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Coefficient of Sliding Friction
by Ron Kurtus (17 July 2019)
The coefficient of sliding friction is a number that indicates how much sliding friction there is between two object for a given normal force pushing them together.
There are two coefficients of sliding friction, depending on whether the objects are static or stationary of if they are kinetic or moving with respect to each other. For a given set of materials, the static coefficient of sliding friction is typically greater than the kinetic coefficient of friction.
There are a number of factors that can affect the coefficient of friction, including surface conditions. Values of the coefficient of sliding friction can be a good reference for specific combinations of materials.
Questions you may have include:
- What is the coefficient relationship?
- What factors affect the coefficient of sliding friction?
- What are the coefficient values?
This lesson will answer those questions. Useful tool: Units Conversion
Coefficient relationship
When a force is applied to an object, the resistive force of sliding friction acts in the opposite direction, parallel to the surfaces.
Static coefficient
When the objects are stationary with respect to each other and an external force pushed on one of them, the resistive force of friction is:
Fss = μssN
and the static coefficient of sliding friction is:
μss = Fss/N
where:
- μss is the static coefficient of sliding friction for the two surfaces (Greek letter "mu")
- Fss is the static force of sliding friction
- N is the normal or perpendicular force pushing the two objects together
Kinetic coefficient
When one object slides over the other, the kinetic coefficient of sliding friction is:
μks = Fks/N
where:
- μks is the kinetic coefficient of sliding friction for the two surfaces (Greek letter "mu")
- Fks is the kinetic resistive force of sliding friction
Relationship of coefficients
The static coefficient is greater than the kinetic coefficient:
μss > μks
and thus
Fss > Fks
Factors affecting coefficient
there are several factors affecting the coefficient of sliding friction.
Independent of velocity
In most cases, the velocity of the sliding object does not affect the coefficient of friction. However, at higher velocities, μks can change. There have not been many experiments to measure the change in μks with respect to the sliding velocity.
Independent of area
Although it may seem counterintuitive, the coefficient of sliding friction is independent of the area of the surfaces in contact, provided the normal force is constant. This holds only when the surfaces are hard and not lubricated.
For example, the sliding friction of a book on its edge is the same as when it is laying down on the table.
The rationale for this rule is that much of the COF is from surface roughness. When an object with a small footprint is pressed against a surface with a given force, the pressure involved is the force divided by the area.
Surface conditions
Other effects like oxidation of a metal surface, dirt, water or grease can dramatically change the coefficient of friction for the given materials.
Effect of oxidation
For example, clean dry steel sliding on steel has a coefficient of friction of μ = 0.78, but if the surface has oxidized, the coefficient changes to μ = 0.27.
Likewise, clean dry copper sliding on copper has a coefficient of μ = 1.21, while oxidized copper has a value of μ = 0.76.
Need to know surface conditions
The biggest problem in using values established by others in such tables is that you do not know the actual surface condition of the materials used or how the values were determined.
Chart of values
The coefficient of friction can range between 0 (zero) and ∞ (infinity).
When close to zero
When μ = 0, there is no friction. If μ is close to 0, there is little friction. For example, leather-soled shoes on slippery ice has a very small coefficient of friction, close to zero. That is why you can easily slide on ice or even take a fall. Even rubber-soled shoes on ice has a very small coefficient of friction.
When close to infinity
Many students and teachers mistakenly think that μ must be less than 1. That is incorrect, since Fr could be many times the normal force.
One extreme example is if you glued an object to another. The resistance to moving the objects would be very large and the coefficient of friction would also be very large. If the glue was so strong that they could never be slid against each other, then μ would equal infinity.
The reason people think that μ must be less than 1 is probably since most listing of coefficients of friction have values less than 1. That is because most materials of interest usually slide relatively easy on each other.
Chart
The following chart lists the static and kinetic coefficients of sliding friction for some typical materials. It is assumed that the surfaces are clean, hard, and without lubrication.
However, since the quality of the surfaces is not mentioned, you should only use these readings as a guide. It is best to measure the coefficients for your specific materials and conditions of use to obtain accurate values.
Coefficient of Sliding Friction |
|||
Material 1 |
Material 2 |
Static |
Kinetic |
| Aluminum | Mild Steel | 0.61 | 0.47 |
| Cast Iron | Cast Iron | 1.1 | 0.15 |
| Copper | Cast Iron | 1.05 | 0.29 |
| Copper | Mild Steel | 0.53 | 0.36 |
| Glass | Glass | 0.9 - 1.0 | 0.4 |
| Glass | Nickel | 0.78 | 0.56 |
| Leather | Oak (parallel grain) | 0.61 | 0.52 |
| Nickel | Nickel | 0.7 - 1.1 | 0.53 |
| Oak | Oak (parallel grain) | 0.62 | 0.48 |
| Oak | Oak (cross grain) | 0.54 | 0.32 |
| Steel (mild) | Brass | 0.51 | 0.44 |
| Steel (mild) | Lead | 0.95 | 0.95 |
| Steel (mild) | Steel (mild) | 0.74 | 0.57 |
| Steel (hard) | Steel (hard) | 0.78 | 0.42 |
| Steel | Zinc (plated on steel) | 0.5 | 0.45 |
| Zinc | Cast Iron | 0.85 | 0.21 |
Summary
Coefficient of friction for a number of materials have been tabulated. These values apply only to hard, clean surfaces sliding against each other. Since various experimental parameters are not listed, considerations should be made in using these tabulated values because they may not directly relate to your application.
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Resources and references
Websites
Friction Resources - Extensive list
Coefficient of Friction - Static friction values (clean vs lubricated) from Engineering Toolbox
Engineering Library - Coefficient of Friction
Engineer's Edge COF - Extensive tables
Approximate Coefficients of Friction - Wikipedia
RoyMech (UK) - Friction Factors - Various lists
Books
Top-rated books on Friction Science
Top-rated books on Friction Experiments
Friction Science and Technology (Mechanical Engineering Series) by Peter J. Blau; Marcel Dekker Pub. (1995) $89.95
Physics of Sliding Friction (NATO Science Series E:) by B.N. Persson, E. Tosatti; Springer Pub. (1996) $358.00
Questions and comments
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