A Cyclosymmetric Beam Model and a Spring-Supported Annular Plate Model for Automotive Disc Brake Vibration

Abstract

This paper discusses two simplified analytical models for automotive disc brake vibration which can be used to complement more complex finite element methods. The first model approximates the brake disc as a simple beam structure with cyclosymmetric boundary conditions. Since the beam model is a one-dimensional approach, modelling of the inner boundary condition of the brake disc, at the interface of the brake rotor and the central hat, is not possible. The second model, which is established based upon Kirchhoff’s thin plate theory, is presented in this paper in order to incorporate the vibrational deformation at the hat-disc interface. The mode shapes, natural frequencies, and forced response of a static disc are calculated using different inner boundary conditions. Among others, the spring-supported boundary condition is proposed and applied in this paper to make appropriate predictions. The predicted results are compared with measurements of the vibration characteristics of a solid brake disc mounted upon a static test rig. These comparisons demonstrate that the most appropriate model for the inner boundary condition of the measured brake disc is the proposed spring-supported inner boundary condition.