In this paper, analytical equations for the central film thickness in slender elliptic contacts are investigated. A comparison of state-of-the-art formulas with simulation results of a multilevel elastohydrodynamic lubrication solver is conducted and shows considerable deviation. Therefore, a new film thickness formula for slender elliptic contacts with variable ellipticity is derived. It incorporates asymptotic solutions, which results in validity over a large parameter domain. It captures the behaviour of increasing film thickness with increasing load for specific very slender contacts. The new formula proves to be significantly more accurate than current equations. Experimental studies and discussions on minimum film thickness will be presented in a subsequent publication.
DowsonDHigginsonGR. New Roller Bearing Lubrication formula. Engineering1961; 192: 158–159.
2.
DowsonDToyodaS. A central film thickness formula for elastohydrodynamic line contacts. In: Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, Leeds, 1978, pp.60–64.
3.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: Part I—theoretical formulation. J Lubr Technol1976; 98: 223–228.
4.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: Part II—ellipticity parameter results. J Lubr Technol1976; 98: 375–381.
5.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: part III—fully flooded results. J Lubr Technol1977; 99: 264–275.
6.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: Part IV—starvation results. J Lubr Technol1977; 99: 15–23.
7.
LubrechtAAVennerCHColinF. Film thickness calculation in elasto-hydrodynamic lubricated line and elliptical contacts: The Dowson, Higginson, Hamrock contribution. Proc Inst Mech Eng, Part J2009; 223: 511–515.
8.
RangerAPEttlesCMMCameronA. The solution of the point contact elasto-hydrodynamic problem. Proc R Soc Lond Ser A, Math Phys Sci1975; 346: 227–244.
9.
ZhuDWangQ. Elastohydrodynamic Lubrication: A gateway to interfacial mechanics—review and prospect. J Tribol2011; 10: 133.
10.
MoesH. Optimum similarity analysis with applications to elastohydrodynamic lubrication. Wear1992; 159: 57–66.
11.
NijenbanningGVennerCHMoesH. Film thickness in elastohydrodynamically lubricated elliptic contacts. Wear1994; 176: 217–229.
12.
ChittendenRJDowsonDDunnJF, et al. A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse. Proc R Soc Lond A Math Phys Sci1985; 397: 245–269.
13.
WheelerJDVergnePFillotN, et al. . On the relevance of analytical film thickness EHD equations for isothermal point contacts: Qualitative or quantitative predictions?Friction2016; 4: 369–379.
14.
MoesH. Lubrication and Beyond. Enschede, University of Twente, 2000.
15.
VennerCHLubrechtAA. Revisiting film thickness in slender elasto-hydrodynamically lubricated contacts. Proc Inst Mech Eng, Part C2010; 224: 2549–2558.
16.
KanetaMKawashimaRMasudaS, et al. Thermal effects on the film thickness in elliptic EHL contacts with entrainment along the major contact axis. J Tribol2002; 124: 420–427. https://doi.org/10.1115/1.1430675.
17.
WolfMSannerAFatemiA. A semi-analytical approach for rapid detection of roller-flange contacts in roller element bearings. Proc IMechE, Part J: J Engineering Tribology2020; 235: 1440–1449. https://doi.org/10.1177/1350650120964295.
18.
ShirzadeganMBjörlingMAlmqvistA, et al. Low degree of freedom approach for predicting friction in elastohydrodynamically lubricated contacts. Tribol Int2016; 94: 560–570.
19.
ShirzadeganMLarssonRAlmqvistA. A low degree of freedom approach for prediction of friction in finite EHL line contacts. Tribol Int2017; 115: 628–639.
20.
OteroJEde la Guerra OchoaETanarroEC, et al. Friction coefficient in mixed lubrication: A simplified analytical approach for highly loaded non-conformal contacts. Adv Mech Eng2017; 9: 1–11. DOI: Available from: https://doi.org/10.1177/1687814017706266.
21.
MasjediMKhonsariMM. An engineering approach for rapid evaluation of traction coefficient and wear in mixed EHL. Tribol Int2015; 92: 184–190.
22.
SharifKJKongSEvansHP, et al. Contact and elastohydrodynamic analysis of worm gears Part 2: Results. Proc IMechE, Part C: J Mechanical Engineering Science2001; 215: 831–846.
23.
JangJYKhonsariMMBairS. Correction factor formula to predict the central and minimum film thickness for shear-thinning fluids in EHL. J Tribol2008; 130: 024501.
24.
PandeyRKGhoshMK. Thermal effects on film thickness and traction in rolling/sliding EHL line contacts—an accurate inlet zone analysis. Wear1996; 192: 118–127.
25.
VennerCHNapelW. Multilevel solution of the elastohydrodynamically lubricated circular contact problem Part I: Theory and numerical algorithm. Wear1992; 152: 351–367.
WangW. 2013) EHL, Full Numerical Solution Methods. In: WangQJChungYW (eds) Encyclopedia of tribology. Boston, MA, Springer US, pp.852–859.
28.
VergnePBairS. Classical EHL versus quantitative EHL: A perspective Part I-real viscosity-pressure dependence and the viscosity-pressure coefficient for predicting film thickness. Tribol Lett2014; 54: 1–12.
29.
BlokH. Inverse problems in hydrodynamic lubrication and design directives for lubricated flexible surfaces. In: Proceeedings of international symposium lubrication and wear, Houston, 1963, 7, Available from:https://ci.nii.ac.jp/naid/10026701153/en/.
30.
VennerCHNapelW. Multilevel solution of the elastohydrodynamically lubricated circular contact problem part II: Smooth surface results. Wear1992; 152: 369–381.
31.
ChittendenRJDowsonDDunnJFTaylorCM, et al. A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. II. General case, with lubricant entrainment along either principal axis of the Hertzian contact ellipse or at some intermediate angle. Proc R Soc Lond A Math Phys Sci1985; 397: 271–294.
32.
EvansHPSnidleRW. The isothermal elastohydrodynamic lubrication of spheres. J Lubr Technol1981; 103: 547–557.
33.
MasjediMKhonsariMM. On the effect of surface roughness in point-contact EHL: Formulas for film thickness and asperity load. Tribol Int2015; 82: 228–244.
34.
CanziAVennerCHLubrechtAA. Film thickness prediction in elastohydrodynamically lubricated elliptical contacts. Proc Inst Mech Eng, Part J2010; 224: 917–923.
35.
MarianMBartzMWartzackS, et al. Non-dimensional groups, film thickness equations and correction factors for elastohydrodynamic lubrication: A review. Lubricants2020; 8. Available from: https://www.mdpi.com/2075-4442/8/10/95.
36.
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.
37.
HamrockBJSchmidSRJacobsonBO. Lubricant Properties. In: FaulknerLL (ed.) Fundamentals of fluid film lubrication. 2nd ed. New York: Marcel Dekker Inc., 2004.
38.
LugtPMMorales-EspejelGE. A review of elasto-hydrodynamic lubrication theory. Tribol Trans2011; 54: 470–496.
39.
DowsonDHigginsonGR. Elastohydrodynamic lubrication, the fundamentals of roller and gear lubrication. Oxford: Pergamon Press, 1966.
40.
JohnsonKL. Regimes of elastohydrodynamic lubrication. J Mech Eng Sci1970; 12: 9–16.
41.
CrookAW. The lubrication of rollers II. Film thickness with relation to viscosity and speed. Philos Trans R Soc Lond Ser A, Math Phys Sci1961; 254: 223–236.
42.
HookeCJ. The elastohydrodynamic lubrication of heavily loaded point contacts. J Mech Eng Sci1980; 22: 183–187.
43.
HookeCJ. The elastohydrodynamic lubrication of heavily loaded contacts. J Mech Eng Sci1977; 19: 149–156.
44.
HamrockBJDowsonD. Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus I—fully flooded conjunction. J Lubr Technol1978; 100: 236–245.
45.
GrubinA. Fundamentals of the hydrodynamic theory of lubrication of heavily loaded cylindrical surfaces. Invest Contact Mach Compon1949; 2: 115–166.
46.
WheelerJDFillotNVergneP, et al. On the crucial role of ellipticity on elastohydrodynamic film thickness and friction. Proc IMechE, Part J: J Engineering Tribology2016; 230: 1503–1515.
47.
HookeCJ. Minimum film thicknesses in lubricated point contacts operating in the elastic piezoviscous regime. Proc IMechE, Part C: J Mechanical Engineering Science1988; 202: 73–84.
48.
SharifKJde LingFMBMartinMJAlanouMP, et al. Film thickness predictions for elastohydrodynamic elliptical contacts over a wide range of radius ratios with consideration of side starvation. Proc IMechE, Part J: J Engineering Tribology2000; 214: 63–78.
