Transient thermal elastohydrodynamic lubrication (EHL) of general elliptical point contacts was investigated numerically in this study. Both entrainment directions along the major and the minor axes of the contact ellipse were considered, together with a transient load impulse. In this study, a Newtonian lubricant was assumed to highlight the thermal influence. The transient solution was achieved at every instant, starting from a steady state thermal EHL solution. At each instant, a multilevel solver was used for pressure and surface deformation, whereas a column-by-column relaxation technique was used for solving temperature. The unknown rigid central distance between the contact bodies was adjusted after each iteration between the transient fields of pressure and temperature, so that in each iteration, only one W cycle was required for pressure and only a few relaxation cycles were required for temperature. With these numerical techniques, the computing time required for a typical transient case was reduced to 12 h on a personal computer with a 3.0 GHz central processing unit. The transient thermal results were compared with those corresponding to isothermal conditions presented in Part 1 of this series of papers. It was found that, in general, the transient behaviour under thermal conditions was similar to that under isothermal conditions, however, the former was weaker than the latter when the slide-roll ratio was large enough.

Transient elastohydrodynamic lubrication of general elliptical point contacts was analysed in the present study based on multi-level techniques. Both entrainment directions along the major and minor axes of the contact ellipse were considered, together with transient load and speed impulses. In this study, only a Newtonian lubricant and isothermal conditions were assumed. The computing time required for a typical case took only approximately 2 h on a personal computer with a 2.8 GHz central processing unit. The predicted film thickness and the pressure were found to be mainly governed by the squeeze-film or separation actions. A sudden load increase resulted in an increase in the contact conjunction and a significant development of the squeeze-film action. Consequently the lubricant film thickness was increased initially around the inlet region and then moved along in the entraining direction towards the exit. A significant increase in the predicted central film thickness was observed, long after the load impulse had ceased. Such a process was found to be mainly governed by the time period of the impulse, and the time taken for the lubricant to move through the contact conjunction in the entraining direction. The speed impulse had similar effects. However, a sudden speed decrease was found to have negligible effect on the predicted film thickness, due to the powerful squeeze-film action.

Transient non-Newtonian elastohydrodynamic lubrication (EHL) of elliptical point contacts was investigated numerically under both thermal and isothermal conditions. The multi-level technique used in Parts 1 and 2 of this series of papers for determining pressure and film thickness and the column-by-column relaxation technique used in Part 2 for temperature calculation were used again in this study. However, both Newtonian and non-Newtonian lubricant properties were considered, with the Ree -Eyring model being adopted in the latter case. The entrainment direction was assumed to be along the minor axis of the contact ellipse. A simplified numerical scheme for the evaluation of the equivalent shear stress and viscosity of the non-Newtonian lubricant was proposed and verified by comparing the steady-state thermal solutions without the simplification. The computing time required for a transient thermal and non-Newtonian case was typically 14 h on a personal computer with a 2.8 GHz central processing unit. For a steel -steel contact, the responses of the EHL films to a transient load impulse were determined for the non-Newtonian lubricant under both isothermal and thermal conditions. The isothermal non-Newtonian results were compared with those in Part 1, and the thermal results were compared with those presented in Part 2. A similar investigation for a glass -steel contact is also reported.

The influence of a transversely or longitudinally oriented surface bump or groove on the lubricating performance and dimple phenomena in the simple sliding point contact composed of a steel ball and a glass disk has been investigated theoretically with numerical solution of the thermal elastohydrodynamic lubrication (EHL) and experimentally with optical interferometry technique. Good agreement has been obtained between the theoretical and experimental results. It has also been discovered that the surface bump or groove is dangerously harmful to the lubricating performance and has a significant influence on the dimple phenomena.

The influence of the transversely and/or longitudinally oriented surface waviness on the lubricating behavior in the rolling/sliding elliptic contact composed of two steel bodies and lubricated with a non-Newtonian lubricant was investigated theoretically with full numerical solution of the thermal elastohydrodynamic lubrication. The entrainment velocity was assumed to be along the minor axis of the Hertzian contact ellipse. The waviness of each surface was given by a sinusoidal function. The non-Newtonian flow of the lubricant was described by the Eyring model with a constant Eyring shear stress at the ambient pressure and temperature. The velocity of the faster surface was assumed to be four times as that of the slower surface in order not only to highlight the thermal and non-Newtonian effects, but also to ensure a cyclic solution when both surfaces were with transversely oriented waviness. Starting from a quasisteady solution, the cyclic time-dependent solution was achieved numerically time step by time step. The results show that the thermal and non-Newtonian effects can be enlarged significantly by the surface waviness, and the worst configuration of the surface topography is that both surfaces are with longitudinal waviness.

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In order to investigate the size effect on elastohydrodynamic lubrication (EHL) of roller pairs, complete numerical solutions for both the Newtonian fluid and the Eyring fluid thermal EHL problems of roller pairs under steady state conditions have been achieved. It can be seen that there is no size effect on the isothermal EHL performance; however, there is a very strong size effect on the thermal EHL performance. Results show that the term of shearing heat is the most important factor for the film temperature when the size of a contact changes. Comparison between the Newtonian solution and the Eyring solution has been made under some operating conditions. It is interesting to see that the effective viscosity of the Eyring fluid is nearly the same as that of the Newtonian fluid when the size of a contact is large enough. The non-Newtonian effect, therefore, can be ignored when the size of a contact is very large. It is equally interesting to see that the thermal effect can be ignored when the size of a contact is very small. In addition, the influence of the velocity parameter, the load parameter, and the slide-roll ratio on the lubricating performance for various sizes of contacts has been investigated.

Due to the imperfect geometry and misalignment, cylindrical roller loading may result in both the roller tilting and skewing. Roller tilting coupled with skewing is important for the working lifetime of the bearings. To investigate the effect of the roller tilting and skewing on the thermal elastohydrodynamic lubrication, a model with non-Newtonian property of the lubricant has been built and a complete numerical solution has been obtained to address the relationship between the tilted and skewed roller effect and the thermal effect. Effects of the tilting angle, the rotating speed, and the applied load are discussed. In addition, profiles of the roller ends and generatrix are modified to reduce the roller tilting coupled with the skewing effect. Results show that, the thermal effect and the uneven distribution of the lubricating performance are the most prominent when both tilting and skewing effect are considered. Larger tilting angle, and heavier applied load causes greater maximum pressure and temperature, and thinner minimum film. Higher rotating speed leads to greater maximum film temperature, although thicker film. Profile modification of the roller’s ends and generatrix may reduce the effect of roller tilting and skewing. These findings provide important insights into the lubricating design in rolling bearings.