Film Thickness Equation Research Articles

Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed U, load W, materials G, and sliding velocity U* and limiting-shear-strength proportionality constant γ on dimensionless minimum film thickness Hmin was investigated. Fourteen cases were investigated for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. The influence of sliding velocity (U*) and limiting shear strength (γ) on minimum film thickness was observed to be small. Hence the film thickness equation obtained for a Newtonian fluid is sufficient for calculations considering non-Newtonian effects. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

A Film Thickness Analysis for Line Contacts Under Pure Rolling Conditions With a Non-Newtonian Rheological Model

The non-Newtonian constitutive equation proposed by Winer and Bair [1] is applied in a conventional isothermal film thickness analysis of line contact lubrication of rolling elements. The present analysis provides four different dimensionless film thickness equations for four different regimes of lubrication. Due to the formulation technique used in deriving the governing pressure-gradient equation, the present study is recommended for high viscosity, high rolling speed, and low limiting shear stress cases where Newtonian models fail to match the experimental data. Comparison of the present film thickness equations with the Newtonian correspondences in each lubrication regime shows a considerable difference, but the analysis suffers from the fact that the limiting shear stress parameters of these high viscosity lubricants need to be determined experimentally. The present analysis assumes a reasonable range of limiting shear stress which is smaller than the corresponding values for low viscosity lubricants which are predominantly Newtonian in behavior (unless severe rolling and/or sliding with high loads is applied).

An Experimental Evaluation of the Hamrock and Dowson Minimum Film Thickness Equation for Fully Flooded EHD Point Contacts

Fifty-seven measurements of the minimum lubricant film thickness separating the elastohydrodynamically lubricated point contact of a steel crowned roller and a flat sapphire disk were made by an optical interferometry technique. The data collected were used to evaluate the Hamrock and Dowson minimum EHD film thickness model over a practical range of contact ellipticity ratio where the major axis of the contact ellipse is aligned both parallel and perpendicular to the direction of motion. A statistical analysis of the measured film thickness data showed that the experimental data averaged 30 percent greater film thickness than the Hamrock and Dowson model predicts.

Theory of the thermomagnetic effects in thin films in a magnetic field of arbitrary magnitude

AbstractThermomagnetic effects of a thin film in a magnetic field normal to the film surface are studied for an arbitrary value of specularity parameter p. Using the solution of the Boltzmann equation for an arbitrary film thickness and magnetic field strength the basic thermomagnetic coefficients are calculated, the Nernst‐Ettingshausen coefficient (N‐E) Q, the thermopower in a magnetic field α(H), and the thermal conductivity in a magnetic field χ. A detailed analysis is given of their dependences on the thickness, magnetic field strength, and the parameter p. It follows from the analysis that in a weak magnetic field the thermopower α and the N‐E coefficient Q are practically p‐independent. The computer calculations show that α and Q oscillate as functions of the magnetic field strength, the oscillations of Q being more pronounced than those of the electronic thermal conductivity. χ varies monotonically with the magnetic field.

Optical Measurement of Oil Film Thickness Between Rollers

Previous research has established that the laser beam diffraction method can be used for measurement of film thicknesses between two adjacent flat surfaces. This paper describes further experimentation on this method, where oil film thicknesses between rollers is measured. Calibration curves are obtained between the experimental (set) gap and the gap dimensions which are deduced from the diffraction patterns when the laser beam is passed through the film. These set versus calculated film thickness curves are extremely linear for films which are less than 1 mm depth, the coefficients of correlation with straight lines being close to unity. Data based upon several oils used with 76.2 mm dia rollers are presented and empirical equations established. These equations allow the researcher to obtain the film thickness between the rollers in terms of oil properties (density, viscosity and refractive index) and the geometry of the light beam (wavelength, distance from oil film to diffraction screen, and diffraction pattern bandwidth). The empirical constants in the equations for film thickness appear to apply to specific oil types, and remain the same for each family or group of oil used. The groups used here were SAE 10 through 40, low viscosity index and high viscosity index groups. Oil films from 7.62 × 10−3 mm up to 76.2 × 10−3 mm thickness were measured using this method.

Lubrication at Elliptical Contacts

The classical hydrodynamic theory for point contacts is extended to cover the general case where the resolved hydrodynamic velocity is not directed along either of the axes of the ellipse of contact. Isobar plots of deduced values of the non-dimensional reduced pressure, q, are shown for some of these cases. A first approximation to an elastohydrodynamic film thickness equation is derived, for this general case, by equating the maximum reduced pressure generated between undeformed bodies to the inverse of the pressure coefficient of viscosity, α. The theory is applicable to the contact conditions that exist between the teeth of hypoid gears, and the variation of lubricant film thickness with pinion offset and gear ratio for a range of hypoid gear sets has been deduced. Experiments have been performed on a crossed cylinders machine, the results of which demonstrate the general validity of the theory.

Film geometry effects in hydrodynamic gear lubrication

The involute gear lubrication problem is analyzed with a first order correction made to the conventional parabolic arc film thickness equation to account for the actual tooth shape and the squeeze action resulting from its time dependence. Both internal and external gears are considered for one pressure angle and a range of gear ratios. The film geometry effect is found to be greater for internal than for external gears and to decrease as the minimum film thickness decreases. Conclusions are drawn concerning the importance of the correction.