Comparative signal processing analyses of a speed-dependent problem as motivated by brake judder problem

The goal of this paper is to investigate a transient problem using several digital signal processing techniques. First, a simple linear mathematical model, where a point mass is connected to a roller trough a contact interface, is developed and the dynamic interfacial force is analytically calculated as a function of the speed. In this model, the contact interface is described with a linear spring and viscous damper, and the system is excited with a base excitation, as defined by the undulations on the roller surface. Due to the time-varying speed characteristics of the roller, the resulting response is transient. Second, the dual-domain analyses of the calculated system response is carried out by using short-time Fourier and wavelet transforms, since single-domain representation leads to a loss of information due to signal's transient characteristics. Third, the Hilbert transform is applied and the envelope curves of the interfacial force response are successfully obtained. Finally, this problem is briefly linked to brake judder phenomenon and its source regimes are briefly explained.