Impact of an irregular friction formulation on dynamics of a minimal model for brake squeal. (July 2018) - Stender, Merten; Tiedemann, Merten; Hoffmann, Norbert; Oberst, Sebastian
Highlights: A temperature-dependent, irregular friction formulation is proposed. Multi-scale dynamics are generated. The friction model increases the vibration responses of the disk brake model. Qualitatively different dynamics arise as multiple scales interact. Abstract: Friction-induced vibrations are of major concern in the design of reliable, efficient and comfortable technical systems. Well-known examples for systems susceptible to self-excitation can be found in fluid structure interaction, disk brake squeal, rotor dynamics, hip implants noise and many more. While damping elements and amplitude reduction are well-understood in linear systems, nonlinear systems and especially self-excited dynamics still constitute a challenge for damping element design. Additionally, complex dynamical systems exhibit deterministic chaotic cores which add severe sensitivity to initial conditions to the system response. Especially the complex friction interface dynamics remain a challenging task for measurements and modeling. Today, mostly simple and regular friction models are investigated in the field of self-excited brake system vibrations. This work aims at investigating the effect of high-frequency irregular interface dynamics on the nonlinear dynamical response of a self-excited structure. Special focus is put on the characterization of the system response time series. A low-dimensional minimal model is studied which features self-excitation, gyroscopic effects and friction-induced damping. Additionally, the employed friction formulation exhibits temperature as inner variable and superposed chaotic fluctuations governed by a Lorenz attractor. The time scale of the irregular fluctuations is chosen one order smaller than the overall system dynamics. The influence of those fluctuations on the structural response is studied in various ways, i.e. in time domain and by means of recurrence analysis. The separate time scales are studied in detail and regimes of dynamic interactions are identified. The results of the irregular friction formulation indicate dynamic interactions on multiple time scales, which trigger larger vibration amplitudes as compared to regular friction formulations conventionally studied in the field of friction-induced vibrations.