University of Huddersfield Repository Ball, Andrew, Wang, Tian T., Tian, X. and Gu, Fengshou A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum, Original Citation Ball, Andrew, Wang, Tian T., Tian, X. and Gu, Fengshou (6) A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum,. In: COMADEM 6, the 9th International Congress on Condition Monitoring and Diagnostic Engineering Management, th nd August 6, Empark Grand Hotel in Xi an, China. This version is available at http://eprints.hud.ac.uk/id/eprint/9476/ The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not for profit purposes without prior permission or charge, provided: The authors, title and full bibliographic details is credited in any copy; A hyperlink and/or URL is included for the original metadata page; and The content is not changed in any way. For more information, including our policy and submission procedure, please contact the Repository Team at: E.mailbox@hud.ac.uk. http://eprints.hud.ac.uk/
A robust detector for rolling element bearing condition monitoring, based on the modulation signal bispectrum, and its performance evaluation against the kurtogram Professor Andrew Ball Pro Vice-Chancellor for Research and Enterprise & Director of The Centre for Efficiency and Performance Engineering
Contents. Introduction. The modulation signal based detector 3. Simulation study 4. Application case studies 5.
. Introduction Bearings are at the heart of almost every rotating machine they have received a lot of attention in the field of vibration analysis because they are common sources of machine faults To keep machinery operating reliably many methods for bearing fault detection and diagnosis have been developed vibration measurement and associated signal processing are the most widely used approach 3
. Introduction A review of signal processing methods High frequency resonance technique Cyclostationary spectral analysis Cepstrum analysis Bispectrum analysis Time-frequency analysis Self-adaptive noise cancellation Minimum entropy deconvolution Empirical mode decomposition Most methods are based on tracking the amplitude variations of characteristic fault frequencies Only limited attention has been given to utilisation of modulation characteristics in extracting the diagnostic information But the Modulation Signal Bispectrum can be used to extract fault features from envelope signals giving reliable bearing fault detection, diagnosis and severity assessment 4
. Introduction Purpose of the research To develop and evaluate a robust detector for bearing fault diagnosis based on modulation signal bispectrum (MSB) analysis The modulation signal bispectrum MSB analysis can be used to suppress random noise and to decompose nonlinear modulation components in a measured signal, eg vibration Advantages of the modulation signal bispectrum include: ) Highly effective suppression of random noise ) Revelation of the weak nonlinear characteristics of signals 5
. The modulation signal based detector Bearing fault frequencies D c Contact Angle φ D r Outer race Inner race Roller Cage Ball Diameter Pitch Diameter Outer race fault frequency: Nr Dr BPFO Fs ( cos ) D Inner race fault frequency: BPFI Ball fault frequency: BSF Nr Dr Fs ( cos ) D c c c s Dr D r Dc DF ( cos ) Cage fault frequency (often called the fundamental train frequency): Dr FTF Fs ( cos ) D c 6
Acc.(m/s ) Acc.(m/s ) Acc.(m/s ) Acc.(m/s ). The -. modulation signal based detector...4.6.8. 4 Small 6outer 8 race fault Envelope analysis is the current state of the art Healthyin industry,. 3 and it can be exemplified as follows: x -3. -...4.6.8.. -...4.6.8.. Acc.(m/s Acc.(m ) Acc.(m/s Acc.(m/s ) Acc.(m/s Acc.(m/s ) ) ) Acc.(m/s Acc.(m/s ) Acc.(m/s Acc.(m/s ) ) ) -. -...4.6.84 Raw data x. -3 -...4.6.8....4.6. -....4.6.84 Filtered x -3.. -...4.6.8. -. Demodulated 4 x -3 -...4.6.8....4.6.8. 4 6 8 3 x -3 3 x -3 4 6 8 Envelope analysis is a time domain technique which involves filtering, demodulating, rectifying and smoothing time data before 4 6 8 Small outer race fault Healthy 4 6 8 3 x -3 4 6 8 3 x -3 3 x -3 4 6 8 3 x -3 4 6 8 4 6 8 6 x -3 4 6 8 transferring to the frequency domain. The challenge is selecting the most -...4.6.8. 4 3 x -3 -. 6 8..4.6.8. 4.. 5 x 6 Rectified & Smoothed x -3 4 6 8 Spectrum of -3 the envelope appropriate filter. 6 x Small outer race fault 4-3 Healthy edges. -. -...4..6.4.8.6..8. 3 4 5 6 4 3 4 5 6 Time(s) Frequency Time(s) Frequency -...4.6.8. 4 6 8..4.6.8. 3 4 5 6 Introduction The MSB detector Time(s) Simulation study Application case studies. 6 x -3 Frequency Acc.(m/s Acc.(m/s ) Acc.(m/s Acc.(m/s ) ) ) -...4.6.8....4.6.8. Small outer race fault 4 Healthy 6 8 3 x -3 4 6 8 BPFO=88.5Hz 7
. The modulation signal based detector The kurtogram is current state Raw of datathe art in bearing.5 monitoring research and hence is our comparator level k.6.6 3 3.6 4 4.6 5 5.6 6 6.6 7 fb-kurt. - K max =.7 @ level 4, Bw= 65Hz, f c =87.5Hz 4 6 8 Frequency.6.5.4 Time(s).3. BPFO=88.5Hz. The Kurtogram reveals a colour map of thresholded Kurtosis across frequency, and hence it allows resonance regions to be identified and envelope filter edges to be selected. -.5...3.4.5.6.7.8.9. Time(s)..5 Envelope of the filtered signal...3.4.5.6.7.8.9. x -6 Fourier transform magnitude of the squared envelope Kmax Maximum kurtosis value Level 4 Optimised filter band at level 4 Bw filter bandwidth of optimised filter f c central frequency of optimised filter 5 5 5 3 35 4 45 5 Frequency 8
. The modulation signal based detector The bearing vibration model It was decided to use ways of evaluating the new method: via simulated data and real data. To simulate bearing fault data, a bearing vibration model is needed. The vibration signature x(t) of a faulty rolling element bearing is comprised of several components, and these are represented in the model as follows: Machinery induced vibration x( t) x ( t) x ( t) x ( t) x ( t) n( t) f q bs s Noise The presence of modulation in the time data means that there will be sidebands in the frequency domain, and these are key to bearing fault detection/diagnosis Impulses produced by bearing fault AM due to the non-uniform load distribution Bearing-induced vibration determined by the bearing structural dynamics 9
. The modulation signal based detector Simulated 5 fault data (a) 5 (a).5 /f.5 o.5. /f o..5 (a) /f o Simulated fault time series -5 and spectra -5 of a rolling element bearing 5 with a 5 /f localised defect i /f /f on r i /f r the (a) outer race, -5 inner race (c) -5 rolling element, and 5 (d) 5cage.5..5..5..5. -5.5..5.5. 5 /f i /f r -5.5..5. 5 /f b /f c.5..5..5..5. /f /f /f b /f c b c -5.5..5. 5 /f c -5.5..5. Time(s) (c) (d) f o 5 5 f i -f r f i f i +f r 5 5 4 x -3 f f b -f c b f b +f c 5 5 3 x -3 f c 5 5 Frequency -5-5.5..5. 5 5.5..5. 5 5 (d) Introduction 5 The MSB detector Simulation study (d) Application 3 x -3 case studies 5 /f 3 x -3 e 5 f o..5.5. 5 5.5.. 5 5 (c) (c).5.5 e f i -f r f i f i +f r 5 5 5 5 4 x -3 4 x -3 f f b -f c b f f f b -f c b f f f b -f c b f f o f o f i -f r f i -f r b +f c b +f c b +f c f i f i f i +f r f i +f r
. The modulation signal based detector Conventional bispectrum (CB) PS( f ) E X ( f ) X * ( f ) Definition of CB: B( f, f ) E X ( f ) X ( f ) X ( f f ) f f f 3 = f + f Phase of CB: CB ( f, f ) ( f ) ( f ) ( f f ) Coherence of CB: Conventional bispectrum offers: Nonlinear identification capability Retention of phase information Noise suppression capability E An average must be performed to suppress random noise But it is limited to f + f = f 3 so it only shows the higher sideband
. The modulation signal based detector The modulation signal bispectrum (MSB) The MSB is based on the CB, but is more attractive in this work because it contains both upper and lower sideband components * * MS c x c x c x c c B ( f, f ) E X ( f f ) X ( f f ) X ( f ) X ( f ) The MSB can itself be modified to enable precise quantification of sideband amplitudes, by removing the influence of the carrier frequency f c. We call this the MSB sideband estimator (MSB-SE), defined as: SE MS c x B f, f B f, f MS c x B MS f c, The MSB-SE only includes the information of sidebands (f c + f x ) & (f c - f x )
. The modulation signal based detector Typical results of the MSB detector - B(f x ) - formed from slices shown along B(f c ), show that the optimal frequency band for detecting a bearing fault is at a specific value of f c. Symptomatic features are labelled *. f o f o 3
. The modulation signal based detector Vibration signal Vibration signal the MSB using Calculate the MSB * using * B ( f, f ) E X ( f f ) X ( f f ) X ( f ) X ( f ) MS c x c x c x c c * * MS c x c x c x c c B ( f, f ) E X ( f f ) X ( f f ) X ( f ) X ( f ) Calculate Calculate the the MSB-sideband estimator using estimator using SE BMS fc, fx SE MS c x B f, f B f, f MS c x MS Calculate the compound MSB slice using B f c MS, c, x Flow chart of the robust MSB detector calculation B f f B MS f c, Calculate the compound MSB slice using N SE B( fc ) i BMS N fc, ifse B( f c ) i BMS fc, if N Calculate the robust MSB detector using Calculate the robust MSB detector using K SE SE k ( x) MS k B( f ) B f B fc, fx x x K k BMS fc, fx fx K 4
3. Simulation study Four different simulation scenarios were developed They use different levels of random noise and different amounts of aperiodic interference, to represent the noisy in-field measurements typically encountered in the vibration-based condition monitoring of rolling element bearings Scenario Low noise signal without impact interferences White noise Aperiodic impact interference Type SNR value Type SNR value Level None -5dB n/a High noise signal without impact interferences Low noise signal with low level impact interferences Level None -3dB n/a Level Level -5dB -db High noise signal with high level impact interferences Type SNR P P Level Level -db -48dB log s / n Type SNR log A / A s n 5
3. Simulation study The extent of white noise contamination Pulse train of impacts from bearing fault -..4.6.8. - -..4.6.8...4.6.8. / f o BPFO=88.5Hz -..4.6.8. -..4 Time(s).6.8. Time(s) (a) (c) (c) (c).5.5 R x R3 x 4.8 SNR=-5dB.8.6 SNR=-5dB.6.4.4...5.5.5 R3.5 x x 4 x 4.8 SNR=-3dB.6.8 SNR=-3dB.4.6 7Hz 75Hz..5.5.5 Frequency.5 x 4 Frequency x 4.8.6.4...4 R R 347Hz 7Hz 7Hz R3 75Hz 75Hz 75Hz 75Hz Simulated structural resonance regions which naturally amplify bearing frequency harmonics Low noise, no impacts High noise, no impacts 6
3. Simulation study The MSB-SE results compared to the Kurtogram results B( f c ) (a)..5 SNR=-5dB R R3 (a) B( f c ).6.4. SNR=-3dB R3 B( f x ) 6 7 8 9 3 f c.5 f o x Kurtogram based Detector MSB based Robust Detector 3x 4x B( f x ) 6 7 8 9 3 f c Kurtogram based Detector MSB Robust based Detector.5 fo x 3x 4x 88.5 77 65.5 354 f x 88.5 77 65.5 354 f x Low noise, no impulses High noise, no impulses 7
3. Simulation study 5 BPFO=88.5Hz 5 + The addition of aperiodic -5 impact interference, -5 along with white noise R3 (a).8 SNR=-dB 5 5.6 R 5 5.4 5-5 -5.. + - + -...3.4.5-5.5.5...3-5.4.5.5-5.5 Time(s) x 4 - - -..4..4..4.8 SNR=-49dB 5 R3 (a) x 4.6.8.4.8 SNR=-dB 5 SNR=-5dB 5-5.6.6..4.4 - -5-5...3.4.5...5.5 Time(s) Frequency - x 4....3.4.5.5.5.5.5 Time(s) Frequency x 4 de Pulse -5 train of impacts from bearing fault Random noise Impacts -..4 -..4 -..4 7Hz 75Hz 75Hz Low noise, low level impacts Low noise, high level impacts x 4 Introduction The MSB detector Simulation.8 study SNR=-5dB Application case studies 5 de + 5 7Hz 7Hz 75Hz 75Hz 75Hz 75Hz 8
B( f c ) B( f c ) (a) 3. Simulation.3 study (a) (a) B( f x ) Performance evaluation of the MSB-SE against the Kurtogram..5 B( f x ) 6 7 8 9 3 f c.5 x..5 SNR=-dB f o Kurtogram based Detector MSB based Robust Detector 88.5 77 65.5 354 f x 3x R3 R 6 7 8 9. 3.5 B( f c ) SNR=-dB B( f x ).. R 4x (a) B( f c ) B( f x ) R R3.3 SNR=-5dB. 6 7 8 9 3 f c f c.5 R f o R3 R3 SNR=-5dB fo x 6 7 8 9 3 f c.5 Kurtogram based Detector Kurtogram based MSB Detector based Robust Detector fo MSB based Robust Detector x 3x x 3x 4x 3x Kurtogram based Detector MSB based Robust Detector 4x 88.5 77 65.5 354 f x 4x Low noise, low level Low noise, high level 88.5 77 65.5 354 88.5 impact interference f x 77 65.5 354 impact interference f x 9
4. Application case studies The first real application: motor bearing fault detection Dynamic brake Supporting bearing Flexible coupling Supporting bearing AC motor Shaft encoder Vibration sensor
4. Application case studies Electric motor bearing with a small seeded outer race fatigue defect (defect simulated by EDM) Specification of NSK Type 66ZZ deep groove ball bearing Parameter Measurement Pitch Diameter 46.4mm Ball Diameter 9.53mm Ball Number 9 Contact Angle
4. Application case studies The motor data reveals clear resonant regions (a) (ms - ).5 -.5 (ms - )..4.6.8..4.6.8 Time (s) x -3.5 R R.5 3 4 5 6 7 8 9 Frequency
o 4. Application case studies f (a) x -7 R B( f c ) Motor bearing fault detection capability Clear x f o showing.5 outer race fault B( f x ) Possible cage damage also apparent (c) Normalised.5.5 Clear x f o showing outer race fault B( f c ).5 3 4 5 6 7 8 9 f c MSB Robust Detector 89.33.5 78.7 68 B( f x ) (c) Normalised.5 f o f cage 3f cage 5f cage f b f o f b f i f o 3f b 3f o f i 89.33 78.7 68 f x Bw= 65Hz, f c =87.5Hz Kurtogram based Detector f cage 3f cage 5f cage R f b f o f b The slices of the first three highest peaks are selected for calculating the MSB detector 3 4 (a) x 5 6 7 8 9-7 f c MSB Robust Detector f cage 3f cage 5f cage f b Bw= 65Hz, f c =87.5Hz f cage 3f cage 5f cage f b f o f o f b f i f b f i f x f o f o 3f b 3f b f i f o 3f b f i 89.33 78.7 68 Frequency R 3f o f i f i 89.33 78.7 68 Frequency R Kurtogram based Detector 3f o 3f o 3
4. Application case studies The second real application - planetary gearbox bearing fault detection Motor Helical gearbox Vibration sensor Planetary gearbox DC Generator 4
4. Application case studies Planetary gearbox specification Sensor position Input Sensor position Bearing position Output Planetary gearbox specifications (David Brown) Bearing position Parameter Specification Ring gear teeth number 6 Planet gear (3) teeth number 6 Sun gear teeth number Transmission ratio 7. Maximum torque 67 Nm Maximum input speed 8 rpm Maximum output speed 388 rpm Specifications of deep groove ball bearing (SKF 68) Input Parameter Diameter (mm) Pitch circle 54 Ball 7.9 Ball number Contact angle Output Inner race fault 5
4. Application (a) case studies (ms - ) Planetary gearbox time data and spectrum (ms - ) (a) (ms - ) (ms - ) - -.4.4....4.6.8..4.6.8 Time (s) R R R3 3 4 5 6 7 8 9 Frequency R4 Note presence of high levels of random noise, in addition to impacts..4.6.8..4.6.8 Time (s) In this case, there are 4 resonance regions R R R3 3 4 5 6 7 8 9 Frequency But when choosing the resonant region(s) to use in the calculation of the MSB-SE, it is always wise to check the coherence R4 6
4. Application case studies MSB-SE coherence for the planetary gearbox Although resonance R4 has high MSB amplitude, it has low coherence and so it is excluded from the calculations of the MSB-SE detector R4 (around 9kHz) R3 (around 6kHz) R (around 4kHz) R (khz-khz) 7
B( f c ) 4. Application case studies Choice of slices and performance evaluation f c (a) B( f x ) B( f c ).5 3 x -3 Clear x f i showing inner race fault (c) Normalised B( f x ).5 f cage 3f cage 5f cage No clear inner race fault feature 3 4 5 6 (a) B( f c ) B( f x ) (c) Normalised 3 x -3 frs fsf f b.5 f cage 3f cage 5f cage 3 4 5 6 f c MSB Robust Detector frs fsf f b f o f fsf i f b 3fsf f o 3f b 4fsf f i 5fsf 3f o 6fsf 3f i 65.7 3.3 95.5 f x Bw= 56.3Hz, f c =573.Hz Kurtogram based Detector f cage 3f cage 5f cage R f o f fsf frs fsf f b i f b f o f fsf 3fsf i f b 3fsf R 3f b 4fsf f o 3f b 4fsf f i 5fsf 3f o 65.7 3.3 95.5 65.7 Frequency 3.3 95.5 Frequency f x Bw= 56.3Hz, f (c) c =573.Hz Kurtogram based Detector ed f o 6fsf The slices of the first three highest MSB peaks Robust are Detector selected for calculating the MSB detector. 65.7 3 43.3 5 6 95.5.5 f x c Bw= 56.3Hz, f c =573.Hz Kurtogram MSB Robust based Detector f cage 3f cage 5f cage f cage 3f cage 5f cage f cage 3f cage frs R fsf f b frs fsf f b 5f cage f b f o f fsf fsf i i f o f f b f b i f o f 3fsf 3fsf f b R f o f o 3f b 4fsf 3f b 4fsf f o f b R3 f i 5fsf 3f o 6fsf f i 5fsf 3f o f i 5fsf 3f o 3f i 6fsf 6fsf f i 3f o R3 3f i 3f i 3f i 3f i 8
The MSB is demonstrably effective in suppressing noise and decomposing the nonlinear modulation components The MSB-SE is effective in the suppression of both stationary white noise and aperiodic impact impulses. Simulated signal and real data studies shows that the capability of the MSB-SE exceeds that of a kurtogrambased detector. The application to signals from a planetary gearbox shows that the new approach can successfully detect bearing faults in circumstances where no other method is able to do so. 9