On the Effect of Friction Law in Closed-Loop Coupling Disc Brake Model

Brake squeal is a complex dynamics instability issue for automobile industry. Closed-loop coupling model deals with brake squeal from a perspective of structural instability. Friction characteristics between pads and disc rotor play important roles. In this paper, a closed-loop coupling model which incorporates negative friction-velocity slope is presented. Different from other existing models where the interface nodes are coupled through assumed springs, they are connected directly in the presented model. Negative friction slope is taken into account. Relationship between nodes' frictional forces, relative speeds and brake pressure under equilibrant sliding and vibrating states is analysed. Then repeated nodal coordinate elimination and substructures' modal coordinate space transformation of system dynamic equation are performed. It shows that the negative friction slope leads to negative damping items in dynamic equation of system. Then the complex eigenvalue analysis is applied to find out the unstable modes of the system. Finally, the presented method is applied on a disc brake system to study the effect of friction character on the stability of the system. Prediction results from models with/ without considering negative friction slope effect is listed and compared with bench test results. It shows that with the introduction of negative friction slope, more unstable modes which correspond to test result can be obtained. So the model prediction results are more correlated with those from test. The accuracy of model prediction results is improved and the closed-loop coupling model is more close to the actual brake system.