Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 1: harmonic excitation

Abstract

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analysed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated. Linearised resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated. Resonance peak is confined in a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. Forced response spectrum exhibits several harmonics because of nonlinear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results. For higher input amplitude, system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibroimpacting contact and leads to a wide frequency range softening resonance. Spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency versus input amplitude allows the identification of the nonlinear damping law during intermittent contact. Simulations of the vibroimpacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results.