Deformable Rough Wide Tapered Land Slider Bearing

Abstract

This paper presents an analytical study of the impact of couple stress on the static and dynamic characteristics of a wide tapered land slider bearing under the influence of an applied magnetic field. A modified, non-dimensional Reynolds equation is derived for the bearing system. Closed-form expressions are obtained for the steady-state fluid film pressure, steady load-carrying capacity, and dynamic characteristics, including the dynamic stiffness and dynamic damping coefficients. Numerical computations demonstrate that a magneto hydrodynamic tapered land slider bearing, lubricated with a couple-stress fluid, offers higher steady load-carrying capacity, dynamic stiffness, and dynamic damping coefficients compared to the corresponding Newtonian fluid case. Additionally, the results indicate that the presence of an applied magnetic field, characterized by the Hartmann number, enhances both the static and dynamic performance of the tapered land slider bearing when compared to the case without a magnetic field.

Introduction

Bearing design is critical for machine efficiency and reliability, requiring optimal bearing size, type, material, and lubricant choice. Traditional lubrication theory assumes lubricants are Newtonian fluids, but many practical lubricants behave as non-Newtonian fluids, often achieved by adding long-chain polymers.

The Stokes couple stress theory extends classical lubrication theory to account for polar effects like couple stresses in lubricants, improving load capacity and reducing friction compared to Newtonian lubricants. Multiple studies have confirmed these benefits in various bearing configurations.

Another important factor is magneto-hydrodynamics (MHD), which studies the effect of magnetic fields on electrically conducting fluids, enhancing bearing performance, especially at high temperatures. Research shows that applying a magnetic field increases the load-carrying capacity of bearings.

Recent investigations explore the combined effects of couple stress fluids and MHD, finding further improvements in static and dynamic bearing characteristics compared to using either effect alone.

The current study focuses on the static and dynamic performance of wide deformable rough tapered land bearings lubricated with couple stress fluids under a transverse magnetic field. The problem assumes a thin fluid film, negligible fluid inertia, and dominance of viscous and Lorentz forces. Governing equations based on these assumptions lead to a modified Reynolds equation describing pressure distribution and load capacity.

Mathematical modeling incorporates:

• Fluid film thickness variation due to bearing geometry and deformation.

• Non-dimensional parameters for film thickness, pressure, and velocity.

• Boundary conditions representing physical constraints of the bearing surfaces.

Results from this analysis will be compared to previous studies considering Newtonian fluids with and without magnetic fields. Preliminary findings align well with earlier work, confirming that couple stress fluids combined with MHD enhance bearing performance.

References

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Copyright

Copyright © 2025 Dr. Pragna A. Vadher, Dr. Gunamani B. Deheri, Dr. Dhinesha Ruwanthi Perera, Rakesh Manilal Patel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.