A Full Numerical Solution for the Thermoelastohydrodynamic Problem in Elliptical Contacts

Paper IX(iii) A full numerical solution for the non-steady state elastohydrodynamic problem in nominal line contacts

The isothermal elliptical contact elastohydrodynamic lubrication (EHL) problem in ball screw with rotating nut was studied.Numerical solution to the problem was obtained for various parameters with a multigrid solver.Based on work mentioned above,the influence of the working parameters such as the rotating speed of screw shaft and the contact force,on the lubricant oil film thickness and pressure is analyzed .The results showed that, with the increasing loads,the pressure became higher,the film thickness became smaller. On the other hand,when the angular velocity was higher,the film thickness was higher, while the pressure spike was closer to the center of the contact. Because of the spinning, the slide-roll ratio was not a constant.

Application of machine learning for film thickness prediction in elliptical EHL contact with varying entrainment angle

The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two models with viscosity constant and variable across the oil film were developed. The results under extremely heavy conditions of dimensionless load W = 52 * 10−5 (pH = 2 GPa) and dimensionless rolling velocity U = 20 * 10−11 are presented. They show that even for pure rolling, but under heavy load and high rolling velocity conditions, the thermal effects significantly reduce the minimum film thickness. The distributions of pressure, film thickness, and temperature for two rolling velocities and various loads are presented. They indicate that under high rolling velocity conditions the thermal effects have a strong influence on a pressure spike.

Thermal elastohydrodynamic lubrication of rolling and sliding contacts with a power law fluid

The film shape, pressure and temperature profiles have been measured in a disk machine under conditions of elastohydrodynamic lubrication. They were obtained with a new design of transducer which enables the various measurements to be accurately inter-related. In the case of the film shape and pressure measurements the corresponding theoretical solutions have been calculated and detailed comparison made. It has been shown that the sharp peaks of pressure near the outlet which are predicted in the theory are in practice considerably attenuated but do occur in the correct positions. The associated dip in film thickness is also much reduced. Johnson’s recent postulate that the position of the pressure spike should be a function of a single parameter has been examined and found to hold for this new range of experimental data.

Paper VII(iv) A full E.H.L. solution for line contacts under slidding-rolling condition with a non-Newtonian rheological model

The paper presents the numerical solution of line contact thermal elastohydrodynamic lubrication (EHL) with bio-based lubricant. The model comprises Reynolds equation, film thickness, load balance and energy equations with appropriate boundary conditions by incorporating viscosity–pressure–temperature and density–pressure–temperature relations. Second-order finite difference scheme is used for the discretised form and their equation. The multigrid method with full approximation scheme is used to solve the Reynolds equation along with multilevel multi-integration method for film thickness equation. The pressure, film thickness and temperature distributions for two rolling velocities and various loads with a bio-based lubricant are presented in detail. The present findings yield a reduction in the minimum film thickness for high speed. Details of pressure spike as a function of relevant parameters are given. The results are compared with earlier findings based on different methods.

In order to understand the influence of the body temperature of contact solids on the lubrication performance of machine components such as gears and roll-bearings, full numerical solution for the non-Newtonian and thermal elastohydrodynamic lubrication (EHL) problem in point contacts has been achieved, assumed that the solid body temperature is different from the temperature of the supplied lubricating oil. The Ree-Eyring rheological model has been used to describe the shear-thinning behavior of the lubricant. The effects of the body temperature, the slide-roll ratio, and the velocity parameter have been discussed. The solutions for the body temperature being higher or lower than the temperature of the supplied oil have been compared with that of the conventional thermal EHL solution, where the temperature of the contact bodies and the temperature of the supplied oil are assumed to be the same. Results show that, if the entrainment velocity is not very high, the solid body temperature plays a dominant role in the EHL behavior, however, the influence of the body temperature decreases as the entrainment velocity increases. Comparisons between the non-Newtonian and Newtonian results have been made under some operating conditions. It has been shown that, comparing with the Newtonian solution, the shear-thinning property of the lubricant can always lead to lower frictional coefficient and lower temperature, but has little effect on the film thickness, no matter the temperature of the contact bodies is lower than, equal to, or higher than that of the supplied oil.

An effective method for calculating elasto-plastic contact pressure and contact patch size under elliptical, circular and line contact conditions

In this paper, an isothermal study of the shut down process of elastohydrodynamic lubrication under a constant load is performed. The surface mean velocity is decreased linearly from the initial steady state value to zero. The details of the pressure and film thickness distributions in the contact area are discussed for the two stages of shut down process, namely the deceleration stage and the subsequent pure squeeze motion stage with zero entraining velocity. The nature of the balance between the pressure, the wedge and the squeeze terms in Reynolds equation enables an analytical prediction of the film thickness change on the symmetry line of the contact in the deceleration period, provided that the steady state central film thickness relationship with velocity is known. The results indicate that for a fixed deceleration rate, if the initial steady state surface mean velocity is large enough, the transient pressure and film thickness distributions in the deceleration period solely depend on the transient velocity. The pressure and film thickness at the end of the deceleration period are then the same and do not depend on the initial steady state velocity. From the same initial steady state velocity, larger deceleration rates provide higher central pressure increase, but also preserve a higher film thickness in the contact area at the end of the deceleration period. Later in the second stage when the axisymmetric pressure and film thickness patterns typical of pure squeeze motion form, the pressure distribution in the contact area resembles a Hertzian contact pressure profile with a higher maximum Hertzian pressure and a smaller Hertzian half contact width. As a result, the film thickness is close to a parabolic distribution in the contact area. The volume of the lubricant trapped in the contact area is then estimated using this parabolic film thickness profile.

A numerical solution to the problem of thermal elastotydrodynamic lubrication of line contacts was obtained by using a finite-difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter, Q: Plots of pressure distribution, films shape, temperature distribution, and flow are shown for some representative cases.

Tapered roller bearings are widely used in high axial-load and radial-load applications. In this study, a numerical analysis is performed to study a finite line contacts EHL problem between a tapered roller and raceway in tapered roller bearings. Converged solutions are obtained for moderate load and material parameters using a finite difference method with non-uniform grids and the Newton-Raphson method. The contours and sectional plots of pressure distribution and film shape are compared. The pressure distribution and film shapes near both ends of the roller are very different from those in the central part and are transversely asymmetric. The maximum pressure and absolute minimum film thickness always occur at the small end of the roller.

A separative roll-type mechanism installed between an automatic fish selector and counting system was devised. The separative state of overlapping fish body was investigated by controlling the peripheral velocity of the first roll on the supply side, and the ratio of peripheral velocities of neighboring rolls, by adjusting the angle of inclination of the line connecting the centers of rolls parallel to each other and the interval distance between neighbor rolls, by controlling the ratio of overlapping fishes body length, and from the relationship between the distance of partitive boards and fish body width. The results were as follows.1. When the ratio of peripheral velocity of neighboring the rolls was 1.00, the peripheral velocity of the first roll was 0.8m/s, and the ratio of overlapping fishes body length was 75%, overlapping fry were perfectly separated.2. When the ratio of peripheral velocity of neighboring rolls was 1.26 and the ratio of overlapping fishes body length was 75%, the separation of overlapping fishes body was not affected by the peripheral velocity of the first roll on the supply side, and the counting error of fry numbers was zero.

Temperature, pressure and film thickness measurements for an offset half bearing