On the modeling and simulation of friction

Two new models for “slip-stick” friction are presented. One, called the “bristle model,” is an approximation designed to capture the physical phenomenon of sticking. This model is relatively inefficient numerically. The other model, called the “reset integrator model,” does not capture the details of the sticking phenomenon, but is numerically efficient and exhibits behavior similar to the model proposed by Karnopp in 1985. All three of these models and the Dahl model are preferable to the classical model, which poorly represents the friction force at zero velocity. Simulation experiments show that the Karnopp model, the Dahl model, and the new models give similar results in two examples. In a closed-loop example, the classical model predicts a limit cycle which is not observed in the laboratory. The Karnopp model, the Dahl model, and the new models, on the other hand, agree with the experimental observation.