Continuously Differentiable Stick-Slip Friction Model with Applications to Cable Simulation Using Nonlinear Finite Elements

摘要

This paper presents a continuously differentiable friction model based on the Quinn regularization of the Coulomb model in order to improve numerical performance for simulating dynamic systems using implicit ODE solvers. The implementation of the friction model for simulations of cable-pulley and cable-winch contact is demonstrated using the nonlinear Absolute Nodal Coordinate Formulation. Frictional contact between the cable and a dynamic surface is implemented using a Lagrange multiplier formulation. Examples of simple a capstan and a motorized pulley system are provided to demonstrate the stick-slip behavior of the model and the performance improvement over the original Quinn model, respectively. Using the ODE solver ode15s, the computation time was reduced by factors of 4.5 to 18.8 depending on the model parameters. The proposed model can be used to model and verify the behavior of dynamics systems in control applications.