Extraction of Frictional Vibration Features with Multifractal Detrended Fluctuation Analysis and Friction State Recognition

Abstract

For the purpose of extracting the frictional vibration characteristics of the friction pair during friction and wear in different friction states, the friction and wear tests of friction pair in different friction states were conducted on a testing machine. Higher-dimensional fractal and multifractal characteristics hidden in time series can be examined by multifractal detrended fluctuation analysis (MFDFA) method. The frictional vibration time-domain signals, the friction coefficient signals and the frictional vibration frequency-domain signals were analyzed and multifractal spectra were acquired by using the MFDFA algorithm. According to the spectra, the multifractal spectrum parameters of these signals were calculated to realize the quantitative characterization of frictional vibration characteristics in different friction states. The analysis shows that it is symmetric in the variation trends of the multifractal spectrum parameters of the frictional vibration signals and the friction coefficient data. Based on the multifractal spectrum parameters of frictional vibration, the principal component analysis (PCA) algorithm was applied to establish the friction state recognition method. The results show that the multifractal spectra and their parameters can characterize the frictional vibrations, and the friction state recognition can be realized based on the multifractal spectrum parameters of frictional vibrations.Symmetry 2020, 12, 272 2 of 22 friction pair [7]. Therefore, the analysis of frictional vibrations is a better means to monitor the friction and wear states of the friction pair in real time during the operation of equipment.The study of the frictional vibration has attracted many scholars' interest. Jaeyong et al. studied the nonlinear behaviors of the frictional vibration by using spring-mass model based on the smooth friction velocity curve. The results show that the nonlinearity and instability of friction may bring forth chaotic frictional vibrations according to the friction curve [8]. Liu et al. showed that the cross correlation coefficient of frictional vibration is opposite to the variations of friction coefficient [9]. Sun D. et al. pointed out that the change law of the defined frictional vibration parameter k is consistent with the change trends of the friction coefficient during the tests [10]. Rouzic et al. studied the squeal noises of a wiper/windscreen contacts. Based on Stebeck's law of friction coefficient, they proved that noises are caused by self-excited frictional vibration [11]. Wernitz and Hoffmann's analysis indicated that irregular frictional vibration states of friction brakes are mainly dominated by intermittency phenomena [12]. Nadim et al. pointed out that the frictional vibration of dry friction has nonlinear characteristics, and the surface morphology of the friction pair change due to abrasive wear and adhesive wear at the interface of the friction pair results in the change of friction coefficient, which is the source of the nonlinear frictional vibration [13]. Recentl...

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