Coefficient of Friction – Meaning, Calculation, Values


Coefficient of friction is a dimensionless number that represents the ratio between the friction force and normal force acting on a body. In this article, you will learn the meaning of friction coefficient, how to calculate it, values for common objects, and specific use cases of friction coefficient.

What Does Friction Coefficient Mean?

Coefficient of friction (COF) depicts the relationship between two surfaces in contact and the normal reaction between them. As a result, its value varies according to the materials in contact. Although the coefficient values are usually between 0 and 1, they could be greater than 1 on some occasions.

A value of 0 means there is no friction between the contact surfaces, which is rare, but possible with superfluidity. A value of 1 means that the frictional force and normal force are equal. But if the frictional force is the predominant force between the materials, the coefficient value exceeds 1.

Generally, the coefficient possesses different values for static friction and kinetic/dynamic friction. The static friction coefficient is the value when there is no relative motion between the objects. The kinetic counterpart is the coefficient when one or both objects are moving.

Two objects in contact showing the friction coefficient (μ) as a function of the normal force (N) and frictional force (Ff).
Courtesy: Universe Today

How to Calculate Coefficient of Friction

Calculating the coefficient of friction is essential in obtaining the right surface combinations per application. In engineering, a typical goal is to select the material combination that minimizes friction, due to its detrimental effects including energy losses and wear. To find the coefficient value (μ), take the ratio of the frictional force (Ff) and the normal force (N).

    \[ \mu =\frac{F_{f}}{N} \]

This is the same formula for calculating the coefficient whether it is static (μs) or kinetic (μk). The difference will be that the frictional force should correspond with the type of coefficient being calculated. Normal force remains the same whether the objects are static or in motion.

COF Values for Common Materials

It is common practice in engineering to empirically determine and document frequently used values for easy and quick reference. The coefficient of friction is one of these values. Apart from varying according to the nature of the materials in contact, the surface condition also influences the COF value.

Material CombinationSurface ConditionStatic Friction Coefficient (μs)Kinetic Friction Coefficient (μk)
Aluminum – AluminumClean and dry1.05 – 1.351.4
Aluminum – AluminumLubricated and greasy0.3
Brass – SteelClean and dry0.510.44
Brass – SteelLubricated and greasy0.19
Cast Iron – Mild SteelClean and dry0.40.23
Cast Iron – Mild SteelLubricated and greasy0.210.13
PTFE – SteelClean and dry0.05 – 0.2
Tungsten Carbide – SteelClean and dry0.4 – 0.6
Tungsten Carbide – SteelLubricated and greasy0.1 – 0.2
Rubber Tire – RoadDry0.90.8
Rubber Tire – RoadWet0.2
Brake Lining – Cast Iron0.40.3
Wood – ConcreteClean and dry0.62
Wood – MetalClean and dry0.2 – 0.6
Copper – Cast IronClean and dry1.050.29
Copper – Mild SteelClean and dry0.530.36
Copper – Mild SteelLubricated and greasy0.18
Chromium – ChromiumClean and dry0.41
Chromium – ChromiumLubricated and greasy0.34
Metal – Ice0.0220.02
Material Combinations and their Friction Coefficient

From the formula, a value above 1 implies that the force that results in relative motion is greater than the normal force. A value of 0 means that there is no friction between the contact surfaces. This is rare, although materials such as Teflon have a coefficient as low as 0.04. The values from the table show that selecting an appropriate material combination and maintaining the surface condition is key to meeting the frictional needs of an application.

Specific Use Cases

This section focuses on specific use cases of the friction coefficient. It also entails how to influence the coefficient value for a given material combination.

Coefficient of Friction for Steel on Steel

Generally, the friction coefficient for greasy steel on a steel surface is 0.05 and 0.1 for the kinetic and static values respectively. As for a dry surface, the kinetic and static values are about 0.4 and 0.6 respectively.

Friction Reducing Gear

High coefficient values are desirable in applications such as milling and grinding, thus, surfaces undergoing these procedures must be kept clean and dry. Although, cooling of the steel may become necessary in the case of excessive heat generation. Other means apart from lubrication can provide cooling. Another scenario that requires more friction is steel-to-steel seals such as in valves. These seals provide more durability than their elastomer counterparts with increased levels of friction. However, they are prone to wear over time. In high-pressure valves, an increase in the steel-on-steel surface area increases the friction coefficient.

Coefficient of Friction for Rubber on Steel

The use of rubber on steel is a popular combination in engineering. In applications such as seals, it helps eliminate wear associated with steel-on-steel surfaces when there is relative motion. For example, rubber on stainless steel has a coefficient of 0.64. In terms of friction, rubber-on-steel and steel-on-steel are equivalent. But the durability of rubber and its compatibility with the process fluid makes designers overlook it whenever longevity is a priority.

Coefficient of Friction for Wood on Wood

The static coefficient of for wood on wood generally lies between 0.25 and 0.55 for a dry surface. Even after lubrication, the value reduces only slightly to 0.20. Thus, the coefficient value for wood on wood is less sensitive to the surface condition relative to other materials such as steel and rubber.