Machine Elements

Friction Fundamentals

All of the effects of friction involve force. The same force which keeps stationary objects in place tends to retard objects in motion. Basic concepts of the two corresponding types of friction are static and dynamic. The first is simply a tangential force associated with a nor­mal force and no work is done. The second involves both force and speed, and energy is expended. A friction element is on a rotating drum; mechanical energy is converted directly to heat at the rubbing surfaces by virtue of friction, giving the immediate effect of increasing the temperature of the rubbing materials.

Classical Approach. The coefficient of friction µ is classically defined as the tangent of the angle of repose of a body on a surface. The angle of repose, ȹ, is the maximum angle with the horizontal to which the plane surface may be inclined before the body slips down the inclined plane under the influence of gravity.

The coefficient of friction is:

 where W_t is the tangential component and P the normal component of the weight W, of the body. While the classical laws for friction are often quoted and are of use in the study of friction theory, they have less significance in practice where heavy pressures are used at high speeds and temperatures. Although friction has been thought to be independent of area and speed, friction elements nevertheless exhibit coefficients of friction which vary with speed, pressure, and tempera­ture. It is not sufficient to talk about the coefficient of friction of two rubbing surfaces as a single unvarying figure.

In the study of commercial friction elements and mechanisms, it is not possible to determine the coefficient of friction in the classical manner, nor does it have the same meaning as in the classical sense. Under dynamic friction conditions the weight of the friction element is replaced by the pressure with which two surfaces are applied to each other. The inclined plane, which appears to be boundless in the classical analogy, is replaced by a drum in the automobile brake and an opposing disc in the clutch. Classically, the static breakaway friction is measured. From a practical standpoint, however, dynamic engagement and breakaway friction conditions are important in a clutch, while kinetic friction of slipping surfaces and static breakaway friction at rest are important in a brake. In a classical example, there is no tempera­ture problem; the temperature of the two rubbing surfaces is assumed to be the ambient temperature, and no heat is generated by the rubbing surfaces.

However, in practical application, the purpose of a friction element is to absorb energy. In fact, the energy to be absorbed in the friction mechanism of an airplane brake is often quite large.

In view of the discrepancy between the classical and practical inter­pretations of friction, it is necessary to re-evaluate the concepts. The phenomena observed by the early French physicist, Amontons, on the effect of pressure and by Coulomb on the effect of velocity were of scientific value but the friction element of today requires evaluation under much more severe conditions.

Mechanism of Friction. Several factors contribute to the phenom­enon of friction. These are adhesion, cohesion, abrasion and elastic deformation.

The friction of adhesion is similar to that involving a fluid or a viscous mass. The friction of one’s hand on glass or on a varnished tabletop is high, but it is friction which increases with the time the hand is allowed to rest on the surface. Here, the pores of the skin adhere to the table top like suction cups, if a very small amount of moisture is present to complete the seal. The adhesion can be broken by spreading a little powder on the hand.

Cohesion, the second factor, is the phenomenon by which surfaces of compatible metals become welded together. Fusion welding causes cohesion over large areas, but the welding resulting from friction occurs over extremely small contact areas. Thus, metal may cohere with metal, but it is difficult to conceive of the coherence of cloth with metal. Nor is it generally conceivable that the resin in a molded brake lining will cohere with the metal brake drum, but resin will cohere with resin. Copper will cohere with copper, and iron or steel will cohere with the same. Most mutually soluble metals, in fact, will cohere.

The third factor contributing to friction is mechanical abrasion. It is the same effect as that required by a cutting tool, which plows through an object, displacing or removing a quantity of metal. In such a manner, a diamond point embedded in a lough material and dragged across a soft surface will score the surface, leaving a trough from which material has been removed or a trench banked by displaced met­al. This effect involves a measurable force, and even though the scratch may be minute, the sum of the forces necessary to make many scratches in a surface is considerable. Friction material manufacturers sometimes find it necessary to include in their composition small amounts of abra­sive material which tend to mark the opposing surface and may contrib­ute to the friction.

The fourth factor is the elastic and plastic deformation induced by a load moving over a surface. The friction force resulting from defor­mation is not very important in the case of two discs engaging each other. It is a well known fact that in the two-shoe internal-expanding brake there is a definite tendency for the brake drum to go out of round, becoming elliptical in shape during braking. The force necessary to maintain the ellipticity of the drum during rapid rotation is considerable, and contributes to the friction force.

Contributing Factors. With the realization that the modern fric­tion mechanism is essentially an engine in which mechanical energy is converted to heat, it is well to survey the interrelation of friction and wear rate of the friction materials. There are several basic factors affecting friction and wear, which must be analyzed and considered. The most important of these is pressure. Many of the organic or molded friction materials exhibit no change in friction with pressure, but some of the sintered-metal materials suffer a decrease in friction as the pres­sure on the lining increases. The coefficient of friction of one material decreases from about 0.3 at 20-psi plate pressure to about 0.22 at 200 psi.

For metallic materials to have friction, decreasing with increasing speed is common. The effect of speed on friction is not limited to sint­ered metal, but is noticeably evident in the cast-iron railroad brake shoe where it is not only a fact that the average friction from a 100-mph stop is much less than from a 40-mph stop, but it is very desirable and necessary. In the case of the railroad wheel, the curve of the retarding force of the brake should be parallel to the curve of the adhesion of the wheel to the rail. For railroad applications, adhesion is expressed as Fa /L where Fa is the force required to cause the wheel to slip on the rail and L is the wheel load.

Adhesion becomes very much lower as the speed of the wheel increases, mainly because high speed causes the pressure of the wheel against the rail to be increasingly variable. If, during a “bounce” of the wheel when the normal pressure is relatively light, the brake shoe should have sufficient friction to grab the wheel, then a slide which would continue until the brake pressure was released would be initiated. This action is fully explained by the great difference between static and dynamic friction of the metal brake shoe against the wheel, and the wheel against the rail. If the wheel is in rolling, not sliding, con­tact with the rail, the friction is high and the lower sliding friction of the brake shoe against the wheel may continue. As soon as the brake shoe is able to grab the wheel and force it into sliding contact with the rail, the system tends to remain in this condition until the brake is released. Therefore, it is advantageous to have the coefficient of friction of brake and wheel dropping with increased speed, as does the adhesion.

There is a parallel to this situation in the case of the automobile, but the treatment is different. Whereas the railroad brake is applied with a mechanical pressure which is not sensitive to the results obtain­ed, automobile brakes are controlled by human beings who gage the pressure to be applied by its effects. If the tires lose their adhesion, the operator releases the brake pressure enough to restore the ground-to-tire adhesion and then increases the pressure to obtain the full effect of rolling braking.

Beyond the effects of speed and pressure, temperature seems to have an independent effect on the coefficient of friction. The magnitude of the effect of temperature varies with the material and may be great­er than that of either pressure or speed. Thus, it is possible for one material to show a moderate increase in friction as temperature increas­es, while another may do just the reverse. To separate completely the effect of pressure and speed changes from the effects of temperature changes is probably impossible, because if pressure is constant and speed is increased, the surface temperature will increase. Similarly, if the speed is kept constant and the pressure is increased, there will be a corresponding increase in the amount of power, resulting in higher temperature.

Wear Rate. The subject of wear is abroad one, since it is affect­ed by many complex interrelated factors. There appears, however, to be a very close relation between the wear of a particular material and the amount of work done in the braking or clutch application. Under conditions which are not extreme, the rate of wear of a constantly dragging friction element will increase in nearly a straight line with increasing speed. Similarly, the work done by a friction element drag­ging at a constant speed and variable pressure will increase in direct relation with pressure.

If, on the other hand, a braking stop is considered in which a vehicle of given weight is decelerated to rest from a given speed, the energy converted to heat during the stop varies with the square of the initial speed. Thus, the energy, and the wear on friction elements, in a stop from 100 mph are four times as much as when the same vehicle is stopped from 50 mph. If, in the same example, the deceleration rate is increased by increasing the pressure, the energy of the stop remains the same, and the wear would at first be expected to be the same. Because energy is absorbed at a faster rate, however, the surface tem­perature will be higher and the wear for the stop will be greater.

Higher temperature of the rubbing surfaces causes higher wear rate. With organic materials such as paper, cloth, cork, and leather, the permissible temperature rise is limited by the possibility of chemical deterioration, which destroys the friction element. Resin-bonded, molded-asbestos friction elements are capable of higher operating temperatures and because their thermal insulating capacity is great, they deteriorate slowly. In the case of metallic friction, materials there are no internal chemical changes before the melting point, and deterioration can only come from oxidation or physical changes. At the same time, however, other characteristics of these materials may have a compensating influ­ence on selection for a particular application.

Surface Temperature. While it is reasonably easy to measure the speed of rubbing surfaces and to estimate the pressure, the temperature of a pair of rubbing surfaces is difficult to determine. Specialists in friction analysis have never come to agreement as to where or how temperature should be measured, nor have they agreed as to what it means if it is measured. It may be said with reasonable assurance of acceptance that there is no such thing as the temperature of the rubbing surfaces. There is, without doubt, a range of temperature.

The lowest temperature of the surface may be the extrapolated value of a curve, which may be determined experimentally by measuring with thermocouples the temperature at a series of points successively closer to the surface. The maximum temperature of the rubbing surfaces will be the melting temperature of the lowest-melting-point major metal. Thus, if the brake lining is pure copper and the drum material pure iron, the maximum temperature of the interface will be the melting temperature of copper. The degree of approach of the minimum temper­ature to the maximum will depend upon the amount of energy to be absorbed by the friction mechanism and upon the time involved.

A cautious and reasonable approach to the temperature question will help in correctly appraising the effects of heavy duty braking un­der extreme energy absorption service. The immediate effect of high temperature in a brake is wear, either on the brake lining or the drum.

High-temperature resistance to wear is increased in molded linings by increasing the amount of inorganic material, such as metals, gra­phite, oxides, and ceramics, in the lining. Near the surface, if the or­ganic binder is destroyed by heat, the ceramic fillers remain and con­tinue to have body and friction properties. The melting temperature of the remaining ceramics is relatively high, and may be higher than that of the steel. If the latter is true, then scoring and general damage to the drum may ensue, because the maximum temperature reached at the surface will be the melting temperature of the drum, instead of the lining. If sintered-metal linings are employed, and the melting point of the matrix metal is substantially lower than that of the drum, it is not likely that the metal lining will damage the drum for reason of high melting point.