A Case Study in Backlash Characterization in Mechanical Systems

The Frequency Response Function (FRF) method using an experimental analysis such as free vibration with shock excitation or forced vibration with step or chirp excitation has proven to be a most efficient way to identify the modal parameters of mechanical structures. However, there is a limitation that only linear dynamic systems can be tested through these methods. The problem becomes more complex when nonlinear systems have to be identified. If the nonlinear system is ‘well-behaved’, i.e. if it shows periodic response to a periodic excitation, ‘skeleton’ identification techniques may be used to estimate the modal parameters, in function of the amplitude and frequency of excitation. However, under certain excitation conditions, chaotic behaviour might occur so that the response is aperiodic. In that case, chaos quantification techniques, such as Lyapunov exponent, are proposed in the literature. This paper deals with the application of the aforementioned nonlinear identification techniques to an experimental mechanical system with backlash. It compares and contrasts Hilbert transforms with Wavelet analysis in case of skeleton identification showing their possibilities and limitations. Chaotic response, which appears under certain excitation conditions and could be used as backlash signature, is dealt with both by a simulation study and by experimental signal analysis after application of appropriate filtration techniques.