# Sliding friction

Sliding friction is defined as the phenomenon of resistance to motion due to the sliding between the surfaces of two material bodies in contact which have a certain surface roughness.

In the case of immobility related to contact, the inclination (angle of friction) of the force exchanged between the common points of two bodies can take any of the values between zero and a maximum, which depends on the conditions that characterize the contact locally.

For this kinematic condition, the inclination of the contact force is determined exclusively by the condition of equilibrium with the other forces urging the body, arbitrarily chosen, and is independent of the characteristics of the contact, as long as the action useful to obtain the equilibrium is developed in contact.

In other words, a tangential action is defined as sliding friction in the case of relative motion; while adhesion is defined as that between elements in contact in the absence of sliding.

## Forms sliding friction

The extent of friction and the friction coefficient depends on the geometric, kinematic and dynamic conditions that arise in contact between the surfaces of the bodies, but in particular, it is extremely sensitive to the chemical and physical state of the parts in contact.

Imperceptible changes in this state can cause as many variations in the friction coefficient of the order of hundreds of times. For this reason, the possibility of encountering significant variations in the friction coefficient for minimal and often uncontrollable causes must always be kept in mind when machines and related mechanisms operating, especially for safety issues. There are at least three forms of sliding friction:

1. dry friction between bodies: between solids with a clean surface (in the chemical meaning, ie at the single monomolecular layer level). For dry bodies, Coulomb experimentally deduced that the frictional resistance is proportional to the perpendicular load and does not depend on the sliding speed or the extension of the contact surface, while it depends only on the nature of the materials. The characteristic manifestation of the sliding friction is the deviation of the perpendicular of the line of action of the contact force so that the force component in the tangent plane is directly opposite to the relative speed of the body to which it is applied (with respect to the body to be where it comes from); the amplitude of the deviation depends only on the nature of the materials. In fact, due to the geometric characteristics, the state of surface finish also influences, that is, the greater or lesser relief of the small and extensive irregularities of the surface;
2. friction between perfectly lubricated bodies: it is characterized by the presence between the two solids of a layer of lubricating fluid which, while being of small thickness, admits sliding of thin fluid layers on the inside, making sure that between the two bodies there is no direct contact. The dynamic connection is established exclusively through the lubricant layer, and therefore the force applied to each of the two bodies follows laws expressing exclusive properties of the fluid. It is for this reason that the friction magnitude of this form, is greatly influenced by the sliding velocity and the temperature of the lubricant, this, in turn, being dependent on the work dissipated by friction within the fluid layer. It can be observed that even the air can creep between the facing surfaces and act as a lubricant, developing significant forces on them due to the rapid relative motion;
3. friction between bodies coated with a layer whose smallness is the extreme conceivable: the thickness of a single molecule, or even of only a few molecules. The coating usually consists of lubricant molecules, for example oils or greases. These molecules have an active end and stick to it orthogonally to the surface with great greed and strength; they can also join together in the form of chain links, together forming a layer similar to that of the threads of a fabric and having a very strong resistance to tearing, neither more nor less than a solid layer.

## Influence of speed

The independence of the friction coefficient from speed is approximate and can be considered admissible only for modest speed variations. In fact, the range of variation of the sliding speed for which there is a fundamental interest in knowing the behavior of the friction coefficient is extremely extensive: from values below one millimeter per second, up to values in the order of a hundred meters per second, as for example happens for wheels and brakes.

Different behaviors of friction can take place, it can be said that starting from the lowest speeds, the friction coefficient between dry bodies first decreases significantly, and then grows already starting from speed values of the order of one centimeter per second. When the speed becomes of the order of one meter per second and more, the friction coefficient value decreases again.

## Influence of pressure

Even pressure can contribute to characterizing the value of the friction coefficient: in fact, it produces an alteration of the shape of the surfaces in contact. Starting from the lowest values to end at values corresponding to the limit of permanent crushing deformation, as in the case of extremely localized (point-like) contacts. For example, enormous pressures occur in the contact between wheel and rail of railway vehicles and in that between the rolling elements of roller and ball bearings.

However, the variation of the friction coefficient as the pressure changes is relatively modest. Often with the increase in pressure starting from very small values, the friction coefficient first slightly decreases while towards maximum pressures there is a significant increase in the friction coefficient.

## Fluidostatic effect of pressure

If on the contact surface between two bodies there is the presence of fluid, among all the forces involved that develop, it is also necessary to consider that of the action of the fluid, in particular the fluidostatic force.

If no trace of the fluid is present at the mating surfaces of two bodies, then the static action of the fluid will be absent. It is observed that during the relative motion, and more easily the faster it is, the instantaneous expulsion of the fluid from limited portions of the surface can occur. This is one of the reasons why there are anomalies and irregularities in the extent of friction.

## Effect of molecular actions

The local load on the contact surface elements expressed as a unitary pressure can also be very large. The extreme proximity of the material elements allows the manifestation to an appreciable extent of molecular actions, of the type of adhesion and cohesion.

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