Dynamics of a simplified nonlinear model offering insights into the hammering type brake squeal initiation process

This article develops a simplified mechanical system model that offers insights into the hammering type brake squeal initiation process while overcoming a void in the literature. The proposed formulation derives a nonlinear two-degree-of-freedom model where a mass is in contact with a rigid frictional surface that moves with constant velocity. The kinematic nonlinearities arise from an arrangement of springs that support the mass, as well as from contact loss between the mass and frictional surface. First, the nonlinear governing equations are numerically solved for several normal force vector arrangements, and a wide range of dynamic responses are observed. Results show that some assumptions made in prior articles are not valid. Second, the nonlinear governing equations are linearized, and the existence of quasi-static sliding motion is sought for selected inclined spring arrangements. Third, the dynamic stability of the linearized system is examined and compared with the results of a nonlinear model. The coupled modes are found even though some contradictions between the model assumptions and linearized system solutions are observed. Finally, the nonlinear frequency responses are calculated using the multi-term harmonic balance method although only the contact loss nonlinearity is retained. Shifts in the resonant frequencies during the motion of the pad are clearly observed. In conclusion, the contact loss nonlinearity is found to be crucial, and as such, it must not be ignored for the squeal source investigation. Finally, the new model offers insight into the squeal initiation process while revealing the limitations of linearized system analyses.