# Coefficients Of Friction

### Friction Factors

Note: I have tried to include a wide range of relevant information on this topic.  It will be noted that friction values in one section do not necessarily agree with values in another section...Please use the linked references at the bottom of the page for more detailed information.

Factors affecting the friction between surfaces

Dry surfaces

1. For low surface pressures the friction is directly proportional to the pressure between the surfaces.  As the pressure rises the friction factor rises slightly. At very high pressure the friction factor then quickly increases to seizing
2. For low surface pressures the coefficient of friction is independent of surface area.
3. At low velocities the friction is independent of the relative surface velocity.  At higher velocities the coefficent of friction decreases.

Well lubricated surfaces

1. The friction resistance is almost independent of the specific pressure between the surfaces.
2. At low pressures the friction varies directly as the relative surface speed
3. At high pressures the friction is high at low velocities falling as the velocity increases to a minimum at about 0,6m/s.  The friction then rises in proportion the velocity 2.
4. The friction is not so dependent of the surface materials
5. The friction is related to the temperature which affects the viscosity of the lubricant

Please refer to... Surface Friction Notes

Static Coefficient of Friction

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.

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Sliding 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..

Friction Coefficients

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

Rolling Friction

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.

• Steel on Steel f = 0,0005m
• Wood on Steel f = 0,0012m
• Wood on Wood f = 0,0015m
• Iron on iron f = 0,00051m
• Iron on granite f = 0,0021m
• Iron on Wood f = 0,0056m
• Polymer on steel f = 0,002m
• Hardrubber on Steel f = 0,0077m
• Hardrubber on Concrete f = 0,01 -0,02m
• Rubber on Concrete f = 0,015 -0,035m

Plain Bearing Friction factors

For values of rolling bearing friction Plain Bearing Friction Values

Rolling Bearing Friction

For values of rolling bearing friction Rolling Bearing Friction Values

Clutch - Brake 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

Friction coefficient Bolted Joints

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

 Female Thread -Nut or Tapped Hole in steel(untreated) Male screw Friction Coefficient (Dry) Friction Coefficient (lub) Untreated Steel 0,12 - 0,18 0,10 - 0,17 Phosphated Steel 0,12 - 0,18 0,10 - 0,17 Cadmium Plated Steel 0,09 - 0,14 0,08 -0,23 Galvanised steel 0,14 - 0,23 0,12 - 0,2 Degreased steel 0,19 - 0,25 Female Thread -Nut or Tapped Hole in steel(Galvanised) Male screw Friction Coeffient (Dry) Friction Coefficient(Lub.) Untreated Steel 0,14 - 0,2 0,12 - 0,18 Phosphated Steel 0,14 - 0,2 0,12 - 0,18 Cadmium Plated Steel 0,1 - 0,16 0,09 - 0,15 Galvanised steel 0,14 - 0,25 0,12 - 0,2 Degreased steel 0,19 - 0,25

Coefficient of Friction Nut/Bolt Face against Clamped surface

 Clamped Surface = Steel Bolt/Nut Mat'l Friction Coeffient (Dry) Friction Coefficient(Lub.) Untreated Steel 0,10 - 0,18 0,08 - 0.15 Phosphated Steel 0,10 - 0,18 0,08 - 0,15 Galvanised steel 0,10 - 0,2 0,09 - 0,18 Clamped Surface -Galvanised Steel Bolt/Nut Mat'l Friction Coefficient (Dry) Friction Coefficient (lub) Untreated Steel 0,10 - 0,18 0,08 - 0,15 Phosphated Steel 0,10 - 0,18 0,08 - 0,15 Galvanised steel 0,16 - 0,22 0,09 - 0,18

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.

 Contact Surfaces slip coefficient Steel On Steel- No treatment 0,15- 0,25 Steel On Cast Iron- No treatment 0,18 - 0,3 Steel On Steel- Machined (Degreased) 0,12- 0,18 Steel On Cast Iron- Machined (Degreased) 0,15 - 0,25 Grit -Sandblasted surfaces 0,48 - 0,55

Friction Factors for Power Screws

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

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

 Screw Material Nut Material Steel Brass Bronze Cast Iron Steel(Dry) 0,15-0,25 0,15-0,23 0,15-0,19 0,15-0,25 Steel (Lubricated) 0,11-0,17 0,10-0,16 0,10-0,15 0,11-0,17 Bronze (Lubricated) 0,08-0,12 0,04-0,06 - 0,06-0,09
2) Thrust collar Friction values (μc)
 Surface Combinations Moving Starting Soft Steel on Cast Iron 0,12 0,17 Hard Steel on Cast Iron 0,09 0,15 Soft Steel on Bronze 0,08 0,10 Hard Steel on Bronze 0,06 0,08

Press Fit Mechanical Joints

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;

• Steel Hub , Steel Shaft unlubricated - force fit ...C. of Friction = 0,07 to 0,16
• Steel Hub , Steel Shaft greased - force fit ...C. of Friction = 0,05 to 0,12
• Steel Hub , Steel Shaft unlubricated - Shrink fit ...C. of Friction = 0,15 to 0,25
• Steel Hub , Steel Shaft greased - Shrink fit ...C. of Friction = 0,08 to 0,16

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.Pc/2

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

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

Testing Methods

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

• Flat block pressed against a OD of rotating ring (FOR)
• Flat block against another flat block (FOF)
• Flat block sliding down an inclined runway(IS)
• Pin pressed against a OD of rotating ring (POR
• Reciprocating loaded spherical end pin pressed on a flat surface(RSOF)

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

Coefficient of Friction

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.

 Effect of oxide film etc on coefficient of static friction Material Clean Dry Thick Oxide Film Sulfide Film Steel-Steel 0,78 0,27 0,39 Copper-Copper 1,21 0,76 0,74

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

Table of friction Values for elements

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)

 Fixed Surface Moving Block Friction coefficient Test Method Static Sliding Silver (Ag) Silver (Ag) 0,5 Incline Plane Gold(Au) 0,53 Incline Plane Copper(Cu) 0,48 Incline Plane Iron(Fe) 0,49 Incline Plane Aluminium(Al) Aluminium(Al) 0,57 Incline Plane Titanium (Ti) 0,54 Incline Plane Gold(au) Silver (Ag) 0,53 Incline Plane Gold(Au) 0,49 Incline Plane Cadmium(Cd) Cadmium(Cd) 0,79 Incline Plane Iron(Fe) 0,52 Incline Plane Cobalt(Co) Cobalt(Co) 0,56 Incline Plane Chromium(Cr) 0,41 Incline Plane Chromium(Cr) Cobalt(Co) 0,41 Incline Plane Chromium(Cr) 0,46 Incline Plane Copper(Cu) Cobalt(Co) 0,44 Incline Plane Chromium(Cr) 0,46 Incline Plane Copper(Cu) 0,55 Incline Plane Iron(Fe) 0,50 Incline Plane Nickel(Ni) 0,49 Incline Plane Zinc(Zn) 0,56 Incline Plane Iron(Fe) Cobalt(Co) 0,41 Incline Plane Chromium(Cr) 0,48 Incline Plane Iron(Fe) 0,51 Incline Plane Maganese(Mg) 0,51 Incline Plane Molybdenum(Mo) 0,46 Incline Plane Titanium(Ti) 0,49 Incline Plane Tungsten(W) 0,47 Incline Plane Zinc(Zn) 0,55 Incline Plane Indium(In) Indium(In) 1,46 Incline Plane Maganese(Mg) Maganese(Mg) 0,69 Incline Plane Molybdenum(Mo) Iron(Fe) 0,46 Incline Plane Molybdenum(Mo) 0,44 Incline Plane Niobium(Nb) Niobium(Nb) 0,46 Incline Plane Nickel(Ni) Chromium(Cr) 0,59 Incline Plane Nickel(Ni) 0,50 Incline Plane Platinum(Pt) 0,64 Incline Plane Lead(Pb) Silver (Ag) 0,73 Incline Plane Gold(Au) 0,61 Incline Plane Copper(Cu) 0,55 Incline Plane Chromium(Cr) 0,53 Incline Plane Iron(Fe) 0,54 Incline Plane Lead(Pb) 0,90 Incline Plane Platinum(Pt) Nickel(Ni) 0,64 Incline Plane Platinum(Pt) 0,55 Incline Plane Tin(Sn) Iron(Fe) 0,55 Incline Plane Tin(Sn) 0,74 Incline Plane Titanium(Ti) Aluminium(Al) 0,54 Incline Plane Titanium(Ti) 0,55 Flat Sliding Tungsten(W) Copper(Cu) 0,41 Incline Plane Iron(Fe) 0,47 Incline Plane Tungsten(W) 0,51 Incline Plane Zinc(Zn) Copper(Cu) 0,56 Incline Plane Iron(Fe) 0,55 Incline Plane Zinc(Zn) 0,75 Incline Plane

Table of friction Values associated with civils and structures

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

 Material 1 Material 2 Friction coefficientSliding Rubber Paving 0,7 -0,9 Masonry Masonry 0,7 -0,9 Masonry Earth 0,5 Earth Earth 0,25 -1,0 Concrete Soil / Rock 0.3 Concrete Steel 0.45 Brick Moist clay 0.33 Brick Dry clay 0.5 Brick Sand 0.4 Brick Gravel 0.6 Brick Brick 0.7 Brick Rock 0.75 Granite Granite 0.6 Limestone Limestone 0.75 Cement Cement Blocks 0.65 Cement Dry Clay 0.4 Cement Wet Clay 0.2 Cement Wet Sand 0.4 Cement Dry Sand 0.50 - 0.60 Cement Dry Gravel 0.50 - 0.60 Cement Dry Rock 0.60 - 0.70 Cement Wet Rock 0.5 Brick Brick 0.65 Wood Wood 0.48

1. Carbide Depot.. Friction Coefficients
2. Supercivilcd Com.. Coefficient of Sliding Friction for various civil Materials
3. Fastener Design Manual...NASA GRC RP-1228 (9,6 Mbyte pdf file) Includes comprehensive table with friction values.
4. Physlinks - Coefficient of Friction...A Table of Friction Coefficients
5. Engineers Edge- Coefficient of Friction...A Table of Friction Coefficients
6. School for Champions...Lots of very useful Notes
7. Bolt Council...Guide to Design Criteria for Bolted and Riveted Joints.(6,7 Mbyte pdf ).  Info on Slip coefficients (P.82) etc
8. Friction coefficients in "Rail- Wheel" contacts .......Downloadable paper providing very theoretical information
9. Hypertextbooks _Physics Factbooks.....Physics Factbook .A page inlcuding a number of very good (school) articles on coe-fficents of friction of different materials
10. Fund'ls of Friction and Wear of Automobile Brake Materials .....Paper Download ..Very informative document
11. Classical Friction...A very simple and clear description of what determines the coefficient of friction.
12. 12 Friction...Brown University-Division of Engineering..Very clear document on friction
13. Rolling Friction...Very useful notes on rolling friction
14. Friction of Rocks...Interesting paper related to earthquakes and the friction forces involved