Multiscale modelling of dynamical systems with friction between randomly rough surfaces

Abstract eng:
Friction induced vibrations are present in many engineering systems, e.g. in brakes and cam follower systems. In these systems, self-excited oscillations may occur. Surface roughness is an important source of uncertainty in friction systems. We present a multi-scale approach to the modeling and simulation of dynamical systems with friction between randomly rough surfaces. In a first step, a stochastic model for the rough surface is identified based on observations obtained directly by a white light interferometer, from which statistical characteristics such as the probability density function, the correlation function and the spectral density of the surface heights are estimated. From these characteristics, sample surfaces can be simulated by Karhunen-Lo`eve expansion or a spectral approach. In a second step, the normal contact problem for samples of the rough surface is solved, where the contact pressure is represented by a polynomial chaos expansion. By repeated solution of the normal contact problem, the coefficients of the the polynomial chaos expansion can be estimated by regression. From the polynomial chaos expansion of the contact pressure and area, a stochastic friction coefficient can be identified by application of the Bowden-Tabor approach. In this way, a stochastic process for the friction coefficient is obtained from the statistical properties of the surface roughness. Finally, on a structural level, vibration systems with friction between randomly rough surfaces are studied, where the classical friction coefficient is replaced by the stochastic process that has been identified previously. As an example, the classical mass on a belt system is considered, where stick-slip vibrations occur. The influence of the stochastic process for the friction coefficient on the limit cycle is studied.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket