Introduction to Friction

Table of Contents
1. Basic concepts and significance
2. Types of friction
3. Dry (Coulomb) friction - detailed view
4. Fluid friction (viscous friction)
5. Internal friction in solids
6. Rolling resistance
7. Energy effects, wear and heat
8. Applications and engineering significance
9. Methods to reduce or control friction
10. Methods to increase friction (when required)
11. Experimental determination of coefficients of friction
12. Simple example (qualitative)
13. Practical notes and engineering judgement
14. Summary
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Friction:

Tangential forces generated between contacting surfaces are called friction forces. Friction occurs in the interaction between all real surfaces. Whenever there is a tendency for one contacting surface to slide or move relative to another, the friction force developed acts in a direction to oppose that tendency. Friction is present throughout nature and in all machines, however accurately constructed or carefully lubricated. A machine or process in which friction is small enough to be neglected is termed ideal. When friction must be taken into account, the machine or process is termed real. In cases of sliding motion between parts, friction causes loss of mechanical energy which is dissipated as heat; friction also contributes to wear.

Basic concepts and significance

Frictional force is a tangential force acting at the contact between two bodies. It depends on the nature of the contacting surfaces and the normal force between them. Friction affects stability, power loss, safety, and service life of structures and machines. Correctly accounting for friction is essential in structural design, machine design, transportation, geotechnical engineering and many other fields.

Types of friction

• Dry (Coulomb) friction: Occurs between unlubricated solid surfaces in contact under sliding or impending sliding conditions. The frictional force is tangent to the surfaces and opposes motion or impending motion. Dry friction is also called Coulomb friction.
• Fluid friction: Occurs in fluids (liquids and gases) when adjacent layers move at different velocities. It depends on velocity gradients and the fluid's viscosity.
• Internal friction: Occurs within solids subjected to cyclic or time-dependent deformation. It is associated with energy dissipation inside a material during loading and unloading (hysteresis) and is related to plastic deformation and microstructural mechanisms.
• Rolling friction (resistance): Resistance encountered when a body rolls over a surface. It is generally much smaller than sliding friction and is related to deformation of the rolling body and/or the surface.

Dry (Coulomb) friction - detailed view

Historical note: The principles of dry friction were developed largely from experiments of Coulomb (1781) and later detailed by Morin (1831-1834).

Static and kinetic friction

Static friction acts when two bodies tend to move relative to each other but remain at rest. It has a variable magnitude up to a maximum called the limiting or maximum static friction. The limiting value is given by the relation

F_s,max = μ_s N

where μ_s is the coefficient of static friction and N is the normal reaction (normal force) at the contact.

Kinetic (dynamic) friction acts when relative sliding motion is occurring. Its magnitude is usually constant (approximately independent of sliding speed for many practical cases) and is given by

F_k = μ_k N

where μ_k is the coefficient of kinetic friction. For most material pairs, μ_s > μ_k; i.e., it generally takes a greater tangential force to initiate motion than to sustain it.

Laws and common observations for dry friction

• The frictional force is independent of the apparent area of contact for a given pair of materials and a given normal load (for many practical dry contacts).
• Frictional force is approximately proportional to the normal reaction: F ∝ N.
• For many common engineering problems the frictional force is approximately independent of sliding velocity (within a moderate velocity range); however, exceptions exist and velocity dependence can be important in some cases.
• Surface roughness and material pair strongly influence the coefficients μ_s and μ_k.

Angle of friction and friction cone

The angle of friction (φ) is the angle between the resultant contact force and the normal to the contact plane when the tangential component equals the limiting friction. It satisfies

tan φ = μ

Conceptually, the friction cone represents the range of directions of the resultant contact force for which no slipping occurs. If the resultant lies inside the cone, the contact remains without slip; if it reaches the cone surface, impending slip occurs; if it lies outside, sliding takes place.

Fluid friction (viscous friction)

Fluid friction arises because adjacent layers of a fluid move at different velocities and shear on each other. The resisting shear stress is proportional to the velocity gradient and the fluid's viscosity. For Newtonian fluids, the shear stress τ relates to the velocity gradient as

τ = μ (du/dy)

where μ (often denoted η in fluid mechanics) is the dynamic viscosity, u is velocity parallel to the layers and y is the coordinate normal to the layers. Fluid friction is central to pipe flow, boundary layers, lubrication theory and aerodynamic/ hydrodynamic resistance.

Fluid friction depends on flow regime: laminar flow follows linear viscous laws while turbulent flow exhibits additional nonlinear resistance depending on Reynolds number and surface roughness.

Internal friction in solids

Internal friction refers to energy dissipation inside a material during cyclic deformation. Highly elastic materials recover deformation with little internal friction; materials that undergo plastic deformation show greater internal friction. Internal friction is important in fatigue, damping, seismic design and materials engineering.

Rolling resistance

Rolling resistance (or rolling friction) arises primarily due to deformation of the rolling object and/or the surface, and due to hysteresis losses. The resisting force is often modelled as proportional to the normal load but with a much smaller proportionality constant than sliding friction. Rolling bearings, pneumatic tyres, and rails are areas where rolling resistance is a key design consideration.

Energy effects, wear and heat

• Energy dissipation: Work done against friction appears principally as heat, increasing temperature at contact zones and in lubricants.
• Wear: Friction produces material removal and surface damage. Wear rate depends on contact pressure, sliding distance, material properties, environment and lubrication.
• Service life and safety: Excessive friction or wear can cause failure; controlled friction can provide stability (e.g. brakes, clutches, foundations).

Applications and engineering significance

• Structures and geotechnical engineering: Friction provides shear resistance at soil-structure interfaces and between blocks, affects bearing capacity, slope stability and retaining-wall design.
• Machine design: Friction determines required power for moving parts, influences bearing selection, lubrication strategy and wear allowance.
• Transportation and brakes: Traction between tyre and road, braking force, and clutch behaviour rely on frictional principles.
• Manufacturing processes: Metal forming, machining and material handling depend on controlled friction and lubrication.
• Everyday devices: Fasteners, screws, frictional brakes, clutches, and shoe soles exploit friction intentionally.

Methods to reduce or control friction

• Lubrication: Use of oils, greases or other lubricants to form a film that reduces direct surface contact and sliding friction. Lubrication regimes include boundary, mixed and hydrodynamic lubrication.
• Smooth surface finish: Reducing surface roughness to lower asperity interactions.
• Rolling elements: Use of ball/roller bearings to convert sliding friction into rolling resistance.
• Low-friction materials/coatings: Use of polymers, PTFE, hard coatings, or surface treatments.
• Alternative supports: Air bearings, magnetic bearings or fluid film bearings to minimise contact.

Methods to increase friction (when required)

• Increase surface roughness or apply high-friction coatings.
• Higher normal load (within safe limits) increases frictional resistance since F = μN.
• Texturing or tread patterns on contact surfaces to increase grip.

Experimental determination of coefficients of friction

Common simple experiments used in engineering teaching and practice:

• Inclined plane test: A block on an adjustable plane is gradually inclined until impending motion is observed. The angle of inclination α at impending motion gives the limiting coefficient as μ = tan α.
• Horizontal pull test (sled or block): A block is pulled by a string and the pulling force is measured when motion begins and during steady sliding to determine μ_s and μ_k.

Simple example (qualitative)

Consider a block of weight W resting on a horizontal surface with normal reaction N = W. If a horizontal force F is applied, the block will remain at rest as long as F ≤ μ_s N. When F exceeds μ_s N, sliding begins and the resisting force becomes F_k = μ_k N.

Practical notes and engineering judgement

• Tabulated values of coefficients μ are available for common material pairs and conditions; these should be used with caution since surface condition, contamination and lubrication alter values.
• Design should include appropriate factors of safety for variation of frictional resistance.
• For precision machines and instruments, frictional effects may be significant even when small; careful lubrication and bearing selection are necessary.
• In geotechnical and structural engineering, interface friction properties are determined by laboratory tests and site investigations; scale and environment matter.

Summary

Friction is a ubiquitous tangential force that opposes relative motion between contacting bodies. Its main types are dry (Coulomb) friction, fluid (viscous) friction and internal friction. Dry friction is characterised by the coefficients of static and kinetic friction (μ_s, μ_k) and the relations F_s,max = μ_s N and F_k = μ_k N. The angle of friction φ satisfies tan φ = μ and helps define the friction cone. Fluid friction depends on viscosity and velocity gradients and is central to lubrication and flow resistance. In engineering practice, friction must be controlled-reduced where it causes power loss and wear, and increased where it provides necessary resistance or stability.