Using a high-speed tribometer, coefficients of friction for bobsled runners were measured over a wide range of loads and speeds. Between 2.8 m/s and 28 m/s (equal to 10 km/h and 100 km/h), the measured coefficients of friction showed a linear decrease with increasing speed. The experiments revealed ultra-low friction coefficients of less than 0.01 after exceeding a sliding speed of about 20 m/s. At maximum speed of 28 m/s, the average coefficient of friction was 0.007. The experiments help to bridge the gap between numerous low-speed friction tests by other groups and tests performed with bobsleds on real tracks. It was shown that the friction data obtained by other groups and our measurements can be approximated by a single master curve. This curve exhibits the largest decrease in friction up to a sliding speed of about 3 m/s. The further increase in speed generates only a small decrease in friction. In addition, friction decreases with increasing load. The decrease stops when ice wear becomes effective. The load point of constant friction depends on the cross-sectional radius of the runner. The larger the radius is, the higher the load is, before the ice shows signs of fracture. It turned out that besides aerodynamic drag (not considered in this work), ice friction is one of the main speed-limiting factors. In terms of runner geometry, a flat contact of runner and ice ensures the lowest friction. The rocker radius of the runner is of greater importance for a low coefficient of friction than the cross-sectional radius.
The precise knowledge of the coefficient of friction
Generally, the number of experiments in the past dealing with friction measurements for the system steel versus ice is limited [
Evans et al. determined low-friction coefficients by sliding steel on an ice cylinder at a sliding speed
Data on ultra-low friction coefficients were published by Niven who measured friction between slider and ring ice at 0.9 m/s and found
De Koning et al. analyzed ice skates [
It is obvious that the measured values vary over a wide range. Up to now, the main problem has been the difficulty of measuring friction over a larger range of high speeds and realistic loads. Thus, the data collected only reflect a small fraction of boundary conditions and, sometimes, seem to be rather far from reality. We therefore introduce a new device for high-speed friction tests at realistic loads. This measuring device allows us to ascertain the precise level of friction between the sled and the ice for bobsled runners with different cross-sectional radii.
All tests were carried out in a tire test stand. The main piece of the stand is a large drum which is 3.8 meters in diameter and open on one side, situated in a cooled cell, see Figure
Test cell with sensor setup and model runner.
The cooling of the test cell and the drum was started two days before the measurements. The air in the cell was constantly circulated, and the temperature was maintained constant at −5°C. One day before the measurement the ice production was started with a flow of distilled water into the rotating drum. The drum turned at 10 km/h and moved the water, until a constant thin film of ice was formed. The ice production was ended at an ice thickness of about 3 cm. On the day of the test, the ice surface was smoothed by a two-stage process. First, the rough spots were removed with a steel blade. Then the final polishing was performed with a smooth low-profile tire. During this process the tire was rotated at constant speed and the drum rotated as well.
By means of a hydrostat the normal force was exerted to the runner. The normal force range between 100 N and 500 N was chosen to simulate a 2-men (man and female) as well as a 4-men bobsleigh. For example, with the selected length of the model runner an applied normal force of about 200 N corresponded to the load of a 4-men bob sleigh. The force range between 200 N and 500 N was selected to simulate curves. Thus, with the used sample geometry of the model runner a pressure range between 20 MPa and 64 MPa was covered.
The bob runners were made of F.I.B.T. steel 1.4057. Figure
Left: schematic of runner. Right: runner after surface finish.
The runners were prepared according to the F.I.B.T. regulations following a procedure used in competition. The runners were first polished with sand paper with decreasing grit size followed by a treatment with diamond slurry. Neither machines nor special grinding fluids were applied.
As a result, the surface of the runner showed low roughness as demonstrated in Figure
Topography of the runner determined with atomic force microscopy.
All force data were measured using a three-axis sensor (K3D120, ME Messsysteme GmbH, Germany) with a maximum load of 1,000 N. The sensor is very compact with a lateral dimension of 120 mm × 120 mm and a height of 30 mm. The sensor comes with integrated electronics allowing the separate evaluation of forces in lateral (
In order to initiate the measurements, the drum was set in motion and the speed was set. Then, the sensor assembly was slowly lowered until the
The speed dependence was recorded between 2.8 m/s and 28 m/s (i.e., 10 km/h and 100 km/h) with increments of 2.8 m/s at a constant load of 500 N, see Figure
Friction as function of speed.
At a constant speed of 14 m/s (
Friction as function of load. The left arrow indicates the equivalent normal force executed by a 2-men bob (130 N), the right arrow that of a 4-men bob (200 N).
The normal forces indicated by the arrows correspond to the loads of either a 2-men bob (women) of 340 kg or a 4-men bob (630 kg). That means that a normal force in the lab-experiment of about 130 N is used to simulate the 340 kg and the lab force of 205 N corresponds to 630 kg.
Depending on the normal force, wear marks were detected on the ice after the tests. Due to surface irregularities, intermitted wear marks were detected for small normal forces, see Figure
(a) Ice after preparation with the low-profile tire. (b) Wear marks on the ice after contact with the runner.
In the experiments analyzing friction as function of speed the lowest coefficients of friction showed an average value of 0.007 at highest speed. With increasing speed, data scatter increased due to higher mechanical noise. When the linear fit is extrapolated to a speed of 33 m/s (120 km/h), the coefficient of friction decreases to a value of 0.005. This value corresponds very well with measurements of Poirier [
In Section
Friction versus speed with results of this work and of others.
Our own data represent the average of the friction coefficients obtained for the 4 mm and the 8 mm cross-sectional radius. The foreign data originate mainly from tests in a pressure range between 1 MPa and 10 MPa and ice temperatures between −2°C and −12°C. One experiment was carried out at 270 MPa. Except the results of Niven, [
The acting load presses the runner onto the ice. Both runner and ice are, to a certain degree, elastic media following Hooke’s law,
Hertzian contact pressure as function of load. The inset shows the mechanical setup of cylinder (model runner) versus flat (ice).
The compressive failure stress of 40 MPa was attained at 200 N for the 4 mm runner and for the 8 mm runner at 400 N. This corresponds well with the findings shown in Figure
Increasing normal force as well as increasing speed decreases the friction force
However, with increasing contact area both influences seem to equilibrate and friction becomes constant for normal forces higher than 200 N (4 mm runner) and higher than 400 N (8 mm runner). A detailed analysis of
While the coefficient of friction at the load point of a 4-men bob is located in the constant section of the friction curve of Figure
With the help of a high-speed tribometer coefficients of friction were determined for the contact of bobsled runner versus ice. The results can be concluded as follows. Ultra-low coefficients of friction can be obtained when the sliding speed is higher than 3 m/s. At The magnitude of friction depends on the contact pressure. For pressures higher than 40 MPa ice fracture prohibits further decrease of friction. Despite ice fracture friction is extremely low. The contact pressure can be increased by additional weights. This measure is more effective for the 2-men bobs, since the friction curve decreases with increasing load. Friction starts to become constant at the load of a 4-men bob. Since the acting pressure, especially in curves, is almost always higher than the compressive failure stress of the ice, the rocker radius of the runner should be carefully adapted to the curve radii of the track in order to realize an adjusted contact. Punctual contacts should be omitted. Measurements and calculation showed that the rocker radius is of greater importance for low friction than the cross-sectional radius. This conclusion is supported by the fact that in this study a flat contact was simulated. The rocker radius was equal to the inner radius of the drum. High loads induce ice fracture. The reduction of the rocker radius would lead to punctual contacts with increased pressure. Thus, ice friction would start at lower normal forces.