Low frequency dynamics of a translating friction element in the presence of frictional guides, as motivated by a brake vibration problem

A simplified translating friction element system is formulated, designed, and evaluated to simulate practical brake vibration (judder) issues. This simplified translating friction element system includes two frictional guides and two actuators to simulate dynamic interactions between the brake pad and the calipers (including the guide pins). First, a two degree of freedom nonlinear model and then a single degree of freedom linear model of the translating friction element problem are developed and solved for eight cases. Second, a simple laboratory experiment is designed, and the measurements are found to correlate well with the predictions of both mathematical models. Third, experiments and mathematical models are utilized to study the effects of the frictional guide and normal load application locations on a shift in the center of contact force. An effective torsional stiffness element is also defined to incorporate the center of contact force concept. Finally, a two degree of freedom nonlinear model of a simplified brake vibration (judder-like) problem is proposed, and the role of calipers on the dynamic response is discussed.