coefficients of friction

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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 necessarilyagree with values in another section...Please use the linked references at the bottom of the page for more detailed information.

Factors Affecting friction..... Static Friction..... Sliding/dynamic/kinetic friction..... Coefficients of Friction.....Rolling Friction..... Plain Bearings Friction..... Rolling Bearing Friction..... Clutch Brake Friction.....Bolted Joints..... Power Screws..... Press Fits.... Test Methods.... Linked Reference Info

Factors affecting the friction between surfaces

Dry surfaces

For low surface pressures the friction is directly proportional to the pressure between the surfaces. As the pressurerises the friction factor rises slightly. At very high pressure the friction factor then quickly increases to seizing

1.

For low surface pressures the coefficient of friction is independent of surface area.2.At low velocities the friction is independent of the relative surface velocity. At higher velocities the coefficent of frictiondecreases.

3.

Well lubricated surfaces

The friction resistance is almost independent of the specific pressure between the surfaces.1.At low pressures the friction varies directly as the relative surface speed2.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.

3.

The friction is not so dependent of the surface materials4.The friction is related to the temperature which affects the viscosity of the lubricant5.

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 dividedby 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 isincreased 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 thesame as the coefficient of friction.

.

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 thecase of a body resting on a flat surface the body starts to move. The sliding frictional resistance is normally different to the static frictionalresistance. The coefficient of sliding friction is expressed using the same formula as the static coefficient and is generally lower than the staticcoefficient of friction..

Coefficients Of Friction http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm

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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 twomaterials is to conduct experiments.

Coefficients of friction are sensitive to atmospheric dust and humidity, oxide films, surface finish, velocity of sliding, temperature, vibration, andextent of contamination. In many cases the degree of contamination is perhaps the most important single variable.. Link Table of Coefficientsof 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 slidingfriction. 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 thecylinder 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 = 0,0005mWood on Steel f = 0,0012mWood on Wood f = 0,0015mIron on iron f = 0,00051mIron on granite f = 0,0021mIron on Wood f = 0,0056mPolymer on steel f = 0,002mHardrubber on Steel f = 0,0077mHardrubber on Concrete f = 0,01 -0,02mRubber 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 resultingfriction between the connected surfaces. Below are provided a small number of values showing approximate values of friction coefficients to beused for steel screw fastened connections. The values are only representative values and should be confirmed against other sources of


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information and preferably testing.

Coefficient of Friction for screw threads

Female Thread -Nut or Tapped Hole in steel(untreated)

Male screwFriction Coefficient

(Dry)Friction Coefficient (lub)

Untreated Steel 0,12 - 0,18 0,10 - 0,17Phosphated Steel 0,12 - 0,18 0,10 - 0,17Cadmium Plated Steel 0,09 - 0,14 0,08 -0,23Galvanised steel 0,14 - 0,23 0,12 - 0,2Degreased 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 - 0,18Phosphated Steel 0,14 - 0,2 0,12 - 0,18Cadmium Plated Steel 0,1 - 0,16 0,09 - 0,15Galvanised steel 0,14 - 0,25 0,12 - 0,2Degreased steel 0,19 - 0,25

Coefficient of Friction Nut/Bolt Face against Clamped surface

Clamped Surface = SteelBolt/Nut Mat'l Friction Coeffient (Dry) Friction Coefficient(Lub.)

Untreated Steel 0,10 - 0,18 0,08 - 0.15Phosphated Steel 0,10 - 0,18 0,08 - 0,15Galvanised steel 0,10 - 0,2 0,09 - 0,18

Clamped Surface -Galvanised Steel

Bolt/Nut Mat'lFriction Coefficient

(Dry)Friction Coefficient (lub)

Untreated Steel 0,10 - 0,18 0,08 - 0,15Phosphated Steel 0,10 - 0,18 0,08 - 0,15Galvanised 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 coefficientSteel On Steel- No treatment 0,15- 0,25Steel On Cast Iron- No treatment 0,18 - 0,3Steel On Steel- Machined (Degreased) 0,12- 0,18Steel On Cast Iron- Machined (Degreased) 0,15 - 0,25Grit -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 MaterialNut Material

Steel Brass Bronze Cast IronSteel(Dry) 0,15-0,25 0,15-0,23 0,15-0,19 0,15-0,25Steel (Lubricated) 0,11-0,17 0,10-0,16 0,10-0,15 0,11-0,17Bronze (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 0,17Hard Steel on Cast Iron 0,09 0,15Soft Steel on Bronze 0,08 0,10Hard 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. Methodsof achieving this type of connection include the engineered interference fit, the taper lock bush and hydraulic fit bush. These keyless shaft/hubconnections 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 intothe 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


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Steel Hub , Steel Shaft greased - force fit ...C. of Friction = 0,05 to 0,12Steel Hub , Steel Shaft unlubricated - Shrink fit ...C. of Friction = 0,15 to 0,25Steel 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 lightlyoiled connections and 0,15 for dry assemblies. These companies can provide surface coating fluids containing particles to increase thecoefficient 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 and0,15-0,20 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 diameterL 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 -abcEngineers edge - press fit calculatgor

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 (PORReciprocating 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 theideal method of determining the coefficient of friction is by trials. A short table is included above the main table to illustrate how the coefficient offriction is affected by surface films. When a metal surface is perfectly clean in a vacuum , the friction is much higher than the normal acceptedvalue 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 DryThick Oxide

FilmSulfide 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 valuessimilar 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 MetalsData 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 avalue for mild steel on mild steel of 0,62 sliding.

Material 1 Material 2

Coefficient Of Friction

Test methodDRY Greasy

Static Sliding Static Sliding

Aluminum Aluminum 1,05-1,35 1,4 0,3

Aluminum Mild Steel 0,61 0,47

Brake Material Cast Iron 0,4

Brake Material Cast Iron (Wet) 0,2

Brass Cast Iron 0,3

Brick Wood 0,6

Bronze Cast Iron 0,22

Bronze Steel 0,16

Cadmium Cadmium 0,5 0,05


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Cadmium Mild Steel 0,46

Cast Iron Cast Iron 1,1 0,15 0,07

Cast Iron Oak 0,49 0,075

Chromium Chromium 0,41 0,34

Copper Cast Iron 1,05 0,29

Copper Copper 1,0 0,08

Copper Mild Steel 0,53 0,36 0,18

Copper Steel 0,8 SPOF

Copper Steel (304 stainless) 0,23 0,21 FOF

Copper-Lead Alloy Steel 0,22 -

Diamond Diamond 0,1 0,05 - 0,1

Diamond Metal 0,1 -0,15 0,1

Glass Glass 0,9 - 1,0 0,4 0,1 - 0,6 0,09-0,12

Glass Metal 0,5 - 0,7 0,2 - 0,3

Glass Nickel 0,78 0,56

Graphite Graphite 0,1 0,1

Graphite Steel 0,1 0,1

Graphite (In vacuum) Graphite (In vacuum) 0,5 - 0,8

Hard Carbon Hard Carbon 0,16 0,12 - 0,14

Hard Carbon Steel 0,14 0,11 - 0,14

Iron Iron 1,0 0,15 - 0,2

Lead Cast Iron 0,43

Lead Steel 1,4 SPOF

Leather Wood 0,3 - 0,4

Leather Metal(Clean) 0,6 0,2

Leather Metal(Wet) 0,4

Leather Oak (Parallel grain) 0,61 0,52

Magnesium Magnesium 0,6 0,08

Nickel Nickel 0,7-1,1 0,53 0,28 0,12

Nickel Mild Steel 0,64; 0,178

Nylon Nylon 0,15 - 0,25

Oak Oak (parallel grain) 0,62 0,48

Oak Oak (cross grain) 0,54 0,32 0,072

Platinum Platinum 1,2 0,25

Plexiglas Plexiglas 0,8 0,8

Plexiglas Steel 0,4 - 0,5 0,4 - 0,5

Polystyrene Polystyrene 0,5 0,5

Polystyrene Steel 0,3-0,35 0,3-0,35

Polythene Steel 0,2 0,2

Rubber Asphalt (Dry) 0,5-0,8

Rubber Asphalt (Wet) 0,25-0,75

Rubber Concrete (Dry) 0,6-0,85

Rubber Concrete (Wet) 0,45-0,75

Saphire Saphire 0,2 0,2

Silver Silver 1,4 0,55

Sintered Bronze Steel - 0,13

Solids Rubber 1,0 - 4,0 --

Steel Aluminium Bros 0,45

Steel Brass 0,35 0,19

Steel(Mild) Brass 0,51 0,44

Steel (Mild) Cast Iron 0,23 0,183 0,133

Steel Cast Iron 0,4 0,21

Steel Copper Lead Alloy 0,22 0,16 0,145

Steel (Hard) Graphite 0,21 0,09

Steel Graphite 0,1 0,1

Steel (Mild) Lead 0,95 0,95 0,5 0,3

Steel (Mild) Phos. Bros 0,34 0,173

Steel Phos Bros 0,35

Steel(Hard) Polythened 0,2 0,2

Steel(Hard) Polystyrene 0,3-0,35 0,3-0,35

Steel (Mild) Steel (Mild) 0,74 0,57 0,09-0,19

Steel (Mild) Steel (Mild) - 0,62 FOR


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Steel(Hard) Steel (Hard) 0,78 0,42 0,05 -0,11 0,029-,12

Steel Zinc (Plated on steel) 0,5 0,45 - -

Teflon Steel 0,04 0,04 0,04

Teflon Teflon 0,04 0,04 0,04

Tin Cast Iron ,32

Titanium Alloy Ti-6Al-4V(Grade5) Aluminium Alloy 6061-T6 0,41 0,38 FOF

Titanium Alloy Ti-6Al-4V(Grade5)

Titanium Alloy Ti-6Al-4V(Grade5) 0,36 0,30 FOF

Titanium Alloy Ti-6Al-4V(Grade5) Bronze 0,36 0,27 FOF

Tungsten Carbide Tungsten Carbide 0,2-0,25 0,12

Tungsten Carbide Steel 0,4 - 0,6 0,08 - 0,2

Tungsten Carbide Copper 0,35

Tungsten Carbide Iron 0,8

Wood Wood(clean) 0,25 - 0,5

Wood Wood (Wet) 0,2

Wood Metals(Clean) 0,2-0,6

Wood Metals (Wet) 0,2

Wood Brick 0,6

Wood Concrete 0,62

Zinc Zinc 0,6 0,04

Zinc Cast Iron 0,85 0,21

Material 1 Material 2

Coefficient Of Friction

Test methodDRY LUBRICATED

Static Sliding Static 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-Page16. I have referred to books including Machinerys Handbook Eighteenth edition, Kempes Engineers Year Book 1980, Concise Metals Handbookby 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 aregenerally different to the values in the table above...

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

Fixed Surface Moving BlockFriction

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


Cadmium(Cd) Cadmium(Cd) 0,79 Incline Plane


Cobalt(Co) Cobalt(Co) 0,56 Incline Plane

Chromium(Cr) 0,41 Incline Plane

Chromium(Cr) Cobalt(Co) 0,41 Incline Plane


Copper(Cu) Cobalt(Co) 0,44 Incline Plane




Nickel(Ni) 0,49 Incline Plane

Zinc(Zn) 0,56 Incline Plane

Iron(Fe) Cobalt(Co) 0,41 Incline Plane



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Maganese(Mg) 0,51 Incline Plane

Molybdenum(Mo) 0,46 Incline Plane

Titanium(Ti) 0,49 Incline Plane

Tungsten(W) 0,47 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





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


Tungsten(W) 0,51 Incline Plane

Zinc(Zn) Copper(Cu) 0,56 Incline Plane



Links to Friction Information

Carbide Depot.. Friction Coefficients1.Supercivilcd Com.. Coefficient of Sliding Friction for various civil Materials2.Fastener Design Manual...NASA GRC RP-1228 (9,6 Mbyte pdf file) Includes comprehensive table withfriction values.

3.

Physlinks - Coefficient of Friction...A Table of Friction Coefficients4.Engineers Edge- Coefficient of Friction...A Table of Friction Coefficients5.School for Champions...Lots of very useful Notes6.Bolt Council...Guide to Design Criteria for Bolted and Riveted Joints.(6,7 Mbyte pdf ). Info on Slipcoefficients (P.82) etc

7.

MD Metric...Datasheet for PTFE8.Friction coefficients in "Rail- Wheel" contacts .......Downloadable paper providing very theoretical information9.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 document11.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 friction13.Rolling Friction...Very useful notes on rolling friction14.

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coefficients of friction

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