A shock filter of vibrtory signl for dmge detection Bechir Bdri ; Mrc Thoms nd Sdok Sssi Abstrct- This pper describes filter tht is designed to trck shocks in the time domin, nd to isolte them from ny other rndom or hrmonics components. This innovtive tool cn be used in the time domin s denoising filter to estimte the proportion of the totl signl energy cused by the shocks nd to quntify the severity of dmge. It cn lso be pplied in the frequency domin nd will llow through envelope or time-frequency nlysis to clerly identify the sources of the shocks even if they re from vrious origins. Keywords Bering, Shock Filter, Signl Processing, Vibrtion, Time-frequency nlysis, Envelop. M I. ITRODUCTIO chines mintennce is conditioned to n dequte monitoring of potentil filures. Mchinery vibrtion consists essentilly of three signl types: Periodic (unblnce, mislignment, blde pss), rndom (friction, noise, fluctution, turbulence) nd shocks (bering fults, ger fults, etc.). The determintion of ech of these types of vibrtion constitutes in itself powerful monitoring technique. One of the most involved mechnisms in rotting mchines filures re the berings. The recognition nd clssifiction of berings defects by vibrtory nlysis remins subject of gret interest in the rotting mchines, becuse the detection of the dmge phenomen nd its propgtion still remin nebulous to dte. Precedent works llowed for the development of simultion softwre generting the vibrtory response cused by defective berings []. The numericl simultor hs been used to generte dtbse covering lrge rnge of defects configurtions. A relevnt review of vibrtion mesurement methods for the detection of defects in rolling element berings hs been presented by Tndon nd Choudhury []. The monitoring methods pplied to berings cn be chieved in number of wys []. Some of these methods re simple to use while others require sophisticted signl processing techniques. In fct, lrge number of defects generte shocks tht cn be nlyzed in either time domin:, Pek, Crest Fctor (CF), Kurtosis (Ku), Impulse Fctor, Shpe Fctor, etc. [], or in frequency domin: spectrl nlysis round bering defect frequencies [-7], frequency spectrum in the high frequency domin, Spike energy [8], enveloping [9], or time-frequency nd wvelet nlysis [], etc. Mnuscript received My,. B. Bdri nd M. Thoms re from the deprtment of Mechnicl Engineering, ETS, Montrel, Qc, HC K, Cnd, mrc.thoms@etsmtl.c S. Sssi is from the deprtment of Physics nd Instrumenttion, Institut tionl des Sciences Appliquées et de Technologie, Tunis, Cedex, Tunisi. The shocks re generlly considered s bnorml phenomen in most rotting mchinery nd s reflecting the effect of defects for which the source must be identified. Usully shock phenomen cn be identified by sclr time descriptors. nd Mx-Pek vlues re quite dequte when the fult is quite developed nd the signl-to-noise is high. Unfortuntely, when the fult is smll nd the signl-tonoise rtio is wek, these two descriptors re not enough efficient lone. The increse in size defect is usully observed more redily by the Pek rther thn by the vlue. Becuse of this, the crest fctor, which is defined by the rtio of the Pek to vlue, is better dpted for monitoring the evolution of shock phenomen. This reltionship between these two descriptors during the evolution of fult is interesting, but it is esier to combine them in only one sclr descriptor such s the Crest Fctor (CF) or the Kurtosis (Ku). In this pper, shock detector, bsed on the Julien Index [-] is described. The min gol of shock filter is to exmine the shock content into signl. The method uses the time wveform nd consists in recognizing the shock pttern of ech defect, insulting it nd treting it seprtely from the originl signl. Thus, the effect of ech defect in the vibrtory signl is treted independently of the others nd will mke it possible to loclize it. The shock descriptor lso llows for counting the number of shocks per unit time, or better, for ech cycle or revolution of the mchine. This simple descriptor my be used by non-specilist to monitor the number of shocks per revolution s the fult progresses. The shock detector llows not only for determining the number of shocks, but lso their loction nd individul mplitudes. It is then possible to use the Fourier trnsform to determine the frequencies t which the shocks occur, similrly to n envelope nlysis which would only rect to shock signls, rther thn to ll the other mnifesttions of modultion phenomen. II. PROCEDURE FOR SHOCK FILTERIG With excellent properties to detect shocks nd fst computing time, Kurtosis hs been found the best time descriptor for evluting energy level of the three s []. ( k ) k Ku () CF pek mx () ISB: 978--68--
with k k k () nd () k being the number of smples in ech. The Shock detector use three consecutive short-time filters sliding on the time signl. The Kurtosis into ech (centrl, left nd right) is computed nd compred to the two others. The procedure consists in scnning the smpled time block with short of n+ smples (Fig. ). t 7 8 9 x Left Left Current vlue during the scn Centrl 6 ) i = Current vlue during the scn 7 8 Right 9 Right Once the Kurtosis hs been evluted for ech of the three s, clssifiction nd selection is conducted: If the energy of the centrl is greter thn the two others into the left nd right, we declre the presence of shock nd the pek mplitude of the signl t position (i) is ssigned to the shock extrctor. Otherwise, there is no shock nd the shock extrctor tkes nul vlue. Then, the scn continues nd the current position vlue is incremented to i+ (figure -b). The procedure continues until the vlue i= mx -(n+) is reched, where mx is the totl number of smples in our signl, nd n is very close to the hlf-length of the short time. The size of the s (R, L nd C) highly depends on the cquisition prmeters, minly the smpling frequency, s well s the nture of the impct. Idelly, the will be the sme s the length of the trnsient response to n impct [6]. If we consider tht the trnsient response is stbilized t, level close to % of the mximum mplitude, the length of the s my be defined s: T () f n with, the dmping rte nd f n, the dominnt bering resonnce (Hz). It is usul to consider bering dmping rte of % nd ccordingly with the bering size dominnt nturl frequency between nd khz [9, 6]. We hve tested the nturl frequency of the bering SKF t khz. This gives T equl to. s. The length of the time is: t 8 9 x 6 Centrl 7 8 9 n T nt (6) fe where t is the time increment nd f e, the smpling frequency. This gives number of smples equl to: fe n (7) f n b) i = 6 Fig. : Identifiction of short time s By considering smpling frequency of 8 Hz, we obtin n = smples. At ech smple (i) of the time signl, the Kurtosis of C centered on i (i-n; i+n) is computed nd compred to the ones clculted on s locted to the left L (i-n; i- n) nd right R (i+n; i+n) of the current smple (i). Figure shows n exmple for time smple centered t i =, nd length of n+ = ; the centrl is represented in ornge nd the s to the right nd left re in green. A Hmming is pplied to ech shock with width equl to the shock length plus twice the short length defined by the shock filter. The different steps of the signl processing re described in Fig.. ISB: 978--68--
Originl signl,, -, -, - determine the proportion (CFR) of shocks (%) present in the originl signl. Tble shows summry of the results. This new descriptor (CFR) gives thus n indiction on the severity of dmge. Clcultion of shock filter,,,,,,, -, -, -,,,,,,,,,,,, -, Signl clen-up,, -, -, -, -,,,,,,,,,, Windowing Shock signl -,,6,7,8,9,,,,,,,, -, -, -,,6,7,8,9,,,,,,,, -,,, -, -, -,,,,,,,,,, Fig. : Originl nd shock signl for defect of.6 mm -, -,,,,,,,,,, Fig. : Signl processing for shock filter III. TIME AALYSIS OF THE SHOCK SIGAL The method previously described ws pplied on two signls recorded on two defective rolling-element berings turning t speed of 7 RPM, one with n inner rce spll of.8 mm nd nother of.6 mm. The results re shown on Fig. nd, respectively. Amp (g) Amp (g),,,, -, -, -, -,,,,, -, -, -,,,,,, Temps (s) Tble : Computtion of the shock/signl rtio Originl (.8 mm) SF (.8 mm) Originl (.6 mm) SF (.6mm) Pek...87.87...6.8 CF.7 7.9 6. 7.6 CFR 6.6 % 8.6 % IV. THE TIME-FREQUECY AALYSIS OF THE SHOCK SIGAL By pplying Short Time Frequency Trnsform (STFT) to the shock signl, it is then possible to determine the frequencies t which the shocks occur. This is prticulrly useful when the source of shocks must be identified since the STFT pplied to the shock signl llows for determining which frequency rnge is excited by shocks. Fig. shows the Fourier trnsform of the signl processed on Fig.. The STFT nlysis from the shock signl reveled to be clerer thn those from the originl signl (Fig.6). As expected, the shock spectrum contins most of its energy in the high frequency rnge. The time-frequency nlysis is thus very useful for identifying the nturl frequencies excited by the trnsient shocks nd the modultion frequencies cuse by the defect. -,,,,,, Temps (s) Fig. : Originl nd shock signls for defect of.8 mm By computing the rtio of Crest Fctor (CF) of the originl signl on the CF of the Shock filter (SF), it is then possible to ISB: 978--68--
where Bd is the bll dimeter; Pd, the dimetrl pitch;, the contct ngle; nd, the rotor ngulr speed. turl frequency Defect size:.6mm Figure : Time-frequency nlysis of the shock signl The Bll Pss Frequency on Outer rce (BPFO) nd the Bll Pss Frequency on Inner ce (BPFI) ppers with their hrmonics when defect develops on outer or inner rce respectively. b Bd BPFO Pd cos (9) b Bd BPFI Pd cos The Bll Spin Frequency (BSF) revels defect on the blls. A defect on blls will excite BSF, since it strikes the inner rce nd the outer rce in the sme revolution. Pd BSF Bd Bd cos Pd () These modultion frequencies cn be esily identified from n envelope nlysis or Hilbert trnsform [9]. The envelope nlysis (lso clled mplitude demodultion) converts the modultion in mplitude or phse from high frequency rnge to low frequency rnge. Fig. 7 shows n exmple of n envelope nlysis performed on the shock signl of Fig. for defect of.6 mm on the inner rce. The presence of the Bll Pss Frequency Inner rce (BPFI) nd one of its nd hrmonic in the shock spectrum indicte tht the shocks re cused by smll defect on the inner rce of the rolling-element bering. The results obtined by this technique re less influenced by noise nd interfering hrmonics, which is very desirble when the signl-to-noise rtio is smll.,8 Figure 6: Time-frequency nlysis of signl of defective bering (.6mm) ) before nd b) fter pplying SF V. THE EVELOP AALYSIS OF THE SHOCK SIGAL The bering frequencies tht re excited by defect re described ccordingly with the bering geometry [7]. At the second stge of degrdtion, these frequencies pper in modultion of the bering nturl frequency [6]. The Fundmentl Trin Frequency (FTF) revels problem on the bering cge nd ppers usully in modultion of other bering frequencies. It is close to % of the rotor ngulr speed. Eq. (8) is only true if the outer rce is fixed. Bd FTF cos (8) Pd,7,6,,,,, BPFI BPFI 6 7 8 9 Figure 7: Envelope spectrum of the shock signl VI. COCLUSIO The present rticle describes the development of signl processing technique in order to extrct the shock content from vibrtory signl. It is clled the Shock Filter (SF). This technique provides clened up signl corresponding only to ISB: 978--68-- 6
the contribution of the shocks, fter hving removed ll the other components in the signl. A prcticl ppliction is presented in order to illustrte its use nd efficiency in dignosis defective rolling-element bering. It is seen tht this new tool provides n estimte of the severity of dmge by compring the shock signl from the originl one. Furthermore the STFT of the shock signl revel the nturl frequencies of the system tht re excited nd n envelope nlysis round the nturl frequency rnge revel the modultion frequencies tht re chrcteristics of the source of dmge. ACKOWLEDGMET The uthors would like to thnk the OR for letting them use the signls from defective rolling-element berings vilble on their site www.cwru.com, s well s the CRSG for their finncil help in this project. REFERECES [] Sssi S., Bdri B. nd Thoms M., 7, A umericl Model to Predict Dmged Bering Vibrtions Journl of Vibrtion nd Control, Vol., o., Doi:.77/77678, 6-68. [] Tndon. nd Choudhury A., 999. A review of vibrtion nd coustic mesurement methods for the detection of defects in rolling element berings, Journl of Tribology Interntionl,, 69-8. [] Hmmock C., 996, Evlution of rolling element bering condition, Vibrtions, Vol, o, pp 8. [] Sssi S., Bdri B. nd Thoms M., 8. Trcking surfce degrdtion of bll berings by mens of new time domin sclr descriptors, Proceedings of the Interntionl journl of Comdem, (), 6-. [] Schiltz R.L., 99, Forcing frequency Identifiction of rolling element berings, Sound nd Vibrtion, Vol., o, p. [6] Berry J., 99, How to trck rolling bering helth with vibrtion signture nlysis, Sound nd Vibrtion, pp. -. [7] Thoms M., Msounve J., Do T.M., Le Dinh C.T. nd Lfleur F, October 99. Rolling element bering degrdtion nd vibrtion signture reltionship, nd interntionl conference on monitoring nd cousticl nd vibrtory dignosis (SFM), Senlis, Frnce, Vol., pp. 67-77. [8] De Priego J.C.M.,. The reltionship between vibrtion spectr nd spike energy spectr for n electric motor bering defect, Vibrtions, Vol 7, o, pp. [9] Sheen Y.T.,, An envelope nlysis bsed on the resonnce modes of the mechnicl system for the bering defect dignosis. Mesurement () 9 9 [] Hongbin M., 99, Appliction of wvelet nlysis to detection of dmges in rolling element berings, Proceedings of the interntionl conference on structurl dynmics, vibrtion, noise nd control, pp -9. [] Bdri B., Thoms M., Archmbult R., Sssi S. nd Lkis A., June 7, Rpid Julien Trnsform: A ew Method for Shock Detection nd Time-Domin Clssifiction, Proceedings of the th interntionl conference of Comdem7, Fro, Portugl, pp 667-676. [] Bdri B., Thoms M., Archmbult R., Sssi S., Lkis A. et Mureithi., October 7, The Shock Extrctor, Proceedings of the th Seminr on mchinery vibrtion, CMVA 7, Sint John, B, p. [] Thoms M., Archmbult R. nd Archmbult J., Oct., A new technique to detect rolling element bering fults: the Julien method, Proceedings of the th interntionl. Conference on cousticl nd vibrtory surveillnce methods nd dignostic techniques, Surveillnce, Senlis, Frnce, R6, p. [] Thoms M., Archmbult R. nd Archmbult J., October, Modified Julien Index s shock detector: its ppliction to detect rolling element bering defect, Proceedings of the th seminr on mchinery vibrtion, CMVA, Hlifx (.S.),.-.. [] Archmbult J., Archmbult R. nd Thoms M., Octobre, A new Index for bering fult detection, Proceedings of the th seminr on mchinery vibrtion, Québec, pges. [6] Swlhi. nd R.B. Rndll,8. Simulting ger nd bering interctions in the presence of fults Prt I. The combined ger bering dynmic model nd the simultion of loclised bering fults. Mechnicl Systems nd Signl Processing, 9 966. BIOGRAPHIES Bechir BADRI (M. Ing), is finishing his Ph.D in mechnicl engineering t the ETS (Montrel). He lso hs M.Ing, grduted in Mechnicl Engineering from ÉTS. Working for more thn yers in the field of vibrtion nd structurl dynmics, he specilizes in the study of berings vibrtion nd mchines monitoring, but especilly in the development of new tools nd methods of signl processing. With this experience, he founded Betvib compny, compny developing new genertion of collectors / nlyzers. Mrc Thoms is professor in mechnicl engineering t the ÉTS (Montrel) since 8 yers. He hs Ph.D. in mechnicl engineering from Sherbrooke university. His reserch interests re in vibrtion nlysis nd predictive mintennce. He is the leder of reserch group in structurl dynmics (Dynmo) nd n ctive member of the Cndin mchinery Vibrtion Assocition (CMVA). He is the uthor of two books: Relibility nd predictive mintennce of mchines nd Simultions of mechnicl vibrtions with Mtlb nd Ansys. He hs cquired lrge industril experience s the group leder t the Quebec Industril Reserch Center (CRIQ) for yers. Sdok Sssi is n expert in vibrtion nlysis nd troubleshooting of mechnicl instlltions nd equipments. He is currently conducting reserch on different res of mechnicl engineering nd industril mintennce. His most significnt contributions re the development of powerful softwre clled BEAT for vibrtion simultion of dmged berings nd the design of n innovtive intelligent dmper bsed on electro nd mgneto rheologicl fluids for the optimum control of cr suspensions. ISB: 978--68-- 7