ROLLING BEARING FAULT DIAGNOSIS USING RECURSIVE AUTOCORRELATION AND AUTOREGRESSIVE ANALYSES
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1 OLLING BEAING FAUL DIAGNOSIS USING ECUSIVE AUOCOELAION AND AUOEGESSIVE ANALYSES eza Golafshan OS Bearings Inc., &D Center, 06900, Ankara, urkey Kenan Y. Sanliturk Istanbul echnical University, Mechanical Engineering Department, 34437, Istanbul, urkey Due to critical role of bearings in global vibration levels of rotating machines, vibration-based fault detection for rolling bearings is considered as one of the most common and reliable approaches in machine condition monitoring. In line with the purpose of fault detection, many diagnosis methods aim to identify the fault repetition period in the vibration signal measured from a system with suspected faulty bearing. Captured vibration signals, however, may suffer from heavy background noise due to environmental conditions. In fact, a signal enhancing/de-noising remains a crucial step in a proper rolling bearing fault diagnosis process. In this paper, a novel rolling bearing fault diagnosis method based on ecursive Autocorrelation (AC) analysis and autoregressive (A) signal modelling is proposed and validated for fault detection in rolling bearings. he results presented here show superior diagnosis results compared to traditional envelope analysis.. Introduction Industrial companies nowadays need well-organized maintenance strategies for optimum productivity. he operating conditions of the industrial machineries can be obtained via the advanced vibration-based condition monitoring tools []. Due to critical role of bearings in global vibration levels of rotating machines, vibration-based fault detection for rolling bearings is considered as one of the most common and reliable approaches in machine condition monitoring. Many diagnosis methods aim to identify the fault repetition period in the vibration signal measured from a system with suspected faulty bearing(s). he envelope spectrum analysis is regarded as an effective method for rolling bearing fault detection. However, it is known that this method may not yield reliable diagnostic information in noisy environments [2] and for high-speed machines [3]. Among a wide range of diagnosis methods, autocorrelation is a very powerful tool in revealing the repetition frequencies in vibration signals, which are valuable for diagnosis purposes [4-6]. Zhang, Yi et al. in [4] illustrated the use of iterative autocorrelation function on raw time domain signals for noise elimination purposes. Wang, W. Y. in [7] investigated the diagnosis ability of autocorrelation of envelope signals and then ensemble averaging for minimizing the background noise. Su, W. et al. in [8] employed enveloping of autocorrelation functions in their proposed rolling bearing fault diagnosis procedure. Linear prediction is basically a way of obtaining a model of the deterministic (periodic) part of a signal, based on a certain number of previous samples. Among the time domain signal representation models, it is proven that the Autoregressive (A) model requires low prior knowledge and can yield very reliable results [9-3]. A modelling is also widely employed for signal enhancing/denoising in the field of rolling bearing fault detection [3].
2 he 23 rd International Congress on Sound and Vibration In this present study, a combination of ecursive Autocorrelation (AC) and Autoregressive (A) signal modelling is proposed for rolling bearing fault diagnosis purposes. he remainder of this paper is organized as follows. First, theoretical background for Autocorrelation A modelling are summarized in Section 2. hen, a brief description of the test rig as well as the experimental results are presented, respectively, in Section 3 and Section 4. Finally, main conclusions of this work are summarized in Section heoretical background 2. ecursive autocorrelation function he autocorrelation function is considered as a strong cyclostationary signal processing tool for analyzing and evaluation of vibration signals in time domain. It is a very useful tool in signal processing for extracting the periodic components, i.e. repeating patterns, in a time domain signal [4]. he autocorrelation function,, for a time domain signal, x(t), is express as [] τ lim xt xt τdt () where and τ are the measurement period and the time delay. For ecursive Autocorrelation (AC) formulation, however, it is more appropriate to write Eq. () as 0 τ lim xt xt τdt (2) hen, the autocorrelation function of an autocorrelation function can be estimated as 0 0 τ2 lim τ τ τ2 dt (3) New autocorrelation functions can be calculated by repeating this process recursively. If this process is carried out r times, the r th order recursive autocorrelation function can be defined as τr lim τr- τr- τr dt (4) 0 Although it is not repeated here for brevity, the AC function can also be expressed in a similar manner for discrete time domain signals, i.e. x(n). 2.2 Autoregressive (A) modelling he A model of a discrete time domain signal, y(n), is expressed as [2] x p n akyn k k where the modelled (predicted) value, x(n), is obtained as a weighted sum of the p number of previous y(n) values. Here, the parameter p determines the order of the A model, a(k). he major issues with A signal modelling are the selection of model coefficients computing algorithm and the model order selection criteria. he four main methods for the estimation of a(k) coefficients can be considered as (i) Least Squares Forward method, (ii) Least Squares Forward Backward method, (iii) Yule-Walker equations and (iv) Burg method. Although the Burg method described in [2] is considered as the most powerful estimation technique [0], the Yule Walker method offers simple and effective estimation process with low prior requirements for its applications [3]. he weighting co- (5) 2 ICSV23, Athens (Greece), 0-4 July 206
3 he 23 rd International Congress on Sound and Vibration efficients, a(k), in Eq. (5) can be obtained by Yule-Walker equations which can be represented in matrix form as [4] 0 p 0 p 2 p p a a a p Since the best choice of model order, p, is not generally known a priori, it is usually necessary in practice to postulate several model orders. Sawalhi, N. et al. in [4] employed the kurtosis value as the criterion for the proper order selection for A models. From rolling bearing diagnosis point of view, however, kurtosis may not give suitable results in vibration signals having small amount of energy level (i.e. low-speed rolling bearings). herefore, the present study proposes the use of Kurtosis MS value as the criterion in A model order selection, which can reflect both the modelled (output) signal energy level and its impulsiveness. 2.3 Proposed fault diagnosis method In the present study, a combination of A-based signal modelling method together with recursive autocorrelation function is employed, yielding a novel rolling bearing fault diagnosis procedure. Figure shows the flowchart summarising the proposed method. As illustrated, first, the captured vibration signal passes through the A modelling process. Autocorrelation function is then calculated for the enveloped A-based enhanced vibration signal. After this operation, the spectrum of resulting autocorrelation function is obtained. It should be noted that the enveloping of the autocorrelation processes is performed recursively in order to obtain smoother and sharper spectrums that may allow one to identify possible fault(s) which may not be visible otherwise by other means. Note that the recursive loop including enveloping and autocorrelation function is repeated until the amplitude of the spectrum of AC at the bearing fault frequency starts to decrease. 2 p (6) ime domain signal y(n) A modelling x(n) Enveloping x (n) AC (t) Autocorrelation function Spectrum of AC Improvement on fault frequency detectability? Yes AC (t) No AC (f) olling bearing fault diagnosis Figure : Flowchart of the proposed bearing fault diagnosis method. ICSV23, Athens (Greece), 0-4 July 206 3
4 he 23 rd International Congress on Sound and Vibration 3. Experimental setup A picture of the test rig is shown in Figure 2. As can be seen, an accelerometer (00 mv/g accelerometer of PCB) is positioned on top of the bearing housing to capture the rolling bearing vibration signals. he speed of the shaft and the amount of axial loading are measured through an optical encoder and force sensor, respectively. 50N load is applied to the bearing along axial direction during the test using a hydraulic piston. he rotating speed of the shaft is 200 PM (20 Hz). One single-row deep grove ball bearing type OS6205 with localized outer race defect is employed in this investigation. A localized fault was artificially introduced to the tested ball bearing. Geometry details of OS6205 type ball bearing are listed in able. he data acquisition (DAQ) system, namely, NI9234, collects the bearing vibration signal with a sampling frequency of 7068 Hz, through a LabVIEW interface. Driver spindle Load monitoring system Accelerometer Force sensor Housing for defective ball bearing Hydraulic loading system Outer ace Diameter Figure 2: olling bearing fault detection experimental setup. able : Geometry details of OS6205 ball bearing. Inner ace Diameter Balls Diameter Number of Balls Bearing Width Contact angle 52 mm 20 mm 7.5 mm 9 5 mm 0 he fundamental fault frequencies for a defective rolling bearing are estimated using the speed of the rotating shaft and the ball bearing geometry. he outer race fault frequency, corresponding to outer race being stationary and inner race rotating with the shaft, can be estimated as β N B D bcos BPFO f r (7) 2 Dp where BPFO, f r, N B, D b, D p, and β are outer race fault frequency, rotational frequency of the shaft, number of rotating balls, ball diameter, pitch diameter and bearing contact angle, respectively. he BPFO for the ball bearing OS6205 rotating at 200 PM (20 Hz) is calculated as 73 Hz. 4. Assessment of the proposed method he performance of the proposed rolling bearing fault diagnosis method described in Section 2.3 is investigated using measured data. Figure 3 presents a vibration signal captured from a system with an outer race defected ball bearing for a time period of s as well as its amplitude spectrum up to 4000 Hz. As can be seen, the localized fault on the bearing outer race excites a few resonances 4 ICSV23, Athens (Greece), 0-4 July 206
5 he 23 rd International Congress on Sound and Vibration including the one around 500 Hz. However, the amplitude spectrum is unable to reveal the characteristics fault frequency (i.e. BPFO) for this tested bearing. Figure 3: Captured vibration signal from the outer race defective bearing in a) time and b) frequency domain. In accordance with the proposed, the captured vibration signal, shown in Figure 3a, is considered as an input in A signal modelling process. As described in Section 2.2, the use of Kurtosis MS as a better indicator compared to Kurtosis is employed to select the optimum order for signal modelling process using A method. Figure 4a shows Kurtosis MS trend for a specific range of A model order, p, in Eq. (5). As seen, no significant improvement is obtained after approximately 30 th A order, hence an order of 33, which has the highest Kurtosis MS is selected in A modelling process as the optimum order. Figure 4b represents the output signal in A modelling process. Figure 4: a) Kurtosis MS criterion for A model order optimization; b) A-based modelled signal. ICSV23, Athens (Greece), 0-4 July 206 5
6 he 23 rd International Congress on Sound and Vibration he enhanced signal in A modelling process is then subjected to enveloping and autocorrelation processes, which are performed recursively. Figure 5 and Figure 6 show the first four orders of recursive autocorrelations and their zoomed plots, respectively. hese results demonstrate that, the recursive approach in autocorrelation analysis enhances diagnostic features of the signal, revealing the repetitive pattern of the signal due to the fault very clearly. It should also be mentioned here that it is neither required nor beneficial to calculate very high orders of AC functions. he highest amplitudes of impulses are likely to be obtained in the second or third orders of the recursive autocorrelation (AC). Figure 5: ecursive autocorrelations for A-based enhanced envelope signal; first four recursive orders, respectively, from a) to d). Figure 6: Zoomed plots of recursive autocorrelations in Figure 5; first four recursive orders, respectively, from a) to d). Figure 7 shows the spectrums of AC functions corresponding to the first four orders. As one may deduce from the time domain recursive autocorrelation function presented in Figure 5, the sec- 6 ICSV23, Athens (Greece), 0-4 July 206
7 he 23 rd International Congress on Sound and Vibration ond order of recursive process yielded the smoother and sharper spectrum compared to other AC orders for the signal used in this work. BPFO 2 BPFO BPFO 2 BPFO BPFO BPFO Figure 7: Spectrums of ACs in Figure 5; first four recursive orders, respectively, from a) to d). he spectrum presented in Figure 7b and the envelope spectrum of the original raw signal are overlaid in Figure 8. In addition, in order to make a better assessment of the effectiveness and performance of the proposed method in this paper, the spectrum presented in Figure 7b as well as the envelope spectrums of the original raw and the A model vibration signals, all in unit normalized form, are overlaid in Figure 9. As seen in both plots, the almost noise-free spectrum obtained using the proposed method here makes the bearing fault frequency much sharper and more visible relative to envelope spectrums. esults in Figure 9 also reveal that the effectiveness of the proposed method is primarily due to the use of AC rather than A modelling. BPFO BPFO Figure 8: Overlaid plot for traditional envelope spectrum and proposed method. Figure 9: Overlaid plot for normalized envelope spectrums. 5. Conclusions A novel method based on recursive autocorrelation (AC) and autoregressive (A) analyses is proposed in this paper for bearing fault diagnosis. In this method, the raw vibration signal is enhanced by both A signal modelling and AC. he proposed method is also validated using a vi- ICSV23, Athens (Greece), 0-4 July 206 7
8 he 23 rd International Congress on Sound and Vibration bration signal captured from a system with a defective outer race ball bearing. he results show that the spectrum obtained using the proposed method makes the bearing fault frequency more visible relative to the envelope spectrum. Furthermore, it is concluded that the best results can be obtained without the need for computing very high order AC spectrums; the first few orders appear to be sufficient to get the best results. Acknowledgment his research work has been supported by OS Bearings Inc., Ankara, urkey. he authors would like to express their appreciations to Mr. Nazmi Saydemir, Mr. Ilker Usta, and Mr. F. Omur Kiyili from OS Bearings Inc. for their contributions during the tests. EFEENCES andall,. B. Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications, John Wiley & Sons, Illinois (20). 2 Golafshan,. and Sanliturk, K. Y. SVD and Hankel Matrix Based De-noising Approach for Ball Bearing Fault Detection and Its Assessment Using Artificial faults, Mechanical Systems and Signal Processing, 70 7, (206). 3 Endo, H. and andall,. B. Enhancement of Autoregressive Model Based Gear ooth Fault Detection echnique by he Use of Minimum Entropy Deconvolution Filter, Mechanical Systems and Signal Processing, 2 (2), , (2007). 4 Zhang, Y., Liang, M., Li, Ch. and Hou, Sh. A Joint Kurtosis-Based Adaptive Bandstop Filtering and Iterative Autocorrelation Approach to Bearing Fault Detection, Journal of Vibration and Acoustics, 35 (5), , (203). 5 Kankar, P.K., Sharma, S. C. and Harsha, S.P. olling Element Bearing Fault Diagnosis Using Autocorrelation and Continuous Wavelet ransform, Journal of Vibration and Control, 7 (4), , (20). 6 Al-aheem, Kh. et al. olling Element Bearing Faults Diagnosis Based on Autocorrelation of Optimized: Wavelet De-noising echnique, he International Journal of Advanced Manufacturing echnology, 40 (3), , (2008). 7 Wang, W. Y. he Diagnosis of Bearing Defects Using Synchronous Autocorrelation echnique, Proceedings of the 5 th International Congress on Sound and Vibration, Adelaide, South Australia, 5 8 December, (997). 8 Su, W. et al. olling Element Bearing Faults Diagnosis Based on Optimal Morlet Wavelet Filter and Autocorrelation Enhancement, Mechanical Systems and Signal Processing, 24 (5), , (200). 9 Dron, J., et al. Fault Detection and Monitoring of a Ball Bearing Bench test and A Production Machine Via Autoregressive Spectrum Analysis, Journal of Sound and Vibration, 28 (3), , (2002). 0 Altmann, J. and Mathew, J. Multiple Band-pass Autoregressive Demodulation for olling-element Bearing Fault Diagnosis, Mechanical Systems and Signal Processing, 5 (5), , (200). hanagasundram, S., Spurgeon S. and Schlindwein F. S. A fault detection tool using analysis from an autoregressive model pole trajectory, Journal of Sound and Vibration, 37 (3 5), , (2008). 2 Broersen, P. Automatic Autocorrelation and Spectral Analysis, Springer, Berlin (2006). 3 Al-Bugharbee, H. and rendafilova, I. A fault diagnosis methodology for rolling element bearings based on advanced signal pretreatment and autoregressive modelling, Journal of Sound and Vibration, 369, , (206). 4 Sawalhi, N., andall,. B. and Endo, H. he Enhancement of Fault Detection and Diagnosis in olling Element Bearings Using Minimum Entropy Deconvolution Combined with Spectral Kurtosis, Mechanical Systems and Signal Processing, 2 (6), , (2007). 8 ICSV23, Athens (Greece), 0-4 July 206
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