Analysis of out-of-plane motion of a disc brake system using a two-degree-of-freedom model with contact stiffness

A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamic interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. The dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffnesses of the pad and disc are equally important. Complex eigenvalue analysis is conducted for the case where the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of the friction coefficient with respect to the normal force makes the system more unstable. Non-linear analysis is also performed to demonstrate various responses. Comparing the responses with experimental data has shown that the proposed model may qualitatively well represent a certain type of brake noise.