Please refer to... Surface Friction Notes

The static friction coefficient (μ) between two solid surfaces is defined as the ratio of the tangential force (F) required to produce sliding divided by the normal force between the surfaces (N)

μ = F /N

For a horizontal surface the horizontal force (F) to move a solid resting on a flat surface

F= μ x mass of solid x g.

If a body rests on an incline plane the body is prevented from sliding down because of the frictional resistance.   If the angle of the plane is increased there will be an angle at which the body begins to slide down the plane.  This is the angle of repose and the tangent of this angle is the same as the coefficient of friction.

When the tangential force F overcomes the frictional force between two surfaces then the surfaces begins to slide relative to each other.   In the case of a body resting on a flat surface the body starts to move.    The sliding frictional resistance is normally different to the static frictional resistance.    The coefficient of sliding friction is expressed using the same formula as the static coefficient and is generally lower than the static coefficient of friction..

A table below shows approximate friction coefficients for various materials.    All values are approximate and are only suitable for guidance only.    The sliding/lubricated values must be used with extreme care.    The only way to determine the accurate coefficient of friction between two materials is to conduct experiments.  

Coefficients of friction are sensitive to atmospheric dust and humidity, oxide films, surface finish, velocity of sliding, temperature, vibration, and extent of contamination.  In many cases the degree of contamination is perhaps the most important single variable..    Link Table of Coefficients of Friction

The friction values provided are obtained by different test methods under different ambient conditions.  This factor can also affect the results. Link Test Methods

When a cylinder rolls on a surface the force resisting motion is termed rolling friction.  Rolling friction is generally considerably less than sliding friction.    If W is the weight of the cylinder converted to force, or the force between the cylinder and the flat surface, and R is radius of the cylinder and F is the force required to overcome the rolling friction then.

center>F = f x W/R

f is the coefficient of rolling friction and has the same unit of length as the radius R -in the example below m (metres)

Typical values for f are listed below

Note: Values for rolling friction from various sources are not consistent and the following values should only be used for approximate calculations.

For values of rolling bearing friction Plain Bearing Friction Values

For values of rolling bearing friction Rolling Bearing Friction Values

The coefficient of friction value is important in the design and brakes and clutches.  
Various values are provided on the following linked page Clutch/Brake Materials

The coefficient of friction is required in calculating tightening torques and resulting bolt tensile forces and stress and in calculating the resulting friction between the connected surfaces.   Below are provided a small number of values showing approximate values of friction coefficients to be used for steel screw fastened connections.   The values are only representative values and should be confirmed against other sources of information and preferably testing.

Coefficient of Friction for screw threads

Coefficient of Friction Nut/Bolt Face against Clamped surface

Coefficient of friction between surfaces clamped by bolts /screws.
These values allow calculation of the shear force necessary to cause slip between surfaces when clamped by bolts.

The following factors are typical friction factors for power screw torque and efficiency calculations..

1) Screw Thread Friction values (μ_s)
(Friction factors apply mainly for screw thread friction (μ_s) - can be applied to collar friction(μ_c)

In mechanical engineering rotary motion can be transferred by mechanical connections between a shaft and hub using only a tight fit.   Methods of achieving this type of connection include the engineered interference fit, the taper lock bush and hydraulic fit bush.   These keyless shaft/hub connections all transfer torque by friction.

The coefficient of friction used for designing these types of connections is dependent on the interface pressure, materials, surface condition, surface coatings etc.   The coefficient of friction is also dependent on the method of installation.   A different value result if the shaft is forced into the hub (force fit) compared to the value if the assemble is completed by heating the hub or freezing the shaft prior to assembly (shrink fit)...

Various values of relevant coefficients of friction are provided below;

The manufacturers of the proprietary keyless hub/shaft systems indicate that their products are based on a coefficient of friction of 0,12 for lightly oiled connections and 0,15 for dry assemblies.    These companies can provide surface coating fluids containing particles to increase the coefficient of friction i.e. coefficient of friction to 0,25 to 0,3. (ref links 1 below)

The American Gear Manufactures Association (AGMA) recommends a value of between 0,12-0,15 for hydraulically expanded hubs and 0,15-0,20 for shrink or press fit hubs.


When calculated the torque to be transmitted it is generally sufficient to use the simple equation

T= μ.π.d².L.P_c/2

d= the shaft diameter
L is the length of the interference joint.
The surface pressure P_c is calculated typically using lame's equation.

Calculators are available for obtaining the transmitted toque very conveniently.
Tribology -abc
Engineers edge - press fit calculatgor

There are a number of test methods for coefficient of frictions as some of which are listed below

It is clear that the different test methods provide different friction results..

Extreme care is needed in using friction coefficients and additional independent references should be used.   For any specific application the ideal method of determining the coefficient of friction is by trials.   A short table is included above the main table to illustrate how the coefficient of friction is affected by surface films.  When a metal surface is perfectly clean in a vacuum , the friction is much higher than the normal accepted value and seizure can easily occur.  

......The links below the tables provide further information.

The level of uncertainty of the information below is indicated by using steel on steel as an example.  Various reference sources provide values similar to the values below.(0,74 Static- 0,42 sliding)   Gieck( 7th ed) provides values of (0,15...0,30 Static - 0,10...0,30 sliding). Concise Metals Data Handbook by J.R. Davis (table 14,1) includes values (0,31 static -0,23 sliding - for steel 1032? on steel 1032?).. The same table includes a value for mild steel on mild steel of 0,62 sliding.

FOR = Flat against rotating Cylinder, FOF = Flat against flat, POF = Pin on flat, IS = inclined surface,SPOF Spherical end pin on flat.

Source of above values.... The values are checked against a variety of internet and literature sources including the links below eg Link 6-Page 16.  I have referred to books including Machinerys Handbook Eighteenth edition, Kempes Engineers Year Book 1980, Concise Metals Handbook by J.R.Davis ASM - (Good source of referenced data) and Kurt Giecks Engineering Formulas 7th Edition.. 1980, etc etc

I provide the table below as a consistent set of values for simple elements using the simplest of test methods. It can be seen that values are generally different to the values in the table above...

Friction tests in air at room temperature. (50% relative humidity)

Notes : Friction is lower when one of the materials is wet

Experimental results in the published literature show that at low normal stresses, as involved in civils design,the shear stress required to slide one rock over another varies widely between experiments.     This is because at low stress rock friction is strongly dependent on surface roughness.ref. link to "Friction of Rocks" below