Friction, classical laws

The frictional properties of TPs, specifically the reinforced and filled types, vary in a way that is unique from metals. In contrast to metals, even the highly reinforced plastics have low modulus values and thus do not behave according to the classic laws of friction. Metal-to-thermoplastic friction is characterized by adhesion and deformation resulting in frictional forces that are not proportional to load, because friction decreases as load increases, but are proportional to speed. The wear rate is generally defined as the volumetric loss of material over a given unit of time. Several mechanisms operate simultaneously to remove material from the wear interface. However, the primary mechanism is adhesive wear, which is characterized by having fine particles of plastic removed from the surface. 

The wear characteristics of one plastic as opposed to another vary widely, even among materials that have good natural lubricity. When an application calls for plastic-to-plastic bearings, shafts, gears, or other wear members, the combination of materials must be chosen carefully. Because plastics are not rigid, they do not behave according to the classic laws of friction. It is these deviations that cause some of the unexpected results when plastics are run against metals. 

The kinetics of combustion reactions turn out to be quite complicated they do not satisfy the classical law of mass action and its kinetic formulation. Neither did Duhem s formal conceptions of the existence of regions of false equilibria and of a special chemical friction, which ignores the molecular mechanism of chemical reactions, correspond to reality. 

The classical laws of friction were noted in the works of da Vinci [69, 70], Amontons [71], Coulomb [72], and Euler [73]. In simplest terms friction is the resistance to motion which occurs whenever an object slides across another surface. The laws of sliding friction may be summarized as ... 

Friction is the force that resists motion when one body slides over another. The classical laws of friction were formulated by Leonardo da Vinci and later by Amontons, with whom they are generally associated [104]. 

It was not until 1934 that it was realized that the classical laws of friction were not obeyed by rubbers and it has, hardly surprisingly, been shown that neither do plastics [6], Further... 

In addition to the surface forces (see Section 4.4), two colliding particles in a liquid medium also experience hydrodynamic interactions due to the viscous friction, which can be rather long range (operative even at distances above 100 nm). The hydrodynamic interaction among particles depends on both the type of fluid motion and the type of interfaces. The quantitative description of this interaction is based on the classical laws of mass conservation and momentum balance for the bulk phases [630-636] ... 

Fundamental to these studies are the classical laws of friction, and the basic relationship (eqn (1)) between friction il force (F) and normal force (N). 

There is scattered evidence in the literature which shows that Amontons classical laws frequently do not apply to solid film lubricants in load ranges of practical importance. This subject has been reviewed elsewhere . The failure of these classical laws has recently been demonstrated for several polymer films by Towle " and Bowers It has been found that for both organic and inorganic solid film lubricants the friction coefficient decreases markedly with increasing load approaching a small asymptotic value at very high loads. The decrease observed is sometimes as much as an order of magnitude. 

The rigidity of even highly reinforced resins is low compared to that of metals therefore, plastics do not exactly behave according to the classic laws of friction. Metal to plastic friction is characterized by adhesion and deformation of the plastic, resulting in frictional forces that are more dependent on... 

In Eyring s theory of chemical reactions (see, e.g., [6]), it is supposed that the motion of the system across the transitory state takes place according to the laws of classical mechanics, without any friction in particular, the inertial motion leads to the independence of the flow from the extent of the intermediate state in the direction of the reaction path. 

The classic Coulomb Law of Friction enjoys wide acceptance in practice due to its simplicity. However, it only reflects reality within a very small range of applications. 

Newton s law in hydrodynamics, or in flnid mechanics, models the viscous friction between fluid elements. It links what is classically called a gradient of velocity (in fact a lineic density) to the local pressure P through a coefficient 77 called dynamic viscosity. This coefficient is a scalar in isotropic media and a tensor otherwise (Phan-Tien 2002). 

To account for the nonideal nature of real soUds and liquids, the theory of Unear viscoelasticity provides a generaUzation of the two classical approaches to the mechanics of the continuum-that is, the theory of elasticity and the theory of hydromechanics of viscous Uquids. Simulation of the ideal boundary properties elastic and viscous requires mechanical models that contain a combination of the ideal element spring to describe the elastic behavior as expressed by Hooke s law, and the ideal element dash pot (damper) to simulate the viscosity of an ideal Newton Uquid, as expressed by the law of internal friction of a liquid. The former foUows the equation F = D -x (where F = force, x = extension, and D = directional force or spring constant). As D is time-invariant, the spring element stores mechanical energy without losses. The force F then corresponds to the stress a, while the extension x corresponds to the strain e to yield a = E - e. 

Term IV is the friction force applied by the fluid on the particle in a steady-state regime. As the Reynolds number is small, we recover here the classical result associated with Stokes law (Chapter 15, Table 15.1). A complementary friction term (IVcorr term) appears on the right-hand side, and is linked to the shear of the velocity field of the fluid flow. 

Classical approaches of Amonton and Coulomb are of great value In formulating the laws of friction. It Is Indeed surprising, considering on one hand, the limited number of experiments and the crude experimental facility available at that time, and on the other hand, the Inadequate knowledge of the mechanism, that the classical work has yielded viable laws of friction. 

This viscometer allows determination of the viscosity of the liquid from the velocity regime of a falling sphere. When a spherical ball (radius r) falls in a viscous liquid under gravity it tends to approach a constant velocity Vi after a transient regime. This is an important hypothesis that has to be checked (Appendix D). The movement of such a ball can be obtained from classical mechanics assuming that the sphere friction can be described by Stokes law (Appendix D). The velocity of the ball is written as... 

The material law of the near surface layer of the friction surfaces was described using the equations of the classical theory of plasticity, taking also into consideration the influence of the state faetors (temperature, strain rate, strain and stress state), which modify the plasticity and the deformability in a veiy wide range. Using unalloyed carbon steel and rapidly solidified, power metallurgy, hypereutectoidal aluminium alloy, the influence of the hydrostatic pressure on the plasticity and deformability was determined experimentally. 

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