An enhanced contact force model with accurate evaluation of the energy dissipation during contact-impact events in dynamical systems

Abstract

The accurate calculation of energy dissipation during impact plays a decisive role in the prediction of the motion status after impact and the maximum contact force. However, how to precisely depict the energy loss and simplify the contact evaluation process meanwhile is an intractable issue. This investigation aims at analyzing the capacity of accurately evaluating the dissipated energy during impact based on the viscous damping factor contingent on frequency dependency and developing a new viscous damping factor by integrating the relative impact velocity from the linearized underdamped vibration system associated with the energy conservation during impact. Two pivotal dissipative coefficients are introduced into the damping force terms in the elastoplastic and plastic contact phases for the sake of compensating the derivation error of the new viscous damping factor. A new contact model with a viscous damper is proposed based on the Hertz contact theory and dimension analysis approach in conjunction with the linearized elastoplastic stiffness from the ML model. A comparative analysis between the novel contact model and the available contact models with viscous damping factors is conducted using an external impact scenario involving two spheres, which proves that the proposed contact model is the most precise viscous contact model in calculating the loss energy during impact. Finally, the slider-crank mechanism with clearance and horizontal granular chain are considered as the numerical example to illustrate the correctness of the new viscous contact model.