 # Actualités

### State Laws of Dry Friction1 dûˋcembre 2022

The elementary property of slippery (kinetic) friction was discovered experimentally from the 15th to the 18th century and expressed by three empirical laws: A 30-pound sled is pulled up a 25-degree icy slope. If the static coefficient of friction between the ice and the trolley is 0.4 and the kinetic coefficient of friction is 0.3, what is the tractive force required to move the trolley constantly? The most commonly used model for dry friction is Coulomb friction. This type of friction can be divided into static friction and kinetic friction. These two types of friction are illustrated in the diagram below. First, imagine a box on a surface. A pushing force is exerted parallel to the surface and constantly increases. A gravitational force, a normal force and a frictional force also act on the box. Of course, there are various explanations for the law of friction. Some are related to the fact that for most reasonable statistical distributions of surface roughness irregularity height, the actual contact surface is approximately proportional to the normal load. This is called the Greenwood-Williamson model, which has many extensions. Other explanations highlight the plastic nature of the contact or the fractal nature of the surface roughness, for example the Archard model. There are changes to the friction law (e.g.

rate and state models with internal variables). Some physicists also claim that the law of friction is essentially wrong and that the coefficient of friction can vary greatly for the same pair of materials in contact. Research in the 20th century focused on understanding the physical mechanisms behind friction. Frank Philip Bowden and David Tabor (1950) showed that at the microscopic level, the actual contact surface between surfaces is a very small fraction of the apparent surface.  This actual contact surface, caused by bumps, increases with pressure. The development of the atomic force microscope (circa 1986) allowed scientists to study friction at the atomic scale, showing that at this scale, dry friction is the product of the shear stress between the surface and the contact surface. These two discoveries explain Monton`s first law (below); the macroscopic proportionality between the normal force and the static frictional force between dry surfaces. Viscous friction is characterized by a viscosity tensor that linearly relates the frictional force and the sliding velocity vectors. The orientations of these vectors generally do not agree for anisotropic viscosity. If the velocity vector rotates 360 degrees and forms a circle, the force vector forms an ellipse, corresponding to the tensor relationship between them, as shown in the figure below.

In most cases, the applied load is supported by the pressure generated in the fluid due to the viscous resistance to friction of the lubricating fluid between surfaces. Proper lubrication allows continuous and smooth operation of the equipment with little wear and tear and without excessive loads or cramps on the bearings. If lubrication fails, metal or other components can rub destructively on each other, causing heat and possibly damage or failure. In 2012, only one study showed the potential for an effective negative friction coefficient in the low load range, meaning that a decrease in normal force leads to an increase in friction. This contradicts the everyday experience in which an increase in normal strength leads to an increase in friction.  This was reported in October 2012 in the journal Nature and concerned friction encountered by an atomic force microscope pen when fired through a graphene layer in the presence of graphene-adsorbed oxygen.  John Leslie (1766-1832) noted a weakness in the views of Amontons and Coulomb: if friction comes from the pulling of a weight upwards from the inclined plane of successive bumps, why is it not compensated by descending the opposite slope? Leslie was equally skeptical of the membership role proposed by Desagulier, who, by and large, should have the same tendency to accelerate as to delay the movement.  According to Leslie, friction should be considered a time-dependent process of flattening and backflow of bumps that creates new obstacles in previous cavities. The work caused by friction can be reflected in deformation, wear and heat, which can affect the properties of the contact surface (even the coefficient of friction between surfaces). This can be beneficial, as with polishing.

Friction work is used to mix and assemble materials, as in friction welding. Erosion or excessive wear of counter-slip surfaces occurs when the work reaches an unacceptable level due to frictional forces. Harder corrosion particles, which get stuck between opposite surfaces in relative motion (friction), increase the wear of frictional forces. When surfaces wear out due to friction caused by work, an object`s surface fit and finish can deteriorate until it stops working properly.  For example, seizure or failure of the bearing may be due to excessive wear due to friction. Friction instabilities can lead to the formation of new self-organized patterns (or “secondary structures”) at the sliding interface, such as: Tribofilms formed in situ, which are used to reduce friction and wear in so-called self-lubricating materials.  The Greeks, including Aristotle, Vitruvius, and Pliny the Elder, were interested in causing and mitigating friction.  They were aware of the differences between static and kinetic friction, with Themistius noting in 350 AD that “it is easier to promote the movement of a moving body than to move a body at rest.”     In the reference frame of the interface between two surfaces, static friction does not work because there is never any displacement between the surfaces.

In the same frame of reference, the kinetic friction is always in the opposite direction of motion and does a negative job.  However, friction can do positive work in some frames of reference. You can see this by placing a heavy box on a carpet and then quickly pulling on the carpet. In this case, the box slides backwards relative to the carpet, but advances relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and the belt accelerates the box in the same direction as the box moves and does a positive job.  The coefficient of friction (COF), often symbolized by the Greek letter ö¥, is a dimensionless scalar value equal to the ratio of the frictional force between two bodies and the force that compresses them during or at the beginning of the slide. The coefficient of friction depends on the materials used; For example, ice on steel has a low coefficient of friction, while rubber on the road surface has a high coefficient of friction. The coefficients of friction range from near zero to more than one.

It is an axiom of the nature of friction between metal surfaces that it is greater between two surfaces of similar metals than between two surfaces of different metals ã therefore, brass has a higher coefficient of friction when moved against brass, but less when moved against steel or aluminum.  The energy losses of a system due to friction are a classic example of thermodynamic irreversibility. A plastic box rests on a steel beam. One end of the steel beam is lifted slowly, increasing the angle of the surface until the box begins to slide. If the box starts to slide, if the beam is at an angle of 41 degrees, what is the static coefficient of friction between the steel beam and the plastic box? Kinetic friction occurs beyond the point of imminent motion when the box slips. For kinetic friction, the amplitude of the frictional force opposite the motion is equal to the coefficient of kinetic friction multiplied by the normal force between the box and the surface. The kinetic coefficient of friction also depends on the two materials touching each other, but is almost always smaller than the static coefficient of friction. If the size of the compressive force continues to increase, the box eventually slips.

When the box begins to slip, the type of friction that counteracts the movement of the box changes from static friction to so-called kinetic friction. The point just before the box slips is called the upcoming movement. This can also be considered the maximum possible static frictional force before hatching. The amplitude of the maximum static friction force is equal to the static coefficient of friction multiplied by the normal force between the box and the surface. This coefficient of friction is a property that depends on both materials and can usually be looked for in tables. The normal force is defined as the net force compressing two parallel surfaces, and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where N = m g {displaystyle N=mg,}.