Accurate modelling of friction coefficient is of primary importance in efficiency, vibration and failure analyses of enclosed gear drives. After showing the influence of surface/lubricant interactions on friction, the authors used a semi-empirical model which can take all these aspects into account. Lubricant is modelled as an Eyring–Reynolds fluid and rough surfaces are described with two parameters via a stochastic approach. A specific two-disc machine is used to perform series of friction measurements on smooth and rough discs. Smooth discs allow to operate under full film lubrication and to measure a reference shear stress of lubricant, whereas rough discs reproduce gear tooth roughness and generate a representative value of friction on asperities. The purpose of this present paper is to describe calculations of this physical-based friction coefficient model and to present the experimental process. On the basis of new results, the impact of a surface finishing process is assessed as well as the consequence of calculating friction coefficient based on oil injection instead of local bulk temperature.
DowsonDHigginsonGR. Elasto-Hydrodynamic lubrication: the fundamentals of roller and gear lubrication. United Kingdom: Pergamon Press, 1966.
2.
BjörlingMHabchiWBairS,et al.Towards the true prediction of EHL friction. Tribol. Int.2013; 66: 19–26.
3.
ZhuDHuYZ. A computer program package for the prediction of EHL and mixed lubrication characteristics, friction, subsurface stresses and flash temperatures based on measured 3-d surface roughness. Tribol. Trans.2001; 44: 383–390.
4.
PeiJHanXTaoY,et al.Mixed elastohydrodynamic lubrication analysis of line contact with Non-Gaussian surface roughness. Tribol. Int.2020; 151: 106449.
5.
ZhangXLiZWangJ. Friction prediction of rolling-sliding contact in mixed EHL. Meas. J. Int. Meas. Confed.2017; 100: 262–269.
6.
WuSChengHS. A friction model of partial-Ehl contacts and Its application to power loss in spur gears. Tribol. Trans.1991; 34: 398–407.
7.
ChimanpureASKahramanATalbotD. A transient mixed elastohydrodynamic lubrication model for helical gear contacts. J. Tribol.2021; 143: 1–15.
8.
LiSKahramanA. A transient mixed elastohydrodynamic lubrication model for spur gear pairs. J. Tribol.2010; 132: 1–9.
9.
AkbarzadehSKhonsariMM. Performance of spur gears considering surface roughness and shear thinning lubricant. J. Tribol.2008; 130: 1–8.
10.
VilleFNéliasDTourloniasG,et al.On the Two-disc machine: a polyvalent and powerful tool to study fundamental and industrial problems related to elastohydrodynamic lubrication. Tribol. Ser.2001; 39: 393–402.
11.
KuzminNF. Coefficient of friction in heavily loaded contact. Vestn. Mashinostroeniya1954; 34: 18–26.
12.
MisharinYA. Influence of the Friction Condition on the Magnitude of the Friction Coefficient in the Case of Rollers with Sliding. In: Proceedings of the International Conference on Gearing, 1958, pp.159–164. London, UK: Institution of Mechanical Engineers, London.
O’DonoghueJPCameronA. Friction and temperature in rolling sliding contacts. ASLE Trans.1966; 9: 186–194.
16.
KelleyBWLemanskiAJ. Lubrication of involute gearing. Proc. Inst Mech. Eng.1967; 182: 173–184.
17.
DrozdovYNGavrikovYA. Friction and scoring under the conditions of simultaneous rolling and sliding of bodies. Wear1968; 11: 291–302.
18.
MatsumotoSMorikawaK. 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: International Gear Conference, 2014, pp.1078–1088.
19.
CastroJSeabraJ. Coefficient of friction in mixed film lubrication: gears versus twin-discs. Proc. Inst Mech. Eng. Part J J. Eng. Tribol.2007; 221: 399–411.
20.
DiabYVilleFVelexP. Prediction of power losses Due to tooth friction in gears. Tribol. Trans.2006; 49: 260–270.
JohnsonKLRobertsAD. Observations of viscoelastic behaviour of an elastohydrodynamic lubricant film. Proc. R. Soc. A Math. Phys. Eng. Sci.1974; 337: 217–242.
HirstWMooreAJ. Elastohydrodynamic lubrication at high pressures. Proc. R. Soc. A Math. Phys. Eng. Sci.1978; 360: 403–425.
25.
HoupertLFlamandLBertheD. Rheological and thermal effects in lubricated E.H.D. Contacts. ASME J. Lubr. Technol.1981; 103: 526–532.
26.
EvansCRJohnsonK,L. The rheological properties of elastohydrodynamic lubricants. Proc. Inst Mech. Eng. Part C J. Mech. Eng. Sci.1986; 200: 303–3012.
27.
GuptaPKChengHSZhuD,et al.Viscoelastic effects in MIL-L-7808-type lubricant, part I: analytical formulation. Tribol. Trans.2008; 35: 269–274.
28.
SottomayorACamposASeabraJ,et al.Experimental evaluation and numerical simulation of MIL-L-23699 traction curves: in memorium of georges tourlonias. Tribol. Ser.2004; 43: 795–806.
29.
OlverAV. Gear lubrication―a review. Proc. Inst Mech. Eng. Part J J. Eng. Tribol.2002; 216: 255–267.
30.
ChangenetCOviedo-MarlotXVelexP. Power loss predictions in geared transmissions using thermal networks-applications to a Six-speed manual gearbox. J. Mech. Des.2006; 128: 618.
31.
LiuHCZhangBBBaderN,et al.Crucial role of solid body temperature on elastohydrodynamic film thickness and traction. Tribol. Int.2019; 131: 386–397.
32.
IsaacGChangenetCVilleF,et al.Thermal analysis of twin-disc machine for traction tests and scuffing experiments. Proc. Inst Mech. Eng. Part J J. Eng. Tribol.2018; 232: 1548–1560.
33.
TallianTE. The theory of partial elastohydrodynamic contacts. Wear1972; 21: 49–101.
34.
MartinKF. A review of friction predictions in gear teeth. Wear1978; 49: 201–238.
35.
HamrockJ. Fundamentals of fluid film lubrication. 1st Ed. US: McGraw-Hill, 1994.
36.
HertzH. Über Die berührung fester elastischer körper. J. für Reine und Angew. Math.1881; 92: 156–171.
37.
CoulombCA. Théorie Des machines simples. Paris: Bachelier, 1821, p.368.
38.
HirstWMooreAJ. Non-Newtonian behaviour in elastohydrodynamic lubrication. Proc. R. Soc. A Math. Phys. Eng. Sci.1974; 337: 101–121.
39.
NewtonI. Philosophiae naturales principia mathematica. 3rd ed. London: Cambridge University Press, 1726, p.572.
40.
EyringH. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys.1936; 4: 283–291.
41.
MooreAJ. The behaviour of lubricants in elastohydrodynamic contacts. Proc. Inst Mech. Eng. Part J J. Eng. Tribol.1997; 211: 91–106.
42.
ForsterNHSchrandJBGuptaPK. Viscoelastic effects in MIL-L-7808-type lubricant, part II: experimental data correlations. Tribol. Trans.1992; 35: 275–280.
43.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts part III — fully flooded results. J. of Lubrication Tech. 1977; 99 (2): 264–275.
44.
BreweDEHamrockBJ. Simplified solution for elliptical-contact deformation between Two elastic solids. ASME J. Lubr. Technol.1977; 99: 485–487.
45.
VogelDH. Das temperaturabhaengigkeitsgesetz Der viskositaet von fluessigkeiten. Phys. Zeitschrift1921; 22: 645.
46.
RoelandsCJAVlugterJCWatermanHI. The viscosity-temperature-pressure relationship of lubricating oils and Its correlation with chemical constitution. ASME J. Basic Eng.1963; 11: 601–610.
47.
DowsonDHigginsonGRWhitakerAV. Elasto-Hydrodynamic lubrication: a survey of isothermal solutions. J. Mech. Eng. Sci.1962; 4: 121–126.
OlverAVSpikesHA. Prediction of traction in elastohydrodynamic lubrication. Proc. Inst Mech. Eng. Part J J. Eng. Tribol.2001; 215: 321–332.
50.
BlokH. The flash temperature concept. Wear1963; 6: 483–494.
51.
SaylesRand ThomasSRT. Thermal conductance of a rough elastic contact. Appl. Energy1976; 2: 249–267.
52.
FrancisHA. Application of spherical indentation mechanics to reversible and irreversible contact between rough surfaces. Wear1977; 45: 221–269.
53.
MannersWGreenwoodJA. Some observations on Persson's Diffusion theory of elastic contact. Wear2006; 261: 600–610.
54.
ISO 4287- Geometrical Product Specification (GPS) – Surface Texture: Profile Method – Terms, Definitions and Surface Texture Parameters, 1997. https://www.iso.org/standard/10132.html
55.
ISO 4288- Geometrical Product Specification (GPS) – Surface Texture: Profile Method – Rules and Procedures for the Assessment of Surface Texture, 1998. https://www.iso.org/standard/2096.html
56.
ISO 16610-21- Geometrical Product Specification (GPS) – Filtration – Part 21: Linear Profile Filters: Gaussian Filters, 2012. https://www.iso.org/standard/50176.html
57.
GreenwoodJAWilliamsonJBP. Contact of nominally flat surfaces. Proc. R. Soc. Lond. A. Math. Phys. Sci.1967; 295: 300–319.
58.
Longuet-HigginsMS. The statistical analysis of a random, moving surface. Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci.1957; 249: 321–387.
59.
BushAWGibsonRDThomasTR. The elastic contact of a rough surface. Wear1975; 35: 87–111.
60.
NayakPR. Random process model of rough surfaces. ASME J. Lubr. Technol.1971; 93: 398–407.
61.
GuptaPKFlamandLBertheD,et al.On the traction behavior of several lubricants. ASME J. Lubr. Technol.1981; 103: 55–64.
