Amonton’s laws of friction

Due to roughness effects, adherence of metals at moderate temperature and pressure is difficult to analyze. When roughnesses undergo plastic deformation, the true area of contact is proportional to the applied load P, and the adherence force F is often proportional to the load (hence the definition of an adhesion coefficient a = F/P), and independent of the apparent area of contact. These two "Laws of adhesion (41) are similar to Amonton s laws of friction. As shown by Gilbreath (42) the adhesion coefficient is very sensitive to adsorption. More precise experiments by Buckley (43,44) on single crystals in ultrahigh vacuum have shown that the adherence force does not increase linearly with the load, and that the position of the knees depends on the adsorption as if the effectively applied load depended on adsorption. 

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 ... 

Assume that Amontons s law of sliding friction can be applied at each elementary area of the interface, such that... 

Examples of materials falling into this class include salts such as sodium chloride, diamond, sapphire and other similar minerals, and solid nonmetallic elements such as krypton. The softer members of the class are generally found to obey Amonton s laws with frictional coefficients falling in the range of 0.5-1.0. The harder, more brittle substances such as sodium chloride tend to suffer extensive surface damage due to cracking but still hold more or less to normal behavior. 

Such a remarkable influence on friction obtained at the expense of only a small power may be of interest in certain applications. It is therefore interesting to study phenomenological laws of friction under these conditions. It is found that Amonton s law of proportionality between normal load and frictional force is approximately valid for given speed, temperature and applied voltage. 

Microscopic Theory of Amontons s Laws for Static Friction. 

The friction parameter generally measured is the coefficient of friction. To measure the friction coefficient, a surface is brought into contact with another and moved relative to it. When the two surfaces are brought into contact, the perpendicular force is defined as the normal force (N). The friction force (F) is that force, which opposes relative movement between the two surfaces. From Amonton s law, the coefficient of friction (/u.) is defined as the ratio of the friction force to the normal force ... 

Friction measurements can offer quantitative insight into changes on the skin surface and the UMT offers technical advances over existing friction measurements. The control of the probe speed and the real-time monitoring of the normal load allow for real-time calculation of the friction coefficient. As seen in Figure 32.1, the control of the load is important because the friction coefficient does not adhere to Amonton s Law. Wolfram18 theoretically deduced that the friction coefficient would relate to the normal load as follows ... 

The earliest attempts to explain Amontons s laws were based on the idea that macroscopic peaks or asperities on one surface interlocked with valleys on the opposing surface [1]. As illustrated in Fig. la, the bottom surface then forms a ramp that the top surface must be lifted up over in order to slide. If the typical angle of the ramp is 9, and there is no microscopic friction between the surfaces. 

Over a wide range of system parameters the dilatancy is smaller than the characteristic length A. Under this condition the generalized Prandtl Tomlinson model predicts a linear increase of the static friction with the normal load, which is in agreement with Amontons s law. It should be noted that, in contrast to the multi-asperity surfaces discussed in Section VII, here the contact area is independent of the load. The fulfillment of Amontons s law in the present model results from the enhancement of the potential corrugation, a2C7oexp(l — Z/K), experienced by the driven plate with an increase of the normal load. 

The linear dependence of friction on load established in solid friction, F = fiW, is explained in terms of the yielding mechanism i.e., the solid surface is not molecu-larly flat and the real contact area between two surfaces increases with an increase of load due to yielding. Thus, the friction has no dependence on the apparent contact area of the two solid surfaces, and Amonton s law holds [38]. 

M. H. Muser, L. Wenning, and M. O. Robbins, Simple microscopic theory of Amontons s laws for static friction. Phys. Rev. Lett, 86, 1295 (2001). 

The pressure-temperature relationship. Charles s law is expressed as the effect of a temperature change on gas volume. However, volume and pressure are interdependent, so the effect of temperature on volume is closely related to its effect on pressure (sometimes referred to as Amontons s law). Measure the pressure in your car s tires before and after a long drive, and you will find that it has increased. Frictional heating between the tire and the road increases the air temperature inside the tire, but since the tire volume doesn t change appreciably, the air exerts more pressure. Thus, at constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature ... 

The further application of Amonton s law will be dealt with later when looking at friction with solids. 

Polymer friction of the bulk polymers and that of the textile polymers follow roughly the same laws, namely that Coulomb s third law of friction (i.e.. that kinetic friction is independent of the speed of sliding) and Amonton s first law (that the frictional force is independent of the area of contact) just do not apply, especially with the thermoplastics. Instead we are faced with the discovery that with a steady increase in the speed of sliding the frictional force can increase until it reaches a point where it can drop dramatically if the friction coelTicient and the linear speed are high enough. But this will of course depend very much on the particular liber type. One illustration of this was found by D. G. Lyne... 

Such behavior is important to the understanding of frictional phenomena. It has been known since Amontons ° in the 17th century that friction, the force required to slide one solid over another, increases in proportion to the load pressing the solids together. This is clearly inconsistent with the Hertz equation for contact area. In the Hertz case, the contact diameter increases with thus the contact area increases with and therefore the friction force should also increase with, at odds with the Amontons observations. However, the behavior shown in Fig. 9.9(b), after sliding causes scratching of the surfaces, is consistent with Amonton s Law. The contact size increases with so that the contact area, and therefore friction, is then proportional to load... 

The general nature of frictional forces was recognized as early as the time of Leonardo da Vinci (in fact, earlier, but not recorded). Since then they have been rediscovered several times and formulated into laws of friction that have served well, even though they are generally found to be limited in their application. The three laws of friction, generally known as Amonton s law, can be stated as follows ... 

Amonton s law says that the frictional force F between two solids is proportional to the load W, forcing them together, i.e., F = pW [32], and does not depend on the apparent contact area A of the two solid surfaces nor on the sliding velocity v. At the same time, the proportional coefficient p, known as the frictional coefficient, depends not on the sliding velocity or on the apparent contact area of the two snrfaces bnt, rather, only on the moving materials according to this law. The proportionality constant p usually lies within a range of 0.5-1.0 [33]. However, the gel friction does not simply obey... 

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