Properties of Friction

Friction is the resistance to motion that takes place when one body is moved upon
another, and is generally defined as “that force which acts between two bodies at their surface
of contact, so as to resist their sliding on each other.” According to the conditions
under which sliding occurs, the force of friction, F, bears a certain relation to the force
between the two bodies called the normal force N. The relation between force of friction
and normal force is given by the coefficient of friction, generally denoted by the Greek letter
μ. Thus:
A body weighing 28 pounds rests on a horizontal surface. The force required to keep it in
motion along the surface is 7 pounds. Find the coefficient of friction.
If a body is placed on an inclined plane, the friction between the body and the plane will
prevent it from sliding down the inclined surface, provided the angle of the plane with the
horizontal is not too great. There will be a certain angle, however, at which the body will
just barely be able to remain stationary, the frictional resistance being very nearly overcome
by the tendency of the body to slide down. This angle is termed the angle of repose,
and the tangent of this angle equals the coefficient of friction. The angle of repose is frequently
denoted by the Greek letter θ. Thus, μ = tan θ.
A greater force is required to start a body moving from a state of rest than to merely keep
it in motion, because the friction of rest is greater than the friction of motion.
Laws of Friction.—The laws of friction for unlubricated or dry surfaces are summarized
in the following statements.
1) For low pressures (normal force per unit area) the friction is directly proportional to
the normal force between the two surfaces. As the pressure increases, the friction does not
rise proportionally; but when the pressure becomes abnormally high, the friction increases
at a rapid rate until seizing takes place.
2) The friction both in its total amount and its coefficient is independent of the areas in
contact, so long as the normal force remains the same. This is true for moderate pressures
only. For high pressures, this law is modified in the same way as in the first case.
3) At very low velocities the friction is independent of the velocity of rubbing. As the
velocities increase, the friction decreases.
Lubricated Surfaces: For well lubricated surfaces, the laws of friction are considerably
different from those governing dry or poorly lubricated surfaces.
1) The frictional resistance is almost independent of the pressure (normal force per unit
area) if the surfaces are flooded with oil.
2) The friction varies directly as the speed, at low pressures; but for high pressures the
friction is very great at low velocities, approaching a minimum at about two feet per second
linear velocity, and afterwards increasing approximately as the square root of the speed.
3) For well lubricated surfaces the frictional resistance depends, to a very great extent, on
the temperature, partly because of the change in the viscosity of the oil and partly because,
for a journal bearing, the diameter of the bearing increases with the rise of temperature
more rapidly than the diameter of the shaft, thus relieving the bearing of side pressure.
4) If the bearing surfaces are flooded with oil, the friction is almost independent of the
nature of the material of the surfaces in contact. As the lubrication becomes less ample, the
coefficient of friction becomes more dependent upon the material of the surfaces.
F = μ × N and μ F
N= ---μ FN---728= = ----- = 0.25
FRICTION AND WEAR 191
Influence of Friction on the Efficiency of Small Machine Elements.—Frict ion
between machine parts lowers the efficiency of a machine. Average values of the efficiency,
in per cent, of the most common machine elements when carefully made are ordinary
bearings, 95 to 98; roller bearings, 98; ball bearings, 99; spur gears with cut teeth,
including bearings, 99; bevel gears with cut teeth, including bearings, 98; belting, from 96
to 98; high-class silent power transmission chain, 97 to 99; roller chains, 95 to 97.
Coefficients of Friction.—Tables 1 and 2 provide representative values of static friction
for various combinations of materials with dry (clean, unlubricated) and lubricated surfaces.
The values for static or breakaway friction shown in these tables will generally be
higher than the subsequent or sliding friction. Typically, the steel-on-steel static coefficient
of 0.8 unlubricated will drop to 0.4 when sliding has been initiated; with oil lubrication,
the value will drop from 0.16 to 0.03.
Many factors affect friction, and even slight deviations from normal or test conditions
can produce wide variations. Accordingly, when using friction coefficients in design calculations,
due allowance or factors of safety should be considered, and in critical applications,
specific tests conducted to provide specific coefficients for material, geometry,
and/or lubricant combinations.