Mathematical Model of Brake Caliper to Determine Brake Torque Variation Associated with Disc Thickness Variation (DTV) Input

Vehicle brake shudder, or judder, is the result of what is termed “brake roughness excitation”. Objectively, this phenomenon is associated with a brake torque variation (BTV). BTV is the dynamic component of brake torque which is applied to the spindle as an input. One of the known mechanical sources of brake torque variation is disc thickness variation (DTV). This source of BTV is associated with the kinematic behaviour of the rotor and caliper from variation in the thickness of the disc rotor. The research documented in this paper is related to brake torque variation caused by disc thickness variation.

A lumped mass-spring mathematical model of the brake caliper system was developed. This was used to characterise the dynamic response of the brake assembly to a disc thickness variation input. The DTV input was represented mathematically as enforced lateral displacements at the inner and outer rotor/pad interfaces. The equations of motion were determined through a Lagrangian approach. The solution of these equations was used to describe the caliper dynamics in terms of displacements and forces for each degree of freedom. An understanding of these outputs permitted the level of brake torque variation to be calculated. The investigation identified the key variables having the largest effect on the level of BTV produced. Hence in summary, a brake caliper mathematical model has been developed which could be used to predict the level of BTV, for a given DTV input, based on the caliper system design variables.