This paper deals with the effects of contact surface shape on the isothermal rolling traction of skewed disks. The pressure distribution for determining the contact surface shape under dry conditions and the isothermal rolling traction under oil lubrication were calculated by using the software TED/CPA. The findings suggest that at low load, the contact surface shape adopts a closed elliptical shape while at high load, it takes on a truncated elliptical or a rectangular shape. This truncation phenomenon is observed. The isothermal rolling traction calculated using published expressions for point contact differs from that calculated by TED/CPA for the closed elliptical case. By curve-fitting the isothermal rolling traction calculated by TED/CPA for the closed elliptical case, an isothermal rolling traction expression for point contact was modified. As a result, the isothermal rolling traction, in the case where the contact surface shape changes from a closed ellipse to a truncated shape with increasing load, can be estimated using both the proposed expression for point contact and Ohta and Matsuyama's expression for line contact.
HoupertLLeendersP. A theoretical and experimental investigation into rolling bearing friction. Proc of the 1985 eurotrib conference. 1985: 1–10.
2.
HoupertL. Piezoviscous-rigid rolling and sliding traction forces, application: the rolling element-cage pocket contact. Trans ASME J Tribol1987; 109: 363–371.
3.
AiharaS. A new running torque formula for tapered roller bearings under axial load. Trans ASME J Tribol1987; 109: 471–478.
4.
ZhouRSHoeprichMR. Torque of tapered roller bearings. Trans ASME J Tribol1991; 113: 590–597.
5.
MartinHM. The lubrication of gear-teeth. Engineering1916; 102: 119–121.
6.
SodaN. Bearing. Tokyo: Iwanami shoten, 1964.
7.
CrookAW. The lubrication of rollers, IV. measurements of friction and effective viscosity. Philos Trans R Soc London Ser A1963; 255: 281–312.
8.
ArchardJFBaglinKP. Nondimensional presentation of frictional tractions in elastohydrodynamic lubrication, part I: fully flooded conditions. Trans ASME J Lubr Technol1975; 97: 398–411.
9.
GoksemPGHargreavesRA. The effect of viscous shear heating on both film thickness and rolling traction in an ehl line contact, part I: fully flooded conditions. Trans ASME J Lubr Technol1978; 100: 346–352.
10.
HamrockBJJacobsonBO. Elastohydrodynamic lubrication of line contacts. ASLE Trans1984; 27: 275–287.
11.
PanPHamrockBJ. Simple formulas for performance parameters used in elastohydrodynamically lubricated line contacts. Trans ASME J Tribol1989; 111: 246–251.
12.
BibouletNHoupertL. Hydrodynamic force and moment in pure rolling lubricated contacts, part 1: line contacts. Proc IMechE Part J: J Eng Tribol2010; 224: 765–775.
13.
OhtaHMatsuyamaD. Rolling traction in isoviscous-rigid, piezoviscous-rigid, and elastohydrodynamic lubrication regimes at line contact. Trans ASME J Tribol2024; 146: 054101.
14.
TevaarwerkJLJohnsonKL. The influence of fluid rheology on the performance of traction drives. Trans ASME J Lubr Technol1979; 101: 266–274.
15.
NogiT. Film thickness and rolling resistance in starved elastohydrodynamic lubrication of point contacts with reflow. Trans ASME J Tribol2015; 137: 041502.
16.
NogiTShiomiHMatsuokaN. Starved elastohydrodynamic lubrication with reflow in elliptical contacts. Trans ASME J Tribol2018; 140: 011501.
17.
BibouletNHoupertL. Hydrodynamic force and moment in pure rolling lubricated contacts, part 2: point contacts. Proc IMechE Part J: J Eng Tribol2010; 224: 777–787.
18.
HookeCJ. The elastohydrodynamic lubrication of heavily loaded contacts. J Mech Eng Sci1977; 19: 149–156.
GuptaPKChenHSZhuD, et al.Viscoelastic effects in MIL-L-7808-type lubricant, part I: analytical formulation. Tribol Trans1992; 35: 269–274.
21.
PandeyRKGhoshMK. Thermal effects on film thickness and traction in rolling/sliding ehl line contacts - an accurate inlet zone analysis. Wear1996; 192: 118–127.
22.
GhoshMKPandeyRK. Thermal elastohydrodynamic lubrication of heavily loaded line contacts- an efficient inlet zone analysis. Trans ASME J Tribol1998; 120: 119–125.
23.
PandeyRKGhoshMK. A thermal analysis of traction in elastohydrodynamic rolling/sliding line contacts. Wear1998; 216: 106–114.
24.
PandeyRKGhoshMK. Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures. Tribol Int1998; 31: 745–752.
25.
AnandanNPandeyRKJaggaCR,et al.Effects of starvation and viscous shear heating in hydrodynamically lubricated rolling/sliding line contacts. Proc IMechE Part J: J Eng Tribol2006; 220: 535–547.
26.
NapelWETMoesHBosmaR. Traction in elastohydrodynamic lubrication at low sliding speeds. Tribology Convention (IMechE)1972: 142–150.
27.
KannelJWWalowitJA. Simplified analysis for tractions between rolling-sliding elastohydrodynamic contacts. Trans ASME J Lub Tech1971; 93: 39–46.
28.
HoupertL. Fast numerical calculations of ehd sliding traction forces; application to rolling bearings. Trans ASME J Tribol1985; 107: 234–240.
29.
SadeghiFDowTAJohnsonRR. Thermal effects in rolling/sliding contacts part 3: approximate method for prediction of mid-film temperature and sliding traction. Trans ASME J Tribol1987; 109: 519–523.
30.
WangJTanJ. Numerical simulation of traction in rolling/sliding contacts. Trans ASME J Tribol1997; 119: 869–874.
31.
KanetaMShigetaTYangP. Effects of compressive heating on traction force and film thickness in point ehl contacts. Trans ASME J Tribol2005; 127: 435–442.
32.
HabchiWBairSVergneP. On friction regimes in quantitative elastohydrodynamics. Tribol Int2013; 58: 107–117.
33.
MasjediMKhonsariMM. An engineering approach for rapid evaluation of traction coefficient and wear in mixed ehl. Tribol Int2015; 92: 184–190.
34.
LiuHCZhangBBBaderN, et al.Simplified traction prediction for highly loaded rolling/sliding ehl contacts. Tribol Int2020; 148: 106335.
35.
LiuHCZhangBBBaderN, et al.Scale and contact geometry effects on friction in thermal ehl: twin-disc versus ball-on-disc. Tribol Int2021; 154: 106694.
36.
HigashitaniYKawabataSBjörlingM,et al.A traction coefficient formula for ehl line contacts operating in the linear isothermal region. Tribol Int2023; 180: 108216.
37.
HigashitaniYKawabataSBjörlingM,et al.A traction coefficient formula for ehl point contacts operating in the linear isothermal region. Tribol Int2024; 193: 109452.
38.
HigashitaniYKawabataSBjörlingM,et al.Effect of entrainment sliding direction to the traction coefficient for elastohydrodynamic lubrication elliptical contacts in the linear isothermal region. Trans ASME J Tribol2024; 146: 124102.
39.
MacLarenAKadiricA. Elastohydrodynamic traction and film thickness at high speeds. Tribol Lett2024; 72: 1–24.
40.
SimpsonMRahmaniRDolatabadiN, et al.An analytical friction model for point contacts subject to boundary and mixed elastohydrodynamic lubrication. Tribol Int2024; 196: 109699.
KakoiKObaraT. A numerical method for counterformal rolling contact problems using special boundary element methods. JSME Int J Ser A1993; 36: 57–62.
43.
HamrockBJSchmidSRJacobsonBO. Fundamentals of Fluid Film Lubrication. 2nd ed. New York: Marcel Dekker, Inc., 2004.
44.
VennerCHLubrechtAA. Multilevel Methods in Lubrication. Amsterdam: Elsevier, 2000.
45.
RoelandsCJA. Correlation aspects of viscosity-temperature-pressure relationship of lubricating oils. Ph.D. thesis, Delft: Delft University of Technology, 1966.
46.
DowsonDHigginsonGR. Elasto-Hydrodynamic Lubrication. SI ed. Oxford: Pergamon Press, 1977.
47.
NSK. Rolling bearings for industrial machinery. Cat. No. 1103. Tokyo: NSK Ltd., 2019.
48.
HertzH. Gesammelte Werke. Band I. Leipzig: Johann Ambrosius Barth, 1895.
49.
MoesH. Lubrication and Beyond. Enschede: University of Twente, 2000.
