# Friction, Coefficient of

## Friction, Coefficient of

the ratio of the frictional force *F* to the reaction *T* normal to the surface of contact that occurs upon application of a load that presses one body against another: / = *FIT.* The coefficient of friction is used in technical calculations to describe the frictional interaction between two bodies (*see*).

A distinction is made between the coefficients of sliding friction and rolling friction, depending on the type of movement of one body with respect to the other. In the case of sliding, in turn, a distinction is made between the coefficients of static friction, limiting friction, and sliding friction, depending on the tangential force (*see* Figure 1 in FRICTION). All these coefficients can vary within wide limits, depending on the roughness and irregularity of the surfaces and the nature of the films covering the surfaces. For an extended contact they change very little with variations in load.

Frictional pairs are classified in two groups, according to the coefficient of sliding friction: friction materials, which have large coefficients, usually 0.3–0.35 (rarely 0.5–0.6), and antifriction materials, with coefficients of 0.15–0.12 without lubrication and 0.1–0.05 with boundary lubrication.

The resistance to free rolling of a solid body such as a wheel is characterized by the coefficient of rolling friction *f _{r}*, =

*T*·

*r*/

_{d}*I*(cm), where

_{m}*T*is the normal component of the wheel’s reaction on the support,

*r*is the dynamic radius of the wheel, and

_{d}*I*is the normal load on the wheel. If a driving or braking torque acts on the wheel, then the coefficient of adhesion of the wheel to the road surface is given by the equation Ψ =

_{w}*T*/

_{x}*I*, where

_{w}*T*is the static friction that arises between the rolling wheel and the road. The coefficients

_{x}*f*and Ψ depend essentially on the nature of the rolling bodies, the character of the films covering them, and the rolling velocity. For metals (steel on steel),

_{r}*f*is usually 0.001–0.002cm.

_{r}For an automobile moving at 80 km/hr, the coefficient of friction *f _{r}* for the wheels on asphalt is 0.02 cm; it increases sharply with speed. The coefficient of adhesion Ψ on dry asphalt is up to 0.8, but in the presence of a film of water it is reduced to 0.2–0.1.

I. V. KRAGEL’SKII