Application Notes Vibration Diagnostics for Industrial Electric Motor Drives
The induction motor is the most widely employed industrial electric-drive. Identifying the vibration problems that can occur in induction-motor drives have an added complexity due to the rotating magnetic-fields in the machine. A basic understanding of the principles involved, together with a simple trouble-shooting guide and the right analysis instrumentation, should be invaluable to the maintenance engineer.
Vibration Diagnostics for Industrial Electric Motor Drives by Glenn H. Bate, B.Sc, M.Sc, Dip. UCL. Bruel&Kjcer
Introduction By far the most widely emplo yed electric motor in indust rial drives, is the induction motor and this applic ation note applies to this type of electric motor. Engineer s should be able to relate some of the principles to synchronous moto rs or gener ator s etc., but , for brevity, only the induct ion motor is specifically discussed. The effects of electronic variable speed drives* are not discussed either; operati on on a mains frequency supply is assume d. 'Magnetic' or 'Mechanical 5 ? The vibratio n problems relati ng to the induction motor are a combinat ion of two groups which can be called 'mechanicaV an d 'magnetic', accord ing to how they arise (this is made clear in the following sections). To help determ ine which of the two groups of vibrati on are present , the main tenan ce engineer can listen for beat s. A bea t is identi fied as an oscillatory ampl itude of vibration , due to closely spaced frequency compon ents alterna tely reinforcing the n cancelling each other, as their relative phas e varies. The absence of beats may indic ate there is only a 'mechanical' problem. Their presence can indicat e a 'mechanical' problem and 'magnetic ' one combined. For example, such compo , • r, i • j , , nen ts in a z-poie ind uct ion motor, 1 '
tud e mod ula tio n of a single frequenc y 7 compone nt, due to a 'magnetic problem alone. How ampli tude modul ation compon ents and beat frequency componen ts can appea r in the induc tion motor is explained later. More can be discove red abo ut the problem by disconnec ting the electric supply (a 'power tri p test '). This will distinguis h the 'mecha nical ' and the 'magn etic' component s of vibrati on, since 'magne tic' compo nents will disappear immediately after electrical power is removed. The effect of the power trip test should be observed by studyi ng the changing ampl itud e of the vibrati on on a spec trum analyzer. Spectrum Analysis Furt her analysis of the vibrati on spectra is requir ed to sepa rate out specific faults, and therefore to deter mine the appro pria te rectification action. Thi s can be done using a high resolut ion spec trum analyzer: typically an FF T (Fast Fourier Transf orm) analyzer with an increased resolution 'zoom' facility. The resolution is needed to pick out the n arrow -ban d and sideband signatures of all the vibration problems occurring with induct ion motor drives. This applic ation note describes what these signat ures are and how or i , /» j ,i ,i -i where to find th em usin g the analyzer. J °
COUld OCCUr at cl os el y Sp ac ed f r e q u e n-
cies of twice rotational speed and twice th e sup ply freq uenc y res pec ti vei ly. J
A Complex Problem Th is s hor t a ppl ic at io n no te c once n, i ,i ^ ,• j i i mi tra tes on the magnet ic problems, t he
Noti ce th at an osci llat ory am pl it ud e of vib rat ion also occu rs wit h amp li -
tr ea tm en t of th e 'mec ha ni ca l' vibr ati on pro ble ms rel at ing to th e ro ta ti ng
2
t=>
f
shaft is brief, concentrating on the resuits rath er tha n the causes. The 'resuits ' are often seen in association with some of the 'magne tic' vibrati on problems , because 'mecha nical ' problems such as unbalan ce, misal ignmen t and loosenes s can affect th e ind uct ion motor magnetic circuit, by causing variati ons in the air-gap. The problem is further complica ted since indus trial electric drives are often moun ted on rails or box stru ctur es as common bases to the driven equi pmen t. This means th at meas ured spect ra can contain compo nents due to gearing, bearings etc., tra nsm itt ed via the structure . Also any spectrum compon ent will vary dep end ing on the mobil ity of the path from the various vibration sources to each mea sur eme nt point. The answer to this complex problem is to identify the specific vibrat ion signatu res , and while this applicat ion note provides info rmat ion on only induction motor vibratio n, Briiel&Kjaer are publishin g a series of applic ation notes relati ng to vibrat ions in shafts, gears, bearings etc..
*
Electronic variable speed drives such as d.c.
link invert ors or cyclo-con vertors achieve , ^ , t, / ,u . r speed control through synthesis oi a varying frequency supply by electronic switching. Due
to this, the current supplied has a degree of harmonic distortion, depending on the sophistica tion of the elect ronics , filters etc.. The dis, ,. ,,, , ' „ ^ . iU
tortion oi the current waveform reflects in the
vibration spectrum, this relationship is made clear in this application note.
'Magnetic' Vibration Induction Motors
in
Principles The induction machine is shown in simplified form in Fig. 1. Cur ren t is produced in the rotor conductors, which is propor tional to the difference in speed between the rotating field, produced by the current in the 3phase stator windings, and the rotor itself. This current produces a rotor field which interacts with the stator field to generate force on the rotor. The field in the rotor rotates in syn chronism with the rotating field in the stator; both advance 2-pole pitches rel ative to the stator, for each cycle of line frequency, i.e. at synchronous speed. The rotor of the induction mo tor does not rotate at synchronous LOUS speed, but instead slips backwards through the rotating field. The rate of slip is the difference between synchro nous speed and rotor speed. Since synchronous speed depends on the line frequency and the number of poles in the machine, it is conve nient to use the per-unit slip as de fined in Fig. 1., and define slip fre quency as per-unit slip x line frequen cy. This definition of slip frequency applies to all motors regardless of the number of poles. The slip fre quency is the actual frequency of the current in the rotor conductors, and the rotating fields advance relative to the rotor by 2-pole pitches for each cycle of slip frequency. Motor torque is produced where bal anced forces exist on either side of the rotor. If the forces of attraction are not balanced, then vibration results. This can be related to current or air-gap variations in induction motors. Current Variations Due to Rotor or Stator Faults Consider a simple coil rotating through a magnetic field as shown in Fig. 2. It is well known t ha t t he force on a current carrying conductor in a magn eti c field can be obt ain ed from the vector cross product of the current vector and the flux density vector. This can of course be applied to the coil in Fig. 2, bu t here a not her more general expression of the force on the coil is given, relati ng to the to tal flux # linking the coil. The relationship given in Fig. 2. shows th at th e force on th e coil, in any arbitrary direction 'x', is directly proportional to the current in the coil and the rate of change of the magnetic flux in the direction of th e force (and not the flux itself). The
Fig. 1. The induction motor stator, rotor & air-gap
Fig, 2, The force on a current carrying coil moving in a magnetic field
term NI is called the magnetomotiveforce (MMF) and the rot ati ng field in the induct ion motor can be defined as an MMF wave in th e cond uct ors, giving rise to a flux wave in the air-ga p. By likening conductors on either side of the rotor to the two sides of the coil, a num ber of broke n bars can be considered as introd ucing an unbal ance of
MMF and thus force between the two sides of the rotor. Thi s force unb ala nce rotat es with the rotor. The equat ion given in Fig. 2 however, reveals t ha t the force unba lan ce is obt ain ed from a multiplication of the MMF unbalance and the rat e of change of m agn eti c flux in the dire cti on of th e force. If the problem can be simplified by neglect-
3
ing other tha n funda ment al components of th e MMF wave, then the unbalance force can be described by the product of two alternating terms of funda ment al frequency, but which are not necessarily in phase, of the form: k sin sa?t sin(sa>t + 6) or, (/e/2)(cos^ - cos(2scvt + 0)) where, to = the line frequency s = the per- unit slip k =an ampl itud e value 0 = a phase angle i.e. t he vibration has a constant part an d a 2 x slip frequency alt erna ting part. Transforming this t o a stationary reference frame requires a frequency multiplication of 1 x RPM. A stationary transducer, positioned for instance on the rotor shaft bearing housing, will therefore measure a vibration with components of 1 x RPM an d 2 x slip frequency sideba nds about a centre frequency of 1 x RPM. By similar reasoning, if the current discontinuity is du e to a fault in the stator windings, e.g. short ed stat or turn s, the n the resulti ng force unbalance does not rotate, an d is of the form: (fe/2)(cos# - cos(2o>£ + 6)) i.e. The vibration has a constan t component and a component at 2 x line frequency. Air-gap Variations Due t o Eccentricity Now consider the relationship given in Fig. 2 wit h regar d to air-gap variations. The flux in the air-gap is generated by the total MMF of the magn etic circuit, such th at the flux:
same MMF will result in greate r flux. T h e travelling s inusoidal flux wave will thu s experience a greater rate of change as it enters this region of the air-gap. The effects of a varying airgap may thu s be similar to the effects of curr ent variation s. The same relationship for the unbalance force re suits, where only funda ment al frequency components of MMF are considered. Stat ic eccentrici ty refers to an eccentricit y which does not travel (e.g. due to bearing wear or misshapen stator), this will produce a vibrat ion force with compo nents at d.c. an d 2 x line frequency. Dynamic eccentricity travels with th e rotor (e.g. due to rotor bow), this will produce a vibration force at 1 x RPM an d 2 x slip frequency sidebands on 1 x RPM. In deed these statements are justified by practical results, but consideration of t he variation of the reluctance as a peri odic funct ion (of space , in th e case of static eccentricity, and of time and space, in the case of dynamic eccentrici ty), suggests different comp onent s to look for as th e best indication of eccentricity. This is dealt with in the section "Advanced Analysis & Other Techni ques" later in this applic atio n note.
the inerti a cons tant of the rotor shaft, some speed varia tion may result . Th e speed variation will be larger for low inerti as, and this can therefore cause a frequency modul atio n of the vibration compo nents whose frequency is referenced to rotor speed. For high inert ias the speed variation and therefore t he degree of frequency modulation will be less. W here sideb ands ar e generated then, t he general case is somewhere between pure amplitude modulation and frequency modul ation . The spacing between each sideban d comp onent is still the modulating frequency, however, in the case of frequency modulation t he number of sidebands can be much greater than two, depending on the modulation index, i.e. the ratio of t he peak frequency (or speed) deviation to the modulating frequency (or the frequency of the torque variatio ns) . See Fig. 3. Slot Fre que nci es The slots carrying t he conductors in the induction motor, also generate a vibrat ion force as they create unbalanced magnet ic forces of attraction, resulti ng from an effective variat ion of reluct ance in the magnet ic circuit as a function of the rat e of stat or and rotor slot passing. The components will be present in a 'healthy' motor of course, since the slots are part of the design, and thes e will always ten d to concentrate t he magnetic field in the slot tee th rath er th an the slot channel , due to higher magnet ic permea bility in the material in the teeth than in the conductors in the channels. Th e vibrations occur at the frequencies given by t he equation in Fig. 4, which repre sents t he principal harmonic content of the resulting force function.
' R o t a t i n g ' o r 'S ta ti on ar y' ? The 'magnetic' problems discussed so far, can also be classified as either a 'rotating' or a 'sta tion ary' problem, according to the vibration produced. A presentation of this with some typical causes is given in Table 1. Fre quenc y Modulation Due to Spe ed Var iat ion s Th e discontinuities in the magnetic forces of attraction giving rise to vibrat ion as discussed, also cause variations in motor torque. Depending on
# F IR where, F m= the total MMF Rm= t he total magnetic reluc tance in the circuit =
Any eccentricity in the air-gap results in a variation of the magnetic reluc tance, which depends on the radial ' ^ rX . «. . • , air-gap length. I his effect is particu, i 4. • ■ J +* K. larly apparent in induction motors, as these require a very nar row air-g ap, compared to synchronous motors or direct curr ent machi nes. Therefo re small defects ca n result in rel ati vel y larger reluctance variations in induetion motors If the air-gap narrows for instance,
then the reluctance decreases and the
\~1
l
I
Type of of Type D m k u m Problem Problem
~ 71 Z I Symptomatic Frequency „« \#;K,„*i~of Vibration Vibration of
Tunirai r a n ^ Typical Cause ly pi ca iu au se 1 Variations Current Variations Air-gap Variations
1
ZJL Static eccentricity, Stator winding Static eccentricity, Stator winding weakness of stator faults Stationary 2 x line frequency Stationary weak ness of stat or faults 2 x line frequency support support Dynamic eccen cracked Dynamic ecce n- Broken Broken or or cracked 1 X P M w with i t h 2 2x x slip frequen xRRPM or1 tricity rotor bar(s), Rotatina slipfre quen- tricity rotor bar(s), orRotating C cy sidebands Loose rotor bar(s) shorted rotor lami Y sid eban ds Loose rotor bar(s) shorted rotor laminations I I „ I I
TYi i OQQt^Of} TmRQvnmn
Table 1. 'Rotating'
and 'stationary'
'magnetic'
vibration
in induction
motors
Fig. 3. Amplitude spectra of sidebands for frequency modulation with various values of modulation index ft
The 'Mechanical' Vibration Problems of the Rotating Shaft A brief description of the 'mechanical' vibration problems resulting from faults occurring on the rotati ng shaft is appropriate, since these problems are often interdependent with 'mag netic' vibrations as described already. For a thorough treatment of shaft and bearing vibrations, please ask your Briiel&Kjaer representative for appli cation notes on these subjects. 1 x, 2 x RP M A guide to the most co mmon shaft vibrations and causes is given here. This is presented in tabular form in Table 2. From this it can be seen that a 1 x RPM component of vibration force may arise from a number of fault conditions. Misalignment and bent shafts can be separated from unbal ance by ascertaining if a large vibra tion compo nent at 2 x RPM is present; this component does not arise in the case of unbalance. To distinFig. 4. Illustration of how the stator and rotor slots distort the magnetic field, concentrating lines of flux density in the air-gap over the slot teeth
guish a bent shaft an d different forms of misalignment, identifying the pre-
5
dom inan t plane of vibr ation (whether axial or radia l), and the relative pha se of the vibrat ion between the two ends of the shaft is the key. Pha se can also be used to distinguish types of unbalance, as indic ated in Table 2. Immediately it is appa rent tha t a 1 x RPM comp onen t can arise from many causes, bot h 'mechan ical' and 'magn etic' , and for a 2-pole indu ctio n motor, 2 x line frequency and 2 x RPM are very close especially on light load (low values of slip).
tru m in the frequency domain is characterized by a large num ber of harmonies, and possibly sub- harm onics of the fund ament al comp onen t. Such a spectr um can result from mechanical looseness, where the harmo nics are of 1 x RPM. Tru nca tio n may also arise in cases of misali gnmen t, and also stiffness non- linear ities. In the case of the indu ction motor rotor and shaft, this may lead to a more compli cated analysis, especially if tru nca tio n of a beat vibra tion occurs, see Fig.5. Thi s will induce strong compon ents at the sum and difference frequencies of the two frequency comp one nts of t he beat, say a) x an d ai2 , and also compo-
Truncation Where tru nca tio n of a vibr ation signal occurs in the time domain , the spec-
Type of Typeof Problem
I
Dominant Dominant Frequency q y
Dominant Dominant Plane
(2)
1x 1x RPM RPM
Radial(2)
1) 1 x , 22x x ((1) RP M RPM 1 x,
Axial
Unbalance
Bent Shaft or MisMis
|
alignment (Angular)
alignment (Angular) ~Z7. ~ ' Misalignment
parallel) (Parallel)
I
Phase Phase
|
Relationship ip
^
Static - 0° Static Unbal. Unbal.-0° Couple-180° Coup le-18 0° Rad. Dynamic-0^180 0 Dynamic-0^180 180°Axial 180°A xial(4) .. . n o RRadial 0°
w "aaiai
1x,2 x (1 ) RPM RPM 2
1X
' *™
Bearings Bearing s in indu ctio n motor s can be of the rolling elemen t type, but for larger machine s they are usually the sleeve typ e. In rolling elemen t bearin gs, local faults produ ce a series of impa cts which can excite resonances in the structure of the bearing housing and the machine casing. These resonances are typically between 1 kHz and 20 kHz. Th e actua l fun dame ntal frequencies associated with the impact re pet iti on rates given in Fig.6 are sometime s seen, bu t are generally low i n level and so lost in the background*. Problems associated with sleeve type i
•
. ..
,
bearings th at give frequency compone nt s
in th e
ra ng e
of in te re st
fo r
th e
induction motor problems discussed Radial
^ ^
180°RRadial °o° a ? w(4) 180°Axial 180
18
° Axial
Mechanical Looseness Mechanical Looseness
nen ts at (2cv x + a>2) & (2co + o^). Additionally these compo nent s will have sideban ds sep arat ed by the difference frequency (w2 - co\). In a 2-pole inductio n motor, this difference will be equal 2 x slip frequency when the beat frequencies are 2 x line frequency 'ma gnet ic' vibration and 2 x RPM 'mechanical' vibration!
{5) i5) RPM
1 x , 22x x RPM 1 x,
Radial Radial
S
° far' are du e to oil wh ir l a n d whi p" The se can give com po ne nts at a fracti o n (0.43 to 0.48) of 1 x
Variable Variable
RPM.
T01662GB0
(1) (2) (3) (4)
A high 2x componen t can be expecte d, depending on the magnitude of the problem and the system mobility For overhung rotors the axial component is often dominant, but axial vibration is always present with a couple The phase relationship.given is theJ approximate Phase difference measured from shaft-end to shaft-end Accelerometers placed at each end of the shaft may be oriente d in opposi te direction s, thus giving a measured phase relationship of 0°for an actual 180° relationship (5) Higher harmonics and also interharm onics of 1 x RPM i.e, 0,5 x 1,5 x RPM etc. can often be present, resulting from the non-linearity caused by truncation
* Env elo pe an alys is on a res ona nce re gio n in the sp ec tr um exc ite d by th e be ar ing fa ul ts , can J & ^ . ' recover the fu nd am en ta l im pa ct rates for accur at e diagno sis
Table 2. Rotating shaft 'mechanical7 vibration problems
Impact Rates f(Hz) (assuming motion) Impact Rates f(Hz) (assuming pure pure rolling rolling motion) For an outer outer -i A race defe defect: race ct:
f / u _ ,
For an inner race ct: race defe defect:
i/ -. ,. n / MHz) = = -£ f fr (( ii MHz) r
For a ball . , defect: defect:
_ n 2
I \
BD PD
f(Hz) = -^ s / R p 3 > (Hz) = — ffrr ( l1 - - f | c ocos BD
+
+
!
-\
!— § - c cos o s / ?0))
PD PD [ /B D „\ 2] T (HZ) = —— frr 11 - - — CCOS S PH BD " (PD BD [[ \PD ° 0) )
cage For a cag e -j x 4 defect: defect:
= f(Hz} Hz ) =
f
1f r /1 BDC 0 S / 3 0 \ ^ fr 1 - r^ T COS 8]
i2 (\ - f§PD
)/
871541 j
Fig. 5. A beat vibration amplitude
6
waveform that is truncated
Fig. 6. Formula for calculating ment bearing frequencies
rolling-ele-
Practical Trouble-shooting The discovery of any of the above vi bration signatures in a spectrum on a spectrum analyzer does not necessarily imply that there must be a problem requiring immediate rectification. There will always be some 'magnetic' or 'mechanical' imperfections in any motor, so the question arises: What is a problem? Standards do exist, like ISO 2372 (and equivalent national stan dards), by which the severity of vibra tion levels can be judged. Whilst it is useful to know thes e, they are often far too crude to judge whether a particular problem will result in breakdown, or is otherwise intolerable in the particular operating environment. For instance, broken rotor bars in an induction mo tor can cause arcing, which is highly dangerous in explosive or inflammable environments. Spectrum Increases By far the most effective means of determining whether a problem exists is spectrum comparison of a current vibration spectrum and the spectrum of the machine in good condition. In creases in frequency components or the appearance of new components are the best indicator that something is going wrong. CPB and Narrow-band Analysis Where spectrum comparison forms part of a regular maintenance pro gramme, a package such as Briiel&K jaers' Type 2515 Vibration Analyzer (an FFT Spectrum analyzer) and Type 7616 Application Software on an IBM Dersonal
COmDUter \
automates j
,
the ,
comparison process, based on constant percentage bandwidth (CPB) spectra*. This is ideal for detecting a developing fault, but for actual diagnosis, use of the Type 2515's capability for narrowband cons tant band width 'zoom' analysis is necessary. Thi s is requi red to pick out the narr ow-ba nd and sideband signatures of the 'magnetic' vibratio n problems and distin guish these from 'mechan ical' vibrat ions. An illust ration of this is given in Fig. 7, where a cons tant band widt h spec trum shows a single peak at aroun d 100 Hz, but the 'zoom' aroun d this compon ent identifies th at it is in fact two components, one at 99,6 Hz, the other at 100 Hz. Th e spe ctr um given is from a 2-pole induction motor driven screw
^^' ^' Narrow-band vibration components rately identified using 'zoom' analysis
compressor, and the two pe aks in question are 2 x RPM and 2 x line frequency compon ents respectively. Fault Prognosis As mention ed, eccentricity 'probl ems' may be prese nt in a healt hy motor, and whether they repre sent any cause for concern may be deter mined by comparing with broa d-ban d vibrati on sta ndar ds and applying engineering judge ment for part icul ar operati ng conditio ns. 'Faul t' development or progre ssion can be followed by observing changes in the narrow -band signa-
due to 'magnetic'
& 'mechanical'
problems,
sepa-
tures . If levels don' t increase the re may be no cause for conce rn, but if regular monitorin g shows increases, then a problem is developing. Tre nding the increases may help decide when the fault must be corrected, but this must be based on experienced judge ment. Eccent ricity problems can occur together with mechanical problems, as a result of poor installati on, or machining or other problems after an overhaul. Broken rotor bars are obviously not pre sen t in a hea lth y motor, and the ir occurrence is in any case an immedi -
* CPB frequency analysis is a powerful tool in detecting general machinery faults as a broad spectr um can be covered while still maint aining resolution at the lower frequencies where it is generally required. For instance a 6% CPB sp ectrum has a resolution of 60 Hz at 1 kHz in the s pectrum and 6 Hz at 100 Hz in the spectrum .
7
ate problem, regardless of environment, since the damage will be progressive, with adjacent bars eventually breaking. This is due to higher thermal and mechanical stresses in the ad jacen t bar s, as the y are forced to carry more curr ent. Th is progressi on will depend on many factors, includ ing motor age and duty cycle. Long star ting and heavy star t-st op duty cycles
normally cause the stresses th at result in broken bars in the first place. Positioning the Transducer The measur ements made depend very much on the positi oning of th e tr an sducer, due to the mechanic al mobility of the motor str uct ure , as has alre ady been stressed. A further practical point is also worth mentioning to aid
the reader seeking the best positioning of the transd ucer: travelling radially around a motor casing, the transd ucer may pass through "valleys" and "troughs" of the measur ed vibration amp litud e, due to th e casing response to the driving vibr atio n force. Differences of eg. 20 dB in rms level are not uncommon.
Advanced Analysis & Other Techniques The problem th at is immediate ly apparent from Table 1, is that there are a number of 'magnetic' faults resulting in the same vibration signature. The discrimination is only between 'stationar y' and 'rota ting ' problems. Further analysis or other differences in signature are needed to distinguish between current and air-gap variations, broken rotor bars and a rotating air-gap eccentricity for instanc e. Unfortunately, resear ch being carri ed out to achieve thi s, is still in infancy. Non-fundamental Components The simple expl anat ion of the the 'magnetic ' vibrations given earlier assumed an MMF wave with only the fundamental frequency component. The reali ty of course is rat her different. Since there is a strong discontinuity in the curre nt in bars surround ing a broken rotor bar, or in the region of an air-gap var iation, the resulting MMF wave is strong in harmonics. The slot frequency components are also pres ent, so inspe ctio n of the relationship in Fig. 2 shows tha t the resultan t vibration force will contain all the compon ents arising from the crossprod ucts of the fund amen tal wave with itself and its harmonics and with the slot frequency comp onen ts. Some resea rchers (see the list of references at the end of thi s appl icat ion note), have carri ed out an analysis of the theor etic al flux densit y wave due to the effects of slott ing, eccentric ity, satur ation effects and the fundamental stator MMF. They have predicted and confirmed experimentally, level changes in the prin cipa l vibr atio n slot harmonics as a result of static eccentricity, and the appea rance of new components around the slot harmonics as a resul t of dynam ic eccentrici ty. Frequencies predic ted are given by: aiX[((nRs ± k e)x(l
8
- s)/p) ± k x]
where, w — line frequency n = any integer R^ = number of rotor slots k e = an eccentri city 'or der', zero for static eccentricity and a low integer value for dynami c eccentr icit y 5 = per-un it slip p = number of pole-pairs k x = zero or even Furthe r work is trying to predict the relati ve magn itu des of these component s as a function of eccentricit y. Thi s will mean limi ts for thes e vibration compo nents can be set for acceptable eccentri city in a motor. It has been claimed by these researcher s, th at these compo nent s are unique to eccentricity. However, the compari son, for inst ance, of the vibration s pectrum around the principal slot harmonics, for a healthy motor and one with broken rotor bars , shows the appearan ce of new components as well as 'slip' sidebands on the principal slot harmonic. As explained, this is due to the MMF wave being rich in harmonics, due to the curre nt discontinui ty at the broken bar, but it also shows th at , even if analysis shows some differences between broken rotor bars and dynamic eccentricity, determining these differences on pract ical meas urem ents will still have to be proven. Until th is is the cas e, engineers must rely on thei r experience and judge ment, to decide which is the more likely fault. Other Techniques There are a number of other techniques th at have been pu t forward to monitor 'magnetic' faults in induction motors. Principally, the monitored paramet ers suggested are: Motor Speed, Axial Flux (using search coils), and Stat or Current (using a clip-on cur-
related, and force (and motor torque) and hence speed, depen d on the product of MMF and rate of change of flux, all these measure essentially the same thin g as vibra tion, which is of course a measure of force. A consensus of opinion seems to have been reach ed between researchers and industry, tha t monitoring stator current or vibration are prefer red, since thes e tec hniq ues are non-invasive, i.e. they require no modification to the motor and can be performed wit hout int err upt ing operation . Sta tor cur ren t analysis is also performed using a spec tru m analyzer. However, rath er tha n using an acceleromete r or proxim ity probe, as in vibration measur ements , a clip-on curren t tran sfor mer is employed. Pro ponents of curre nt analysis seem to have concentrat ed on detecting broken rotor bars , and this is indeed a common and impor tant fault in induction motors. The analysis method used is the detection of 'slip' sidebands on the line frequency compon ent of sta tor current, similar to those sidebands on 1 x RPM in the vibration spectrum. The effect of eccentricit y, and whet her thi s can be diffe renti ated from broken rotor bars using this method, does not seem to have been addre ssed yet. The main advant age of cur ren t analysis however, is th at the degree of damage, i.e. the number of broken rotor bars , can be est ima ted from the absolute magn itud e of the sideban d cornponents, taking a number of other experience based factors (data) into consideration. This is not practical in the case of vibr ation analysi s, since the magnitude of the measured components depends so much on the mechanical mobility of the partic ular tran smi ssio n pat h, betwee n the source of the vibration and the point at which
rent transformer on the supply). Since current (or MMF) and flux are inter-
the transduc er is placed. Notice two points though: Firstly, there are cer-
tain theoretical configurations in which rotor bars could break, where current analysis would not detect the fault, but vibration analysis would. Secondly, vibration analysis is already employed to detect a wide variety of problems in rotating machinery, for which current analysis is irrelevant.
Final Notes and Conclusions This application note has shown that vibration analysis is capable of detecting and distinguishing between 'mechanical' and 'magnetic' faults in in duction motor drives. Of particular in teres t has been the detect ion of the 'magn etic ' faults. Thes e can be disti nguished as arising from either a 'stationa ry' or a 'rot ati ng' problem. Furthe r distingui shing be tween possible
Fig. 8. The Type 2515 Vibration Analyzer. (An advanced portable single channel FFT analyzer that features a built-in preamplifier for direct connection of accelerometers)
winding faults or eccentricity problems is not so clear-cu t and further research is needed to ensure the accuracy of int erpr eta tio n. This also applies to the techn ique of stat or curr ent
analysis. As a final 'trou ble-s hooti ng' guide, Table 3 is a pres ent atio n of all the vibration compone nts dealt with in the tex t and the possible causes, but also gives some compo nents tha t have
Symptom atic Frequency
Dominant Plane
1 x RPM
Radial
Bent Shaft or Angular Misalign ment
1 x,2 X RPM
Axial
Parallel Misalignment
1 x,2 x RPM
Radial
See Table 2 for more info rmat ion
Mechanical Looseness
1 x, 2 x, 3 x, 4 x RPMeXc. also 0,5 x, 1,5 x RPMeXc.
Radial
High number of harmonics and possible interharmonics characterizes truncation
Vibration Cause Unbalanced Rotor Shaft
Damaged Bearings
Rolling
Element
Oil Whirl and Whip in Sleeve Bearings Static Eccentricity
Induced resonance in the bear ing housing and machine casing in the range 1 to 20 kHz typically
Dynamic Eccentricity
Broken or Cracked Rotor Bar, Loose Rotor Bar, Shorted Rotor Laminations, Poor End-Ring Joints
See Table 2 for more information
0,43 to 0,48 x RPM
Radial
Sleeve Bearings are common in larger mo tors
2 x line frequency and compo nents at co x [nR s (1 -s)/p ± k A ]
Radial
Can result from poor internal alignment, 1) bearing wear, or from local stator heating (Vibration worsens as motor heats up) Referred to as "loose iron" Difficult to differentiate between this group using only vibration analysis, but they will also be apparent at no load as well as on load
2 x line frequency
Radial
2 x line frequency and compo nents spaced by 2 x line fre 1 quency at around 1 kHz "
Radial
Can have high amplitude but not usually de structive. The high frequency components 1 may be similar to static eccentricity "
1 x RPM with 2 x slip frequency sidebands and components at co x[((nR s ± fce)x(1-s)/p) ± k,]
Radial
Can result from rotor bow, rotor runout, or 2 from local rotor heating ' (Vibration worsens as motor heats up)
Shorted Stator Laminations/Turns Loose Stator Laminations
Type of unbalance can be determined from phase relationships (see Table 2)
Resonance is excited by impacts of local faults in the bearing. Also frequencies due to fundamental impact repetition rates (see Fig.6), which are generally lost among other signals + noise at lower frequency however
Weakness/Looseness of Stator Support, Unbalanced Phase Resistance or Coil Sides,
Comment
1 x W/Wwith 2 x slip frequency sidebands and components similar to those given above for 1 dynamic eccentricity "
Radial
The slip sidebands may be low level, requir ing a large dynamic range as well as fre quency selectivity in measuring instrumen tation. Typical spectra are shown in the ap pendix showing that these components in the region of the principal vibration slot har monics also have slip frequency sidebands
1) Local stator heating may be caused by shorted laminations 2) Local rotor heating can be caused by shorted laminations or broken or cracked rotor bar(s) t Observed components (see main text)
Table 3. A trouble-shooting guide as a summary of all the induction motor vibrations discussed in the application note 9
been observed (identified with a f)»
It is hoped th at this applic ation note
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Expert Sy st em s The experience of engineers in the field can be partly reprod uced by collecting a compu ter based dat a base, in a system using this and other programme d knowledge (such as the trou ble-shooting guide), the n designing inference proc edu res , to res ult in an 'exper t syst em'. Such sys tems have already been applied, appa rent ly suecessfully, to the diagnosis of elect ric motor problems using vibrat ion analysis (see references). As research continue s and remain ing question s are answered, exper t systems must have an impo rta nt role to play. The curr ent stat e of the art however, as this application note makes clear, means th at a knowledgeable and experienced maintena nce engineer is probably best equippe d to assess a complex problem.
sideration of the relationship given in Fig. 2, forces and thu s vibrati on magnitude s, vary according to the square of curre nt. Thus the magnitudes are load power dependent; at high load powers the current in the motor conductors is higher. Also per- unit slip, even for a motor on norma l load is typica lly 0.03 to 0.05, i.e. a small value. On light loads therefore, not only will the mag nit ude of vib rat ion componen ts be lower, but the spacing of sidebands will be even smaller. In such circumst ances it may be necessary to use an analyzer with greater dynami c range and frequency resolution , such as the Brtiel&Kjger Type s 2033 or 2032/34 single or dual channel analyzers. The worst case is a motor runni ng freely, the n the per- unit slip is typically 0.005. Note also tha t a varying load
♦ ♦ W jr ,,"ir""IT^"*1'"";"" ' '^Sf" " r " n "' ' r "*j™g mf r j * m mm » « * « HMHI f: '•"""::; ;;;;;:'' ;:;;; " :;: ;;;* Fig 9 The TyPe2032 Dual Channel Signal Analyzer. (Features truly extensive postprocessing)
prob lem could make analys is very difficult. Meas urem ent tra nsd uce rs are also very imp ort ant , especially when measuri ng low level signals. The unique Delta Shear® design of Briiel&Kjser accelerom eters makes them particu larly insensit ive to environme ntal influences which might otherwise disto rt the vibrati on signal and give false readings or obscure impor tan t signature s.
References [1] J.R .Ca mer on, W.T. Thom pson , A.B. Dow, "Vibration and curr ent monitoring for detect ing air-gap eccentric ity in large induc tion motors", Proc. IEE , Vol. 133, Pt. B, N2 3, May 1986, pp 155-163.
[5] B.G. Gaydon, "An ins tru ment to detect induct ion motor circuit defects by speed fluctua tion measurem ents" , Testmex Conf., IE E , Wembley 1979, Conference Publ n. 174, pp 5-8.
[2] J.E . Corley, G.D. Darby, "Developendent and impl emen tati on of an expert system to diagnose motor vibratio n problems ", Proceed ings Of The Fiftee nth Turb omach iner y Sympos ium, 1986, pp 111-118.
[6] C. Harg is, B.G. Gaydo n, K. Kamash ,"Th e detecti on of rotor defects in induc tion motors" , Proc. Int. Conf. on Electric al Machines, Design and Applica tions, IEE , London , May 1982, Publ n. 213, pp 216-220.
[3] H.M. Conolly, R.J. Jacks on, I. Lodge, I. Rober ts, "Dectec tion of int ert urn faults in generator rotor windings using air-gap search coils", Proc. of Int. Conf. on Electric al Machines - Design and Applica tions, IEE, London, Conf. Pub ln. 254, Septe mber 1985, pp 11-15.
[7] J.H. Maxwell, "Indu ctio n motor magnetic vibratio n", Proc. Vibration Ins tit ute , Machin ery Vibration Monitorin g and Analysis Meeting, Hous ton, Texas, Apr. 19-21, 1983.
[4] R.L. Eshl eman , "The role of sum and difference frequencies in rofating machine ry fault diagnosis", I Mech E , Engla nd, publn . C272/80, 1980, pp 145-149. 10
[8] J. Penm an, M.N. Dey, A.J. Tait , WE . Bryan, "Conditi on monitoring of electrical drives", IE E Proc, Vol. 133, Pt. B, N°3, May 1986, ppl4 2-14 8. [9] J. Penm an, J.G. Hadwick, B. Barke r, "Det ect ion of faul ts in
electrical machines by examination of the axially direct ed fluxes", Thi rd Int conf. on Elec. Machines, Brussels , 1978. [10] J. Pen ma n, J.G. Hadwic k, A.F. Stron ach, "Prot ecti on str ate gy agai nst th e occu rrenc e of fault s in electrical machines", Proc . of secon d Int . Conf. on De velopments in Power System ProConf. tection , IE E, London, Publ n. 185, Jun e 1980, pp 54-58. [11] R.B. Randa ll, "Freque ncy analysis", Brtiel&Kjger, Denmark, 1987. [12] P.J. Tavner, B.G. Gaydon, D.M. Ward, "Monito ring of generators and large motors" , IE E Proc, Vol. 133, Pt. B, N°3, May 1986, ppl6 9-180 . [13] P.J. Tavner, J. Penm an, "Condit ion monitoring of electrical machines", Researc h Stud ies Press , Letchworth, Hertfor dshire , Engl and, John Wiley & Sons INC., 1987.
[14] W.T. Tho ms on, D. Ran kin , "Case histories of on-line rotor cage fault diagnosis", Conf. Conditi on Monito ring '87, Dept . Mech. Eng., Universit y College Swansea, Pine rich Pres s, Mumbles, Swansea, UK.
[15] D. Traver, D. Foley, "Diagnosi ng gear and motor problem s with signat ure analysis", AS ME Publ n. DE-7, 1987, pp 3945.
[16] S. Willi amson, A.C. Smi th, "Ste ady sta te analysis of thre ephas e cage motors with rotor- bar and end-ring faults", IE E Pr oa , Vol. 129, Pt . B., JNb3, May 1982.
A Bruel & Kjaer Typ e 2032 Dual Channe l Signal Analyzer was used to perform F FT frequency analysis; spectra , ceps tra and envelope spect ra were plott ed on a Type 2319 Graphi cs Plotter , directly from the Type 2032. The first two figures show the identification of the motor speed and slip frequency sideband compo nents in a baseba nd spec trum to 50 Hz (Fig. Al ) and the correspon ding ceps trum (Fig. A2). Th e rema ini ng four figures show the baseb and spe ctr um to 1.6 kHz (Fig. A3), a "zoom" on this spe ctru m arou nd the second princi pal slot harm oni c (Fig. A4), the corre spondin g cep stru m (Fig. A5), and finally, the envelope spe ctru m from a
thi rd octave filter cen tre d on 800 Hz (Fig. A6). The figures ill ustrat e t he presence of the motor speed (1 x RPM) and the 2 x slip frequency sidebands and the modul atio n of the princip al vibrat ion slot harmon ics by these compo nent s. T he ceps tra of Fig. A5 identifies particul arly clearly the motor speed sideba nds on the princip al vibrat ion slot ha rmonic s. Th at these sideband s also have their own slip frequenc y sid eban ds can be seen on the zoom spect ra in Fig. A4 and the envelope spe ctr a of Fig. A6.
Appendix A series of figures is pre sen ted here depicting the identificat ion of broken rotor bars using tap ed vibrat ion signals recorded on a Briiel&Kjser Type 7005 Portab le Inst rum ent at ion Tap e Recorder. In accordance with the main text and Table 3 in partic ular, two spectra l regions are conc entr ated on—t he region arou nd the motor speed (1 x RPM) and the region aroun d the princip al slot harmo nics. The moto r conc erne d has 2 pai rs of poles and 28 rotor slots. It is runn ing at 24.875 Hz from a nom ina l 50 Hz supply, the first principal vibrati on slot har moni c is ju st over 696 Hz. Thr ee rotor bars in the motor are broken.
Fig. Al. Baseband spectrum to 50 Hz showing the motor rotational speed component with 2 x slip frequency sidebands
Fig. A2. Cepstrum of the baseband 50 Hz spectrum showing the peak at 2 x slip frequency
11
Fig. A3. Baseband spectrum to 1.6 kHz showing both the motor speed component and the region around the principal vibration slot harmonics
Fig. A4. Zoom spectrum centred around the second principal vibration slot harmonic, showing 2 x slip frequency sidebands on the component at this frequency
Fig. A5. Cepstrum of the 1.6 kHz baseband spectrum, clearly identi fying the motor speed (1 x RPM) periodicity in the baseband spectrum
Fig. A6. Envelope spectrum from a third octave filter centred, on 800 Hz, showing not only the (1 x RPM) modulation present in the region of the principal vibration slot harmonics, but also the 2 x slip frequency modulation
BO 0269-12