Model-based predictions of complex vibrations and NVH phenomena in brake systems continue to be challenging. Even high dimensional FEM and MBS models only provide a small portion of the results gained through measurements. The reasons for this are manifold.

One potential source of these inadequacies is the very simple formulation of the friction forces in the above mentioned models. Due to time and financial constraints, complex eigenvalue analyses are used to describe stability behaviour for NVH characterization, and the coefficient of friction in the models is assumed to be constant. Recent studies and measurements have demonstrated that the coefficient of friction is a system variable with surprisingly dynamic properties. For this purpose, new and complex friction laws can be found in the literature, making use of additional parameters in differential formulations. To use such friction laws in linear systems, the initial system must be embedded in an expanded state space. This augmented dimensioning is a very common method, which can be used to approximate nonlinear friction effects in a linear space.

The method is used in the EKS “Expert Group Simulation Brake Noise” to perform principle investigations on the influence of various friction models on the stability of friction-induced vibrations. This paper describes the fundamentals to express nonlinear and differential friction laws using simple models in the frequency domains. First analyses of the impact on the stability limits are presented. Such analyses will be expanded for complex brake models in the future.

Ostermeyer, G.-P.; Völpel, A.; Müller M. - TU Braunschweig, Institute of Dynamics and Vibrations