The Z-properties chart

Dynamic friction modeling has received considerable attention, and diverse models have been put forward. Some of the most widely applied models are state-variable models, which incorporate one or more internal states governed by nonlinear differential equations. As empirically motivated nonlinear differential equations, state-variable friction models exhibit a surprising variety of behavior. Most of these models are dissipative for motions on all scales, while others are nondissipative for very small motions; some show true sliding for very small applied forces, while others show purely elastic displacement under the same conditions; and some show hysteresis with nonlocal memory, while others do not. In this article the Z-properties chart is introduced. This chart provides a means for comparing and contrasting the properties of the state-variable friction models under the condition referred to as presliding, where the dynamics of the state variables play their greatest role. The friction state is often designated z(t) and thus the name "Z-properties chart".