An engineering approach on sliding friction in full-film, heavily loaded lubricated contacts

Abstract

Various schemes to approximate the sliding friction coefficient in heavily loaded lubricated contacts with different rheologies are studied. Rather than using complex full numerical thermo-hydrodynamically lubricated solutions to calculate the friction coefficient, in this paper the emphasis is on rather simplified approaches which are suitable for providing the user with physical insight of the phenomenon and at the same time fulfilling the most advanced engineering applications.The simplification of the equation for the lubricant velocity distribution for an assumed Hertzian contact with a fixed parallel film thickness and different fluid rheologies leads to simple solutions with comparable results to the recently obtained (through full numerical simulations) friction master curves from Jacod.Point-by-point models with thermal effects are included using the simplified model for the oil and wall temperature calculation from Olver and Spikes. The results are compared with full numerical solutions from literature and good agreement is found. A one-dimensional scheme is extended to a two-dimensional model where the integration of the varying viscosity with pressure and temperature is included. The wall surface temperature calculation is then carried out using a fast Fourier transform convolution approach. NOTATION a half-width of the elliptical Hertzian contact, rolling direction (m) A area of pressure (m 2 ) A A constant in the oil-temperature calculation (-) bVogel constant, half-width of the elliptical Hertzian contact (transverse direction) (m) E 0 reduced elasticity modulusthermal conductivity of the oil (W/m K) p pressure (Pa) p 0 maximum Hertzian pressure (Pa) p m mean pressure (Pa) _ q q generated heat flow (N m/s) S slide-roll ratio ¼ ðu 2 À u 1 Þ= u u T temperature ( 8C) u 1 velocity, lower surface (m/s) u 2 velocity, upper surface (m/s) u ucoefficient in the Reynolds viscositytemperature law &0:05 (K À 1 ) _ g g shear strain rate ðu 2 À u 1 Þ=h c (s À 1 ) Z lubricant viscosity (Pa s) Z 0 lubricant viscosity at the contact inlet and ambient temperature (Pa s) lVogelPoisson's ratio (-) r lubricant density (kg/m 3 ) t shear stress (Pa) t c generalized characteristic Jacod et al.shear stress ¼ 2 u uSZ p 0 =ðh c t f Þ (-)The MS was

Friction coefficient in mixed lubrication: A simplified analytical approach for highly loaded non-conformal contacts

“…Unlike bath temperature, inlet temperature is initially unknown and the use of a thermal factor u t is therefore needed to consider the shear heating effects in the inlet zone, which is calculated with equation (15). The Newtonian central film thickness at bath temperature, h Ncb , can be calculated using the formulae in Table 1, developed by Hamrock and Dowson for point contact and by Hamrock for line contact.…”

A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

“…The resulting two-dimensional model provides information on the temperature distributions of the lubricant and the contacting surfaces, along with other parameters of interest, such as the friction coefficient and the film thickness distribution. These results are more useful to designers in industry than those obtained with the analytical models [15][16][17][18][19] and they also contribute to a greater understanding of the complex physical phenomena involved under TEHL.…”

“…14 Olver and Spikes 15 developed a one-dimensional thermal network for TEHL point contact. Later on, Morales-Espejel and Wemekamp, 16 Echa´varri et al, 17 Paouris et al 18 and Shirzadegan et al 19 used this approach to account for thermal effects in analytical models and calculate an average value of the temperature of the lubricant within the high-pressure contact zone. Morales-Espejel et al 16 also presented a simple extension to a two-dimensional case.…”

Film Thickness and Friction Relationship in Grease Lubricated Rough Contacts

“…The traction behaviour of lubricating oils is well documented [19][20][21][22]. It is known that the traction coefficient depends on the low shear viscosity, the limiting shear modulus and the limiting shear stress that the lubricant can withstand [19,21].…”