Perturbation Stability of Frictional Sliding with Varying Normal Force

Abstract

In many systems, the normal force at friction contacts is not constant, but is instead a function of the system’s state variables. Examples include machine tools, friction dampers, brake systems and robotic contact with the environment. Friction at these contacts has been shown to possess dynamics associated with changes in normal force. In an earlier paper, the authors derived a critical value of system stiffness for stability based on a linearized analysis of constant velocity sliding (Dupont and Bapna, 1994). In this paper, the domain of attraction for the steady sliding equilibrium point is characterized for a system in which normal force is coupled to tangential displacement. Perturbations consisting of sudden changes in the displacement and velocity of the loading point are considered. These perturbations can be viewed as either actuator disturbances or changes in control input. The effect and interaction of the frictional and geometric parameters are elucidated. The results are applicable to the design and analysis of systems in which steady motion without friction-induced limit cycles is desired.