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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 necessarily agree 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
1.
2.
3.
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
For low surface pressures the coefficient of friction is independent of surface area.
At low velocities the friction is independent of the relative surface velocity. At higher velocities the coefficent of
friction decreases.
Well lubricated surfaces
1.
2.
3.
4.
5.
The friction resistance is almost independent of the specific pressure between the surfaces.
At low pressures the friction varies directly as the relative surface speed
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.
The friction is not so dependent of the surface materials
The friction is related to the temperature which affects the viscosity of the lubricant
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.
.
Sliding
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.
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 of 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
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)
Friction Coefficient Friction Coefficient
Male screw
(Dry)
(lub)
Untreated Steel
0,12 - 0,18
0,10 - 0,17
Phosphated Steel
0,12 - 0,18
0,10 - 0,17
Cadmium Plated
0,09 - 0,14
0,08 -0,23
Steel
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)
Friction Coeffient
Friction
Male screw
(Dry)
Coefficient(Lub.)
Untreated Steel
0,14 - 0,2
0,12 - 0,18
Phosphated Steel
0,14 - 0,2
0,12 - 0,18
Cadmium Plated
0,1 - 0,16
0,09 - 0,15
Steel
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
Friction Coeffient
Friction
Bolt/Nut Mat'l
(Dry)
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
Friction Coefficient Friction Coefficient
Bolt/Nut Mat'l
(Dry)
(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
Steel On Steel- No treatment
Steel On Cast Iron- No treatment
Steel On Steel- Machined (Degreased)
Steel On Cast Iron- Machined (Degreased)
Grit -Sandblasted surfaces
slip coefficient
0,15- 0,25
0,18 - 0,3
0,12- 0,18
0,15 - 0,25
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)
Nut Material
Screw Material
Cast
Steel Brass Bronze
Iron
0,150,150,150,15Steel(Dry)
0,25
0,23
0,19
0,25
0,110,100,100,11Steel (Lubricated)
0,17
0,16
0,15
0,17
0,080,040,06Bronze (Lubricated)
0,12
0,06
0,09
2) Thrust collar Friction values (µc)
Surface Combinations
Soft Steel on Cast Iron
Hard Steel on Cast Iron
Soft Steel on Bronze
Hard Steel on Bronze
Moving
0,12
0,09
0,08
0,06
Starting
0,17
0,15
0,10
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 theie coefficient of friction to 0,25 to 0,3. (ref links 1 & 2 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.
Testing Methods
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.
Coefficient Of Friction
Material 1
Material 2
DRY
Static
Greasy
Sliding
Static
Aluminum
Aluminum
1,051,35
Aluminum
Mild Steel
0,61
Brake Material
Cast Iron
0,4
Brake Material
Cast Iron (Wet)
0,2
Brass
Cast Iron
Brick
Wood
Bronze
Cast Iron
Bronze
Steel
Cadmium
Cadmium
Cadmium
Mild Steel
Cast Iron
Cast Iron
Cast Iron
Oak
Chromium
Chromium
0,41
Copper
Cast Iron
1,05
Copper
Copper
1,0
Copper
Mild Steel
0,53
Copper
Steel
Copper
Steel (304 stainless)
0,23
Copper-Lead Alloy
Steel
0,22
-
Diamond
Diamond
0,1
0,05 0,1
Diamond
Metal
0,1 -
0,1
1,4
0,47
Test
method
Sliding
0,3
0,3
0,6
0,22
0,16
0,5
0,05
0,46
1,1
0,15
0,07
0,49
0,075
0,34
0,29
0,08
0,36
0,18
0,8
SPOF
0,21
FOF
0,15
Glass
Glass
0,9 - 1,0 0,4
0,1 - 0,6
Glass
Metal
0,5 - 0,7
0,2 - 0,3
Glass
Nickel
0,78
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
Leather
Wood
0,3 - 0,4
Leather
Metal(Clean)
0,6
Leather
Metal(Wet)
0,4
Leather
Oak (Parallel grain)
0,61
Magnesium
Magnesium
0,6
Nickel
Nickel
0,7-1,1
Nickel
Mild Steel
Nylon
Nylon
0,15 0,25
Oak
Oak (parallel grain)
0,62
0,48
Oak
Oak (cross grain)
0,54
0,32
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)
0,250,0,75
Rubber
Concrete (Dry)
0,6-0,85
Rubber
Concrete (Wet)
0,450,75
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
Steel(Mild)
Brass
0,51
Steel (Mild)
Cast Iron
Steel
Cast Iron
0,4
0,21
Steel
Copper Lead Alloy
0,22
0,16
0,090,12
0,56
SPOF
0,2
0,52
0,08
0,53
0,28
0,64;
0,12
0,178
0,072
0,19
0,44
0,23
0,183
0,133
0,145
Steel (Hard)
Graphite
0,21
0,09
Steel
Graphite
0,1
Steel (Mild)
Lead
0,95
Steel (Mild)
Phos. Bros
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
Steel (Mild)
Steel (Mild)
-
0,62
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
Titanium Alloy Ti-6Al4V(Grade 5)
Aluminium Alloy 6061-T6
0,41
0,38
FOF
Titanium Alloy Ti-6Al4V(Grade 5)
Titanium Alloy Ti-6Al4V(Grade 5)
0,36
0,30
FOF
Titanium Alloy Ti-6Al4V(Grade 5)
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
Zinc
Cast Iron
0,85
0,1
0,95
0,5
0,34
0,3
0,173
0,090,19
FOR
,32
0,04
0,21
Coefficient Of Friction
Material 1
Material 2
DRY
LUBRICATED
Test
method
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-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
Static
Silver (Ag)
Aluminium(Al)
Gold(au)
Cadmium(Cd)
Cobalt(Co)
Chromium(Cr)
Copper(Cu)
Iron(Fe)
Test
Method
Sliding
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)
0,57
Incline
Plane
Titanium (Ti)
0,54
Incline
Plane
Silver (Ag)
0,53
Incline
Plane
Gold(Au)
0,49
Incline
Plane
Cadmium(Cd)
0,79
Incline
Plane
Iron(Fe)
0,52
Incline
Plane
Cobalt(Co)
0,56
Incline
Plane
Chromium(Cr)
0,41
Incline
Plane
Cobalt(Co)
0,41
Incline
Plane
Chromium(Cr)
0,46
Incline
Plane
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
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)
Incline
Plane
0,49
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
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
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
Nickel(Ni)
0,64
Incline
Plane
Platinum(Pt)
0,55
Incline
Plane
Iron(Fe)
0,55
Incline
Plane
Tin(Sn)
0,74
Incline
Plane
Aluminium(Al)
0,54
Incline
Plane
Titanium(Ti)
0,55
Flat
Sliding
Copper(Cu)
0,41
Incline
Plane
Iron(Fe)
0,47
Incline
Plane
Tungsten(W)
0,51
Incline
Plane
Copper(Cu)
0,56
Incline
Plane
Iron(Fe)
0,55
Incline
Plane
Zinc(Zn)
0,75
Incline
Plane
Molybdenum(Mo) Iron(Fe)
Lead(Pb)
Platinum(Pt)
Tin(Sn)
Titanium(Ti)
Tungsten(W)
Zinc(Zn)
Links to Friction Information
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Friction Joint Theory... An informative article
RingFeder ...Keyless Shaft Hub Connection-including relevant friction values
Carbide Depot.. Friction Coefficients
NORD-SKG.. Download manual with various Calculations involving sliding and rolling
friction
Supercivilcd Com.. Coefficient of Sliding Friction for various civil Materials
Fastener Design Manual...NASA GRC RP-1228 (9,6 Mbyte pdf file) Includes
comprehensive table with friction values.
Physlinks - Coefficient of Friction...A Table of Friction Coefficients
Engineers Edge- Coefficient of Friction...A Table of Friction Coefficients
FrictionCenter- Coefficient of Friction...A Table of Friction Coefficients
School for Champions...Lots of very useful Notes
Investigation of the press fit joints by tribology aspect...A Very Informative paper
Bolt Council...Guide to Design Criteria for Bolted and Riveted Joints.(6,7 Mbyte pdf ). Info
on Slip coefficients (P.82) etc
MD Metric...Datasheet for PTFE
Friction coefficients in "Rail- Wheel" contacts .......Downloadable paper providing very
theoretical information
Hypertextbooks _Physics Factbooks.....Physics Factbook .A page inlcuding a number of
very good (school) articles on coe-fficents of friction of different materials
3M Mill Rolls Coef't of Fr'n Study .."...Coefficient of friction values for real applications
NACA Research Memorandum .....Paper Download ..Friction value and surface damage of
several corrosion resistant materials
Wear Research Paper .....Paper Download ..A study of the tribological behaviour of
polyamide 66 with varying injection-moulding parameters
Fund'ls of Friction and Wear of Automobile Brake Materials .....Paper Download ..Very
informative document
Friction in Metal Forming...Chapter 4-aces, Tribology, DimensionalCharacteristics,
Inspection and Product Quality Assurance ..
Classical Friction...A very simple and clear description of what determines the coefficient of
friction.
12 Friction...Brown University-Division of Engineering..Very clear document on friction
Rolling Friction...Very useful notes on rolling friction
co-design-5. Mechanics of Screw Threads ...Web page include screw friction values
This Page is being developed
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Last Updated 07/05/2007