A continuous contact force model for impact analysis in multibody dynamics

TL;DR

This paper introduces a novel continuous contact force model for impact analysis in multibody dynamics, incorporating energy dissipation via hysteresis damping and providing an approximate dynamic equation for better simulation accuracy.

Contribution

The work develops a new contact force model based on Hertz law with hysteresis damping, offering an improved approximation method for impact analysis in multibody systems.

Findings

The model accurately predicts impact forces and energy dissipation.

Surface geometry significantly affects system response.

The model outperforms existing contact models in simulations.

Abstract

A new continuous contact force model for contacting problems with regular or irregular contacting surfaces and energy dissipations in multibody systems is presented and discussed in this work. The model is developed according to 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 between deformation velocity and deformation is founded on the approximate dynamic equation, then it is utilized to calculate the energy loss due to the damping force. The model is established through modifying the original formula of the hysteresis damping parameter derived by combining the energy balance and the law of conservation of linear momentum. Numerical results of five different continuous contact models reveal the capability of our new model as well as the effect of the geometry of the contacting surfaces on the dynamic system response.