, if it is from sloppy manufacturing tech­
niques, the forces exist even at no load.
Since the unbalance magnetic pull is dependent upon slip,
and as described in the basic theory section of this paper, slip is
present even at no load, it makes sense that these modulation
forces can also exist at no load. At no load, however, the slip and,
therefore, the forcing frequency is very low. Typical no load slip
frequencies are between 0.001 Hz and 0.003 Hz (0.06 rpm to
0.18 rpm), whereas, full load slip values typically range between
0.25 Hz to 0.5 Hz ( 15 rpm to 30 rpm). As a result, during no load
operation the time for the revolving point of minimum air gap
71
UNDERSTANDING THE VIBRATION FORCES IN INDUCTION MOTORS
to come under the influence of maximum flux density will be ap­
proximately five to seventeen minutes. However, during full
load operation, this time is only between two and four seconds!
It is for this reason, extremely low frequency, that a beat cannot
be heard at no load.
It is, therefore, possible to ascertain the slip frequency mod­
ulated electromechanical forces during a no load run by monitor­
ing a vibration component continuously for up to approximately
15 minutes. In addition, the no load slip speed can be deter­
mined by aiming a strobe light, set at exactly 60 Hz for hvo pole
motors, exactly 30 Hz for four pole motors , etc. , at the shaft end
keyway. One can then see the keyway start to lag behind the
strobe very slowly. The time required for the keyway to make
one complete revolution is the no load slip speed. An example
of using this technique is demonstrated in Case History Number
3.
For modulation forces to be eliminated, a perfectly symmetri­
cal machine, both electrically and mechanically would have to
be manufactured. As this is not possible, the motor should be
made as symmetrical as tolerances allow.
The vibration troubleshooting chart presented in Table 1
should be beneficial when motor vibration problems occur. It
covers most of the common occurrences in a simplified way;
however, because of the multitude of electrical and mechanical
factors which may precipitate a vibration problem, it is often
necessary to perform a basic analysis based on fundamental con­
cepts, most of which are discussed herein. Since not all combi­
nations of electrical and mechanical problems can ever be
accounted for, it is very important to understand the nature,
origin, and behavior of the forces discussed here.
Table 1. Vibration Symptoms and Causes for Squirrel Cage Induction Motors.
II) Poor be" I"' to bHrlna
fte(J.Itf'C V(D
C nl'd)
t
frauton•ot lto uth"..
hDUII!nallt
1ttl!ltOIIti-\vibr8t\Dn-rp\\h.de
notprc>pOttl-l tobtll��neeeotrKtl-.
"-VI I III tltflll t ln-.dtlplee of tllletl-1
Frequeney
a)o\lwhlrl
lr�v.
frequM�Cyc_,tyfal l e aros.n:l40
toUiof tht rotatl-l frequmc:y
IHUIU l n d if
lffllf'ltle
t IIIJ*10'illf'lwhhlll
b)poor Ialani bearing
._..
� -..rotorbllrt.
�IIIU!Ckogreater ln thhorhonul
dlreetlon than tha ¥ertlut.
c""INiend tllll
diep!Hftlfnlllt lltelllngronu\uln
Sl.ob·
C aul d leld to ber brut., . .
....,_,_,_
(lllt-1\Mtbeeorrectedbyrel""'l"'.
har-lcr"onenc:eM)'c-evlbra·
tlonat1/Z,1/3,1/4, etc., o f
rotatl-1 frequene v .
o)lkln·UI'Iiflltllltotor
e��reet..,.tng
-.:h ...tu
tlvfornd•
h•ft bolllit
h er et
nsewb\y gr Qii! IMr-l el
l e chn t
he
roto rhe et1141.
ITit��ullotatl-1
plD
S ft fnt
Frequency
�tltldeUeady,
llllltl llloflr-llt bll,.,p:���t
ct.,..ir!ll, il!IPI'opll' "''..,.ng, etc.
t�oat c_,cal.llt of vlbratlon,
Ohm procb:u -vnttlc dt..-,-rrv
teapondtraodlly
....:le•celtlvel2tlllz vlbret1Qn.
to"-1-ewlohtt.
Addltlonof lar��t of bel.ne:t
wllhta h-t\Ute eff�t.
Mey aho
e)heua!Yerotor core
create el!cesslvesllp related
HC"'trleltylllth
llledJittlDI'I.
reQ*t toJour,t
..
Plllchl"9eccentrlcltv, achlnlng ltt
llr
end / or l -• r o to r lMinttl_on ... •fl.
IMIIaoiiECII"IIICAI.c) for ... ttlpleJof
rotJtl-1 frequvq' .nd IECIIANICAL k)
c
)lll!pt�r blll � l"f
tll!l:hnlquea
-·
Clll'lo�rly flex ahaft •• In the lnstM"Ct
of.-ddlns�t.tance welehta to endtof
rotOt"for�hnce ln center Cif rotor,
bl�hdlve totorbtlrt
orendrlna•
d)Crltlultpeed l•ne•r
op��ratlngepeed
tec::hnhfJel.
lrokenrotorbl>rtotciii"'MCtl.,...to the
rndtlnfl.
Sh-'4'et ......r llfJIII\et
tl- tll p fr....,.no:y wlth •o<ld etlllfl o f
Dlfflcult to batancetl!li"'lnotlllll
l
twlcellnefr�ve�t .
Ylbretlon�eklneer
totetlonel lp.edd.srlngc::ooetdowl.
Clllt"'-1\lfro-l..,.opllt i)'IIWCh lned
rotorlurhee endtml!erNrl>tort.. t.,..
Ylbretlonlt lns-ltl� to nor.t
tl- , broken r otorblt l , etc.
behmelng�thoda.
c-.ell
fr
1111\elao
vrelltedlliOdulatlon.
Multlple�ofRotetlonal
f)EilC::HIIV.brlt\ngehllt811C:H/Ot
eRuulve tetenl elur..-.:ea
SheftYibntlonis oftentrllter ln the
F requenc y
horhontel dlrec::tlon thin the wrtleal
t)OUt of rOIR!jouriiDh
dlrec::tlon.
Vlbr•tlonciiMOtberecb!edbynor��tl
blll-lllllt
l hochbeloweectrtelnyelu..
ftllqlllV
ltiC NV ehobe2 or 11ote tl11ee
rotltl-1.
t)lotor r!A:I
Posaible�rtdlc::tabiiYibretlon-.lltuM
endphase engle.
Locat overheetlng effectl
biiNideqtjllte oll fll•
ean c::eus- therNI bow .
h)Mhallgrllln
l! t
thlcknns
Loed re,l on of be
n l��t i lltlrved llf
hmt-lun t , II too hl>t, Wl"OIIt tt.,. of
oil , etc.
Cen differentlite ftOIII trobltlence 6Je to
the bc::t that MIIB\1,_-.t often eppe.ltl
ulnereuedYibntlon elso etZ•,3•,
c)OUtllftDUI'Idrotllr
ftftf.*IC'VVI bratlon .
fr�y.
slip r�leted 111ocle
ll tlonof t11ice 11,.
lffect laproport!Oilll to the
ft�V·
stiffness of the C::lll
l4' i"11 rldlallylnd
beer I no•
KIV•Isopl"o:dlc:e
SH•IsoEUCTIIOMECIIANICAL
e)...:fi'ECWIWt)for1tiiiK
the dtgree ofml"llar-"Jt.
IJDefectlve .ntl·frletlon
U.WIIy produce1 twlc• rot•tl ... t
.w:lhlther...,ltlplesof rotetlonel
tlltatl...
t frequeoc:v.
CW�alsoproduee.u\tlp\es of rotetlonel
d)lhc:h.,.lc•tl-tena�aof
ftllq.lel'ley andfrequencies euoc:htted with
bel!lrlna•�tstructur•
Vlbr•tlonhlghl!ltii4'POf"l fftt.w:l
f!U'Idlltlont.
the�r of bllltsendblll tr.ln rotetlan
MIIY IIIlO eppur 11 11Jitlp\e11 of rotlt!Dnlll
frotq�.���ney ofton et6to50tillll!lrotetl0111l
Multiples o f Ro utlonRI
Vibration h un�teadye11 bearlngdeterlor·
f r.,...ncy
a)Non- slnusoldlll o r iU\ tlpt
e
rotl t l-l fr�v
t•..,te:
OUtllf rcudrotor lnllddltlon
t ll the r
lltotbeil'lgfl'CIIf'ltrlclllth,.spect
totheloul"nlts.
ltcxl.olatl...,. of vlbr•tlon
rctated t o all p frequency.
AdjacentbearingYlbratlon Is hlghelt.
Olffleutt toMkebatance correctlonon
rotor body.
I)St l tor bore not r....-d
k)LOOie rotor l•lnatillnl
onsheft
SttllsoiLECTRO·
Mf.CIIAIIIC"L 1) endMECH"IUtAL C) for
b) RlltMnot centered l n t
he
Se nsl tln to s tet
ll t lllndlngcii<Q!Ctl­
l rdvolt -.
111Uitiple1 of rotationlli freq.!ef�Cy.
IJ E c
centri cjourn11h
S-itl��ottOUitMWindlngc-tions:
and volt-.
lrratic:: andmprtdlc::table responsato
belance eorreetl-.
Vlbretion camotbe rotduced by nor1111l
1
betarw:••thochbrtow e cert•ln v•lue.
a)lnherent��qn��t lc forces
frequentyllll)'olsobeZotlllOr8t!IIII!S
e�duetolllndlna
tot•tionet.
clrcult orphtseinbelenc..
CIIIISH lttc:al ata tor he a tlng.
V\t1r1tion
�HIIOIOrheiUUp.
Unlt fa i lsl n •s hort per lodl>f t l•.
72
PROCEEDINGS OF THE NINETEENTH TURBOi\IACHINERY SYI\IPOSIUI\1
CONCLUSIONS
\Vhile squirrel cage induction motors have been used wide­
spread in industry for over .50 years, it appears that the recent
trend in long term reliability on major machines has now been
instituted on motors. As a result, users are evaluating motors in
the same manner thev evaluate higher speed compressors' and
turbines· mechanical perf(mnance. In the purchasing stage, it is
important to recognize that stringent specifications alone do not
guarantee a well running and reliable machine. A thorough un­
derstanding of induction motors must be known and employed
when making up job specifications. The following aspects of
motor procurement should he f()Jlowed in order to assnre the
user of a well running and reliable motor:
Write detailed motor specifications which rely on standards
already published, if applicable to the motor application. Keep
in mind that vibration and manufacturing tolerances do uot have
to be overly stringent for a good operating machine. Also, re­
member that a motor is a "completely different animal" from a
turbine or compressor and, therefore, not all requirements can
he interchanged.
Submit the job speciHcations to motor vendors ff1r com­
ments. Qualify various motor manufacturers to ascertain their
manufacturing, quality control and testing capabilities.
Contact other users of identical motors to learn of their ex­
periences. Judgement has to be made here since a particular
machine can b � either the "greatest" or a "piece of junk," de­
pending upon who is talking. It helps to have a specific list of
questions available and lllake certain that all failures are fully
explained to determine responsibility.
• Evaluate the motor bids from a technieal and an economic
standpoint. Know the various mam!lilC'turers' major design fea­
tures and drawbacks.
A comprehensive design review should he made as soon as
the initial electrical and mechanical designs are finalized. ff pos­
sible, crosscheck the motor starting characteristics and the lat­
eral critical speed analysis. Get satis±twtory explanations on sig·
nificant deviations between results.
• Develop a complete and comprehensive shop inspection
and witness test plan. It is most important to utilize qualiHecl in­
spectors knowledgeable .in motor marmlacturing and construc­
tion. \Vitness agents must be knowledgeable in motor design,
and electrical a1-1d mechanical testing. It is easy to understand
that more than one person may be required to satisfactorily com­
plete the inspection and witness testing.
In order to understand the vibration f(Jrces within a motor, it
is important that the basic operating principles of motor theory
be knovvn. Vibration hJrces in motors can he of three ty pes:
mechanical, electromagnetic, or electromechanical. As this pre­
sentation is geared towards the mechanical engineer, onl�' the
latter hvo cases were reviewed. Electromagnetic vibration con­
sists of 60 Hz (line frequency) and 120 Hz (twice line frequency)
f(m.·es. Electromechanical forces consist of a unbalanced mag­
netic pull f(>rce working in combination with an electromagnetic
force so that the resulting vibration is modulating at a frequency
in relation to slip speed.
Lastlv, five actual case histories of motors exhibiting various
vibrati(;!l problems are presented. Each case is detailed in terms
of the troubleshooting and corrections necessary w·hich resulted
in well running machine.
•
•
Demonstration of vibration modulation at one times slip
speed
•
Case History 1
Three identical 125 0 hp, 6900 Volt, 3600 rpm, induction
motors were placed in service in 1978 at a waste water concen­
trator plant f(,r a utility company. The units were driving vapor
compressors having a connected load inertia of four times the
listed "allowable NE�JA \VK2 to accelerate without injurious
temperature rise." Over the next Hve years, numerous rotor fail­
ures occurred on all three motors, with at least two failures per
unit. Each time, the rotor was repaired and placed back into
service.
Vibration measurements were subsequently recorded on one
of the repaired motors after it had been in service for two
months. lVIaximnm unfiltered vibration levels on the bearing
housing modulated between 1. 6 and .3. 4 mils. The frequency of
the modulation was determined to be twice slip frequency ·with
a very strong twice line frequency vibration component of 0. .3 0
ips which was also modulating at twice slip fi·equency (Figure
.5 ). A higher harmonic of bar passing freqnency was also noted
in the u;1filtered value.
•
•
FIVE CASE HISTORIES
Rotor bar breakage on a compressor driver
Rotor Thermal bow clue to smeared laminations
Stator core 120 Hz vibration transmitted to shaft and bear­
ing housings
Demonstration of non linear damping of oil film
•
•
•
�
Figure .5. Opposite Drive End Bearing Housing Horizontal vw­
ration as Measured by Accelerometer.
The f(>llowing month, the motor was shut down and trans­
ported to a service shop for inspection and repair. \Vheu the
rotor was pulled from the stator, numerous cracks were noted in
the end ring and rotor bar to end ring joints (Figures 6 and7).
Additionally, the rotor cage \Vas extremely loose, such that the
service shop started to swage the bars at an attempt to tighten
the rotor cage (Figure il). Reportedly, this had been the exact
condition of all the rotors which had previously hti!ed. \Vork was
stopped when it was decided that an analysis and assessment of
this problem should be ped(mned.
A review of the rotor design was made, and it was discoYered
that to compensate for the loose cage, the manufacturer utilized
a balance/support ring assembly. This assembly was bolted to
the end ring and the ID was then shrnnk to the shaft, thereby
containing tl1e radial looseness of the rotor cage. A cross section
of the rotor construction is shown is Figure 9. Restraining a loose
item is acceptable on a mechanical 1;1achine, however, on an
electrical machine, certain electrical and thermal parameters
were neglected.
Each time a motor is started, a large current flows in the rotor
hars and end ring. The heat generat�d during this start is almost
UNDERSTANDING THE VIBRATION FORCES IN INDUCTION MOTORS
Figure 6. View of Crack in Rotor End Ring after Motor was Dis­
assembled at Service Shop.
73
Figure 8. Service Shop Worker Attempting to Tighten Rotor
Cage by Swaging Rotor Bars. Swaging is the act ofmechanically
displacing har material ill a manner such that it becomes tighter
in the slot.
ROTOR SHAFT
Figure
7.
Crack in Rotor Bar to End Ring Braze.
equal to the amount of energy imparted to the rotating system.
This heat, of course, is greater when accelerating high inertia
loads such as this. The temperature rise of the bars and end ring
results in an axial growth of the bars pushing the end ring assem­
blies awav from the rotor core. Stresses are created due to cen­
trifugal f;rces acting- on the end ring and bars along with temper­
ature gradients on the bars due to skin effect. These factors
create bending stresses at the bar protrusion section and at the
Figure .9. Original Rotor Cross Section Showing Balance Bing/
Support Bing Assembly.
brazed bar joints to the end rings. For these reasons, it is impor­
tant to allow an unrestrained and predictable axial growth of the
rotor bars. The end ring balance/support ring assembly the man­
ufacturer utilized on this machine mav have avoided a balance
problem; however, it did not allow for the design
- considerations
just mentioned.
Once this problem \Vas identified, the motor manufacturer de­
signed and assembled new rotors utilizing a tight cage, larger
74
PROCEEDINGS OF THE NINETEENTH TURBOMACHINERY SYMPOSIUM
end rings for the high inertia starting, and a balance ring which
was allowed to slide on the shaft. Problems have not been re­
ported on these machines since.
Case History 2
During acceptance testing of a 1500 hp, 3600 rpm motor, no
load coupled vibration levels on a dynamometer stand were very
low. Maximum unfiltered levels of 0.80 mils on the shaft and
0.25 mils on the bearing housing were measured. When the
motor was placed under load, the corresponding vibration levels
gradually increased over a four hour period and stabilized at un­
filtered levels of 2.5 mils on the shaft and 0.75 mils on the bear­
ing housing. Filtered rotational speed vibration levels showed
approximately the same increase in shaft vibration and a corres­
ponding phase angle change of almost 180 degrees.
Even though the measurements exhibited classic signs of a
rotor thermal instability (Bow), the manufacturer stated that the
vibration acceptance criteria of 2.0 mils had not been guaran­
teed under loaded conditions. They felt that since the motor vi­
bration was below 2.0 mils under no load, the motor was accept­
able. During initial discussions, they stated that this condition
was the result of vibration influence from their dynamometer;
however, this was disproved from a review of the vibration
spectra which clearly confirmed original suspicions of a thermal
bow.
The rotor was disassembled from the stator and inspected
very thoroughly. As discussed earlier, the rotor core is made up
of thousands of cylindrical laminated steel sheets held in com­
pression axially and shrunk onto the shaft. Each of these lami­
nated sheets are insulated from one another in order to limit
rotor surface eddy current losses and thereby reducing stray
load losses. Since the laminated core is placed on the shaft, it is
effectively shorted at the core ID. Local currents cannot flow un­
less a short occurs at a different radial location, most often at the
core OD. One method of lamination shorting at the core OD can
come from excessive burrs touching one another or piercing the
coreplate of an adjacent lamination.
An inspection of this rotor's core OD, as viewed under a mag­
nifying glass, showed areas of the rotor with "smeared" lamina­
tions over approximately 30 percent of the core surface. In these
areas, localized eddy currents were circulated, thereby increas­
ing the rotor surface temperatures nonuniformly and resulting
in a thermal bow. Since the surface losses increase with slip, the
rotor did not bow until the machine was loaded, when the sur­
face eddy currents were highest. The smearing of laminations
was caused by a dull lathe cutting tool, which was subsequently
corrected. The entire rotor 0D was then turned down to a lesser
diameter and the motor then reassembled. When the vibration
was again measured ·with the machine under load, levels did not
increase by more than 10 percent over the test duration, while
the phase angles did not change more than 10 degrees over a
four hour test.
The vibration data shown in Figure 10 was recorded both be­
fore and after the repair procedures.
¥
MAXIMUM SHAFT VIBRATION
REPAIRED RO'rOR-END OF HEAT RUN
2.35
if
Ol
-'
....
::0:
z
....
MAXIMUM SHAFT VIBRATION
FULL LOAD-END OF HEAT RUN
w
CJ
�
�
�
2.35
0
MAXIMUM SHAJ!'T VIBRATION
FULL LOAD-START OF HEAT RON
0
100
300
200
FREQUENCY IN HZ
400
500
Figure 10. Vibration Data Recorded Both Before and After Re­
pairs.
fore, the magnetic force occurs at exactly hvice line frequency.
As the stator core is the primary forcing function, the decision
was made to isolate it from the bearing housing.
The frame construction was a fairly standard cast frame which
is line bored to accept the stator core (Figure 11). In order to
maintain close air gap tolerances, ribs on the frame ID are bored
concentric with the end bell rabbit fits. In this machine, there
were six ribs into which the stator core and winding were
shrunk. As these ribs extend along the entire axial length of the
frame, the core vibration easily transmits to the end of the frame
which supports the bearing housing. To isolate the core vibra­
tion, notches were machined into the ribs as shown.
Case History 3
Figure 11 . Cost 500 Frame Showing the Ribs in Which the Stator
Core is Placed. To limit the transmission of the 120 Hz vibration
from the stator core, each of the six ribs were notched as shown
in the cross section. T his tends to isolate the core from the end
frame to which the bearing housings are mounted.
A 600 hp, 2300 Volt, NEMA 5000 frame motor was experiencing
very high vibration, modulating at two times the slip frequency
on both bearing housings and all shaft probes. Additionally, the
twice line frequency vibration component was predominant and
was also modulating at two times slip frequency.
It is important to note that twice line frequency vibration is
present on all induction motors no matter how many poles. On
a two pole motor such as this, it inherently results from the rotat­
ing magnetic field passing a single point of the stator twice in
one voltage cycle (sine wave). The resulting stator and rotor at­
traction forces are independent of the voltage polarity, there-
\Vhen the motor was assembled, the twice line frequency vi­
bration was lower; however, the excessive modulation was still
present. Only when another frame was modified was the cause
identified and corrected which resulted in reduced vibration
levels. It was discovered that in addition to the 120Hz vibration
problem, the original frame was improperly bored so that it was
deflecting excessively in one direction simulating an out of
round stator. The maximum shaft vibration is shown in Figure
12 both before and after the modifications to the frame.
�------·
75
U N D E RSTANDING THE VIBRATION FORCES IN I N DUCTION MOTORS
0
0
·
·
·
: J.IO'l'OR AS �AliPRox. ::14 <*-m
�
:
:
:
:
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
·
:·
·
·
·
·
2
r·
.50
. UlfFIL'I'�REJ? � VI�TII?N TR�ND:
.
.
WITH MO'f'OR AT NO LOAD
.
1000
. ..
..
.
TIME
HIJn.JTES
4.5
5.0
10. 5
l2
3000
2000
4000
� �-------,
.
.
.
.
.
.
1lmiiLiiii!E 1IElGIJl' OF 51 IlK-IN •
•
·
· · · · : · · · · AiU:D :m OOi F:Nii'oi.> �- · :· · · · · : · · · ·
Figure 12 . Plot Showing Instantaneous Peak to Peak Shaft Vibra­
tion Levels Modulating at 2 x the Slip Speed During a No Load
Slip Cycle .
:
2
Case History 4
A two pole, 1250 hp motor had undergone vibration testing
at the motor manufacturers plant without any problems. Unfil­
tered vibration levels reached a maximum of 1.13 mils on the
shaft and 0.50 mils on the bearing housing during the full load
dynamometer testing. Predominant vibration was noted to be
at running speed with no excessive 120Hz or slip frequency ef­
fects noted. The motor was very stable throughout the load test
as amplitudes, both filtered and unfiltered, and phase angles did
not change significantly.
Contract requirements stated that an unbalance response test
for the determination of the first lateral critical speed was to be
performed for this rigid shaft rotor. (The calculated first lateral
critical speed was 4250 rpm) To do this, the motor was run at an
overspeed up to 4200RPM and allowed to coastdown freely
while plotting the filtered shaft vibration and corresponding
phase angle. The critical speed would show an increase or peak
at a given speed as well as a phase angle change. During the first
coastdown, shaft vibration reached a maximum of only 1.20 mils.
As this value was fairly low, an unbalance was placed on each end
of the rotor in phase with one another to excite the first mode.
The residual unbalance (RU) tolerance of the rotor was 19 gm­
in. The second coastdown was performed with an unbalance of
51 gm-in placed on each end of the rotor. This time, the maxi­
mum amplitude was 1.4 mils. The decision was made to add 95
gm-in per end (6 times RU). The machine was then being
brought up to overspeed and a sudden increase in shaft vibration
up to 5.0 mils occurred at 4150RPM. The occurrence was ex­
tremely rapid and the amplitude and phase angle characteristics
did not indicate a true critical speed. Upon bearing disassembly,
there was a "polish" on the top bearing halves due to their being
contacted by the shaft journals. The maximum probe vibration
during each of the three coastdowns performed is shown in Fig­
ure 13.
Once the bearings were "scotchbrited" and reassembled, the
unbalance response tests were repeated but only up to adding
the unbalance weights of 51 gm-in. All commercial obligations
had been satisfied as there were no critical speeds within 20 per­
cent of operating speed, and nothing in the customer specifica­
tions stated that the addition of five times the residual unbalance
tolerance could not cause a vibration increase. The motor was
accepted following an explanation from the manufacturer stating
that the 98 gm-in unbalance resulted in a nonlinear behavior of
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Figure 13. Rotor Unbalance Response Curves with Rotor in the
'f\s Balanced" and Unbalanced Conditions of 51 gm-in and 96
gm-in.
the oil film perimeters. The unbalance caused the shaft journal
displacements to exceed the linear portion of the oil film and per­
mitted the shaft to contact the bearing.
This motor was subsequently installed and has been in service
for approximately two years without any knovvn problems.
Case History 5
Three 700 hp, 3567 rpm motors were purchased as the drivers
for feedwater pumps. As the first motor was undergoing accep­
tance testing, vibration measurements with the machine under
no load were well below the user specified levels of 0.10 ips on
the bearing housings (filtered, all frequencies) and 2.0 mils on
the shaft (unfiltered).
The motor was briefly loaded for instrumentation verification
by use of a dynamometer and immediately an audible "beat" was
noted whose frequency corresponded directly to one times slip
PROCE E DINGS OF THE NINETEENTH TURBO MACHINERY SYMPOSIUM
76
frequency. Shaft vibration spectra was recorded as shown in Fig­
ure 14. It is quite common for a beat or vibration modulation of
twice slip frequency to occur on 1:\vo pole motors, and as long as
this is not excessive, should not be a concern. Due to machining
and assembly tolerances, always present is a point of minimum
air gap in the motor. This \'1-ill come under the influence of max­
imum flux density 1:\vice in one slip cycle, producing the unbal­
anced magnetic pull force whose frequency is 1:\vice slip speed.
When this is superimposed onto other vibration frequency com­
ponents, the result is a modulation of that component at 1:\:\.ice
slip frequency. As the motor exhibited a modulation ofonce slip
frequency, an unusual situation was occurring on this machine.
What cannot be shown in Figure 14 is the 100 percent modula­
tion of all the vibration components. Zooming into the 60 Hz
PROX PROBE lY
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Figure 14. Full Load Shaft Vibration Spectra from 0-400 Hz, 5070 Hz, and 110-130 Hz. T he latter two plots differentiate the run­
ning speed from the line frequency components and multiples
thereof
REFERENCES
l.
STA'IUS : PADSI!D
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o
component revealed that one and 1:\vo lines slip speed sidebands
were prevalent. Overall vibration levels at this time were not ex­
cessive; therefore, electrical performance testing was com­
pleted during which the vibration was not monitored. When the
machine was again run under no load, the overall vibration
levels had increased significantly and were now above the
aforementioned specified values. Because of this, the motor was
disassembled and inspected thoroughly.
As was stated previously, it is normal for vibration modulation
to occur at 1:\:\.ice slip frequency as a result of manufacturing toler­
ances of the machine. In this instance, there is a force whose fre­
quency is one times slip frequency. This can occur if there is a
multiple dissymmetry, such as when a mechanical dissymmetry
and magnetic dissymmetry occur simultaneously bel:\veen the
stator and rotor. An example of this would be a rotor not
adequately centered in the stator and also exhibiting excessive
unbalance. For instance, when a magnetic pole lines up with a
point of minimum air gap, the mechanical unbalance is 180 de­
grees from this point; therefore, the magnetic pull will tend to
equalize the mechanical unbalance and the resulting force will
be negligible for one half cycle of slip. During the other half
cycle, the magnetic pull will be in phase with the mechanical
unbalance and the resulting force will, therefore, occur once in
one cycle of slip.
On this motor, the significant vibration increase from one no
load test to the next pointed to a mechanical shift from its origi­
nal residual unbalance condition. An inspection of the rotor re­
vealed significant end ring cross section variations over its entire
circumference. This leads to nonuniform resistivity in the end
ring, producing a variation in the induced current circuit and ,
hence, air gap flux dissymmetry. Since these 1:\vo problems, ex­
cessive unbalance and magnetic variation , were occurring
simultaneously, the resulting electromagnetic force occurred
once per cycle of slip. Actions for correction of this problem
included machining of the end ring eliminating the variation and
rebalancing the rotor. The motor was subsequently tested, and
vibration levels were low, thermally stable and repeatable. Mod­
ulation at one times slip speed was still present , however, to a
much lesser degree (down to 35 percent instead of the original
100 percent).
Sommers, Ernest W. , "Vibration in Two Pole Induction
Motors Related to Slip Frequency" Transaction, AlEE,
(April 1955).
2. Brozek, B., " 120 HERTZ Vibrations in Induction Motors,
Their Cause and Prevention," IEEE, Catalog #71C35-IGA,
Paper PLI-7, 1-6 (1971).
3. Brozek, B., "Discussion of Two Pole Motor Vibration" , Un­
published (May 1984).
4. Liwschitz-Garik, M. and Whipple, C. C., "Electric Machin­
ery - AC Machines," Second Edition (1961).