Development of a compliant dashpot model with nonlinear and linear behaviors for the contact of multibody systems

A comprehensive dashpot model with hysteresis damping factors that can provide a convenient calculation approach for the elastoplastic impact behavior in multibody systems is studied in this paper. At the beginning of contact, the nonlinear hysteresis damping factor in the elastic phase is derived by approximately solving a nonlinear vibration system. When impact happens at a relatively high speed with a large load, elastoplastic deformation is inevitable, and Hertz contact stiffness cannot represent the actual contact stiffness. In order to describe the contact stiffness in the elastoplastic or plastic phase correctly, a static elastoplastic contact model is adopted to calculate the contact stiffness by approximately linearizing the relationship between load and deformation. When the contact comes into the elastoplastic phase, the impact behavior can be treated as a linear vibration system, and the linear hysteresis damping factor can be obtained from this linear system. The energy dissipation in different contact phases can be described by a nonlinear and a linear hysteresis damping factors. Such a nonlinear hysteresis damping factor can make up for the deficiency of the static elastoplastic contact model when describing the energy dissipation in the elastic contact phase. Simulation results show that the proposed dashpot model is more harmonious with the static elastoplastic contact model compared to the existing dashpot models. A slider-crank mechanism with a clearance joint and a Hopkinson incident bar are exemplified in the present work by using experimental data to validate the effectiveness of the proposed dashpot model.