Analysis of complex modal instability of a minimal friction self-excited vibration system from multiscale fractal surface topography

Abstract In order to reveal the stability and nonlinear characteristics of the friction self-excited vibration system from the perspective of microscopic multiscale fractal surface topography, a minimal two-degree-of-freedom mathematical model of the disc brake system is established in this paper. Considering the fractal characteristics of rough surface topography, the fractal contact stiffness of contact surfaces is introduced into the system model from the perspective of microscopic contact, and the effects of two important surface fractal parameters, fractal dimension D and fractal roughness G, on the stability and nonlinearity of the system are analyzed. Further finite element analysis and brake noise test improve the analysis of system stability and noise intensity by different surface topographies. The results show that the system stability can be improved with the increase of fractal dimension within a certain range, and the system will be in a stick state with the further increase of fractal dimension. With the increase of fractal roughness, the unstable modal coupling region of the system is increasing, which can reduce the stability of the system. The unstable region of the system is dependent on fractal dimension and fractal roughness, and has different sensitivity to them.