Mechanical Models of Friction That Exhibit Hysteresis, Stick-Slip, and the Stribeck Effect.

Abstract

In this dissertation, we model hysteretic and friction phenomena without introducing friction or hysteresis per se. We use a combination of masses, springs, and dashpots and the frictional phenomena emerge as the result of their interaction. By using physical elements, we can understand the physical mechanisms that lead to hysteretic energy dissipation and phenomena, such as stick-slip behavior and the Stribeck effect. Furthermore, we study the origins of butterfly hysteresis, which arises in optics and ferromagnetism. We define the multiplay model for hysteresis with nonlocal memory, which consists of N mass/spring/dashpot with deadzone elements. The advantage of this model is that its hysteresis map can be inverted analytically. Second, we investigate the origins of stick-slip friction by developing an asperitybased friction model involving the frictionless contact between a body and a row of rigid, rotating bristles. This model exhibits hysteresis and quasi-stick-slip friction. The hysteretic energy-dissipation mechanism is the sudden release of the pivoted bristles. The discontinuous rotating bristle model is an approximation of the rotating bristle model that exhibits exact stick-slip and hysteresis. We next develop an asperity-based friction model in which the vertical motion of the body leads to the Stribeck effect. The friction model is hysteretic and the energy-dissipation mechanism is the sudden release of the compressed bristles. We show that this bristle model is a generalization of the LuGre model. The final contribution of this dissertation is a framework for relating butterflyshaped hysteresis maps to simple hysteresis maps, which are typically easier to model and more amenable to control design. In particular, a unimodal mapping is used to transform simple loops to butterfly loops.