TELKOMNIKA, Vol.10, No.8, December 2012, pp. 2139~2150 e-ISSN: 2087-278X accredited by DGHE (DIKTI), Decree No: 51/Dikti/Kep/2010
2139
Bearing Fault Diagnosis Based on Laplace Wavelet Transform Hui Li, Yingjie Yin Department of Electromechanical Engineering, Shijiazhuang Institute of Railway Technology Shijiazhuang, Hebei, China *corresponding author, e-mail:
[email protected],
[email protected]
Abstract The roller bearing characteristic frequencies contain very little energy, and are usually overwhelmed by noise and higher levels of structural vibrations. Therefore, envelope spectrum analysis is widely used to detection bearing localized fault. In order to overcome the shortcomings in the traditional envelope analysis in which manually specifying a resonant frequency band is required, a new approach based on the fusion of the Laplace wavelet transform and envelope spectrum is proposed for detection and diagnosis defects in roller element bearings. The basic principle is introduced in detail. Laplace wavelet transform is self-adaptive to non-stationary and non-linear signal. The methodology developed in this paper decomposes the original times series data in intrinsic oscillation modes, using the Laplace wavelet transform. Then the envelope spectrum is applied to the selected daughter wavelet that stands for the bearing faults. The experimental results show that Laplace wavelet can extract the impulse response from strong noise signals and can effectively diagnose the faults of bearing. Keywords: fault diagnosis, Laplace wavelet transform, bearing, envelope spectrum, signal processing Copyright © 2012 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction The roller element bearing is an important component for power transmitting systems within the machine tool or gearbox drive train. Monitoring the condition of the bearing component provides advantages in the safety, operation and maintenance areas. Therefore, the predictive maintenance philosophy of using vibration information to lower operating costs and increase machinery availability has been the subject of intensive research throughout industry. Since most of the machinery in a predictive maintenance program contains rolling element bearings, it is imperative to establish a suitable condition monitoring procedure to prevent malfunction and breakage during operation. The hertzian contact stresses between the rolling elements and the races are one of the basic mechanisms that initiate a localized defect. When a rolling element strikes a localized defect, an impulse occurs which excites the resonance of the structure. Therefore, the vibration signature of the damaged bearing consists of exponentially decaying sinusoid having the structure resonance frequency. The duration of the impulse is extremely short compared with the interval between impulses, and so its energy is distributed at a very low level over a wide range of frequency and hence, can be easily masked by noise and low-frequency effects. The periodicity and amplitude of the impulses are governed by the bearing operating speed, location of the defect, geometry of the bearing, and the type of the bearing load [1]. The rolling elements experience some slippage as the rolling elements enter and leave the bearing load zone. As a consequence, the occurrence of the impacts never reproduce exactly at the same position from one cycle to another, moreover, when the position of the defect is moving with respect to the load distribution of the bearing, the series of impulses is modulated in amplitude. However, the periodicity and the amplitude of the impulses experience a certain degree of randomness [2,3]. All these make the bearing defects very difficult to detect by conventional FFT-spectrum analysis that assumes that the analyzed signal to be strictly periodic. A method of conditioning the signal before the spectrum estimation takes places is necessary. A commonly used method is envelope detection. To overcome the modulation problem, several signal envelope demodulation techniques have been introduced. In high-frequency
Received October 10, 2012; Revised November 9, 2012; Accepted November 17, 2012
2140
e-ISSN: 2087-278X
resonance technique (HFRT), an envelope detector demodulates the pass-band filtered signal and the frequency spectrum is determined by FFT technique [4]. Another well-established method is based on the Hilbert transform [5] or Teager Kaiser energy operator (TKEO) [6,7]. The envelope analysis technique is widely accepted as a powerful tool in the detection and diagnosis of bearing faults. The resonance frequency oscillation of the impacts and the possibly suppressed impact periodicity are two modulations of the vibrations that both reduce the amplitude of the power spectrum peaks, which therefore are more likely to be suppressed below the overall noise level. A popular countermove is to remove the resonance frequency modulation with the envelope method, which consists of a band-pass filter followed by a demodulation and a fast Fourier transformation. In the traditional envelope analysis technique, the fault is identified through the peak value of envelope spectrum. However, the central frequency of the filter is determined with experience while forming an envelope signal, which will make great subjective influence on the diagnosis results [2,3]. Bearing faults by their nature are time localized transient events. To deal with nonstationary and non-linearity signals, time-frequency analysis techniques such as the short time Fourier transform (STFT) [8], Wigner-Ville distribution (WVD) [9,10] and wavelet transform (WT) [3,11,12,13] are widely used. The STFT [8] uses sliding windows in time to capture the frequency characteristics as functions of time. Therefore, a spectrum is generated at discrete time instants. An inherent drawback with the STFT is the limitation between time and frequency resolutions. A finer frequency resolution can only be achieved at the expense of time resolution and vice-versa. Furthermore, this method requires large amounts of computation and storage for display. The WVD [14] is a basic time-frequency representation, which is part of the Cohen class of distribution. The difficulty with this method is the severe cross terms as indicated by the existence of negative power for some frequency ranges. In addition, the WVD of discrete time signals suffers from the aliasing problem, which may be overcome by employing various approaches. The wavelet transform provides powerful multi-resolution analysis in both time and frequency domain and thereby becomes a favored tool to extract the transitory features of nonstationary vibration signals produced by the faulty bearing [15,16]. The wavelet analysis results in a series of wavelet coefficients, which indicate how close the signal is to the particular wavelet. In order to extract the fault feature of signals more effectively, an appropriate wavelet base function should be selected. Morlet wavelet is mostly applied to extract the rolling element bearing fault feature because of the large similarity with the impulse generated by the faulty bearing [3]. The impulse response wavelet is constructed and applied to extract the feature of fault vibration signal in [17]. A number of wavelet-based functions are proposed for mechanical fault detection with high sensitivity in [18], and the differences between single and double-sided Morlet wavelets are presented. An adaptive wavelet filter based on single-sided Morlet wavelet is introduced in [19]. The Laplace wavelet is a complex, single-sided damped exponential formulated as an impulse response of a single mode system to be similar to data feature commonly encountered in health monitoring tasks [20]. It is applied to the vibration analysis of an actual aircraft for aerodynamic and structural testing [21], to diagnose the wear fault of the intake valve of an internal combustion engine [22], and to acquire modal parameters with high precision for the rotor crack detection [23-25]. In this paper, an alternative approach for detecting localized faults in the outer and inner races of a roller element bearing using the envelope spectrum of the Laplace wavelet transform (LWT) is investigated. The shape parameters of Laplace wavelet ensure a large similarity between the wavelet function and the generated fault impulse. The methodology developed in this paper decomposes the original times series data in intrinsic oscillation modes, using the Laplace wavelet transform. Then the envelope spectrum is applied to the selected intrinsic oscillation mode that stands for the bearing faults. The techniques are demonstrated by the experiments on a gearbox with a roller bearing under simulated crack on the inner race or the outer race. The characteristic frequencies related to the bearing defect can be effectively extracted. This approach is applied in the research of the faults detection and diagnosis of the roller bearing. The experimental results show that this method based on Laplace wavelet transform and envelope spectrum can effectively diagnose the faults of bearing. To address the issues discussed above, this paper is organized as follows. Section 1 gives a brief introduction of bearing fault detection. Section 2 introduces the Laplace wavelet TELKOMNIKA Vol. 10, No. 8, December 2012 : 2139 – 2150
TELKOMNIKA
e-ISSN: 2087-278X
2141
transform. Section 3 presents the method and procedure of envelope analysis technique based on Laplace wavelet transform. Section 4 describes the experimental set-up. Section 5 gives the applications of envelope analysis technique based on Laplace wavelet transform to fault diagnosis of roller bearing. Finally, the main conclusions of this paper are given in Section 6.
2. Laplace wavelet transform The Laplace wavelet is a complex, analytical, and single sided damped exponential, and it is given by [20]
− ψ (t ) = Ae 0 ,
ξ 1−ξ 2
ωc t
e − jωct , t ≥ 0 t
