Continuous contact force model with an arbitrary damping term exponent: Model and discussion

Abstract

More than twenty continuous contact force models have been presented for modeling contact-impact problems; however, there was no uniformity regarding the value of the damping term exponent in these models. A new type of continuous contact force model is proposed in this research, in which the value of the damping term exponent can be arbitrary. Then, the effect of the value of the damping term exponent on the model accuracy is investigated by comparing the simulation and experimental results. As it is almost impossible to obtain an analytical solution based on the system dynamic equation, according to the rule of energy equivalence, an approximate dynamic equation is developed by introducing an equivalent indentation and equivalent velocity. Based on the system dynamic equation and the approximate dynamic equation, a primary formula for the hysteresis damping factor of the model can be obtained. Through nondimensional analysis, new models for different values of the damping term exponent are established by modifying the primary formula. The comparison between the simulation results and published experimental data demonstrates the validities of the new models and reveals that the influence of the value of the damping term exponent on the model accuracy can be considered to be negligible.