THE PROBLEMS OF HYDRODYNAMIC NON-ISOTHERMAL LUBRICATION
Authors: WIERZCHOLSKI Krzysztof 
Published: November 2018

The classical hydrodynamic theory of slide bearing lubrication has been constituted on the assumption of constant pressure and viscosity perpendicular to the thin oil layer thickness. These fundamental assumptions are in contradiction to contemporary achievements connected with new devices such as micro-bearing, nano-bearing, magnetic bearings, artificial joints in humanoid robots, micro-motors. Therefore, new methods of measurements and calculations using AFM and a new mathematical computer programs are needed. Energy conservation equations after boundary layer simplifications confirm the fact that temperature gradient variations across the film thickness have the same order of magnitude as the variations in longitudinal or circumferential directions. The fact that temperature gradient variations across the bearing gap height can be significantly large are evident, despite the temperature differences across the film thickness that are negligibly small. This statement cannot be compliant with the assumption of a constant viscosity value in the gap height direction. It has been proven that hydrodynamic pressure is not constant across the film thickness for non-Newtonian oils with Rivlin Erickson constitutive equations. For pseudo-plastic non-Newtonian oils, the apparent dynamic viscosity significantly decreases with shear rate increases. However, for pseudo-plastic oils, the shear rate increments during the oil flow are strictly connected with the average flow velocity increments. Therefore, the apparent dynamic viscosity depends strongly on the oil velocity gradients. It is evident that flow velocity gradients across the film thickness have intensive variations, particularly in regions where gap height attains the least value. In these places, the dynamic viscosity attains the largest variations in gap height directions. If gap height in micro-bearing is smaller than one micrometre, than the largest oil dynamic viscosity increments caused by the velocity variations across the film thickness are located near the superficial layer of the movable journal surfaces in the case of the hydrodynamic lubrication by rotation, but in the neighbourhood where each of two come near lubricated surfaces during the squeezing. Hence, in these places, dynamic viscosity increases across the film thickness and attains the local maximum values. A gap height smaller than one micrometre has the largest oil dynamic viscosity increments caused by the adhesion force variations across the film thickness located near the motionless sleeve surfaces. In a similar manner, the influences on the viscosity variations caused by the cluster points of concentrations of nano particles as oil inhibitors or oil additives smaller than 5 nm occurring in micro-bearing gaps and the cluster concentration regions of collagen fibres occurring in human joint gap are observed. This paper describes and comments on the above-mentioned problem of oil viscosity changes in the gap height direction, and it presents the apparent dynamic viscosity functions for Newtonian and non-Newtonian oils as well indicates the largest viscosity variations in bearing gap height direction and gives examples of initial calculation results.