Automotive brake squeal analysis with rotating finite elements of asymmetric disc in time

The new finite element brake squeal model is proposed where the finite elements of a real brake disc rotate in time. Contact nodal forces between the rotating disc and stationary pads are allocated to the moving contact area at every time step. When the proposed model is applied to an asymmetric automotive brake disc, it becomes the periodic time-varying brake system. The stability boundary of the discrete time-varying system is numerically calculated by the Floquet theory. Also, the quasi-static linearized eigenvalue analysis is conducted to show that the unstable modes repeatedly appear at the short interval of the disc rotation angle. The results are consistent with the angle-dependent local phenomenon of squeal termed squeal periodicity in the squeal experiment. In the nonlinear time-domain analysis, the squeal vibration increases and then decays in time for the rotating mode shape functions. It demonstrates that the rotation of an asymmetric disc can change the nonlinear squeal behavior as well as the linear stability character drastically.