Question

what observation and experiment can you cite to show excitence of friction?

Answer 1

Forces affect the motion and speed of a football in the game, and different forces can help or hinder motion in the game at different times. Some forces are in direct contact with objects, while other forces are not. For example, the force of friction slows the football down when it rubs against another object. Friction is a force that resists motion between two bodies in contact. You can observe friction when you roll a football on the ground. The ball will eventually come to a complete stop after rolling, because the friction caused by the football dragging on the ground depletes the force that was initially enacted upon it.

Answer 2

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.

Keywords:1. Introduction

Modelling of dry friction has been the subject of active scientific research since Coulomb's hypothesis (Coulomb 1785). It appears in many, if not all, mechanical systems commonly met in engineering practice, including wheels, brakes, valves, cylinders, bearings, transmissions and others. Therefore, reliable predictions of their dynamic responses require robust dry friction models. In general, there are many different types of dry friction models and it is crucial to appropriately choose one that best suits the modelled problem. For example, if one considers the dynamics of a system where the relative velocity practically remains constant, there is no need for sophisticated dry friction models and even the simplest one described by the Coulomb law will suffice. However, the systems with dry friction can often exhibit more complex dynamical behaviour, such as chaotic or even stochastic responses (Den Hartog 1931; Tolstoi 1967; Shaw 1986; Popp & Stelter 1990; Wojewoda 1992; Feeny & Moon 1994; Wiercigroch 1994; Oestreich 1998; Bogacz & Ryczek 2003). Then, the chosen model must account for the transition from static to dynamic friction and should provide a means of guiding the system through zero relative velocity. Such a model should also describe hysteretic dynamical behaviour of dry friction arising from the pre-sliding displacement, the frictional lag or the non-reversibility of friction force, and other characteristic frictional phenomena like the Stribeck effect or the varying breakaway force. However, it is not easy to include all these frictional effects in a single model. It is especially difficult to define a mechanism governing the switch between the stick phase (pre-sliding) and the macroscopic sliding phase. Recently, several friction models including the above-mentioned properties have been suggested (Armstrong-Hélouvry 1991; Powell & Wiercigroch 1992; Armstrong-Hélouvry et al. 1994; Canudas de Wit et al. 1995; McMillan 1997; Liang & Feeny 1998a; Al-Bender et al. 2004); however, they are too complicated to be applied in practical engineering problems.

In this paper, we propose a simple approach to modelling of the hysteretic effects. A mathematical description of our model has been developed on the basis of experimental studies and other well-known friction characteristics. Its main advantage is a good approximation of the real nature of the friction force during macroscopic sliding motion of arbitrary type, i.e. regular, chaotic and stochastic responses. Thus, during the experimental studies, we have concentrated more on the pure sliding case (the oscillations with very short stops) rather than stick–slip motion.

The paper is organized as follows. In §2 the physical properties of the friction force are briefly described. Section 3 concerns a problem of friction modelling, which is exemplified by several existing friction models (static and dynamic). A description of the proposed model is presented in detail in §4. In §5 the experimental results and the numerical simulations performed using tested friction characteristic are compared. Section 6 contains the discussion and conclusions.

2. Friction phenomena

Friction force is a reaction in the tangential direction between a pair of contacting surfaces. Dry friction phenomenon can be treated as a result of various factors, i.e. physical properties of the material of frictional surfaces, its geometry and topology, relative velocity, and displacement of the bodies in contact.

The first description of dynamical behaviour of friction force, assuming that its constant value is independent of velocity, was formulated by Coulomb (1785). Newer experiments (from the beginning of the twentieth century) show nonlinear dependencies on the contact velocity rather than the constant one (see Stribeck 1902; Rabinowicz 1951).