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Properties of Friction

Friction, Laws of Friction, and Rolling Resistance

Friction is the resistance to motion that occurs when one body moves upon another. It is defined as the force acting at the surfaces of contact that resists relative sliding.

For sliding motion, the friction force F is proportional to the normal force N. This relationship is expressed by the coefficient of friction, denoted by μ:

F = μ × N
μ = F / N

Example:
A body weighing 28 lb rests on a horizontal surface. If a force of 7 lb is required to keep it in motion:

μ = 7 / 28 = 0.25

Angle of Repose

When a body rests on an inclined plane, friction prevents it from sliding until a critical angle is reached. This angle is called the angle of repose, denoted by θ.

At this condition:

μ = tan θ

The angle of repose provides a practical experimental method for determining the coefficient of friction between two surfaces.

A greater force is required to start motion than to maintain it, because static friction is greater than kinetic friction.

Laws of Friction (Dry or Unlubricated Surfaces)

  1. For moderate pressures, friction is directly proportional to the normal force. At very high pressures, friction increases rapidly and may lead to seizure.
  2. For moderate pressures, friction is independent of the apparent area of contact, provided the normal force remains constant.
  3. At very low sliding speeds, friction is nearly independent of velocity. As speed increases, friction generally decreases.

Lubricated Surfaces

For well-lubricated surfaces, the laws of friction differ significantly from dry contact:

  1. Friction becomes almost independent of pressure when surfaces are fully flooded with lubricant.
  2. At low pressures, friction varies approximately with speed. At high pressures, friction is high at low speed, reaches a minimum, then increases again.
  3. Friction is strongly affected by temperature due to changes in lubricant viscosity and thermal expansion of bearing components.
  4. With adequate lubrication, friction depends little on surface material. As lubrication deteriorates, material properties become increasingly important.

Influence of Friction on Machine Efficiency

Friction reduces the efficiency of mechanical systems. Typical efficiencies of carefully manufactured machine elements are:

  • Plain bearings: 95–98%
  • Roller bearings: ~98%
  • Ball bearings: ~99%
  • Spur gears (including bearings): ~99%
  • Bevel gears (including bearings): ~98%
  • Belting: 96–98%
  • Roller chains: 95–97%

Coefficients of Friction

Representative values of static and sliding friction are available for various material combinations under dry and lubricated conditions.

For example:

  • Steel on steel (dry): static ≈ 0.8 → sliding ≈ 0.4
  • Steel on steel (lubricated): static ≈ 0.16 → sliding ≈ 0.03

Because friction is sensitive to surface condition, load, speed, and lubrication, design calculations should include appropriate safety factors. Critical applications should rely on testing whenever possible.

📘 Tribology & Friction Engineering Books

Rolling Friction (Rolling Resistance)

When a body rolls on a surface, the resisting force is known as rolling resistance. Let:

  • W = load on the wheel (lb)
  • r = wheel radius (in)
  • f = coefficient of rolling resistance (in)

Rolling resistance = (W × f) / r

Typical values of f:

  • Wood on wood: 0.06 in
  • Iron on iron: 0.02 in
  • Iron on granite: 0.085 in
  • Iron on asphalt: 0.15 in
  • Iron on wood: 0.22 in

The rolling resistance coefficient has units of length and is not directly comparable to sliding friction coefficients. These values should be used only for approximate calculations.

📘 Rolling Resistance & Machine Design References

Source: Google Books

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