# Specific Problems in Measurement of Coefficient of Friction Using Variable Incidence Tribometer

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## Abstract

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## 1. Introduction

## 2. Motivation and Goals

## 3. Description of Measurement Chain

## 4. Recommendations from Standards

^{2}. The weight of the sled is 200 g. The sled also has clips for attaching the test material. For the measurement to be carried out, the smooth increasing of the inclination angle of the skid from horizontal position to 45° is required. The velocity of the tilting of the skid should be 1.5 ± 0.5°/s. The indication of the inclination angle of the skid should be with resolution at least 0.5°. Tilting should be triggered until the moment when the movement of the sled is initialized. After the movement of the sled is initialized, the skid tilting is immediately turned off and the angular position of the inclined skid is read with resolution of 0.5°. The ASTM D4918-97 standard [27] states that five measurements are required to determine the static coefficient of friction, from which the arithmetic mean and the standard deviation should be determined.

## 5. Questions and Problems Connected with Measurement

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- How to determine the moment of initialization of the movement of the sled on the skid when measuring the static coefficient of friction? Subjective observation can introduce gross errors in the measurement process, and the measurement process will thus be impaired.
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- What should the tilting velocity of the tribometer skid be in terms of the achievable uncertainty of measurement?
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- How many measurements are needed? The measurement process should not be lengthy due to the economic aspects of the measurement, but this consideration should not lead to the detriment of the achievable uncertainty of the measurement.
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- How to determine the uncertainty of the measurement of friction coefficients?
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- Is it possible to determine the kinetic coefficient of friction using this measurement principle? How to proceed with this measurement?

## 6. Model of Measurement of Static and Kinetic Coefficients of Friction and Uncertainty of Measurement

## 7. Design of Concept of Measurement Device

- The sensing of the inclination angle and the automatic evaluation of the measured value of the inclination angle of the skid to eliminate the complicated and inaccurate reading of the inclination angle of the skid.
- The sensing of the moment of the initialization of the motion of the slipping sled on the skid and the subsequent automatic turn off of the inclination of the tribometer skid in order to eliminate the subjective approach of the measuring person by which gross errors are introduced into the measurement.
- The possibility of adjusting the skid inclination velocity in intervals from 0.5°/s to 3°/s. The creation of the automatic control of the skid inclination velocity to the selected value of the skid inclination velocity.
- The sensing of the overpassed path of the slipping sled along the skid when measuring the kinetic coefficient of friction using adjustable sensors for various adjustments to the overpassed path of the sled.

#### 7.1. Sensing of Inclination Angle of the Skid

#### 7.2. Sensing of Initialization of Motion of Sled on the Inclined Skid

## 8. Experimental Examination of the Influence of Parameters of Measurement Chain on the Result of Measurement of the Static Coefficient of Friction and the Balance of Uncertainties of Measurement

## 9. Experimental Examination of Impact of Parameters of Measurement Chain on the Result of Measurement of Kinetic Coefficient of Friction and Balance of Measurement Uncertainties

_{P}and the gravity acceleration g are constant but the time of the body motion Δt and the inclination angle of skid α

_{T}are probably correlated variables.

_{T}and Δt indicates that there is a functional dependence between these variables, and, therefore, their covariance had to be considered in determining the uncertainty of the kinetic coefficient of friction.

_{T}, Δt) has a component cov

_{A}(α

_{T}, Δt) evaluated by Method A and component cov

_{B}(α

_{T}, Δt) evaluated by Method B.

_{T}and the time of overpassing the path Δt is determined by Relation (17) and has a value of cov

_{A}(α

_{T}, Δt) = −0.00476606 rad·s.

_{B}(α

_{T}, Δt) = −8.3474 × 10

^{−9}rad·s was found. After substituting this value into Relation (16), it was possible to obtain the standard uncertainty of kinetic coefficient obtained by Methods A and B (Figure 16).

## 10. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Method of inclined plane for the measurement of the static coefficient of friction; (

**b**) arrangement of measurement device for the measurement of friction using the inclined plane.

**Figure 3.**(

**a**) Uniform accelerated movement of a body on a skid; (

**b**) friction force while increasing the force applied in the direction of body movement.

**Figure 5.**(

**a**) Realized concept of a variable incidence tribometer; (

**b**) application of the resistive position sensor for sensing of inclination angle of the tribometer platform.

**Figure 6.**(

**a**) Location of the sensor for the identification of the moment of the initialization of the motion of the sled on the tribometer skid; (

**b**) location of laser optical barriers on the tribometer skid.

**Figure 7.**(

**a**) Surface roughness measurement of the skid; (

**b**) Surface roughness measurement of the sled.

**Figure 8.**(

**a**) Arithmetical mean deviation of the assessed profile of the skid; (

**b**) Arithmetical mean deviation of the assessed profile of the sled.

**Figure 9.**Mean values of the static coefficients of friction at different velocities of skid tilting with standard deviations (100 measurements).

**Figure 10.**Standard deviations of the static coefficients of friction at different inclination velocities of the skid (100 measurements).

**Figure 11.**Cumulative standard deviations of the static coefficients of friction at different inclination velocities of the skid.

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## Share and Cite

**MDPI and ACS Style**

Kelemenová, T.; Dovica, M.; Božek, P.; Koláriková, I.; Benedik, O.; Virgala, I.; Prada, E.; Miková, Ľ.; Kot, T.; Kelemen, M.
Specific Problems in Measurement of Coefficient of Friction Using Variable Incidence Tribometer. *Symmetry* **2020**, *12*, 1235.
https://doi.org/10.3390/sym12081235

**AMA Style**

Kelemenová T, Dovica M, Božek P, Koláriková I, Benedik O, Virgala I, Prada E, Miková Ľ, Kot T, Kelemen M.
Specific Problems in Measurement of Coefficient of Friction Using Variable Incidence Tribometer. *Symmetry*. 2020; 12(8):1235.
https://doi.org/10.3390/sym12081235

**Chicago/Turabian Style**

Kelemenová, Tatiana, Miroslav Dovica, Pavol Božek, Ivana Koláriková, Ondrej Benedik, Ivan Virgala, Erik Prada, Ľubica Miková, Tomáš Kot, and Michal Kelemen.
2020. "Specific Problems in Measurement of Coefficient of Friction Using Variable Incidence Tribometer" *Symmetry* 12, no. 8: 1235.
https://doi.org/10.3390/sym12081235