Amontons law of friction

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. 

Neither departure from Amontons laws of friction nor the occurrence of values greater than 0.2 for the coefficient of friction should be regarded as aberrations from a fundamentally ideal mode of frictional behavior. The theoretical basis of friction can be extended to these cases. To avoid the restrictions imposed by a limiting value of 0.2 for... 

Since the contact area is proportional to the normal force, we obtain an equation known as Amontons law of friction [31] ... 

The Young s modulus of the film can be obtained from the tangential traction for a sphere-plane contact given by the Hertz theory and Amontons law of friction (49) ... 

For both the Bowden-Tabor and the Greenwood-Williamson models, the assumption that friction is proportional to the true contact area directly leads to Amontons law of friction. Except for very soft elastic materials, one will always expect a mixture of elastic and plastic deformations. There may even occur a paradoxical situation in which deformation occurs plastically initially at low loads... 

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. 

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 ... 

Amontons law of macroscopic, dry friction states that the friction force is proportional to the load and does not depend on the apparent contact area ... 

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 ... 

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 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... 

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 ... 

It is now accepted that friction between two solid surfaces is due to the opposition of surface asperities on the one hand and surface adhesion on the other. Friction is independent of the contact area (Amontons law). The friction force is measured as the resistance opposed to the movement of a body submitted to both a vertical pressure P and a horizontal force F (Fig. 17). The friction coefficient is defined by the relation = F/P. 

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]. 

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... 

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 ... 

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. 

Figure 3 shows the total load dependence of the friction force measured for modulation amplitudes of 50nm and lOOnm. The contact location was arbitrarily chosen on the same surface. Both curves are described by the same Amontons law. The friction coefficient defined by the slope of the linear fit is )li=0.087 0.001. When plotted as the friction force versus the total load, the intercept is zero. It is important at this point to specify that the error associated to the friction coefficient arises from the fitting analysis of our data, which therefore, determines the precision of the experiment and not the overall acuracy of the experiment. Indeed, the main source of uncertainty in our measurements originates in the precision in the cantilever metrics measured by optical microscopy and SEM which is of the order of 3% to 5%. Some other sources (19,28), like the position of the laser spot on the backside of the cantilever affects the absolute accuracy of the friction measurements to an extend that is difficult to evaluate. We expect the overall accuracy on the friction measurement to be less than 60%(25). Nevertheless, since the crucial experimental conditions were optimized and kept constant from an experiment to the other, the comparison remains valid. 

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. 

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. 

One important factor that affects the fiber-on-fiber friction is the normal force. According to the Amontons law, the friction coefficient should be a constant and is independent of the normal force. However, the fiber-on-fiber friction does not obey the Amontons law. Figure 19.4 shows the effect of normal force on the friction coefficient between fibers. The friction coefficient of fibers decreases with increase in normal force. This behavior may be explained by the elastic deformation of surface asperities on fibers. The relationship between fiber-on-fiber friction force and normal force can be described by using an empirical equation ... 

The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

Although friction between objects is a matter of everyday experience, it is curious that Amontons law, although of fairly good general validity, seems... 

Thus if Amontons law is obeyed, the initial velocity is determined entirely by the coefficient of friction and the length of the skid marks. The mass of the vehicle is not involved, neither is the size or width of the tire treads, nor how hard the brakes were applied, so long as the application is sufficient to maintain skidding. 

Substances in this category include Krypton, sodium chloride, and diamond, as examples, and it is not surprising that differences in detail as to frictional behavior do occur. The softer solids tend to obey Amontons law with /i values in the normal range of 0.5-1.0, provided they are not too near their melting points. Ionic crystals, such as sodium chloride, tend to show irreversible surface damage, in the form of cracks, owing to their brittleness, but still tend to obey Amontons law. This suggests that the area of contact is mainly determined by plastic flow rather than by elastic deformation. 

TWo limiting conditions exist where lubrication is used. In the first case, the oil film is thick enough so that the surface regions are essentially independent of each other, and the coefficient of friction depends on the hydrodynamic properties, especially the viscosity, of the oil. Amontons law is not involved in this situation, nor is the specific nature of the solid surfaces. 

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