It is nrmterically shown that tlte elastohydrodynamic lubricashon~s that, in elastol~ydrodynan~ic line contacts, the central film tion (EHL) filnt tltickness ltas a linlit ut~der an assumed limiting tliickness is of ntolecular scale and part of the cottract area is in shear stress of the cotttact-lubricant interface in isotlzermal pure non-continuum film lubricatior~ when the equivalent cylinder crrrrolling line contacts. Tlte prediction of the central film thickness vature radirrs is less than the critical one. This critical radi~rs lintit is made, and well ntatcl~es experiments. The present theory depends on the load and the contact-lubricant inrerjacial lin~iting shear stress at low pressures.
KEY WORDSFinal manuscript approved June 12,2002 Elastohydrodynamic Lubrication; Film Thickness Limit; Review led by Danyluk Interfacial Limiting Shear Stress C = dimensionless ambient interfacial limiting shear stress, T I O / ( E ' @ .~) = qo/(kE'Gn.4) E l , E, = Young's elasticity moduli of the cylinder and plane surfaces, respectively E' = equivalent Young's elasticity modulus, l / E 1 = 1/2[1 -v:)/E1 + (1 -v,2)/E2] fo(r), f , (~) = functions, Eqs.[3] and [4] (3 = material parameter, a E' G, = shear elasticity modulus If, = central film thickness /I,,,,, = central film thickness limit H,m,, = dimensionless central film thickness limit, hc,,,x/R, Eq.[19] k = 71al7ro~~ K , n and Urn = variables dependent on C, Eqs.[13]-[I51 K,, n , and Ub I =variables having the values of K, n and Urnrespectively when Cp is substituted for C P = film pressure I'h = maximum Hertzian pressure, J -PS = lubricant solidification pressure T;,, nz,,, = variables dependent on G , U and W, Tables 3 and 4 R = equivalent cylinder curvature radius %a = critical equivalent cylinder curvature radius less than which for the equivalent cylinder curvature radius, the non-continuum film is generated in line contact EHL I = time T =lubricant temperature II = rolling speed Ub = the rolling speed which makes the interfacial slippage start to occur in the inlet zone "d = the rolling speed beyond which the central film thickness remains constant II = the rolling speed which is used for prediction of the central film thickness limit U = operational parameter, I~~U / ( E ' R ) " / I = dimensionless form of u b ,~u b / ( E I R ) ? Eq. 1 I I] UP = dimensionless form of ~c , , ,~n t l~/ ( E ' R ) , Eq.[18] n1 = load per unit axial length W = operational parameter, UJ/(E'R) x = coordinate v , , v, = Poisson's ratios of the cylinder and plane surfaces, respectively a = lubricant viscosity-pressure index Q d = interfacial limiting shear stress-pressure proportionality 7 = shear stress 7 a = shear stress at the contact-lubricant interface no = ambient interfacial limiting shear stress 7r = interfacial limiting shear stress ROC = required or critical ambient interfacial limiting shear stress which prevents the interfacial slippage in the inlet zone TIOCP = critical ambient interfacial limiting shear stress for the speed of U,,, Eq. [I71 11 = lubricant viscosity ' lo = ...