The accurate prediction of friction coefficient and power losses in the gear mesh is a key subject to several gear-related fields of study. However, there is still not a unified method for large ranges of operating conditions, different gear geometries and lubricant types. The current paper meets this demand by modelling partial EHL friction with an asperity-fluid load sharing approach where fluid traction is calculated with the Ree-Eyring equation and the reference stress behaviour is predicted from piezoviscosity coefficient. It will be shown that only an accurate description of the lubricant’s viscosity behaviour is required to compute friction in gears. Finally, mesh power losses are predicted considering thermal effects and numerical predictions are compared to experimental results showing good agreement.
Jurkschat T, Lohner T, Michaelis K, et al. Experimentelle Bestimmung des Reibungsverhaltens von Schrägverzahnungen mit Flankenmodifikationen. In: Proceedings of the 57.GfT – Tribologie-Fachtagung. Göttingen, Germany, September 2016.
2.
FernandesCMMarquesPMMartinsRCet al.Gearbox power loss. Part II: Friction losses in gears. Tribol Int2014; 88: 309–316.
3.
AnderssonMSosaMOlofssonU. The effect of running-in on the efficiency of superfinished gears. Tribol Int2016; 93: 71–77.
4.
Ohlendorf H. Verlustleistung und Erwärmung von Stirnrädern. PhD Thesis, Technische Universität München, 1958.
5.
Wimmer AJ. Lastverluste von Stirnradverzahnungen – Konstruktive Einflüsse, Wirkungsgradmaximierung, Tribologie. PhD Thesis, Technische Universität München, 2005.
6.
VelexPVilleF. An analytical approach to tooth friction losses in spur and helical gears-influence of profile modifications. J Mech Des2009; 131: 101008–1–101008–10.
7.
Doleschel A. Wirkungsgradberechnung von Zahnradgetrieben in Abhängigkeit vom Schmierstoff. PhD Thesis, Technische Universität München, 2003.
8.
XiYBjörlingMShiYet al.Traction formula for rolling-sliding contacts in consideration of roughness under low slide to roll ratios. Tribol Int2016; 104: 263–271.
ZiegltrumALohnerTStahlK. TEHL simulation on the influence of lubricants on load-dependent gear losses. Tribol Int2016; 113: 252–261.
11.
XuHAndersonNMaddockDet al.Prediction of mechanical efficiency of parallel-axis gear Pairs. J Mech Des2007; 129: 58–68.
12.
LiSKahramanA. A method to derive friction and rolling power loss formulae for mixed elastohydrodynamic lubrication. J Adv Mech Des Syst Manuf2011; 5: 252–263.
13.
TallianT. The theory of partial elastohydrodynamic contacts. Wear1972; 21: 49–101.
14.
Matsumoto S and Morikawa K. The new estimation formula of coefficient of friction in rolling-sliding contact surface under mixed lubrication condition for the power loss reduction of power transmission gears. In: Proceedings of the international gear conference 2014. August 2014, Lyon, France: Woodhead Publishing, pp.1078–1088.
15.
Robbe-Valloire F. Theoretical prediction and experimental results for mixed lubrication between parallel surfaces. In: Dowson D (ed.) Boundary and mixed lubrication – science and applications, vol. 40. Vienna, Austria: Elsevier Science, 2002, pp.129–137.
16.
FaraonISchipperD. Stribeck curve for starved line contacts. J Tribol Transact ASME2007; 129: 181–187.
17.
MasjediMKhonsariM. Theoretical and experimental investigation of traction coefficient in line-contact EHL of rough surfaces. Tribol Int2014; 70: 179–189.
18.
DiabYVilleFVelexP. Prediction of power losses due to tooth friction in gears. Tribol Transact2006; 49: 260–270.
19.
JohnsonKTevaarwerkJ. Shear behaviour of elastohydrodynamic oil films. Proc R Soc Lond Ser A (Math Phys Sci)1977; 356: 215–236.
20.
Sottomayor AG. Reologia de um lubrificante Não-Newtoniano no interior de um contacto termoelastohidrodinâmico: Determinação dos parâmetros reológicos de um lubrificante. PhD Thesis, Faculdade de Engenharia da Universidade do Porto, 2002.
21.
BjörlingMHabchiWBairSet al.Towards the true prediction of EHL friction. Tribol Int2013; 66: 19–26.
22.
Sharif K, Morris S, Evans H, et al. Comparison of non-Newtonian EHL models in high sliding applications. In: Dalmaz G, Lubrecht A, Dowson D, et al. (eds) Tribology research: from model experiment to industrial problem, Tribology series, vol. 39. Lyon, France: Elsevier, 2001, pp.787–796.
23.
BerceaMPaleuVBerceaI. Lubricant oils additivated with polymers in EHD contacts: Part 1. Rheological behaviour. Lubricat Sci2004; 17: 1–24.
24.
BairSWinerW. High shear stress rheology of liquid lubricants at pressures of 2 to 200 MPa. ASME J Tribol1989; 112: 245–252.
25.
JacodBVennerCLugtP. Extension of the friction mastercurve to limiting shear stress models. ASME J Tribol2003; 125: 739–746.
26.
HirstWMooreA. Elastohydrodynamic lubrication at high pressures. II. Non-Newtonian behaviour. Proc R Soc Lond Ser A (Math Phys Sci)1979; 365: 537–565.
27.
ClarkeAWeeksIEvansHet al.An investigation into mixed lubrication conditions using electrical contact resistance techniques. Tribol Int2016; 93: 709–716.
28.
StewardJ. The compliance of solid, wide-faced spur gears. J Mech Des1990; 112: 590–595.
OlverA. Testing transmission lubricants: the importance of thermal response. Proc IMechE, Part G: J Aerospace Engineering1991; 205: 35–44.
31.
ISO/TR 15144-1. Calculation of micropitting load capacity of cylindrical spur and helical gears – Part 1: Introduction and basic principles, 2nd Edition, International Organization for Standardization, September 2014.
32.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: Part III – Fully flooded results. J Tribol1977; 99: 264–275.
33.
van LeeuwenH. The determination of the pressure–viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Proc IMechE, Part J: J Engineering Tribology2009; 223: 1143–1163.
34.
Mann U. Schmierfilmbildung in Elastohydrodynamischen Kontakten. PhD Thesis, Technische Universität München, 1995.
35.
HöglundE. Influence of lubricant properties on elastohydrodynamic lubrication. Wear1999; 232: 176–184.
36.
BairS. Choosing pressure-viscosity relations. High Temp High Pressure2015; 44: 415–428.
37.
GoldPWSchmidtADickeHet al.Viscosity-pressure-temperature behaviour of mineral and synthetic oils. J Synthetic Lubricat2001; 18: 51–79.
38.
Michaelis K. Die Integraltemperatur zur Beurteilung der Freßtragfähigkeit von Stirnradgetrieben. PhD Thesis, Technische Universität München, 1987.
39.
HiliJOlverAVEdwardsSet al.Experimental investigation of elastohydrodynamic (EHD) film thickness behavior at high speeds. Tribol Transact2010; 53: 658–666.
40.
Hinterstoißer M. Zur Optimierung des Wirkungsgrades von Stirnradgetrieben. PhD Thesis, Technische Universität München, 2014.
41.
Morales-EspejelGWemekampAW. Ertel-Grubin methods in elastohydrodynamic lubrication-a review. Proc IMechE, Part J: J Engineering Tribology2008; 222: 15–34.
42.
SpikesHJieZ. History, origins and prediction of elastohydrodynamic friction. Tribol Lett2014; 56: 1–25.
43.
BairSVergnePKumarPet al.Comment on “history, origins and prediction of elastohydrodynamic friction”. Tribol Lett2015; 58: 1–8.
44.
SpikesHJieZ. Reply to the comment by Scott Bair et al. on “History, origins and prediction of elastohydrodynamic friction” by Spikes and Jie in Tribology Letters. Tribol Lett2015; 58: 1–6.
45.
BobzinKBrogelmannTStahlKet al.Friction reduction of highly-loaded rolling-sliding contacts by surface modifications under elasto-hydrodynamic lubrication. Wear2015; 328-329: 217–228.
46.
LohnerTMayerJMichaelisKet al.On the running-in behavior of lubricated line contacts. Proc IMechE, Part J: J Engineering Tribology2015; 231: 441–452.
