Laws of friction

The basic law of friction has been known for some time. Amontons was, in fact, preceded by Leonardo da Vinci, whose notebook illustrates with sketches that the coefficient of friction is independent of the apparent area of contact (see Refs. 2 and 3). It is only relatively recently, however, that the probably correct explanation has become generally accepted. 

Here we have neglected derivatives of the local velocity of third and higher orders. Equation (A3.1.23) has the fonn of the phenomenological Newton s law of friction... 

DaVinci s experiments on friction also formed the basis for what today are called the first two laws of friction ... 

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. 

Scientific studies of friction can be traced back to several hundreds years ago when the pioneers, Leonardo da Vinci (1452-1519), Amontons (1699), and Coulomb (1785), established the law of friction that "friction is proportional to the normal load and independent of the nominal area of contact, which are still being taught today in schools. Since then, scientists and engineers have been trying to answer two fundamental questions where friction comes from and why it exhibits such a behavior as described above. Impressive progress has been made but the mystery of friction has not been resolved yet. In an attempt to interpret the origin of... 

It would appear that no account of friction is complete without first stating Leonardo da Vinci s (or Amonton s) laws and Coulomb s law of friction and pointing out that, in general, polymers do not obey them. The laws are ... 

Figure 11.1 Amontons Law of Friction the frictional Force does not depend on the contact area and is proportional to the load.

For both cases, the assumption that friction is proportional to the true contact area Areai directly leads to Amontons law of friction. 

Friction is the tangential resistance offered to the sliding of one solid over another, due to dry friction. Friction is an apparently simple phenomenon with very complex mechanisms that take place on a variety of length scales, from atomic to nano and up. The study of friction is part of the engineering-scientific discipline of tribology,3 which is the scientific study of friction, wear, and lubrication (6). It was Leonardo da Vinci (1452-1519) who discovered the first two laws of friction, namely, that the area of contact has no effect on friction and that friction is proportional to the load. These two laws were rediscovered later by Guillaume Amontons (1663-1705), and later Charles-Augustin Coulomb (1736-1806), added the third law ... 

Bowden and Tabor (7) suggested a physical explanation for the observed laws of friction. They determined that the true area of contact is but a small fraction of the apparent area of contact, because the surfaces of even the most highly polished material show irregularities appreciably larger than atomic dimensions called in the literature asperities, as shown in Fig. 4.3. Thus, with increasing normal load, more asperities come in contact and the average area of contact grows, as shown in Fig. 4.4... 

The proportionality between the area of real contact and the applied load supplies at last a rational explanation of the well-known Amontons 1 or Coulomb s2 law of friction, that the frictional force F is directly proportional to the total load P pressing the surfaces together. The meaning of this law has long been mysterious. Under ordinary circumstances the law holds fairly accurately, i.e. there exists a nearly constant coefficient of friction, /x = F/P. The frictional force is naturally proportional to the total area of these bridges consequently the frictional force should be proportional to the load. 

A first approach to take into account the solvent s effect on the absolute mobility of an ion was made by Walden. It is based on the Stokes law of frictional resistance. Walden s rule states that the product of absolute mobility and solvent viscosity is constant. It is clear that the serious limitation of this model is that it does not consider specific solvation effects, because it is based on the sphere-in-continuum model. However, it delivers an appropriate explanation for the fact that, within a given solvent, the mobility depends on temperature to the same extent as the viscosity (in water, for example, the mobility increases by about 2.5% per degree Kelvin). The mobilities do not deviate too... 

A third central issue concerns the relationship between friction and the normal force or load L that pushes the two objects together. The macroscopic laws of friction found in textbooks were first published by the French engineer Amontons about 300 years ago [14], albeit the first recorded studies go back even further to the Italian genius da Vinci. Both found that the friction Fj between two solid bodies is (i) independent of the (apparent) area of contact and (ii) proportional to L. These laws can be summarized in the equation... 

Coulomb contributed what is often called the third law of friction, i.e. that is relatively independent of sliding velocity. The experiments discussed in Section I.D show that the actual dependence is logarithmic in many experimental systems and that often increases with decreasing velocity. Thus there is a fundamental difference between kinetic friction and viscous or drag forces that decrease to zero linearly with v. A nearly constant kinetic friction implies that motion does not become adiabatic even as the center-of-mass velocity decreases to zero, and the system is never in the linear response regime described by the fluctuation dissipation theorem. Why and how this behavior occurs is closely related to the second issue raised above. 

Fig. 1.27 Illustration of Newton s Law of friction. A linear velocity gradient results of sliding liquid layers...

Liquids for which Newton s Law of friction according to equation (1.41) does not apply, are known as non-Newlonian fluids. 

A borderline case of viscoelastic behavior is the so-called linear viscoelastic behavior. which is observed upon small deformations / and deformation rates . For such behavior the viscous contribution follows the Newton Law of friction (r = )... 

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 defined as the resistance encountered when one body moves tangentially over another and they are in contact. Friction often embraces two classes of relative motion sliding and rolling. In industrial processes, frictional energy is usually dissipated as waste heat. The friction force is represented by F and the friction coefficient by p. Under many sliding conditions, the p for a given pair of materials and fixed conditions of lubrication is mostly constant. The three laws of friction are ... 

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