A continuous contact force model for impact analysis in multibody dynamics

Abstract

A new continuous contact force model for contact problems with complex geometries and energy dissipations in multibody systems is presented and discussed in this work. The model is developed according to the Hertz law, and a hysteresis damping force is introduced for modeling the energy dissipation during the contact process. As it is almost impossible to obtain an analytical solution based on the system dynamic equation, an approximate dynamic equation for the collision system is proposed, achieving a good approximation of the system dynamic equation. An approximate function relating the deformation velocity and indentation depth is determined based on the approximate dynamic equation and is utilized to calculate the energy loss due to the damping force. Then, a primary formula of the hysteresis damping parameter is derived by combining energy balance and the law of conservation of linear momentum. The new model is developed by modifying the primary formula through nondimensional analysis. The comparison with published experimental data and the analysis of the simulation data of eight different continuous contact models reveal the capability and high precision of the new model as well as the effect of the geometry of the contacting surfaces on the dynamic system response.