Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 2: random excitation

Abstract

Non-linear dynamic behaviour of a normally excited preloaded Hertzian contact (including possible contact losses) is investigated using an experimental test rig. It consists of a double sphere plane contact loaded by the weight of a rigid moving mass. Contact vibrations are generated by a external Gaussian white noise and exhibit vibroimpact responses when the input level is sufficiently high. Spectral contents and statistics of the stationary transmitted normal force are analyzed. A single-degree-of-freedom non-linear oscillator including loss of contact and Hertzian non-linearities is built for modelling the experimental system. Theoretical responses are obtained by using the stationary Fokker–Planck equation and also Monte Carlo simulations. When contact loss occurrence is very occasional, numerical results show a very good agreement with experimental ones. When vibroimpacts occur, results remain in reasonable agreement with experimental ones which justify the modelling and the numerical methods described in this paper. The contact loss non-linearity appears to be rather strong compared to the Hertzian non-linearity. It actually induces a large broadening of the spectral contents of the response. This result is of great importance in noise generation for many systems such as mechanisms using contacts to transform motions and forces (gears, ball-bearings, cam systems, to name a few). It is also of great importance for tribologists preoccupied with preventing surface damage.