Non Linear Dynamic Behaviour of an One-Sided Hertzian Contact Excited by an External Gaussian White Noise Normal Excitation

Abstract

The system under study consists of a randomly excited single-degree-of-freedom non linear dynamic system. More precisely, we investigate the vibratory response of a moving mass preloaded by a normal force acting through a Hertzian contact. This study includes possible contact losses, and then vibroimpacts dynamic behaviour. The random excitation consists of an external Gaussian white noise normal force superimposed on the static one. Theoretical responses, in particular the spectral densities of the elastic restoring force, are obtained by using Monte Carlo simulations. In order to describe statistics of the stationary response, we have used the stationary Fokker-Planck equation. In order to validate theoretical results, we have also built an experimental test rig allowing us to simulate the studied non linear system. This test rig consists of a double sphere plane contact loaded by the weight of a rigid moving mass. Experimental results show a good agreement with experimental ones.

The contact loss non linearity appears to be rather strong compared with the Hertzian non linearity. It actually induces a large broadening of the spectral contacts of the response. This is of great importance in noise generation for many systems such as mechanisms using contacts to transform motions and forces. It can be also of great importance for tribologists preoccupied with preventing damage.