The use of additives (polyisobutylene, ethylene-propylene, lithium hydroxy stearate, hydrophobic silica, etc.) changes lubricants’ rheology due to which they show pseudoplastic and dilatant nature, which can be modelled as cubic stress fluid model (Rabinowitsch fluid model). The present theoretical analysis investigates the effects of non-Newtonian pseudoplastic and dilatant lubricants on the squeezing characteristics of a sphere and a flat plate. The modified Reynolds equation has been derived and an asymptotic solution for film pressure is obtained. The results for the film pressure distribution, load carrying capacity, and squeezing time characteristics have been calculated for various values of pseudoplastic parameter and compared with the Newtonian results. These characteristics show a significant variation with the non-Newtonian pseudoplastic and dilatant behavior of the fluids.

Squeeze film between a sphere and plate is observed in various machine elements such as ball bearings, cam and followers, and gears. The mechanical action (squeezing, shearing, etc.) leading to the generation of high pressure at the contacts [

The objective of this paper is to extend the results [

The physical configuration of a sphere-plate system is shown in Figure

Schematic diagram of squeeze film between a sphere and a plate.

Under the assumptions of hydrodynamic lubrication applicable to thin film as considered by Dowson [

Integrating (

The modified Reynolds equation (

As (

Substituting (

The load carrying capacity can be obtained by integrating the film pressure over the squeezing film area as follows:

The squeezing time can be calculated by integrating (

Based on the Rabinowitsch fluids model, the effects of non-Newtonian rheology on the squeeze-film characteristics between a sphere and a plate are investigated using a dimensionless parameter

In order to analyze the non-Newtonian effects of fluids on the squeeze-film performance of sphere-plate system, various squeeze-film characteristics are presented with the following values:

pseudoplastic parameter

sphere parameter

Variation of dimensionless pressure with respect to the dimensionless radius

Figure

Variation of the dimensionless maximum film pressure with respect to the minimum film thickness

Figure

Variation of the dimensionless load capacity with respect to the dimensionless minimum film thickness

Figure

Variation of dimensionless squeeze time with respect to the squeezed film thickness

Based on the Rabinowitsch fluid model (cubic stress model) for non-Newtonian pseudoplastic and dilatant fluids, the effects of lubricant additives on the performance characteristics of squeezing film between a sphere and a plate are presented avoiding the inertia and cavitation effects. The analytical solution for pressure distribution is obtained using a classical perturbation technique. Based on the present theoretical analysis, the following results have been drawn.

Dilatant lubricants increase the pressure and load carrying capacity significantly, whereas the case is reversed with the pseudoplastic lubricants.

On comparing with the Newtonian case, dilatant lubricants increase the squeeze time, whereas the pseudoplastic lubricants decrease it.

As the squeezing time of the sphere-plate system is significantly increased with the dilatant lubricants, it is expected that the use of additives can reduce the vibration in the sphere-plate systems.

Bar denotes the dimensional quantities

Film thickness defined in (

Minimum film thickness,

Initial minimum film thickness

Film pressure,

Dimensionless perturbed film pressures

Radial coordinate,

Radius of sphere

Time,

Components of velocity

Load capacity,

Design parameter

Coefficient pseudoplasticity

Viscosity of lubricant

Stress component.

The authors, hereby, thank Dr. M. Fillon (Director of Research, Centre National de la Recherche Scientifique, University of Poitiers) and Dr. V. K. Kapur (Former Professor and Chairman, KNIT, Sultanpur, India) for providing useful materials and guidelines to enhance the content of the paper.