Investigation of the Influence of ODE Based Friction Models on Complex FEM Brake Models in the Frequency Domain

In today’s research and development of brake systems the model-based prediction of complex vibrations and NVH phenomena plays an important role. Despite the efforts, the high dimensional computational simulation models only provide a limited part of the results gained through experimental measurements. Several reasons are discussed by the industry and academic research.

One potential source of these inadequacies is the very simple formulation of the friction forces in the simulation models. Due to a significant shorter computation time (by orders of magnitude), the complex eigenvalue analysis has been established, in comparison to the transient analysis, as the standard method in the case of industrial research, where systems with more than one million degrees of freedom are simulated. The coefficient of friction in the models is usually assumed to be constant, although it is known that the coefficient of friction is dependent on various system variables like temperature, pressure and velocity. Furthermore, well-known friction phenomena such as time lag behaviour, hysteresis, and the fading effect, can be observed in experimental measurements. 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. For this purpose, the state vector is extended by the new state variables like coefficient of friction or friction force, pad and disc temperature, wear and so on. This method will be referred to in this paper as the “Method of the Augmented Dimensioning” (MAD).

The method was used to perform principle investigations on the influence of various friction models onto the stability behaviour of friction-induced vibrations in the case of minimal models. This paper analyses embedded ODE based friction models in common FEM-tools, in order to describe the influence of dynamic friction laws on the stability in commercial FEM brake models of high order.