A continuous contact force model for impact analysis

Abstract

Hunt and Crossley proposed a general expression of the contact force in 1975. The dissipative force term of the general expression has two exponents: the exponent of indentation depth and that of velocity. Because it is almost impossible to obtain an analytical solution based on the general expression, more than twenty continuous contact models have been developed based on the simplification of the general expression. In these studies, the exponent of the indentation depth was set as 0.25, 0.5, 0.65, 1.0 or 1.5, and the exponent of the velocity was set to 1.0. This paper proposes a new continuous contact force model with arbitrary values of the exponents of the indentation depth and velocity. The model is based on the general expression of the contact force. Considering the rule of energy equivalence, an approximatedynamic equation is developed by introducing the equivalent indentation and equivalent velocity. Subsequently, a new continuous contact force model is constructed based on the system dynamic equation and approximate dynamic equation. The influences of the two exponents on the performance of the continuous contact force models are investigated by analyzing the simulation results. Moreover, the validity of the new model is demonstrated by comparing the simulation results with two published experimental datasets. The comparison also indicates that the performance of the continuous contact model can be enhanced by selecting appropriate values of the two exponents.