A Differential-Algebraic Contact Model With Nonlinear Compliance

Modeling of compliant contact is an important issue for simulation and control of mechanical systems. Empirical results in the literature show that, in some mechanical systems such as biological tissues, the relation between the contact force and the indentation is characterized by the following three features: (i) continuity of the force at the time of collision, (ii) Hertz-like nonlinear force-indentation curve, and (iii) non-zero indentation at the time of loss of contact force. The conventional Hunt-Crossley (HC) model does not capture the feature (iii) as the model makes the contact force and indentation reach zero simultaneously. This paper proposes a compliant contact model based on a differential-algebraic equation that satisfies all the three features. The behaviors of the model and the effect of parameters in the model are investigated through numerical simulations.