Precision of Tribometer Testing on Laboratory-Grown Dendritic Snow for Evaluating Cross-Country Ski Performance.
Tribometers play a crucial role in measuring friction and wear. A full-scale ski-snow tribometer was developed by the Department of Civil and Environmental Engineering at the Norwegian University of Science and Technology to test ski-snow friction with greater precision using the OAV Dovetail Linear Air Bearing. The precision of the tribometer varied based on snow type, speed, and surface preparation.
International ban on fluorine-containing waxes and ski bases has led to increased research on minimizing ski-snow friction. Despite this, quantifying ski-snow friction in a precise and representative way still remains a challenge, and manufacturers rely mostly on full-scale field testing. Although laboratory studies for friction have been conducted, there are still some limitations with the current setups, such as severe polishing and limited sample size. To address these limitations, a modified linear tribometer was produced, capable of testing full-sized cross-country skis at speeds up to 8 m/s on testbeds made with laboratory-grown dendritic snow. This setup provides better control and can produce the same type of snow repeatedly, allowing for more precise measurements of ski-snow friction.
Consisting of a mobile carriage driven by a servo motor, the modified tribometer carriage includes a fork, air bellow, the OAV Dovetail Linear Air Bearing, two vertical load cells, a horizontal load cell, and a system for data acquisition and transmission. During a run, there is a phase of acceleration, constant speed, and deceleration, with the length of the constant speed phase varying from 2.50 to 5.50 m depending on the chosen acceleration of the motor. The vertical load can be adjusted from 50 N to 800 N, and the applied load is distributed over the entire length of the binding with the center of mass approximately 12 cm behind the front of the binding, which is similar to a skier's weight distribution and center of mass over the ski.
Fig 1. Schematic of the friction track with the carriage optimized for cross-country skis. Insert a) shows the ‘frictionless’ sliding OAV Dovetail Linear Air Bearing and the position of the load cells while insert b) shows the detailed components of the carriage.
The force from the air bellow is transmitted through the fork to the two vertical load cells, which sit on top of the OAV Dovetail Linear Air Bearing. The ski is connected to the bottom of the air bearing, which can slide without friction, and the angle of the OAV Dovetail Linear Air Bearing is adjusted with a screw and digital level. The resistance force of the ski on the snow is measured by a horizontal load cell placed between the housing and slider of the air bearing.
The OAV Dovetail Linear Air Bearing allows for the ski-snow friction to be measured with incredibly accurate precision. The sliding mechanism of the air bearing allows for the ski to glide without any friction. The air bearing in the modified tribometer provides greater control for the precise measurements, which is critical for developing and testing new ski wax and base materials that align with the international ban of fluorine-containing waxes and ski bases.
The motor controller gradually reduces acceleration during the second half of the acceleration phase using a sinusoidal ramp (S-ramp) to reduce the impact of inertia. The horizontal force during acceleration is significant due to the added inertia force of the ski and slider. The air dragis negligible due to the measured air drag being less than 0.4% of the total force when compared to the average friction force.
Fig 2. Illustration of the collected data a) Carriage speed, b) horizontal force, c) vertical force. The highlighted area is the measurement area.
The horizontal force is the ski-snow friction force, while the normal force is measured by two vertical load cells. The friction coefficient is calculated by dividing the horizontal force by the vertical force. Vibrations during the measurement are reduced by removing data points at the start and end of the measurement area. The spectral analysis is used to identify the major frequency and average amplitude of the force data.
The precision of the tribometer was assessed at three levels. At level 1, the precision of the friction measurement unit was determined by measuring the coefficient of friction for 50 consecutive runs on a single track. The variation of the measurement series around their linear trendlines was used to estimate the standard deviation and the relative standard deviation for each track. At level 2, the precision within a single testbed was determined by running the test ski 50 times on different parallel tracks within the same testbed. The standard deviation of all μ measurements was calculated around the value of μfit,i, and the relative value for the standard deviation was obtained. The variation between different testbeds was determined at level 3 by finding the linear fit for all measurements in all the tracks of all the testbeds and calculating the standard deviation of the μ measurements around this line.
The text notes that tribometer snow tracks polish over time until an ice-like surface is obtained, and the coefficient of friction for a classic roller ski was measured as a comparison. The accuracy of the tribometer was assessed by comparing the absolute μ values obtained in the test to those obtained in other studies.
Since the friction level variations for different snow surfaces and ski properties are generally large, the authors complemented the comparison of friction values from different studies by testing the rolling resistance of a classic roller ski. The results showed that the reported tribometer's accuracy is acceptable at the friction level of a roller ski, which is generally comparable to that of a racing cross-country ski. Additionally, the standard deviation of the 50 roller ski runs at 6 m/s was 0.000227, indicating a high precision of 0.96%. The results suggest that the reported tribometer can achieve high precision even at lower friction levels, and the precision within a single track is relatively high, especially for aged snow.
The authors found that the dendritic structure of new snow changes more rapidly than aged snow, resulting in a greater reduction in the pore space and an increase in density over 50 runs. The surface topography of the new snow testbed also showed a reduction in the visibility of dendritic features after the test, while aged snow appeared more polished and flatter.
S. B. Auganæs, A. F. Buene, and A. Klein-Paste, “Laboratory testing of cross-country skis – Investigating tribometer precision on laboratory-grown dendritic snow,” vol. 168, p. 107451, 2022, doi: 10.1016/j.triboint.2022.107451.
This material is based on work supported by Department of Civil and Environmental Engineering at the Norwegian University of Science and Technology.