EHL Film Thickness Limitation Theory Under a Limiting Shear Stress

Abstract

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 = ...

Contact‐fluid interfacial shear strength and its critical importance in elastohydrodynamic lubrication

“…where p is the fluid pressure, p s is the fluid solidification pressure, t l0 is the bulk fluid shear strength at ambient pressure, and a tl is the bulk fluid shear strength-pressure proportionality. The correctness and accuracy of equation (2) for predicting the shear strength of the usual fluid at both low and high pressures were confirmed by both the experimental results of Hoglund and Jacobson (1986) and the researches of EHL by Zhang et al (2001aZhang et al ( , 2002bZhang et al ( , 2004a. Equation (2) usually predicts much lower shear strengths of the fluid at low pressures than equation (1).…”

“…The analytical EHL results based on equation (2) as obtained by Zhang et al (2001aZhang et al ( , b, 2002bZhang et al ( , 2004a are qualitatively different from those based on equation (1) as obtained by Jacobson and Hamrock (1984) and Shieh and Hamrock (1991). Actually, the analytical EHL results based on equation (2) incorporating the fluid shear strength and contact-fluid interfacial slippage effects are very fresh and seem of a milestone in the research of EHL as can be found from the researches of EHL by Zhang et al (2001bZhang et al ( , 2002bZhang et al ( , 2004a. Zhang (2003aZhang ( , 2004aZhang ( , 2002a proposed that precisely to say, in isothermal EHL, the material shear strength of effects is actually the contact-fluid interfacial shear strength instead of the fluid shear strength due to the maximum value of the fluid film shear stress across the film thickness occurring at the contact-fluid interface instead of within the fluid film in this EHL and thus the fluid film slippage occurring at the contact-fluid interface caused by the fluid film shear stress at the contact-fluid interface exceeding the contact-fluid interfacial shear strength.…”

“…Besides by the present theory as shown above, the prediction equation for the contact-fluid interfacial shear strength in EHL expressed by equation (2) has also been supported and verified by a lot of other researches. Zhang et al (2001aZhang et al ( , 2002bZhang et al ( , 2004a developed the EHL theory based on the assumption of the contact-fluid interfacial shear strength predicted by equation (2). His theory well matches the experimental EHL film thickness obtained by Kannel and Bell (1971) and validates this prediction equation for the contactfluid interfacial shear strength in EHL.…”

“…the contact-fluid interfacial slippage in EHL. Kaneta et al (1996) experimentally observed dimples of sliding EHL point contacts at medium loads; Zhang et al (2002b) suggested that these dimples be caused by the combined effect of the contact-fluid interfacial slippage and fluid film viscous heating in EHL.…”

“…4.2 Mixed rheologies in isothermal EHL of ideally smooth concentrated contacts due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects Zhang et al (2002bZhang et al ( , 2004a analytically showed that in isothermal EHL of ideally smooth line contacts, due to the contact-fluid interfacial shear strength and contact-fluid interfacial slippage effects, the EHL film thickness especially in the Hertzian contact zone is usually extremely low and on the nanometer scale even in pure rolling for severe operating conditions, i.e. the condition of heavy loads, high rolling speeds and high bulk fluid temperatures.…”