A contact force model considering constant external forces for impact analysis in multibody dynamics

A continuous contact force model, which considers the influence of constant external forces, is presented for the dynamic analysis of a multibody system. In this model, the Hertz contact law is applied to represent the nonlinear nature of contact, and a damping force is derived for evaluating the energy loss during impact. Together with the restitution coefficient, the external force influence factor defined in this paper is required for calculating the hysteresis damping factor associated with damping force. Moreover, the expression of hysteresis damping factor is deduced based on the energy-based method, which is adopted frequently in literature, and then it is improved by a weighted combination method with an exponential function due to the fact that the energy-based method has great errors when the restitution coefficient is low. Meanwhile, the exponential function is obtained by fitting the parametric surface of hysteresis damping factor gained from a numerical approach. Finally, four contact force models, including the new model, are utilized to compare the dynamic response of a special bouncing ball. The results illustrate that the described model is more suitable for impact analysis in multibody dynamics. In addition, the external forces and the energy loss are the main reasons for the multibody system to enter a steady contact state from repeated impact state.