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The slipperiness of ice is well known while, for ice skating, its mechanism still needs further investigation, where the complex interactions including the thermal conduction of the skate–meltwater–ice system, the ploughing and the frictional melting of ice to the friction force are still unclear. This study presents a theoretical framework and a simplified analytical solution to unveil the friction mechanism when a curved skate sliding on ice. The theory is validated by experiments and the effects of these various factors, including the sliding velocity, the ice temperature, the supporting weight, and the geometry of the skate blade to the friction are revealed in detail. This study finds that the contribution of friction force from the ploughing deformation through skate indentation and that from the fluid friction through the shear motion of the meltwater layer is comparable with each other, which thus clarifies how the ploughing deformation of the ice substrate together with its frictional melting regulates the friction during skating.


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How ploughing and frictional melting regulate ice-skating friction

Show Author's information Feng DU1( )Peng KE1Ping HONG2
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
Beijing Sports University, Beijing 100084, China

Abstract

The slipperiness of ice is well known while, for ice skating, its mechanism still needs further investigation, where the complex interactions including the thermal conduction of the skate–meltwater–ice system, the ploughing and the frictional melting of ice to the friction force are still unclear. This study presents a theoretical framework and a simplified analytical solution to unveil the friction mechanism when a curved skate sliding on ice. The theory is validated by experiments and the effects of these various factors, including the sliding velocity, the ice temperature, the supporting weight, and the geometry of the skate blade to the friction are revealed in detail. This study finds that the contribution of friction force from the ploughing deformation through skate indentation and that from the fluid friction through the shear motion of the meltwater layer is comparable with each other, which thus clarifies how the ploughing deformation of the ice substrate together with its frictional melting regulates the friction during skating.

Keywords: coefficient of friction, skating, ice friction, ploughing, frictional melting

References(58)

[1]
Kietzig A M, Hatzikiriakos S G, Englezos P. Physics of ice friction. J Appl Phys 107: 081101 (2010)
[2]
Liefferink R W, Hsia F C, Weber B, Bonn D. Friction on ice: how temperature, pressure, and speed control the slipperiness of ice. Phys Rev X 11(1): 011025 (2021)
[3]
Hong J L, Talalay P, Zhang N, Fan X P. Controlling mechanism of temperature dependence of kinetic friction of ice. J Tribol 142(8): 081704 (2020)
[4]
Weber B, Nagata Y, Ketzetzi S, Tang F J, Smit W J, Bakker H J, Backus E H G, Bonn M, Bonn D. Molecular insight into the slipperiness of ice. J Phys Chem Lett 9(11): 2838–2842 (2018)
[5]
Böttcher R, Seidelmann M, Scherge M. Sliding of UHMWPE on ice: experiment vs. modeling. Cold Reg Sci Technol 141: 171–180 (2017)
[6]
Yun C, Choi J W, Kim H, Kim D, Kim H. Sliding on ice: real contact area, melted film thickness, and friction force. Int J Heat Mass Transfer 160: 120166 (2020)
[7]
Baurle L, Szabo D, Fauve M, Rhyner H, Spencer N D. Sliding friction of polyethylene on ice: tribometer measurements. Tribol Lett 24(1): 77–84 (2006)
[8]
Persson B N J. Ice friction: Role of non-uniform frictional heating and ice premelting. J Chem Phys 143: 224701 (2015)
[9]
Oosterkamp T H, Boudewijn T, van Leeuwen J M J. Skating on slippery ice. Europhys News 50: 28–32 (2019)
[10]
Ovaska M, Tuononen A J. Multiscale imaging of wear tracks in ice skate friction. Tribol Int 121: 280–286 (2018)
[11]
Tikanmäki M, Sainio P. Experiments on friction of dry and wet ice. Cold Reg Sci Technol 172: 102990 (2020)
[12]
Tuononen A J, Kriston A, Persson B. Multiscale physics of rubber-ice friction. J Chem Phys 145(11): 114703 (2016)
[13]
Marmo B A, Blackford J R, Jeffree C E, Ice friction, wear features and their dependence on sliding velocity and temperature. J Glaciol 51(174): 391–398 (2017)
[14]
Spagni A, Berardo A, Marchetto D, Gualtieri E, Pugno N M, Valeri S. Friction of rough surfaces on ice: experiments and modeling. Wear 368–369: 258–266 (2016)
[15]
Irbe M, Gross KA, Viba J, Cerpinska M, Unveiling ice friction and aerodynamic drag at the initial stage of sliding on ice: Faster sliding in winter sports. Tribol Int 160: 106967 (2021)
[16]
Kietzig A M, Hatzikiriakos S G, Englezos P. Ice friction: the effects of surface roughness, structure, and hydrophobicity. J Appl Phys 106: 024303 (2009)
[17]
Maeno N, Arakawa M, Adhesion shear theory of ice friction at low sliding velocities, combined with ice sintering. J Appl Phys 95(1): 134–139 (2004)
[18]
Lever J H, et al. Revisiting mechanics of ice–skate friction: from experiments at a skating rink to a unified hypothesis. J Glaciol 68(268): 337–356 (2022)
[19]
Lever J H, Asenath-Smith E, Taylor S, Lines A P. Assessing the mechanisms thought to govern ice and snow friction and their interplay with substrate brittle behavior. Front Mech Eng-Switz 7: 690425 (2021)
[20]
Ribeiro I d A, de Koning M, Grain-boundary sliding in ice Ih: tribology and rheology at the nanoscale. J Phys Chem C 125(1): 627–634 (2021)
[21]
van Leeuwen J M J. Skating on slippery ice. SciPost Phys 3(6): 042 (2017)
[22]
Wagner W, Riethmann T, Feistel R, Harvey A H. New equations for the sublimation pressure and melting pressure of H2O ice Ih. J Phys Chem Ref DATA 40(4) (2011)
[23]
Nagata Y, Hama T, Backus E H G, Mezger M, Bonn D, Bonn M, Sazaki G. The surface of ice under equilibrium and nonequilibrium conditions. Acc Chem Res 52: 1006–1015 (2019)
[24]
Slater B, Michaelides A. Surface premelting of water ice. Nat Rev Chem 3: 172–188 (2019)
[25]
Benet J, Llombart P, Sanz E, MacDowell L G. Premelting- induced smoothening of the ice-vapor interface. Phys Rev Lett 117: 096101 (2016)
[26]
Le Berre M, Pomeau Y. Theory of ice-skating. Int J Non- Linear Mech 75: 77–86 (2015)
[27]
Lozowski E, Szilder K, Maw S. A model of ice friction for a speed skate blade. Sports Eng 16(4): 239–253 (2013)
[28]
van Dongen M E H, Smeulders D M J, Ice speed skating: Onset of lubrication by frictional heating. EPL 134(3): 34005 (2021)
[29]
Lozowski E P, Szilder K. Derivation and new analysis of a hydrodynamic model of speed skate ice friction. Int J Offshore Polar Eng 23(2): 104–111 (2013)
[30]
Bonn D. The physics of ice skating. Nature 577(7789): 173–174 (2020)
[31]
Canale L, Comtet J, Niguès A, Cohen C, Clanet C, Siria A, Bocquet L. Nanorheology of interfacial water during ice gliding. Phys Rev X 9(4): 041025 (2019)
[32]
Replace it by: Du F, Analytical theory of ice-skating with flat contact. Tribol Lett 71: 5 (2023)
[33]
van Leeuwen J M J. The friction of tilted skates on ice. SciPost Physics 8(4): 059 (2020)
[34]
von Schleinitz J, Wörle L, Graf M, Schröder A. Modeling ice friction for vehicle dynamics of a bobsled with application in driver evaluation and driving simulation. Tribol Int 165: 107344 (2022)
[35]
Gross K A, et al. Surface hierarchy: macroscopic and microscopic design elements for improved sliding on ice. Lubricants 9(10): 103 (2021)
[36]
Penny A, Lozowski E, Forest T, Fong C, Maw S, Montgomery P, Sinha N. Speedskate ice friction: review and numerical model - Fast 1.0. Phys Chem Ice 495–504 (2007)
[37]
Lozowski E P, Szilder K, Poirier L. A bobsleigh ice friction model. Int J Offshore Polar Eng 24(1): 52–60 (2014)
[38]
Makkonen L. A thermodynamic model of sliding friction. AIP Adv 2(1): 012179 (2012)
[39]
Lienhard IV J H, Lienhard V J H. A Heat Transfer Textbook, 3rd edition. Cambridge (USA): Phlogiston Press, 2000.
[40]
Thiévenaz V, Séon T, Josserand C, Solidification dynamics of an impacted drop. J Fluid Mech 874: 756–773 (2019)
[41]
Natale M F, Santillan Marcus E A, Tarzia D A, Explicit solutions for one-dimensional two-phase free boundary problems with either shrinkage or expansion. Nonlinear Anal- Real 11(3): 1946–1952 (2010)
[42]
Poirier L, Lozowski E P, Thompson R I. Ice hardness in winter sports. Cold Reg Sci Tech 67 (3): 129–134 (2011)
[43]
Lugt P M, Morales-Espejel G E. A review of elasto- hydrodynamic lubrication theory. Tribol Trans 54(3): 470–496 (2011)
[44]
Gong R Z, Li D Y, Wang H J, Han L, Qin D Q. Analytical solution of Reynolds equation under dynamic conditions. Proc IMechE Part J: J Engineering Tribology 230 (4): 416–427 (2015)
[45]
Chien S Y, Cramer M S, Untaroiu A. Compressible reynolds equation for high-pressure gases. Phys Fluids 29(11): 116101 (2017)
[46]
Ashmore J, del Pino C, Mullin T. Cavitation in a lubrication flow between a moving sphere and a boundary. Phys Rev Lett 94(12): 124501 (2005)
[47]
Ince S T, Kumar A, Paik J K, A new constitutive equation on ice materials. Ships Offshore Struc 12(5): 610–623 (2016)
[48]
Stamboulides C, Englezos P, Hatzikiriakos S G, The ice friction of polymeric substrates. Tribol Int 55: 59–67 (2012)
[49]
Itagaki K, Lemieux G E, Huber N P, The double twist connection and the S3 blue phase. J Phys (Paris) 48: 297 (1987)
[50]
Kietzig A M, Hatzikiriakos S G, Englezos P, Ice friction: the effect of thermal conductivity. J Glaciol 56(197): 473–479 (2010)
[51]
de Koning J J, de Groot G, van Ingen Schenau G J. Ice friction during speed skating, J Biomech 25(6): 565–571 (1992)
[52]
Scherge M, Böttcher R, Spagni A, Marchetto D, High-speed measurements of steel–ice friction: experiment vs. calculation. Lubricants 6(1): 26 (2018)
[53]
Mielonen K, Jiang, Yu V, Joel D, Alexander H, Leo S, Mika P, Tapani A. Sliding friction of hierarchically micro–micro textured polymer surfaces on ice. Cold Reg Sci Technol 163: 8–18 (2019)
[54]
Jansons E, Irbe M, Gross K A, Influence of weather conditions on sliding over ice at a push-start training facility. Biotribology 25: 100152 (2021)
[55]
Poirier L, Lozowski E P, Maw S, Stefanyshyn D J, Thompson R I. Experimental analysis of ice friction in the sport of bobsleigh. Sports Eng 14(2–4): 67–72 (2011)
[56]
Houdijk H, Wijker A J, De Koning J J, Bobbert M F, De Groot G. Ice friction in speed skating: can klapskates reduce ice frictional loss? Med Sci Sport Exer 33(3): 499–504 (2001)
[57]
Formenti F, Minetti A E. Human locomotion on ice: The evolution of ice-skating energetics through history. J Exp Biol 210: 1825–1833 (2007)
[58]
Federolf P A, Mills R, Nigg B. Ice friction of flared ice hockey skate blades. J Sports Sci 26(11): 1201–1208 (2008)
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Publication history

Received: 29 May 2022
Revised: 12 September 2022
Accepted: 26 October 2022
Published: 23 March 2023
Issue date: November 2023

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© The author(s) 2022.

Acknowledgements

This research was primary supported by National Key R&D Program of China (2020YFF0304600).

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