I got a couple of questions regarding the modeling part of the work.
You mentioned that you used Boundary Element Method (BEM) for the contact problem solution and I am wondering, how did you apply BEM to the ski side? Have you used a standard BEM with half-space approximation or have you adjusted the this theory to take into account the finiteness of the ski thickness? If so, do you have any reference to the algorithm? Have you used BEM to describe snow deformation as well?
And a second question is regarding the multi-scale modeling part. How was this realized? Is there any paper on this as well? That would be very helpful!
Thanks for very good questions Aydar. We are currently writing up a paper on the Macro-scale contact mechanics of cross-country skis. We are taking measurements of the ski-camber profile using a SkiSelector (https://www.facebook.com/skiselector/) which is a macro-scale stylus that record the geometry of the ski under a given loading condition. We do a lot of these measurements and then we train an ANN to learn what the profiles look like within the boundaries of the measurement conditions. When we perform the contact mechanics calculations, we need to include both force- and moment balance. But we consider the ski as a/the rigid body that the ANN predicts based on the SkiSelector recording. The counter surface is, however, treated as an elastic half-space and we use the reduced elastic modulus of the ski-base material and the counter surface, i.e. stone if replicating the SkiSelector measurement or numerical snow, if modelling the more realistic situation.
Congratulation, thank you very much for this talk. I have some questions and comments regarding the slide titled “Glide wax and surface texture” at minute 38:50.
The questions first : have you tried to compute the contact area reduction of the surface texture? If so, what method did you use? Do you think that the texture have an impact on the hydrodynamics of the lubricant layer? If so, what do you think this impact is? (for instance, parallel textures allows for water rejections while perpendicular texture water trapping).
Here I post my comments. In my lab we realized experiments with textured sliders gliding on ice (not snow) very similar to the texture presented in your slide (they are 100 microns wide, 10 microns deep and separeted by 250 microns), when the textures where parallel to the movement the friction coefficient was lower than when they were perpendicular. More interesting however was to look at the dependency of the friction coefficient with sliding speed. For perpendicular texture at temperatures close to the metling temperature, we clearly observed a decrease in friction proportional to 1/v, which is compatible with friction models of the like of Oksanen & Keinonen (1982). For parallel structures, a sligh increase of friction proportional to approximately v^1/2 was observed. When fitting the model to experimental data we find a higher contact area for perpendicular textures than for parallel textures. Our interpretation of the result is that perpendicular texture, having higher friction, produces more water at increasing velocity, hence are well described by lubrication models. The parallel textures on the other hand are less sensible to lubrication due to their lower friction. However we were not yet able to directly measure the presence of this water layer, nor to measure the real contact area (which is the only difference between the two sliders). That is why I asked you the questions earlier.
Again, thank you for your talk and I am looking forward to hear again from you.
The texture certainly has an impact on the hydrodynamics of the lubricant layer. I do, however, believe that the hydrodynamics of the water film in this contact generally is completely different than in slider/journal bearings. First of all, the snow surface is porous, really porous and cannot sustain a highly pressurized fluid other than locally around the “summits” of the snow grains. In bearing hydrodynamics, the contacting bodies are normally capturing the entrained lubricant which, due to its viscosity (even for a gas such as air) cannot leak to the edges very easily and therefore makes up a load-carrying film. In cross-country skiing, the water film at the top of the snow grains is more of an easily sheared layer as long as the water spots are not growing too large in size because then they generate a lot of suction and the capillary forces make it hard to break the water bridges that are forming. A ski-base texture that makes the contact area(s) as small as possible and prevents water spots from coalescence and bridging is, therefore, wanted.
Your answer is indeed very helpful, and I thank you a lot for it.
In the experiments we realized, we used ice (for the moment) in order to get rid of the snow porosity problem. So we expect that the produced meltwater remains in contact with the slider (even though we do not consider squeeze out flow which must play an important role).
We manage to have a good fit between the experimental data and the basic friction model (that only considers a couette flow and energy balance). It does not consider the grooves’ geometry at all except for the contact area, and adjusting this contact area we are able to fit the data surprisingly well. The only result that we have is that for perpendicular groove, a higher contact area is observed implying a higher friction coeffcient. We do not find a plausible physical explanation for that difference. If you would like to discuss more in detail our results, I would be very glad. If you want, I can provide you with a poster that briefly summarizes our early findings.
The key points, we belive, is to find a way to couple the hydrodynamics equation within the slider’s geometry (which take into consideration the surface texture) and couple them with an energy balance that generates the lubricant layer and find a way to estimate the contact areat between the slider and ice (we are preparing an experimental setup with interferometry to measure it) in lack of being able to compute it from basic principles. Since we are not a lab specialized in tribology, I would like to request your expertise in the field to orient our choice of modelling the problem.
Here are then my questions: would you use Reynolds equation coupled with a thermal balance to take into account the energy used to melt the ice into a water layer? Or would you use some kind of more complex flow equation? Do we need to use some theoretical model (such as Greenwood & Williamson) to derive contact areas and include it to the model?
I thank you a lot in advance for your future answer and for replying to my previous post.
Very interesting
Indeed 🙂
Its a great talk, thank you Andreas!
I got a couple of questions regarding the modeling part of the work.
You mentioned that you used Boundary Element Method (BEM) for the contact problem solution and I am wondering, how did you apply BEM to the ski side? Have you used a standard BEM with half-space approximation or have you adjusted the this theory to take into account the finiteness of the ski thickness? If so, do you have any reference to the algorithm? Have you used BEM to describe snow deformation as well?
And a second question is regarding the multi-scale modeling part. How was this realized? Is there any paper on this as well? That would be very helpful!
Thanks for very good questions Aydar. We are currently writing up a paper on the Macro-scale contact mechanics of cross-country skis. We are taking measurements of the ski-camber profile using a SkiSelector (https://www.facebook.com/skiselector/) which is a macro-scale stylus that record the geometry of the ski under a given loading condition. We do a lot of these measurements and then we train an ANN to learn what the profiles look like within the boundaries of the measurement conditions. When we perform the contact mechanics calculations, we need to include both force- and moment balance. But we consider the ski as a/the rigid body that the ANN predicts based on the SkiSelector recording. The counter surface is, however, treated as an elastic half-space and we use the reduced elastic modulus of the ski-base material and the counter surface, i.e. stone if replicating the SkiSelector measurement or numerical snow, if modelling the more realistic situation.
The multi-scale effect is considered the same way as scales are separated in homogenisation (two-scale or reiterated homogenisation, see e.g. https://doi.org/10.3390/lubricants6030078, https://doi.org/10.3390/lubricants6040087, https://doi.org/10.1243/13506501JET426)
Congratulation, thank you very much for this talk. I have some questions and comments regarding the slide titled “Glide wax and surface texture” at minute 38:50.
The questions first : have you tried to compute the contact area reduction of the surface texture? If so, what method did you use? Do you think that the texture have an impact on the hydrodynamics of the lubricant layer? If so, what do you think this impact is? (for instance, parallel textures allows for water rejections while perpendicular texture water trapping).
Here I post my comments. In my lab we realized experiments with textured sliders gliding on ice (not snow) very similar to the texture presented in your slide (they are 100 microns wide, 10 microns deep and separeted by 250 microns), when the textures where parallel to the movement the friction coefficient was lower than when they were perpendicular. More interesting however was to look at the dependency of the friction coefficient with sliding speed. For perpendicular texture at temperatures close to the metling temperature, we clearly observed a decrease in friction proportional to 1/v, which is compatible with friction models of the like of Oksanen & Keinonen (1982). For parallel structures, a sligh increase of friction proportional to approximately v^1/2 was observed. When fitting the model to experimental data we find a higher contact area for perpendicular textures than for parallel textures. Our interpretation of the result is that perpendicular texture, having higher friction, produces more water at increasing velocity, hence are well described by lubrication models. The parallel textures on the other hand are less sensible to lubrication due to their lower friction. However we were not yet able to directly measure the presence of this water layer, nor to measure the real contact area (which is the only difference between the two sliders). That is why I asked you the questions earlier.
Again, thank you for your talk and I am looking forward to hear again from you.
Daniel
The texture certainly has an impact on the hydrodynamics of the lubricant layer. I do, however, believe that the hydrodynamics of the water film in this contact generally is completely different than in slider/journal bearings. First of all, the snow surface is porous, really porous and cannot sustain a highly pressurized fluid other than locally around the “summits” of the snow grains. In bearing hydrodynamics, the contacting bodies are normally capturing the entrained lubricant which, due to its viscosity (even for a gas such as air) cannot leak to the edges very easily and therefore makes up a load-carrying film. In cross-country skiing, the water film at the top of the snow grains is more of an easily sheared layer as long as the water spots are not growing too large in size because then they generate a lot of suction and the capillary forces make it hard to break the water bridges that are forming. A ski-base texture that makes the contact area(s) as small as possible and prevents water spots from coalescence and bridging is, therefore, wanted.
I hope this helps, cheers, Andreas
Dear M. Almqvist,
Your answer is indeed very helpful, and I thank you a lot for it.
In the experiments we realized, we used ice (for the moment) in order to get rid of the snow porosity problem. So we expect that the produced meltwater remains in contact with the slider (even though we do not consider squeeze out flow which must play an important role).
We manage to have a good fit between the experimental data and the basic friction model (that only considers a couette flow and energy balance). It does not consider the grooves’ geometry at all except for the contact area, and adjusting this contact area we are able to fit the data surprisingly well. The only result that we have is that for perpendicular groove, a higher contact area is observed implying a higher friction coeffcient. We do not find a plausible physical explanation for that difference. If you would like to discuss more in detail our results, I would be very glad. If you want, I can provide you with a poster that briefly summarizes our early findings.
The key points, we belive, is to find a way to couple the hydrodynamics equation within the slider’s geometry (which take into consideration the surface texture) and couple them with an energy balance that generates the lubricant layer and find a way to estimate the contact areat between the slider and ice (we are preparing an experimental setup with interferometry to measure it) in lack of being able to compute it from basic principles. Since we are not a lab specialized in tribology, I would like to request your expertise in the field to orient our choice of modelling the problem.
Here are then my questions: would you use Reynolds equation coupled with a thermal balance to take into account the energy used to melt the ice into a water layer? Or would you use some kind of more complex flow equation? Do we need to use some theoretical model (such as Greenwood & Williamson) to derive contact areas and include it to the model?
I thank you a lot in advance for your future answer and for replying to my previous post.
Best regards,
Daniel