Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3294-3299 3294 www.etasr.com Bella et al.: Industrial Bearing Fault Detection Using Time-Frequency Analysis Industrial Bearing Fault Detection Using Time-Frequency Analysis Yasmina Bella Electrical Engineering Department Ferhat Abbes Setif 1 University Setif, Algeria b_yasmina2014@ univ-setif.dz Abdelhak Oulmane Department of Mechanical Engineering Polytechnic School of Montreal Montreal, Canada abdelhak.oulmane@polymtl.ca Mohammed Mostefai Electrical Engineering Department Ferhat Abbes Setif 1 University Setif, Algeria mostefai@ univ-setif.dz Abstract—Time-frequency fault detection techniques were applied in this study, for monitoring real life industrial bearing. For this aim, an experimental test bench was developed to emulate the bearing rotating motion and to measure the induced vibration signals. Dedicated software was used to analyze the acquired measurements in the time-frequency domain using several distributions with varying resolution. Results showed that each fault type exhibits a specific behavior in the time-frequency domain, which is exploited in the localization of the faulty component. Keywords-time-frequency domain; industrial bearing; nondestructive test; vibration analysis I. INTRODUCTION Enhancement of the production system dependability is a major issue faced by competitive industrial companies. In this context, the predictive maintenance can play a fundamental role in improving the production system reliability and economic efficiency. In fact, the predictive maintenance is a corrective action applied on the equipment, systems or installations based on the previous knowledge of the operation conditions or performances. Hence, using fault monitoring algorithms can provide real time information about the system health and allows a reliable maintenance decision-making tool [1]. In rotating machinery, the fault monitoring of the rolling element bearings (REBs) is of great practical interest. Actually, bearing damage causes 40% of the total amount of failures in an induction motor [2]. A comprehensive review of the recent advances of REBs monitoring techniques can be found in [3]. Current signature analysis method for the diagnosis of bearing faults forms an area of increasing scientific interest. The main idea beyond this technique is detecting faults based on the change of the stator current spectrum of the induction motor. This change causes a variation of the load and irregularities in the magnetic field. The latter affects the mutual and self- inductance and leads to side bands across the line frequency. Despite the advantages of the current signature method, mechanical vibration signal analysis remains more immediate, simple and rich source of information for understanding the defected bearings (DBs) behavior [4]. Vibration signals acquired from bearings can be either stationary or non- stationary. The stationary signals are characterized by time- invariant statistical properties (moments, densities etc.), however, the statistical properties of a non-stationary signal variy over time [5, 6]. In fact, bearing vibration signals are almost always non-stationary since they are inherently dynamic (e.g. speed and load condition change over time) [7]. Joint time-frequency analysis is an effective approach for addressing this issue, using signals which are presented in a time- frequency amplitude/energy density 3D space. Hence, both the constituent frequency components and their time variation properties can be detected [8-10]. Several time-frequency analysis methods are developed, e.g. short time Fourier transform [11], wavelet transform [12, 13], bilinear/quadratic time-frequency distributions including Cohen and affine classes distributions based on Wigner-Ville distribution [14-16]. In the same context, adaptive optimal kernel methods allow adaptive kernel modification and make the time-frequency distribution suitable for signal structures identification [17]. To suppress the cross-terms and improve time-frequency resolution, the reassignment method has been proposed in [18]. In order to deal with the non-linearity and non-Gaussianity of signals, time-varying higher order spectrum methods such as Wigner higher order spectrum were developed [19]. It is worth mentioning that most of the above mentioned time-frequency analysis methods have been applied to machinery fault diagnosis [20, 21]. In this paper, time-frequency vibration analysis method is used for fault detection of real world industrial bearings motivated by the promising results in induction motor condition monitoring field [22, 23]. For this aim, a bearing experimental test bench has been developed and the acquired vibration signals were examined using T-F ANALYSIS toolbox. The used approach consists of comparing several time-frequency bearing performances under different operation conditions. II. NON-DESTRUCTIVE BEARING TESTING BASED ON TIME- FREQUENCY ANALYSIS Vibration analysis is one of the most usual non-destructive methods utilized to evaluate the bearing conditions in an operating machine. Different bearing faults induce different patterns in the time-frequency plane. In this section we give the frequency values associated to each type of bearing element defect (cage, ball, inner and outer raceways). Thereafter, in order to overcome the drawbacks of the traditional spectral ana app mo bea the A. the spe wh Ind do mo and cag am vib fau usi wh fre inn mo fro can fre not but cau ph equ def B. a mo Engineerin www.etasr alysis techniq proaches are i ore precise d aring. This se e experimental Bearings Fau The rolling s e presence o ecifically, vibr hen the surfac dustrial bearin main. In fact oving over the d cause vibrat ge or the balls mplified. By ex brational signa ult occurs. Th ing the formulf 1 2ff D 2Df N 2f N 2 here: f is th equency, f t ner raceway fa Fig. 1. However, b otion, the char om their calcu n be perform equency with t t only increas t also generat used by the enomenon can ual to the sh fects frequenc Vibration An A straightfor time-varying odulating it ng, Technology r.com ques, quadrat introduced. Th discrimination ection represen l study. ult Frequencie surface damag of high force rations are pro ce of one com ngs exhibit sp , as the inner e running sur tions. When th s are defected, xamining the al, specific fr he bearing fau las given in [191 D . f 1 2 . f 1 . f 1 the cage faul the outer race ault frequency. Representation because of th racteristic freq ulated values ed by compa the theoretica ses the amplit tes harmonics e amplitude n be recogniz haft rotation f cies [24]. nalysis Tools rward way to signal x(t) with a win y & Applied Sci tic time-frequ hese techniqu n between d nts the theoret es ge is caused by es at the con oduced by the mponent strik pecial behavio r or outer rin rface excite th he outer or the the amplitude frequency spe requencies are ult frequencies 9] as follows ( lt frequency, eway fault fre . of ball bearing ch he bearing c quencies may b (1%-2%). He aring the mea l ones. The b tude of the vi s associated to modulation. zed by an am frequency f0 a obtain the freq is to locali ndow function ience Research B uency distribu ues allow easie defect and n tical backgrou y fatigue becau ntact points. e impacts that kes another su or in the freq ngs rotate, the he bearing stru e inner racewa e of the vibrati ectrum of a be e amplified w s can be calcu (see Figure 1): (1a (1b (1c (1df the ball equency and f haracteristics. components s be slightly dif ence, fault iso sured charact earing deterio ibration freque o these freque The deterio mplitude modu around the be quency spectru ize the signa n h [25], b h V Bella et al.: Ind utions er and normal und of use of More occur urface. quency e balls ucture ay, the ions is earing when a ulated : a) b) c) d) fault the sliding fferent olation eristic oration encies encies oration ulation earing rum of al by before per the as f whe rep h a sign be e as f tech dom rep freq met signP whe Kˆ( freq       whe f(ξ, (for givW dist freq φ(t, Wig g an osc For foll Vol. 8, No. 4, 20 dustrial Bearing rforming the s frequency con follows: F t, f = x ere ∗ denotes resentation aro and we perform nal as well. H estimated by c follows: S t, f |F On the other hniques that mains simult resentations. quency distrib thod for the nals in many pt, f K ere z(u), Z(f (u,v,t,f) are th quency transfo 2iπξ(s τ)e f (ξ,τ        ere f(ξ,τ) ,τ)=f(−ξ,−τ). I r example f(ξ en by (6): t, f z Z f To reduce th tribution, we quency using ,f)=g(t)H(f). T gner-Ville distφ t nd h are even Another distr cillatory interfe r this distributif ξ,τ e Hence, the C lowing: 018, 3294-3299 g Fault Detectio short-time Fou ntent of the sig x u h∗ u t s the complex ound t, we sim m a Fourier t owever, the sp computing the t, f | r hand, time-f study a signa taneously, u For instance, butions is co analysis and practical applicK u,v,t, f K^ u,v, t, f Z f ) are the he transition k ormation is the *ττ)z(s )z (s 2   is the ob f the function ξ,τ)=1), we ge z t u2 z∗ tZ∗ f he oscillatory apply a sep g the follow This distribut tribution, is git , f W t and real windo ribution that erence effect i ion, the functio⁄ Choi-William on Using Time- urier transform gnal in the reg e du x conjugate [3 mply move by t transformation pectrogram of squared magn frequency ana al in both tim using variou , the class o onsidered the d processing cations: z u z∗ v du u Z∗ v dudv studied sign kernels. A spe e Cohen class g 2iπfττ )e dξdfdτ 2  bservation w n f(ξ,τ) is inde et the Wigner t u2 e de dν inferences of parated smoot wing time-fre tion, known iven by (7): t , f f dt ows with h(0)= allows the m s the Choi-Wi on f has the fo s distribution 3295 -Frequency An m (STFT) to o gion of the win (2) 3]. For the spe translation win n on the wind f the signal x(t nitude of the S (3) alysis include me and frequ us time-frequ of quadratic most approp of non-statio dv v (4) nal and K(u,v ecial class of given by: (5) window veri pendent of ξ a r-Ville distrib du (6) f the Wigner- thing in time equency win by the smoo df (7) =g(0)=1. minimization o illiams distribu ollowing form: (8) n is given by nalysis obtain ndow ectral ndow owed t) can STFT, es the uency uency time- priate onary v,t,f), time- ifying and τ bution -Ville e and ndow: othed of the ution. y the P( wh dis dif the the equ the ded dec vib off fre tim    aut pro net A. bea 2). cal dat bea ide Engineerin www.etasr 2 (t, f ) π |        Actually, if wf ψ,τ here a is a con stribution and , | | We emphasiz fferent resolut e signal under II A general de en the theoret uations of the e developed t dicated expe cisions about bration measur fers a wide ra equency analy me-frequency d It provides dimensions ( It detects an generate a lo It supervises process produ T-F ANALY tomatic clas ocessing throu tworks. Bearing Des Computation We used th aring is a sing . The technic lculate the the ta sheet provid TABL P & W Bea Inner diam Outer dia Pitch diam Widt Contact A Operating s Operating s PW100#5 be aring was coll entified as o ng, Technology r.com 2 2 22σ (s t ) / τσ e z( τ |   we choose the nstant. This d has the follow ze that each tim tion quality w study as illust I. EXPERIME escription of th tical fault freq previous secti theory, we lau erimental test the faulty st rements using ange of metho ysis. The adva domain are: a represent (amplitude-tim nd follows th w vibration po s machines i uces high amp YSIS toolbox, ssification of ugh usage of cription and T n he Pratt & W gle row ball m al specificatio eoretical fault ded by the con LE I. BEARI aring ID meter meter meter h Angle speed 1 speed 2 earing is used lected from Bo one of the y & Applied Sci *τ τs )z (s )e 2 2   kernel functio distribution is wing form: ∗ s me-frequency which allows a trated below. ENTAL STUDY he bearing str quencies are c ion. In order t unched severa t bench. Fin tate, we eval g T-F ANALY ods in time, fr antages of sig tation of the me-frequency) he developme ower. in which the plitude of perio also offers m f rotating m f Fourier desc Theorical Fau Whitney PW1 model with rad ons of bearin t frequencies nstructor (Tabl ING TECHNICAL S PW100#5 BRG 2.8347” 3.9292” 3.04 0.625” 0 1000 2000 for the shaft o ombardier Com most problem ience Research B 2iπfτe dsdτ (9) on as: (10 called Born-J (11 distribution g accurate analy Y STEPS ructure is give calculated usin to take advanta al experiments nally, for m luated the acq YSIS toolbox w frequency and gnal analysis e signal in ent of defects e normal ope odic shocks. more applicatio machinery, criptors and n lt Frequencies 00#5 bearing dial contact (F ng that we ne are taken from le I). SPECIFICATIONS G roller bearing ” 2.8350” ” 3.9272” 4165” ” 0.630” 0o 0rpm 0rpm of the gearbox mpany and has matic compo h V Bella et al.: Ind 0) Jordan ) gives a ysis of en and ng the age of s in a making quired which time- in the three s that erating ons in image neural s g, this Figure eed to m the g x. This s been onents. Fur bea sum freq 1 3 B. Me de the foll sup is c enti 360 bea (Ta rota and can exte bea B whi acc for on t was mo only bea use disa bea Vol. 8, No. 4, 20 dustrial Bearing rthermore, the aring defects mmarized in quency. TABLE II fr 16.66Hz 7 33.33Hz 15 Experimental Several tests echanics Depar Montreal. The applied mec lowing eleme pported at its e connected to a ire system is 00rpm and su ams each. The able III). The t ating machine d gears. All be n be easily dis ernal clampin aring sizes. Fig. 2. TABLE Components Base Motor Couplings Bearing House S Three acceler ich were conn celerometer A3 monitoring th the side of the s positioned h tor and thus t y the data fro aring fault diag ed for equipm assembled in aring (Figure 4 018, 3294-3299 g Fault Detectio e frequencies are calcula Table II wh I. BEARING T fCF f .64Hz 108 5.28Hz 216 l Tests and Me s on the bea rtment Labora e test bench w chanics sectio ents: A rotor ends by an ass a gearbox via s driven by a upported by a test bench is test bench is d ry such as dam earings are mo sassembled. W ng sleeve assem Pratt & Whitne III. TEST BEN Specific 2 H-Beams W 2Hp, 3600rpm 7/8inch SNL 510 – H310 rometers were nected to a co 3 was position he bearing fau e bearing for m horizontally on test equipmen om A1 were gnosis. The re ment monitor order to remo 4, left). Then, on Using Time- s associated w ated using ( here f is the THEORETICAL FAU fORF fIR 8.32Hz 91.7 6.64Hz 183.4 easurement Ac aring were c atory at the Ec was designed a on. The latte system cons sembly of two a transmissio a 2HP electr a set of two 6 1750mm long designed to tes maged bearing ounted on a cl We have design mbly to fit al ey bearing conside NCH TECHNICAL cations W8x8 67lb/ft m, 575Volts h-linch – 1210EKTN9 used, A1, A2 mputer for da ned horizontal ults, A2 was po monitoring the n the spindle nt condition. W analyzed, as w est of sensors ring. The te ove the shaft as illustrated 3296 -Frequency An with the diff (1a)-(1d) and e bearing rot ULT FREQUENCIE RF fBF 71Hz 99.54 42Hz 199.0 cquisition carried out in cole Polytechn at the laborato er consists of sisting of a o SKF bearing n belt system ric motor rate 67lb/ft H-weig g and 210mm st typical defec gs, mass imba lamping sleeve ned an interna ll Pratt & Wh ered for test. SPECIFICATIONS Manufacturer Prometo Toshiba Rex Omega SKF Canada 2 and A3 (Figu ata acquisition ly over the be ositioned verti shaft faults an for monitorin We emphasize we are condu ’ information est bench can along with th d in the lower nalysis ferent d are tating ES F 4Hz 8Hz n the nique ory of f the shaft s that m. The ed at ghted wide cts in alance e and al and hitney rs a ure 3) n. The earing ically nd A1 ng the e that ucting were n be he old right Fig ord the tes Sp spe the 50 sig spe dis no exc ben F wit dec t1a are pro con Engineerin www.etasr gure 4, the ne der to insure e stretch bench sts were carrie p2) of 1000rpm eed range was e fault frequen 0rpm to 2200 gnal is less ma eed, the amp stinguishable f acceleration i cessive noise, nch. Fig. 4. Assem Ro Sp1 Sp2 Experimenta thout taking in celeration i.e. a-t1b and t2a-t e acquired usi ocessed using F For fault dia nsidered: sam ng, Technology r.com ew bearing is successful ins h is reassemb ed out at two m and 2000rp s decided afte ncy reacts wel 0rpm [26]. At arked, less amp plitude genera from the back is generated. F there is an im Fig. 3. Expe mbling and disasse TABLE IV otating speed (rp 1000 2000 al results are p nto considerat we only deal t2b (Figure 5) ing NI PMA6 TF-ANALYS Fig. 5. Speed agnosis purpo mpling freque y & Applied Sci expanded by sertion into th bled and carefu different rota pm respective er the fact that ll over the ran t low and hig plified by the d ated by the f kground noise For high rotati mminent risk o erimental test ben embling of the bea V. TEST SPEE pm) Rotati presented in a tion the times with the follow ). The accelera 61115 Portable SIS software. diagram for PW1 oses, only thre ency, time w ience Research B heating to 110 he shaft. There fully calibrated ational speeds ely (Table IV) t the peak fac nge of rotation gh-speed rang defect, i.e. for fault is not c e and for low- ional speeds, d of damaging th nch. arings from the be EDS ing speed (Hz) 16.66 33.33 chronological of acceleratio wing time inte ation measure e Monitor and 00#5 ee parameters window length h V Bella et al.: Ind 0◦C in eafter, d. The (Sp1, ). The ctor of n from ge, the r high- clearly -speed due to he test ench. order on and ervals: ements d then s were h and freq betw is o dom pos was win pos C. dist ana dist bett 1) pre dist non def a fr Fro alm fIRF Vol. 8, No. 4, 20 dustrial Bearing quency windo ween time and obtained in the main and vice ssible resolutio s applied unde ndow lengths n sitive integer [ Discussion an For different tributions obt alyzed. By adj tributions of C ter resolution o Measurement From Figures sents a bette tribution. The n-stationary s fects in bearing frequency peak om the spectru most equal to F value, which Fig. 6. Fig. 7. C Fig. 8. Sp 018, 3294-3299 g Fault Detectio ow length. It w d frequency re e time domain e versa. Henc on for a partic er the conditio need to satisfy 3]. nd Validation rotational spee tained by th djusting the so Choi-William of the signal. t Results for T s 6 and 7, th er resolution e signal modu ignal. The la g. The signal s k, which corr um graph, we n the inner race has a value of Born-Jordan dist Choi-Williams dis pectrum frequenc on Using Time- was essential esolution becau n then it is los ce, in order cular case a m on that both t y the equation of Results ed values, the he time-frequ oftware param s and Born-Jo Time-Period t1 he distribution compared to ulation indicat atter confirms spectrum grap responds to th notice that the eway calculat f 91.71Hz (Tab tribution for speed stribution for spee y analysis for spe 3297 -Frequency An to find a trad use if the prec st in the frequ to obtain the manual trial me time and frequ 2n−1, where n graphs of diff uency method meters for diff ordan one see 1a-t1b (Sp1) n of Choi-Wil o the Born-Jo es the presen s the presenc ph (Figure 8) s he value of 9 e peak frequen ted fault frequ ble II). d of 1000rpm. ed of 1000rpm. eed of 1000rpm. nalysis de-off cision uency best ethod uency n is a ferent d are ferent eks a liams ordan ce of ce of shows 91Hz. ncy is uency 2) val Ch tha mo pre fro the We fre fre the and is c spe the sm Engineerin www.etasr Measuremen For this time lue of 2000rp hoi-Williams d at the modu odulations are esence of defe om the spectru e fault frequen e noticed th equency trans equency fault. e percentage o d the experim calculated by (% Δf The experim eeds of 1000rp e theoretically Fig. 9. Fig. 10. Fig. 11. S The validity mall difference ng, Technology r.com nt results for T e-period, the pm (Sp2). Ac distribution gr lation numbe present at low ects. As in Sp um (Figure 1 ncy fIRF (Table hat for differ sformations i To validate t of relative err mental value of (12): mental fault fre pm and 2000rp fault frequenc Born-Jordan dis Choi-Williams di Spectrum frequenc of the measu e between the y & Applied Sci Time-Period t2 rotation speed ccording to th aphs (Figures er has almos w frequency, p1, the peak f 1) correspond e II), which e rent rotating indicate the the obtained r ror between th f fault frequen 1 equency fIRFex pm is 0.77% a cy respectively stribution for spee istribution for spe cy analysis for sp urements is d e theoretical a ience Research B 2a-t2b (Sp2) d is doubled he Born-Jorda 9 and 10), we st doubled. which confirm frequency of 1 ds approximat equals to 183. speeds, the apparition o results we cal he theoretical ncy (%ΔfIRF) w 100 (12 xperimental for ro and 0.23% les y (Table V). ed of 2000rpm. eed of 2000rpm. eed of 2000rpm. emonstrated b and measured h V Bella et al.: Ind to the an and e note These ms the 183Hz tely to 42Hz. time- f fIRF lculate value which 2) otating ss than by the d fault freq Rot 1 2 isol obt calc obt sho imp vibr incl mon spe tran dec mai hum [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] Vol. 8, No. 4, 20 dustrial Bearing quencies, whic TABLE V. ating speed fr T 1000rpm 2000rpm In this paper, lation method tained results culated resul tained results a ows the effect portant inform ration measur lude the stud nitoring whic ectrum of cri nsportation. In cisions (syste intenance, and man and mater E. L. Bonaldi, G de Oliveira, L. signature an http://dx.doi.org S. Patidar, P. techniques for International Jo 5, pp. 1803-180 S. Nandi, H. diagnosis of ele Conversion, Vo S. Choi, B. Aki fault-diagnosis digital-signal-pr Electronics, Vo F. E. H. Mont diagnosis of Mechanical Sys 2008 S. Guoji, S. M experimental a diagnosis of gea No. 1, pp. 76-89 C. Li, V. San element bearing transform guid Transactions, V L. Cohen, Time S. Qian, D. Che ] P. Flandrin, T 1998 ] A. Prudhom, J. frequency vibra by bearing curr 84, No. A, pp. 7 018, 3294-3299 g Fault Detectio ch is less than SUMMARY TA Theoretical fIRF 91.71 Hz 183.42 Hz IV. CO , a time-freque d was applie are valid in ts. The diff and the theore tiveness of th mation about rements. Furth dy of fault s h provides im itical applica n fact, real ti em stop, cur d control law r rial disasters. REFER G. Lambert-Torre . E. 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