Exponential Data Fitting for Features Extraction in Condition Monitoring of Paper-based Wet Clutches

Wet clutches play a critical role in automotive driveline systems as wet clutches may degrade while the driveline is running. Sudden failure of the running wet clutch causes unpredictable breakdown of the driveline. This is mainly due to friction material degradation. To avoid the latter, the friction material degradation history must be monitored. Unfortunately, such degradation is difficult to measure directly while the driveline is still running. Consequently, relevant features representing the friction material degradation level must be investigated. In this paper, damping ratio and torsional natural frequency at certain vibration modes are found to be relevant features. These are extracted with an exponential data fitting approach, wherein the free torsional vibration signal is modelled as a sum of exponentially damped sinusoids solved in a Total Least Squares (TLS) sense. 2 IOMAC'09 – 3 International Operational Modal Analysis Conference quency range, all frequencies are relatively constant. An appropriate method is obviously needed to extract the aforementioned modal parameters from such signal. In order to avoid uncertainties due to the inherent limitations of the discrete Fourier transform (Kay and Marple 1981) when applied to such short transient signal, a time-domain identification approach therefore was selected here. Figure 1 : A representative torsional vibration captured post-engagement, (a) Signal in time domain, (b) Energy spectral density, and (c) Time-frequency map In the time domain approach, identification of parameters from the aforementioned signal constitutes an exponential data fitting problem. This can be solved using either non-linear least squares minimisation or using a state-space approach. The first approach is an iterative method with possibly many local minima, so that the convergence is not guaranteed. In contrast, the second one is a non-iterative method. Although the latter approach is suboptimal, it nevertheless has a unique solution. There are several non-iterative time-domain methods commonly used in operational modal analysis, such as Ibrahim Time Domain (ITD) method and its variants (Mohanty and Rixen 2004). However, these methods may not be very robust to noise since signal and noise are well not separated. As a consideration, the Hankel Total Least Squares (HTLS) method was implemented because of its robustness and accuracy for estimating the parameters of such signals (Van Huffel 1993, Van Huffel et al 1994). 2 DESCRIPTION OF HTLS METHOD Principally, this method assumes that the stationary signal yn can be modelled as a sum of K exponentially damped complex values, sampled at uniformly distributed times tn = n.Ts, n = 0, 1,....,N – 1 (Papy 2005). ( ) 1 0 e e 1 1 ,N , n a z c y n t di . j i K