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With the arrival of powerful computers and sophisticated numerical methods the calculation of film thickness and pressure fields in elastohydrodynamically lubricated (EHL) contacts is now a common task. Complete moving-roughness solutions are easily found in literature including thermal effects, non-Newtonian rheology, and mixed-lubrication. Therefore, the pioneering days of analytical and semi-analytical EHL solutions lead by Ertel, Grubin, Crook, and others might be perceived as unfit for modern problems. However, it is important to recognise that despite their apparent simplicity these solutions have provided engineers with substantial insight of the lubrication problem. The present paper reviews Ertel—Grubin methods and shows the potential they still have in providing engineers with physical understanding and practical solutions in modern lubrication problems, including friction, transient effects, roughness, minimum film thickness, and shear thinning. The review is, however, not exhaustive.

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

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Rolling bearing friction is an important measure of bearing performance. With increasing industrial trends of energy savings and CO2 footprint reduction, rolling bearing friction has become a very important parameter in the machinery design and selection process. Particular importance have high-speed applications like spindles or electrical vehicle traction drives and gearboxes. Since handling thermal effects has become an important problem to solve in these applications, oil lubrication is gaining interest due to its cooling capacity. Bearing friction is made of rolling, sliding and drag losses components in oil lubricated bearings. In this paper the emphasis is given to the drag losses component, which becomes the most critical in oil bath in medium and high-speed applications. An engineering model is derived for the calculation of this component for medium and potentially high speeds. The results are compared with experimental measurements (in-house and literature). In general, good agreement is found between the engineering model and the experimental results.