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A theoretical aspect of hydrodynamic lubrication of two symmetric rollers by power law fluids is analyzed. The effect of fluid convective inertia, which is significant in case of high speed bearing, is taken into account. The effect of hydrodynamic pressure and temperature on the lubricant consistency m is assumed to vary with pressure and the mean temperature. The squeezing motion of the surfaces is also incorporated along with inertia and thermal effects. The Reynolds equation and the energy equation (with convection and conduction), which are coupled through m, are solved simultaneously. Various bearing characteristics such as pressure, temperature, load and drag etc. are obtained and a comparison between results (with and without inertia) is also made. It is noted that the effect of inertia is to increase pressure, temperature, load and drag etc. and to displace the position of pressure peak slightly towards the center line of contact of the rollers. An attempt is also made to study the variation of film thickness with load, speed, Eckert number, pressure, and temperature viscosity exponents.

With the advancement of lubrication technology, precise prediction of performance characteristics of bearings is the first and inevitable step for stability of mechanical systems. Most of the existing theoretical analyses of hydrostatic thrust bearings lubricated with non-Newtonian fluids have considered the lubricant inertia, only in the recess and land regions but did not account either for the inertia of lubricant in the supply region or the surface roughness of the bearings. This could be a cause for the deviation between the theoretical results and the experimental data under certain conditions. In this work, combined influence of surface roughness as well as lubricant inertia in the supply region, on the static properties of a hydrostatic stepped thrust bearing lubricated with a non-Newtonian fluid, has been discussed using Rabinowitsch fluid model. Surface roughness effects have been accounted for using Christensen theory of rough surfaces. It is expected that the current study could bridge the gap between the experimental and theoretical studies. Solution for momentum equation has been obtained by means of average inertia approach. Analytic expressions for film pressure have been derived for radial and circumferential roughness patterns. Mathematica 11.0 has been used for numerical computations, wherever necessary. Results for film pressure and load carrying capacity have been plotted and discussed. It is observed that the present results are in a better agreement with the experimental data. [ABSTRACT FROM AUTHOR]

A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operator arising in two-dimensional point contact problem is analyzed and developed in discontinuous Galerkin finite volume (DG-FVEM) framework. We derive a discrete DG-FVEM formulation of the problem and prove existence and uniqueness results for it. Optimal error estimates in H¹ and L² norm are derived under a light load parameter assumptions. In addition, the article provides a complete algorithm to tackle all numerical complexities appear in the solution procedure. Numerical outcomes are presented for light, moderate and relative high load conditions. The variations of load parameter and its effect on the evolution of deformations and pressure profile are evaluated and described. This method is well suited for solving elastoehydrodynamic lubrication point contact problems and can probably be treated as commercial software. Furthermore, the results give a hope for the further development of the scheme for extreme load condition, observes in a more realistic operating situation which will be discussed in part II. [ABSTRACT FROM AUTHOR]