Hysteretic effects of dry friction: modelling and experimental studies

Abstract

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

On the mathematical basis of solid friction

“…ρ = 0. Some numerical simulations and experiments are given in [12,50], showing periodic, quasi-periodic, and irregular motions, suggesting that further in-depth analytical studies are an interesting subject for future work; note that the analysis in [50] introduces hysteresis and static friction using multiple switching laws, instead of nonlinear sticking as introduced here, and various multi-period orbits are identified in numerical and experimental data. In simulations similar to those in section 8 but not shown here, periodic left-right slip and periodic stick-slip oscillations are found at a wide range of parameters.…”

“…Models of a dynamically evolving friction force are traceable from Dahl [13] through various developments to, for example, the LuGre model [7,4,37] where a friction force F = ksz + csż + cv evolves according to the deflection z of bristles on the surface, with stiffness ks and damping cs, including a viscous friction coefficient c, and Stribeck velocity vstr below which speed dependence is seen; bristle models capture the key effects of friction and yield a smooth force law, and have inspired many variations on the model, usually bringing with them more coefficients connected with nonlinearities, giving dependence on acceleration or forming alternative models of asperities. For example in [50] it was proposed to switch the contact force between accelerative, decelerative, and static modes, requiring several quantifiers of effects including compliance or friction memory and hysteresis, Stribeck velocity dependence, dwell times in stick-slip transition, and static friction.…”

“…The information required to reverse stick-slip motion is lost to the environment through heat and sound, and it remains a challenge to show how the small, and even atomic, scale, interactions involved in this (e.g. [23,35,4,37,41,50]) reproduce large scale dynamics. A full characterization of these problems is beyond our scope here, though we refer to the literature a little further in section 9.…”

Is Extreme Learning Machine Effective for Multisource Friction Modeling?

“…For each source of friction is the Coulomb friction, the Stribeck effect is described by and the Stribeck velocity is , while denotes a coefficient of viscous friction [6]. The function , influences the shape of the characteristics.…”

“…This problem is important for applications, and it constitutes an interesting benchmark for modeling techniques. Although several memoryless models of friction as a function of relative speed of moving surfaces are available [6], parametrical identification of these models is difficult because of high nonlinearity. The problem becomes more complex if several sources of friction are present in the plant, acting together against the motion.…”