Fault severity diagnosis of rolling element bearings based on kurtogram and envelope analysis

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1 Fault seveity diagnosis of olling element beaings based on kutogam and envelope analysis Fengshou Gu, Xiange Tian, Zhi Chen, Tie Wang, Ibahim Rehab and Andew Ball Abstact Faults in olling element beaing ae among the main causes of beakdown in otating machines. Vibation is an effective technique fo machine condition monitoing. Vibation signals fom a defective beaing with a localized fault contain a seies of impulsive esponses, which esult fom the impacts of the defective pat(s) with othe elements. Most eseaches caied out have focused on fault location identification. Howeve, limited wok has been epoted fo fault seveity estimation, which is citical to make decision fo maintenance actions. To impove cuent diagnostic capability, this pape pays moe attention to beaing fault seveity diagnosis. It models the vibation souces fom beaing defects as an impact pocess with constant size but thee diffeent lengths coesponding to oute ace fault, inne ace fault and olle fault, espectively. Then an expeimental study was followed to evaluate this model. Moeove, the conventional envelope analysis of the measued vibation signals fom the tested faulty beaings is optimized by spectal kutosis (SK) fo automatic and eliable fault detection and fault categoy diagnosis. In the meantime, the diagnostic paametes fo fault seveity estimation: oot mean squaed (RMS) values and kutosis amplitude ae developed based on the model esults and subsequently evaluated to be ageed vigoously with tested fault cases. Keywods kutogam, envelope analysis, beaing fault diagnosis, elastic defomation, geomety defomation I. Intoduction Rolling element beaings ae key components in moden machiney. Detection and diagnosis of thei faults ae vey impotant, as it pevents any futhe deteioation of othe components which may lead to catastophic failues. Fo a clea diagnosis of the beaing fault, a numbe of techniques have been poposed to sepaate deteministic components fom the beaing component. Dalow exploed high fequency esonance technique (HFRT), which is also widely known as envelope analysis []. Antoni applied cyclostationay spectal analysis to fault detection and diagnosis in olling element beaings [, 3]. Futhemoe, cepstum analysis, bispectum analysis and time-fequency analysis ae also intoduced to beaing fault diagnostic. D. Ho and R.B. Randall investigated the efficient application of self-adaptive noise cancellation (SANC) in conjunction with envelope analysis in ode to Fengshou Gu, Xiange Tian, Ibahim Rehab and Andew Ball Univesity of Huddesfield UK F.Gu@hud.ac.uk, u7888@hud.ac.uk Zhi Chen, Tie Wang Taiyuan Univesity of Technology P.R. China emove discete fequency masking in beaing vibation signals []. Baszcz applied SANC to denoise wind tubines vibation signal fo oute ace fault diagnosis [5]. N. Sawalhi, R. B. Randall and H. Endo pesented an algoithm fo enhancing the suveillance capability of SK by using the minimum entopy deconvolution (MED) technique. The MED technique effectively deconvolves the effect of the tansmission path and claifies the impulses, even whee they ae not sepaated in the oiginal signal [6]. S. Zhao applied empiical mode decomposition (EMD) and the Appoximate Entopy (ApEn) method fo quantitative diagnosis of a spalllike fault of a olling element beaing [7]. Baszcz poposed a new method named potugam, which is based on the kutosis of the envelope spectum amplitudes of the demodulated signal, athe than on the kutosis of the filteed time signal. The advantage of the method is the ability to detect tansients with smalle signal-to-noise atio (SNR) compaing to the SK based kutogam [8]. Howeve, most of these woks ae fo fault detection and fault type diagnosis and limited investigations ae on fault seveity estimation, which is citical to make decisions fo maintenance actions. To impove cuent diagnostic capability, this pape pays moe attention to beaing fault seveity diagnosis. II. Chaacteistic fequencies of beaing faults Rolling element beaing consists of an inne ace, an oute ace, olling elements and a cage, which holds the olling elements in a given elative position, as pesented in Fig.. In ode to find the chaacteistics of the vibation esponses due to faults, the beaing ings ae assumed to be isolated continuous systems. It is futhe assumed that: () All olles ae equal in diamete; () Thee is in pue olling contact between olles, inne ace and oute ace; (3) Thee is no slipping between the shaft and the beaing; () Oute ace is D c D Figue. Rolling element beaing components Oute ace Inne ace Cage

2 stationay and inne ace otates. The elative velocity between olles, inne ace and oute ace ae zeo because they ae in pue olling contact. Race suface fatigue esults in the appeaance of spalls on the inne ace, oute ace o olling elements. If one of the aces has a spall, it will almost peiodically impact with olling elements. The fault signatue is epesented by successive impulses with a epetition ate depending on the faulty component, geometic dimensions and the otational speed. The peiod between impacts is diffeent fo all the listed elements and depends on the geomety of the beaing, the otational speed and the load angle. Fo a fixed oute ace beaing, the theoetical chaacteistic fault fequencies can be calculated using ()-(), and a deivation of these equations is pesented in [9]. Fundamental cage fequency: D FC Fs ( cos) () Dc Oute ace defect fequency: N D FRPO Fs ( cos) () Dc Inne ace defect fequency: N D FRPI Fs ( cos) (3) Dc defect fequency: Dc Fs D FRS ( cos ) () D Dc whee, D c is pitch cicle diamete, D is olle diamete, is contact angle, N is numbe of olle and F s is shaft otational fequency. In pactice thee is always slight sliding and slippage, especially when a beaing is unde dynamic loads and with sevee wea. Theefoe, these fequencies may have a slight diffeence fom calculated ones above. III. Vibation esponses to diffeent sizes of fault The beaing fequency equations povide a theoetical estimate of the fequencies to be expected when vaious defects occu on the beaing elements, based upon the assumption that an ideal impulse will be geneated wheneve a beaing element encountes the defect. Fo localised beaing faults such as spalling and pitting, shap foce impacts will be geneated. These impacts will excite stuctual esonances and the esulting vibation will be measued by the tansduce mounted extenally on the machine casing []. Howeve, due to the diffeent geomety of the contact between the localised fault and the beaing component, the contact-stiffness can change because of the diffeent geometical popeties in contact zones. On the othe hand, a damaged beaing (paticulaly a small damage at an ealy stage of damage development) usually poduces small amplitudes of vibation in high fequency bands due to impulsive impacts[]. (db) Figue. Schematic diagam of geomety defomation d cd Figue 3. Geomety defomation fo two kinds of contact Time(s) Figue. Fequency esponses of diffeence pulse heights The contact defomation is composed of geometic defomation and elastic defomation. Elastic defomation occus along the contact sufaces of a beaing s olling elements and aceway sufaces unde loading. Geometic defomation caused by defect is elated to defect location and size. While elastic defomation is elated to load and defect size. Half-sine pulse of diffeent heights Fequency esponses of diffeent pulse heights 6 8

The total defomation includes geomety defomation g and elastic defomation e. g e (5) As shown in Fig., if the width of fault is d and adius of cicle is, the chod height can be expessed as d cd.

3 The total defomation includes geomety defomation g and elastic defomation e. g e (5) As shown in Fig., if the width of fault is d and adius of cicle is, the chod height can be expessed as d cd. (6) Thee ae two kinds of contact model between beaing components as shown in Fig. 3, which ae contact between a convex and a concave suface (C and C) and contact between two convex sufaces (C and C3). If the chod height fo C, C and C3 ae defined as cd, cd and cd 3. The geomety defomation of concave-convex contact and concave-concave contact ae given out by (7) and (8), espectively. cd cd (7) cd cd3 (8) Futhemoe, consideing that the fault on inne ace ceates concave-concave contact wheeas the fault on the olle has both concave-concave and concave-convex contact. The vibation impact fom the inne ace defect may ceate the highest esponses when the sizes of the faults ae the same ove diffeent aces. Fom the elationship it is easy to undestand that geomety defomations on diffeent components have a elationship as shown in (9). (9) go g gi Based on this elationship, Fig. illustates half-sine pulses of thee diffeent heights:, and and thei fequency esponses. It is obvious that when the amplitude is highe, the fequency esponse inceases. This shows that when the fault size is the same, the fault on inne ace may poduce the highest esponses wheeas the fault on the oute ace will cause the lowest esponses. Taking into account the elastic defomation, it is easy to undestand the impulsive diffeences between diffeent fault seveities. As fault degee inceases, the load aea will decease while elastic defomation e will incease, which will esult in the gowth of impulse height. IV. Signal pocessing based on kutogam The envelope spectum is a vey efficient diagnostic tool fo the afoementioned faults, as the infomation about the fault is extacted fom the spacing between impulses but not fom the excited fequencies. The pocess of obtaining the envelope spectum is often named as signal demodulation. Howeve, the quality of the demodulated signal depends on the fequency band selected fo the demodulation, which equies two paametes bandwidth and cental fequency []. SK is a poweful tool fo detecting the pesence of tansients in a signal, even when they ae buied in stong additive noise, by indicating in which fequency bands they ae taken place. The Kutogam optimization consides a vaiety of bandwidths and cental fequencies. It is basically a cascade of SK obtained fo diffeent values of the Shot Time Fequency Tansfom (STFT) window length. The SK of the complex envelope can be calculated [] as, K ( () whee the subtaction of is used to enfoce K ( in the case is complex Gaussian (instead of 3 fo eal signals). Then, equation fo kutogam of a signal based on STFT can be pesented as (), n K x ( f, n) () whee, n denotes the window length of STFT. n V. Test ig desciption The expeimental data analysed in this pape was collected fom the beaing test ig illustated in Fig. 5. It is composed of moto, coupling, shaft, beaings and bake. DC Moto Vibation senso Beaing Coupling Figue 5. Photo of beaing test ig Shaft Moto Beaing type is NSK N6 cylindical olle beaing and its geometic dimensions ae listed in Table I. One Sinocea piezoelectic acceleomete is mounted on the housing of the N6 beaing vetically to measue the vibation. The fequency ange of acceleomete is fom.5 Hz to khz and the sensitivity is 8.8 mv/ms. 3

Defect fequencies in expeiment calculated accoding to equation ()-(9) ae listed in Table II. TABLE I.

FAULT CHARACTERISTIC FREQUENCIES Fault type Defect fequency (Hz) Oute ace 85.8 Inne ace 39. 9.7 Fig.

In expeiment, defect was made on olle, inne ace and oute ace with thee diffeent seveities (3%, 6% and %) on each component, sepaately.

4 Defect fequencies in expeiment calculated accoding to equation ()-(9) ae listed in Table II. TABLE I. SPECIFICATION OF NSK TYPE N6 CYLINDRICAL ROLLER BEARING Paamete Measuement Pitch Diamete 59 mm Boe Diamete 3 mm Diamete mm Numbe 9 Contact Angle TABLE II. FAULT CHARACTERISTIC FREQUENCIES Fault type Defect fequency (Hz) Oute ace 85.8 Inne ace Fig. 6 gives out the photo of defect olling beaing with 3% olle fault, 6% inne ace fault and % oute ace fault, espectively. In expeiment, defect was made on olle, inne ace and oute ace with thee diffeent seveities (3%, 6% and %) on each component, sepaately. (a) 3% olle fault (b) 6% inne ace fault (c) % oute ace fault Figue 6. Photo of fault beaing VI. Signal pocessing esults and discussion In this section, expeimental data pocessing esults ae discussed based on mechanical vibation model. Same baseline signal is applied to oute ace, inne ace and olle fault fo compaison. Fig. 7 shows aw vibation signals fo baseline, inne ace and oute ace at fou kinds of conditions, espectively. It can be seen that the vibation amplitudes of oute ace ae smalle than inne ace and olle fo thee kinds of fault seveities. In the meantime, the vibation amplitude of olle is highe than inne ace at % damage but simila at both 3% damage and 6% damage. Fig. 8- give out envelope analysis esults of thee kinds of fault. Fom the figues, it is obvious that chaacteistic fequencies and thei hamonics ae significant, which veifies that filte paametes can be optimised by kutosis maximum pinciple effectively. The amplitude of inne ace fault fequency gows with the damage seveity while the oute ace and olle fault do not have such good tend. Envelope analysis esults indicate it can be applied fo fault detection and ecognise the fault type by fault chaacteistic fequencies. Oute Race Inne Race. 3% damage (m/s ). (m/s ) (m/s ) (m/s ) (m/s ).5 6% damage -.. Figue 7. Vibation signals in the time domain 5 x - 3% damage Figue 8. Envelope analysis esults fo oute ace defect Figue 9. Envelope analysis esults fo inne ace defect % damage Oute Race % damage..5 (m/s ) x -3 % damage x -3 3% damage Inne Race % damage % damage

5 (m/s ) (m/s ) (m/s ) x -3 3% damage x -3 6% damage Figue. Envelope analysis esults fo olle defect x -3 % damage seveity, which povides decisive efeence fo taking maintenance actions. VII. Conclusion In this pape, an adaptive filte technique has been developed by combining SK with envelope analysis fo olling beaing fault detection and diagnosis. The adaptive filte is applied to impove SNR. The filte paametes including band width and cental fequency ae optimised by a maximal SK citeion. Then, the filteed vibation signal is analysed by envelope analysis fo fault featue extaction. The effectiveness of the poposed method has been evaluated based on expeimental data sets fom thee types of faults and thee levels of damage seveities. The diagnostic esults show that not only the types of fault can be identified coectly but also the seveity is estimated with a good degee of accuacy % damage 6% damage % damage Fault seveity Mean Kutosis of thee tests 6 Oute ace Inne ace Mean RMS of thee tests 3% damage 6% damage % damage Fault seveity Figue. Mean RMS and Kutosis compaison esults Fig. demonstates mean RMS and kutosis compaison of thee tests esults. RMS value inceases geatly with the damage seveity and shows obvious diffeence between thee kinds of faults. But % damage does not follow the pediction because the motion between beaing components includes slippage. In addition, kutosis esults can also sepaate oute ace fault. Howeve the diffeence is tiny between inne ace and olle fault, showing that the RMS is the bette choice fo fault diagnosis. When thee is a same size fault on oute ace, inne ace and olle, the fault impulse amplitude of oute ace is constant and smalle and wavefom impulse is less spikiness, while the inne ace fault fequency is modulated at shaft fequency and olle fault fequency is modulated at cage fequency. With same size on thee components sepaately, the oute ace impulse has lowest peakedness compaed with inne ace fault. On the contay, olle fault has the lagest defomation and should have highest peakedness which is not eality in expeimental esults. This may be caused by the high level noises in olle vibation which will impact the kutosis value. The expeimental data analysis esults show that the RMS and kutosis value can be elied on to pedict beaing fault Refeences [] M. S. Dalow, R. H. Badgley and G. W. Hogg, Application of high fequency esonance techniques fo beaing diagnostics in helicopte geaboxes, Technical Repot, US Amy Ai Mobility Reseach and Development Laboatoy, 97, pp [] J. Antoni, Cyclic spectal analysis in pactice, Mechanical Systems and Signal Pocessing, vol., 7, pp [3] J. Antoni, Cyclostationaity by examples, Mechanical Systems and Signal Pocessing, vol. 3, 9, pp [] D. Ho and R. B. Randall, Optimisation of beaing diagnostic techniques using simulated and actual beaing fault signals, Mechanical Systems and Signal Pocessing, vol. (5),, pp [5] T. Baszcz, Decomposition of vibation signals into deteministic and nondeteministic components and its capabilities fo fault detection and identification, Intenational Jounal of Applied Mathematics and Compute Science, vol. 9, 9, pp , ISSN (Pint) 6-876X. [6] N. Sawalhi, R. B. Randall and H. Endo, The enhancement of fault detection and diagnosis in olling element beaings using minimum entopy deconvolution combined with spectal kutosis, Mechanical Systems and Signal Pocessing, vol., 7, pp [7] S. Zhao, L. Liang, G. Xu, J. Wang and W. Zhang, Quantitative diagnosis of a spall-like fault of a olling element beaing by empiical mode decomposition and the appoximate entopy method, Mechanical Systems and Signal Pocessing, vol., 3, pp [8] T. Baszcz and A. Jablonski, A novel method fo the optimal band selection fo vibation signal demodulation and compaison with the Kutogam, Mechanical Systems and Signal Pocessing, vol. 5,, pp.3 5. [9] Tomasz Baszcz and Nade Sawalhi, Fault Detection Enhancement in Rolling Element Beaings Using the Minimum Entopy Deconvolution, Achives of Acoustics, vol. 37,, pp.3-. [] T. Igaashi and H. Hamada, Studies on the vibation and sound of defective olling beaings (Fist Repot: Vibation of Ball Beaings with One Defect), Bulletin of the Japan Society of Mechanical Enginees, vol. 5, 98, pp.6-8. [] N. Tandon and A. Choudtuy, An analytical model fo the pediction of the vibation esponse of olling element beaings due to a localized defect, Jounal of Sound and Vibation, vol. 5(3), 997, pp [] R. B. Randall and J. Antoni, Rolling element beaing diagnostics A tutoial, Mechanical Systems and Signal Pocessing, vol. 5,, pp

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