Research Article www.acsami.org
Effect of Different Bearing Ratios on the Friction between Ultrahigh Molecular Weight Polyethylene Ski Bases and Snow Sebastian Rohm,* Christoph Knoflach, and Werner Nachbauer Department of Sport Science, University of Innsbruck, Fuerstenweg 185, 6020 Innsbruck, Austria
Michael Hasler, Lukas Kaserer, and Joost van Putten Centre of Technology of Ski and Alpine Sports, Fuerstenweg 185, 6020 Innsbruck, Austria
Seraphin H. Unterberger and Roman Lackner Department of Material Technology, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria ABSTRACT: The purpose of this study was to analyze the effect of surfaces with different bearing ratios, but similar roughness heights, on the friction between ultrahigh molecular weight polyethylene (UHMWPE) and snow. On a linear tribometer positioned inside a cold chamber, the different samples were tested over a wide range of velocities and snow temperatures. The surface roughness was measured with a focus variation microscope and analyzed using the bearing ratio curve and its parameters. The surface energy was investigated by measuring the contact angles of a polar (water) and nonpolar (diiodmethane) liquid. The friction tests showed that the bearing ratio had a major effect on the friction between UHMWPE and snow. For temperatures close to the melting point a surface with wide grooves and narrow plateaus (nonbearing surface) performed well. For cold conditions, the friction was less for a surface with narrow grooves and wide plateaus (bearing surface). Interpretations of the results are given on the basis of mixed friction, with lubricated friction being dominant at higher snow temperatures and solid−solid interaction at lower ones. KEYWORDS: bearing ratio, surface roughness, UHMWPE, snow, friction
1. INTRODUCTION In competitive skiing every hundredth of a second counts, and therefore, the right treatment of the ultrahigh molecular weight polyethylene (UHMWPE) ski base can decide between victory and loss. One important step in ski preparation is the stone grinding of the base, resulting in different surface roughnesses. Depending on the snow conditions, the optimum grinding settings may differ significantly. Different studies have been conducted to measure the influence of the surface roughness on the friction between ski and snow. Shimbo1 showed that the optimum surface roughness depends on the ambient temperatures. At +3 °C rougher surfaces had less friction and at −2 °C smoother skis were gliding better. Giesbrecht et al.2 found an optimum arithmetic mean roughness Ra in the range of 0.5−1 μm for snow temperatures from −2.6 to −4 °C. One of the most extensive analyses of the surface roughness influence showed that depending on the snow condition a different surface roughness was optimal.3 Colbeck4 introduced the idea that a roughness-induced increase in static contact angle can lead to a decrease in capillary suction and consequently to a decrease in snow friction. The above listed publications focused on the variation of Ra and the grinding direction. However, Ra only gives information © XXXX American Chemical Society
about the variation in height, but does not provide any information about the slopes, shapes, and sizes of the asperities.5 Rohm et al.6 stated that the surface texture, flat with grooves or sinusoidal, might have an influence on the friction between steel and snow. A more complex way to describe surfaces is the analysis of the bearing area or AbbottFirestone curve.5,7 This curve shows the ratio of air to material, called material ratio Rmr, dependent on the surface height z, starting at the highest peak (0% Rmr) and ending at the lowest pit (100% Rmr). The parameters of the bearing area curve give access to both size and proportion of the valleys and the plateaus of a surface. The aim of this study was to investigate the effect of different bearing area curves of the surfaces on the friction between UHWMPE and snow, while keeping the arithmetic mean roughness Sa constant.
2. EXPERIMENTAL METHODS 2.1. Sample. Two wooden skis without camber and side cut were used. The dimensions of the skis were 114 × 5 cm. The front and the Received: March 2, 2016 Accepted: April 26, 2016
A
DOI: 10.1021/acsami.6b02651 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces back of the skis had a radius of 20 cm, leaving a running length of 100 cm (Figure 1). The surface material was sintered UHMWPE (IS CB 7515 C10, Isosport, Austria). It was fixed to the bottom of the skis with a double-sided cello tape.
running direction. Out of these ten values a mean angle was calculated. The apparent surface energies were calculated out of the mean contact angles using the OWRK method.10 For each ski, the measurement was done five times in 20 cm steps. The measurements were carried out at room temperature on freshly waxed skis (section2.1). 2.4. Friction Tests. Tribometer. The friction was tested under laboratory conditions with a large-scale linear tribometer positioned in a cooling chamber (Centre of Technology of Ski and Alpine Sports, Austria). This testing device consists of a 24 m long trough filled with a layer of snow on which a ski, fixed on a measuring sledge, is moved by an electric motor. Via two spring-loaded bars, the desired normal force Fn was adjusted. After acceleration, the velocity was kept constant and the friction force Fr as well as the normal force Fn were measured by load cells (S2M, HBM, Austria) with a sampling rate of 8192 Hz. The accuracy of the load cells is 0.1%.11 For the calculation of the coefficient of friction μ the arithmetic mean values Fr and Fn Fr were used (μ = Fn ). A more detailed description of the test facility can be found in Nachbauer et al.12 To guarantee reproducible results, each test was conducted on a freshly prepared snow surface. The snow was sieved, placed in the through, pressed, and straightened by a steel blade. The thickness of the snow layer was kept constant at 30 mm. Afterward, the snow was compacted by rolling a polyethylene cylinder (diameter = 40 cm) loaded with a normal force of 460 N over the snow surface. The snow temperature TS was measured with PT1000 sensors at four points along the track (0, 5, 10, and 15 m). The snow density ρ was determined by weighing a 14.4 cm3 snow cube, taken from the track at the 10 m point. The grain shape and size were determined with a macroimage of single snow grains taken from the surface of the track at 10 m. The snow hardness was measured with a spring-loaded aluminum cone at 5 and 10 m. Out of the measured values the mean values were calculated. Test Procedure. The tests were performed at three different snow temperatures of −2.6, −11.1, and −19.0 °C. The velocity dependency was measured in 5 ms−1 steps ranging from 5 to 20 ms−1. The normal force was set to 146 N. The snow grains were round and had a mean diameter of 0.25 mm. Table 1 shows that, with decreasing snow temperature, the snow density slightly decreased while the hardness slightly increased.
Figure 1. Bottom and lateral view of the wooden skis. All dimensions in cm. The three “x” (“1”, “2”, and “3”) in the top view mark the surface analysis positions. The skis were grinded by a ski grinding machine (Race NC, Wintersteiger, Austria) in running direction. To get surfaces with similar roughness depths, but different surface topographies, all grinding parameters, except the dressing speed, were kept constant. This parameter stands for the velocity of the cutting diamond while it carves the negative structure into the grinding stone. The carved stone is then used to grind the structure into the ski base. The used grinding parameters are standard for cross-country skis. Before each test the skis were cleaned with a brass brush and then coated with liquid wax, paraffin solved in a solvent (HWK, Austria), using fuzz-free paper. After the solvent evaporated, the skis were cleaned with a nylon brush. The waxing procedure was performed at room temperature. 2.2. Surface Analysis. Surface analysis was carried out with a focus variation microscope (Infinite Focus G4, Alicona, Austria). It uses the principle of focus variation to create a three-dimensional “3D” image of the surface.8 Each ski was measured at three different positions: 32, 57, and 82 cm from the ski tip (marked by “x” and “1”, “2”, and “3” in Figure 1). At each position two areas were scanned. The measurements were carried out after the friction tests at room temperatures with freshly waxed skis (section 2.1). The first area with a size of 8.8 × 8.7 mm was scanned using an objective with a magnification of 20. The 3D image had a lateral resolution of 2.5 μm and a vertical resolution of 100 nm. The analysis was done with the IFM 4.1 × 64 (Alicona, Austria) software. To separate waviness and roughness, the surface data were filtered using a Gaussian filter with a threshold of Lc = 1.5 mm. To quantify the average groove depth, the surface parameters Sa (arithmetic mean roughness), Sz (maximum height), and S10z (ten-point height) were used. The surface texture was analyzed using the density function of the surface heights, the bearing ratio curves, and the bearing ratio parameters. The bearing ratio curves were obtained by computing the cumulative density function of the surface heights.9 The second area with a size of 4.3 × 1.3 mm was scanned by an objective with a magnification of 50. The 3D image had a lateral resolution of 1.5 μm and a vertical resolution of 50 nm. This highresolution image was used to analyze the microroughness which superimposed the roughness caused by the grooves in the running direction.5 It was quantified by the arithmetic mean roughness in running direction Ra0°. In contrast to the surface parameters Sa, Sz, and S10z this parameter depends on the analysis direction. The calculations of Ra0° were done according to Rohm et al.6 (α = 0°, l = 4 mm, i = 1 mm, and Lc = 800 μm). 2.3. Surface Energy. The effect of the surface roughness on the static contact angle was measured with the Mobile Surface Analyzer (Krüss, Germany) using a polar (water) and a nonpolar (diiodmethane) liquid. The droplet volume for both fluids was 1 μL. The angle of both droplets was measured ten times perpendicular to the
Table 1. Snow Characteristics for the Respective Snow Temperatures Measured before the Tests snow temperature Ts (°C) snow density ρ (kg m−3) snow hardness H (N)
day 1
day 2
day 3
−2.6 454 20.1
−11.1 387 23.3
−19.0 392 24.2
Before each test the skis were waxed according to section 2.1. To cool down, the ski was put into the cooling chamber for at least half an hour before the test. While cooling down, the temperature of the ski base was measured using an infrared thermometer (A350 IR thermometer, Artech, China). After 20 min the desired temperatures were reached. Each setting was measured on a separated sliding track 15 times. Out of the 15 measurements, the last 10 were used to calculate the arithmetic average μ̅ and the standard deviation sμ. For the first few runs, μ usually differed from the other values because additional effects, like the compression of the snow, influenced the measured values (Figure 2).
3. RESULTS 3.1. Surface Analysis. Examples of the large-area images of each ski type, both taken at point 1 in Figure 1, are shown in Figure 3. In Table 2, mean values and standard deviations of the measured roughness parameters are displayed. No difference in Sa, Sz, and S10z were measured, meaning that the groove depths were comparable. However, the density function, the bearing B
DOI: 10.1021/acsami.6b02651 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 2. Two examples of the measured coefficient of friction μ dependent on the run number. μ̅ for the runs 6−15 are indicated by the dotted lines.
Figure 3. Two-dimensional (2D) large-area images with pseudocolors of the bearing (ski 1) and nonbearing (ski 2) surfaces. Each color represents a different height which is defined by the scale on the right. The pictures were taken 32 cm from the ski tip (point 1 in Figure 1). The grinding and running direction were from left to right.
Figure 4. Mean bearing ratio curve (top) and the mean density function (bottom) of the bearing (ski 1) and nonbearing (ski 2) surfaces. Δz for the density function was set to 0.2 μm.
description the surface of ski 1 was further referred to as a bearing surface and the surface of ski 2 as a nonbearing surface. Examples for the high-resolution pictures of the skis are illustrated in Figure 5. The corresponding roughness parameters in running direction Ra0° are displayed in Table 2. Ra0° for ski 2 was higher, emphasizing the result gained out of the bearing ratio parameters, saying that the plateaus were more peaked. 3.2. Contact Angle. In Table 3 the results of the contact angle measurements are displayed. No significant difference in any value could be observed. With a contact angle between water and ski of more than 90°, the surfaces were hydrophobic. 3.3. Friction Tests. Figure 6 shows the effect of surfaces with different bearing ratios on the friction between ski and snow at different velocities and snow temperatures. For snow
ratio curves (Figure 4), and the bearing ratio parameters (Table 2) were completely different. Vvc was smaller, while Vmc was larger for ski 1. Both values indicated that the plateaus on the ski 1 surface were broad and the grooves were narrow. This was further confirmed by a high Svk/Sk ratio.8 With a Vvc/Vmc ratio over 1 and a small Svk/Sk value, the surface of ski 2 had big grooves and small plateaus. Spk value further suggests that the plateaus of ski 2 were more peaked. The results achieved from these parameters were confirmed by the density function p(z) (Figure 4, bottom). p(z) values for ski 1 were high at positive z values (broad plateaus), peaking at z = 5.2 μm. For ski 2, the maximum p(z) value was at z = −2.0 μm with over 50% of the area being under z = 0 μm (big grooves). For a comprehensible
Table 2. Mean Values and Standard Deviations of the Average Roughness Parameters, the Bearing Ratio Parameters, and the Parameter Describing the Roughness in the Running Direction ski 1 average roughness parameter
bearing ratio parameters
high resolution
arithmetic mean roughness Sa (μm) maximum height Sz (μm) ten-point height S10z (μm) core roughness depth Sk (μm) reduced peak height Spk (μm) reduced valley height Svk (μm) core material volume Vmc (mL/m2) core void volume Vvc (mL/m2) ratio Vvc/Vmc arithmetic mean roughness Ra0° (nm) C
3.6 55 44 9.0 1.4 6.55 4.9 4.4 0.89 443
± ± ± ± ± ± ± ± ± ±
ski 2
0.3 12 13 0.3 0.1 0.01 0.4 0.3 0.01 16
3.48 48 42 12.6 2.2 2.8 4.08 5.4 1.29 554
± ± ± ± ± ± ± ± ± ±
0.06 20 10 0.3 0.2 0.1 0.07 0.1 0.03 20
DOI: 10.1021/acsami.6b02651 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
temperatures close to the melting point of water (Ts = −2.6 °C), μ̅ for the nonbearing surface (ski 2) was smaller than that for the bearing one (ski 1). The biggest gap of Δμ̅ = 0.012 was measured for a velocity of 20 ms−1, whereas at 5 ms−1 no big difference was observed. At Ts = −11.1 °C, μ̅ for the bearing surface was slightly lower than that for the nonbearing surface at 5 ms−1 (Δμ̅ = 0.0032). For higher velocities no distinction between the two skis was observed. At Ts = −19.0 °C the opposite of −2.6 °C was measured. Friction for the bearing surface was smaller than that for the nonbearing surface. The difference was largest at 5 ms−1 (Δμ̅ = 0.0045) and decreased with increasing velocity. Friction always increased with velocity. The highest and lowest μ̅ values were both measured at −2.6 °C. Consequently, at this snow temperature the dependence of the friction on the velocity was the highest.
Figure 5. High-resolution 2D images with pseudocolors of the bearing (ski 1) and nonbearing (ski 2) surfaces. Each color represents a different height which is defined by the scale on the right. The pictures were taken 57 cm from the ski tip (point 2 in Figure 1). The grinding direction was from left to right.
4. DISCUSSION The differences in surface texture, illustrated by the bearing ratio, had a major effect on friction between UHMWPE and snow. The surface with good performance on warm snow had wide grooves and narrow plateaus (nonbearing surface), leaving little area on the top. The surface which performed well on cold snow was the opposite, with narrow grooves and wide plateaus (bearing surface). In the measured temperature range the load of the slider is supported by both the surface asperities and a lubricating water layer.13 This water layer may consist of quasi liquid water (QLW),14,15 free water distributed around the contact points of snow grains,16,17 and meltwater caused by frictional heating.13,15 Within this so-called mixed friction region, different types of interactions like solid−solid interaction, wet friction, and capillary suction coexist.18,19 These interactions are summed up by the measured friction coefficient μ and their fraction depends on several factors like the snow temperature and the velocity. For the tested snow temperature close to the melting point (Ts = −2.6 °C), the amounts of QLW and free water are high and meltwater is generated more easily. With increasing water− lubricant the contribution of wet friction and capillary suction on the total friction increases. The friction in the water film,13,20 as well as the capillary suction,21 increases with increasing contact area between ski, water, and snow. For the bearing surface the contact area may have increased faster than that for the nonbearing surface with increasing water amount, leading to a higher total friction force of the bearing surface.6 Similar contact angles were measured for both surfaces. Since the contact angle is a measure for the capillary suction,4,15 we conclude that the difference in friction was not caused by the change in hydrophobicity. At −19.0 °C the bearing surface exhibited lower friction than the nonbearing one. At this snow temperature, especially at low velocities, the amount of water (QLW, free water, and generated meltwater) is smaller.12 The contribution of solid− solid interaction to the total friction is higher than that for snow temperatures closer to the melting point.22 During solid−solid interaction, elastic as well as plastic deformations of the materials occur.23 According to refs 24 and 25, the amount of plastic deformation depends on the peak sharpness of the two frictional partners. The rougher surface in running direction and the sharper peaks of the nonbearing surface may have led to higher plastic deformation of the UHMWPE/wax and the
Table 3. Measured Contact Angle Parameters of the Bearing (ski 1) and Nonbearing (ski 2) Surfacesa θWater (deg) θDiiodmethane (deg) σ mN m−1
ski 1
ski 2
104 ± 3 62 ± 3 27 ± 2
106 ± 2 61 ± 2 28 ± 1
θWater, contact angle between water and ski; θDiiodmethane, contact angle between diiodmethane and ski; σ, apparent surface energy of the ski. a
Figure 6. Coefficient of friction μ̅ for the bearing (ski 1) and nonbearing (ski 2) surfaces dependent on the velocity v for three snow temperatures.
D
DOI: 10.1021/acsami.6b02651 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces Notes
snow grains and, therefore, to a higher friction compared to the bearing surface. Besides the conditions described above, where the surface texture of the UHMWPE affected the snow friction, similar friction was found for the following conditions: At −19 °C for the highest velocity, at −11.1 °C for all velocities, and at −2.6 °C for lower velocities. For these conditions, the abovedescribed effects of the solid−solid interaction at −19 °C and the lubricated friction at −2.6 °C seemed to cancel each other out. Meltwater caused by frictional melting depends among others on the heat output and thereby on the velocity.20,26 Higher velocities cause higher heat output which generates more meltwater, while for lower velocities the opposite happens. At −19 °C and the highest velocity, the effect of the solid−solid interaction on the friction of the bearing surface might have been counteracted by the higher amount of meltwater. At −2.6 °C and lower velocities, less meltwater was present. The fraction of the lubricated friction might have been reduced in favor of an increased share in solid−solid interaction. For the assessment of the practical relevance of the observed μ differences, the equation of motion of a skier modeled as a mass point sliding down an inclined plane of 9° was solved. The start velocity was 5 ms−1, the gliding distance was 300 m, and the end velocities were about 20 ms−1 depending on the different μ values. The drag area (cd·A) was assumed to be 0.27 m2.27 To get a continuous velocity-dependent friction force, the measured μ values were linear interpolated. At −2.6 °C, the nonbearing surface was 0.40 s faster than the bearing one. At −11.1 and −19 °C, on the other hand, the bearing surface was 0.06 and 0.22 s faster than the nonbearing one. These time differences indicate that the surface texture of the ski base may be decisive for the outcome of a ski race.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was funded by the project “K-Regio: Skitechnologie” of the Land Tirol.
5. CONCLUSION In this work we showed that the average roughness parameters (e.g., Sa and Sz) are insufficient to characterize the gliding properties of ski base surfaces. The newly introduced bearing ratio curve and its parameters proved to be a suitable expansion for describing the effect of surface texture on the snow friction. Especially the ratios between the core void volume Vvc and the core material volume Vmc (Vvc/Vmc) and between the reduced valley height Svk and the core roughness depth Sk (Svk/Sk) were useful to distinguish different surfaces. The analyses displayed that for a surface with wide grooves and narrow plateaus friction was less for snow close to the melting point. For cold snow, a surface with narrow grooves and wide plateaus was superior. The friction results were interpreted with different dominant friction processes at different snow conditions. To further reduce snow friction, future research will focus on the systematic adaption of surface textures for a variety of snow conditions by improving established or developing new preparation processes.
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REFERENCES
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