Assessment of point and line contact stiffness formulations leading to the initiation of hammering type brake squeal

This article proposes a refined nonlinear mathematical model to conceptually investigate the brake pad kinematics and dynamics in order to reveal certain important aspects that have been ignored in prior studies. In particular, the proposed model is formulated as a three degree-of-freedom mass positioned on a rigid frictional surface moving at constant velocity. The mass is assumed to make planar motion in vertical plane, two translations and one rotation. The interfacial contact is first examined by a point contact model with linear translational springs at edges and then the line contact is defined over the entire interface. Furthermore, kinematic and clearance nonlinearities are included. The nonlinear governing equations with point contacts at edges are numerically solved at certain angular arrangements of normal force vectors. Then, the line contact interface is solved again for the same normal force vector arrangements. Comparison reveals that the line contact approach provides more meaningful results. Finally, a linearized system model and the existence of quasi-static sliding motion are examined over a range of the normal force vector arrangements. Overall, inclusion of the rotational degree of freedom in the source model is crucial and the importance of pad-disc separation is clearly explained by the proposed formulation. This leads to a better understanding of the hammering type brake squeal source mechanisms while overcoming the limitation of prior minimal order models.