This article provides a comprehensive explanation of the basic concepts of the coefficient of friction, calculation methods, the difference between the static and kinetic coefficient of friction, and representative case studies of coefficient of friction testing.
Links to case-study videos of coefficient of friction measurement are also provided at the end of the article.
This guide is useful for a wide range of readers, from those learning about coefficient of friction testing for the first time to quality control professionals in the manufacturing industry.
Introduction: Purpose of Coefficient of Friction Testing
The coefficient of friction is an index that indicates how difficult it is for two contacting objects to slide against each other.
In coefficient of friction testing (also referred to as friction testing or a COF test), the force required to cause sliding (= maximum frictional force) is measured. By applying the measurement results to a calculation formula, the coefficient of friction is determined.
The coefficient of friction obtained in this way is used for various purposes, including:
- Evaluating conveyance stability in manufacturing processes
- Quantifying operability
For example, the following types of coefficient of friction measurement are conducted in research, development, and quality control environments:
- Evaluation of operability and writing feel in product development (e.g., smartphone screen protectors and writing instruments)
- Quality testing of lubricating oils and greases to reduce energy loss and mechanical load caused by friction
- Slip resistance testing of flooring materials for safety verification (see related article: What Is C.S.R., Which Quantifies Slipperiness?)
- Slip property evaluation of films and paper to prevent wrinkles or slippage during conveyance
In this article, we explain the fundamental concepts of frictional force and the coefficient of friction, as well as the equipment, COF measurement methods, and case studies used in coefficient of friction testing.
What Are Frictional Force and the Coefficient of Friction?
Before introducing specific coefficient of friction measurement methods, we will briefly explain friction.
(If you are already familiar with friction, please skip to the section “Methods for Measuring Frictional Force and the Coefficient of Friction.”)
Friction is the phenomenon in which a force that resists motion is generated when two contacting objects attempt to slide against each other. This resisting force is called frictional force. When an object is stationary, the frictional force generated at the contact surface is equal in magnitude to the force applied to initiate motion. However, there is a limit to the frictional force that a contact surface can generate. When the applied force exceeds this maximum value (maximum frictional force), the object begins to slide.
The maximum frictional force is influenced by:
- The slip resistance property of the contact surface (coefficient of friction)
- The force exerted on the object perpendicular to the contact surface (normal force*1)
In physics, the following relationship is established:
Maximum Frictional Force (N) = Normal Force (N) × Coefficient of Friction *2
*1 The normal force refers to the reaction force exerted perpendicular to the contact surface. When an object exerts force on a surface, the surface exerts an equal reaction force back on the object. When an object is placed on a horizontal surface, the normal force equals the object’s weight converted into force.
*2 N (newton) is the SI unit of force and is used for both frictional force and normal force.
When evaluating sliding characteristics, it is often necessary to obtain the coefficient of friction (COF) as the test result. Because the relationship between the coefficient of friction, maximum frictional force, and normal force follows the formula above, measuring the maximum frictional force and the normal force allows the coefficient of friction to be calculated. (The reason coefficient of friction measurement is required is that it eliminates the influence of mass, enabling comparison of slip resistance properties.)
Coefficient of Friction = Maximum Frictional Force (N) / Normal Force (N)
For example, if a 200 g object is placed on a horizontal surface and begins to move when pushed with a force of 1.5 N: (Static) Coefficient of Friction = 1.5 / 1.96133 = 0.765 (using 1 kgf = 9.80665 N)
When an object is placed on a horizontal surface, the normal force (N) can be calculated using the following formula: Normal force (N) = weight (kg) × gravitational acceleration (m/s²)
Note: The gravitational acceleration on Earth varies depending on location, but the internationally agreed standard value is 9.80665 m/s².
Difference Between Static and Kinetic Coefficient of Friction
The coefficient of friction represents the slip resistance property of materials. There are two types:
- Static coefficient of friction (also called static friction coefficient): Indicates resistance to motion just before sliding begins.
- Kinetic coefficient of friction: Indicates resistance while sliding is occurring.
In general, the coefficient of friction is highest immediately before motion begins. After sliding starts, the value typically decreases slightly and stabilizes.
The kinetic coefficient of friction is often calculated as the average value within a specified sliding distance. In some standards, the calculation range is defined.
For example, the following graph shows the results of coefficient of friction testing between printed paper sheets. The vertical axis represents the coefficient of friction (frictional force (N) / normal force (N)), and the horizontal axis represents elapsed time. The graph shows that the coefficient of friction peaks at the onset of motion and then decreases slightly during sliding.
Frictional force is also classified according to the state of motion. The frictional force just before sliding begins is called static frictional force, and the frictional force during sliding is called kinetic frictional force.
Accordingly:
Static Coefficient of Friction = Static Frictional Force (N) / Normal Force (N)
Kinetic Coefficient of Friction = Kinetic Frictional Force (N) / Normal Force (N)
[Key Points Covered So Far]
● Frictional Force: The force that resists motion when two contacting objects slide against each other
● Maximum Frictional Force: The maximum limit of frictional force that a contact surface can generate (influenced by the coefficient of friction and the normal force)
● Normal Force: The reaction force acting perpendicular to the contact surface (for an object placed horizontally, this equals the gravitational force)
● Coefficient of Friction (COF): An index that indicates the slip resistance of the contact surface (Coefficient of Friction = Maximum Frictional Force / Normal Force)
● Static Coefficient of Friction: The coefficient of friction at the onset of sliding (when an object begins to move from a stationary state).
● Kinetic Coefficient of Friction: The coefficient of friction during sliding motion (generally calculated as the average value over a specified interval)
Methods for Measuring Frictional Force and the Coefficient of Friction
The general coefficient of friction measurement method involves measuring frictional force and normal force, then applying: Coefficient of Friction = Maximum Frictional Force (N) / Normal Force (N)
In many cases, weights are used to maintain a constant normal force while sliding the object horizontally and measuring frictional force. This horizontal COF test method is described in:
- JIS P 8147 (2010): Paper and Paperboard — Determination of Static and Kinetic Coefficient of Friction*3
- JIS K 7125 (1999): Plastics — Film and Sheeting — Determination of Coefficient of Friction*4
Although adherence to standards is not always mandatory, they can serve as reference COF measurement methods.
Frictional force is measured using force measuring devices such as force gauges or load cells. The system requires a drive mechanism capable of moving at a constant horizontal speed.
If only the static coefficient of friction is required, recording the maximum value during the test may be sufficient (with some exceptions). However, to measure the kinetic coefficient of friction, continuous data recording is necessary. For example, IMADA provides graphing software capable of recording continuous data. When combined with optional functions, it can calculate the average kinetic frictional force within a specified range and automatically convert it into the coefficient of friction.
>>Click here to learn more about specific COF testing units
*3 JIS P 8147 (2010), “Paper and Paperboard — Determination of Static and Kinetic Coefficients of Friction” (Watch the measurement video)
*4 JIS K 7125 (1999), “Plastics — Film and Sheeting — Determination of the Coefficient of Friction” (Watch the measurement video)
Important Considerations in Coefficient of Friction Testing
When conducting coefficient of friction testing, many factors must be considered. Here we explain three fundamental points:
- Surface condition affects measurement results
- Comparison requires consistent test conditions
- The coefficient of friction is defined between two contacting materials
Surface Condition Variability
The coefficient of friction is highly sensitive to surface condition. If the same sample is repeatedly tested, friction may alter the surface, causing changes in the measured coefficient of friction.
A clear example is sandpaper. The following graph shows repeated coefficient of friction measurements between sandpaper and plywood without replacing samples. Due to abrasion of the plywood surface, both the static coefficient of friction and the average kinetic coefficient of friction decreased by the tenth measurement compared to the first.
The magnitude of change (a decrease of 0.02–0.04 in coefficient of friction) must be evaluated case by case. The key point is that repeated testing changes the coefficient of friction. The direction of change is not always downward. For example, in coatings with high slip properties, repeated friction may remove the coating and increase the coefficient of friction.
In addition to repeated testing, contamination such as skin oils can alter surface condition. Oils act as lubricants and may affect measurement results. Therefore, avoid touching the contact surfaces during sample setup.
Maintaining Consistent Test Conditions
When comparing coefficient of friction measurement results, all test conditions except the comparison variable must be standardized. These include:
- Sliding speed
- Temperature
- Humidity
- Contact area
- Normal force
Although theory suggests that the coefficient of friction is independent of normal force, in practice the value may vary depending on applied force.
The following graph shows coefficient of friction measurement results between a smartphone screen protector and a stylus pen under varying weight conditions (40 g / 60 g / 80 g). The coefficient of friction changes as the applied force changes.
The Coefficient of Friction Is a Property Between Two Materials
The coefficient of friction is not an intrinsic property of a single material; it represents the interaction between two contacting materials. For example, inquiries such as “We would like to measure the coefficient of friction of stainless steel” are common. However, the measured value varies significantly depending on the material paired with the stainless steel.
The following graph shows frictional force–time results measured between stainless steel and various materials under constant normal force. Even when testing the same stainless steel, the frictional force differs depending on the opposing material.
Even when two identical materials exhibit high resistance to sliding, changing the mating material can result in unexpectedly low friction. If material selection or coefficient of friction testing is conducted without considering actual use conditions, unexpected slipping or sticking problems may occur in the final product. Therefore, COF testing should be performed using material combinations that reflect real product applications.
Summary of Important Considerations for Coefficient of Friction Testing
– Do not perform repeated friction tests on the same sample unless intentionally required.
– Avoid touching the contact surfaces of the sample during setup.
– When comparing coefficient of friction measurement results, ensure that test conditions are consistent.
– Conduct testing using material combinations that reflect actual product use conditions (except when testing in accordance with specific standards).
Case Studies of Coefficient of Friction Measurement
As mentioned earlier, coefficient of friction testing is used for various purposes. Below are three representative case studies:
- Paper coefficient of friction testing
- Plastic film coefficient of friction measurement
- Smartphone screen protector and stylus COF testing
Paper Coefficient of Friction Testing
Paper COF testing is conducted to evaluate:
- Conveyance stability in printing, bookbinding, and packaging processes
- Writing smoothness
In some cases, paper-to-paper COF measurement is performed. In other cases, paper-to-rubber COF testing is conducted to evaluate roller conveyance performance. Here we introduce the horizontal method specified in JIS P 8147 (2010). This test is intended to measure the coefficient of friction between paper sheets; however, by changing one of the specimens, it can also be applied to coefficient of friction measurement between paper and other materials, such as plastic film.
| Step 1: Cut specimens from the sample (Left image: lower specimen; Right image: upper specimen). | Step 2: Place the lower specimen on the test platform and attach the upper specimen to the underside of the weight. Align them in overlapping contact. | Step 3: Pull the weight at a constant speed, measure frictional force, and calculate the coefficient of friction. |
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The following graph shows frictional force measured according to horizontal method specified in JIS P 8147 (2010). As described earlier in [Difference Between Static and Kinetic Coefficient of Friction], the frictional force peaks at the onset of motion and then decreases slightly during sliding.
IMADA’s software can automatically calculate static and kinetic coefficient of friction values within specified intervals.
>> Watch the paper coefficient of friction testing video and view details of the COF testing unit
About the Inclined Plane Method
JIS P 8147 (2010) also specifies a coefficient of friction testing method called the inclined plane method.
The inclined plane method is intended to measure the static coefficient of friction. In this method, the specimen and a weight are placed on the test platform, and the platform angle is gradually increased. The coefficient of friction is then calculated based on the angle at which sliding begins.
(For detailed test procedures and calculation methods, please refer to the JIS standard.)
Plastic Film Coefficient of Friction Measurement
The coefficient of friction of plastic films is measured for quality control and improvement purposes, such as evaluating conveyance stability in roll transport and packaging lines, as well as handling performance during packaging and display operations. In addition, for products such as smartphone screen protectors, coefficient of friction testing is also used to evaluate the sliding feel of fingers or stylus pens.
The representative standard is JIS K 7125 (1999).
The measurement procedure is similar to that for paper:
| Step 1: Cut specimens from the sample. (Left image: lower specimen; Right image: upper specimen) | Step 2: Place the lower specimen on the platform and attach the upper specimen to the underside of the weight. | Step 3: Pull the weight at constant speed and calculate the coefficient of friction. |
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Differences between JIS K 7125 and JIS P 8147 include specimen fixation methods, weight mass, and test speed.The coefficient of friction is calculated as: Maximum Frictional Force (N) / Normal Force (N)
(Normal force is calculated as weight mass (kg) × gravitational acceleration (m/s²).)
If you would like to see more detailed information, such as measurement videos and example configurations of COF testing units, please visit IMADA’s product and service website via the link below.
Smartphone Screen Protector and Stylus COF Testing
For flat specimens such as paper or film, placing the specimen under a weight allows straightforward coefficient of friction measurement.
However, for non-flat samples, specialized fixtures are required. The example unit shown measures COF between a smartphone screen protector and a stylus pen. The stylus stands vertically on the specimen without load, and normal force is controlled by placing weights on a plate above the sample.
| Step 1: Install the lower specimen and mount the upper sample in the holder. | Step 2: Balance the counterweight and apply weights to control normal force. | Step 3: Slide the sample horizontally at constant speed and measure frictional force. |
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This measurement setup enables COF testing for:
- Pen on paper
- Lipstick on artificial skin
- Ball-on-plate lubrication testing
If you would like more detailed information, please visit IMADA’s product and service website using the links below.
>>View the writing instrument coefficient of friction testing video and COF testing unit details
>>View the lubricant coefficient of friction testing video (ball-on-plate method) and COF testing unit details
Summary
This article has comprehensively explained the fundamentals of coefficient of friction testing, including calculation formulas, the difference between static and kinetic coefficient of friction, COF measurement methods, and representative case studies.
The coefficient of friction is an essential index for evaluating slip characteristics and surface interaction. If you require consultation regarding coefficient of friction testing methods or measurement equipment, IMADA provides technical support.
In addition, our product and service website features numerous coefficient of friction testing videos. Please visit the link below to explore our case studies.
View coefficient of friction testing case study videos (IMADA Product & Service Website)
