Enhanced performance of step slider bearings with couple stress and magnetic fluid lubrication incorporating sinusoidal magnitude: A theoretical investigation

Dipali K. Chauhan; Jimit Patel; G. M. Deheri

doi:10.15282/jmes.19.2.2025.4.0832

Authors

Dipali K. Chauhan Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa - 388 421, Anand, Gujarat, India. Phone: +91 2697265190, Fax.: +91 2697265192
Jimit Patel Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa - 388 421, Anand, Gujarat, India. Phone: +91 2697265190, Fax.: +91 2697265192
G. M. Deheri Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, Anand, Gujarat, India

DOI:

https://doi.org/10.15282/jmes.19.2.2025.4.0832

Keywords:

Step Slider Bearing, Load Carrying Capacity, Magnetic Fluid, Couple Stress, Sinusoidal Magnitude of Magnetic Field

Abstract

Step slider bearings play a critical role in tribological applications, particularly within high-precision mechanical systems, where their operational efficiency is significantly influenced by the nature of the lubricant and its rheological response to external field variations. This theoretical investigation examines the behavior of a step slider bearing, taking into account the effects of couple stress and magnetic fluid as a lubricant. A sinusoidal model is employed to modulate the magnetic field's intensity, aiming to optimize bearing performance. The Reynolds equation governing the step slider bearing is adapted to incorporate the Neuringer and Rosensweig theory for magnetic fluid flow and the Stokes micro-continuum principle for couple stress effects. Through the solution of the modified Reynolds equation under appropriate boundary conditions, parameters such as pressure, load carrying capacity (LCC), center of pressure, and frictional force are quantified. Visual displays are used to present the study's results. The outcomes indicate a significant increase in load compared to systems without magnetic fluid. In addition, the increase in this couple stress and the parameters of magnetization will increase the load capacity and friction force. On the other hand, a decrease in the coefficient of friction is observed. The effect of magnetic fluid lubrication is found to increase the LCC by at least 28.48% with the inclusion of couple stress. In precision bearing systems used in aerospace, robotics, and micro-mechanical devices, enhanced load-carrying capacity and friction regulation can be achieved by utilizing ferrofluids subjected to well-tuned magnetic fields.

References

[1] G. Ramanaiah, P. Sarkar, “Slider bearings lubricated by fluids with couple stress,” Wear, vol. 52, no. 1, pp. 27-36, 1979.

[2] R. C. Shah, N. I. Patel, “Impact of various and arbitrary porous structure in the study of squeeze step bearing lubricated with magnetic fluid considering the variable magnetic field,” Journal of Engineering Tribology, vol. 229, no. 5, pp. 646-659, 2015.

[3] P. S. Rao, S. Agarwal, “Theoretical study of couple stress fluid film in rough step slider bearing with assorted,” Journal of Nanofluids, vol. 7, no. 1, pp. 92-99, 2018.

[4] N. B. Naduvinamani, S. Patil, S. S. Siddapur, “On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid,” Industrial Lubrication and Tribology, vol. 69, no. 5, pp. 666-672, 2017.

[5] N. B. Naduvinamani, A. Siddangouda, “A note on porous Rayleigh step bearings lubricated with couple stress fluids,” Proceedings of the Institution of Mechanical Enginers, Part J: Journal of Engineering Tribology, vol. 221, no. 5, pp. 615-621, 2007.

[6] P. I. Andharia, H. M. Pandya, “Effect of longitudinal surface roughness on the performance of Rayleigh step bearing,” International Journal of Applied Engineering Research, vol. 13, no. 21, pp. 14935-14941, 2018.

[7] G. Maiti, “Composite and step slider bearings in micropolar fluid,” Japanese Journal of Applied Physics, vol. 12, no. 7, pp. 1058-1064, 1973.

[8] G. M. Deheri, J. R. Patel, N. D. Patel, “Shliomis model-based ferrofluid lubrication of a rough porous convex pad slider bearing,” Tribology in Industry, vol. 38, no. 1, pp. 57-65, 2016.

[9] B. N. Hanumagowda, T. Cyriac, H. S. Doreswamy, A. Salma, “Analysis of static and dynamic characteristics of Secant slider bearing with MHD and couple stress fluid,” Malaya Journal of Matematik, vol. 8, no. 2, pp. 581-587, 2020.

[10] G. S. Nada, “A study of finite hydrodynamics slider bearings lubricated with ferrofluids,” Engineering Research Journal- Faculty of Engineering, vol. 52, no. 2, pp. 16-25, 2023.

[11] J. Anthony, S. Elamparithi, “Effect of MHD and surface roughness on porous step slider bearing lubricated with couple stress fluid,” International Journal of Heat and Technology, vol. 41, no. 1, pp. 135-142, 2023.

[12] M. M. Munshi, A. R. Patel, G. M. Deheri, “Analysis of rough porous inclided silder bearing lubricated with a ferrofluid considering sip velocity,” International Journal of Research in Advent Technology, vol. 7, no. 1, pp. 387-396, 2019.

[13] R. C. Shah, “Ferrofluid lubrication of porous- rough circular squeeze film bearings,” The European Physical Journal Plus, vol. 137, no. 2, pp. 1-16, 2022.

[14] R. C. Shah, R. B. Shah, “Static and dynamic performance of ferrofluid lubricated long journal bearing,” Zeitschrift für Naturforschung A, vol. 76, no. 6, pp. 493-506, 2021.

[15] R. C. Shah, D. B. Patel, “On the ferrofluid lubricated exponential squeeze film bearings,” Zeitschrift für Naturforschung A, vol. 76, no. 3, pp. 209-215, 2021.

[16] G. M. Deheri, J. R. Patel, “Magnetic fluid based squeeze film in a rough porous parallel plate slider bearing,” International Journal of Engineering, vol. 9, no.3, pp. 443-448, 2011.

[17] N. D. Patel, G. M. Deheri, “Based parallel plate porous slider bearing with slip velocity,” Journal of the Serbian Society for Computational Mechanics, vol.5, no. 1, pp. 104-118, 2011.

[18] S. Shukla, G. M. Deheri, “Effect of slip velocity on magnetic fluid lubrication of rough porous Rayleigh step bearing,” Journal of Mechanical Engineering and Sciences, vol. 4, no.1, pp. 532-547, 2013.

[19] M. E. Shimpi, G. Deheri, “Analysis of squeeze film performance in porous rough rectangular plates under the presence of a magnetic fluid lubricant,” Acta technica corviniensis- Bulletin of Engineering, vol. 4, no. 1, pp. 49-54, 2011.

[20] M. E. Shimpi, G. M. Deheri, “Surface roughness effect on a magnetic fluid-based squeeze film between a curved porous circular plate and a flat circular plate,” Journal of the Brazilian Society Mechanical Sciences and Engineering, vol. 36, no. 2, pp. 233-243, 2014.

[21] J. R. Patel, M. E. Shimpi, G. M. Deheri, “Ferrofluid-based squeeze film for a rough conical bearing with deformation effect,” International Conference on Research Invoations in Science, Engineering & Technol - Kalpa Publications in Computing, vol. 2, no. 6, pp. 119-129, 2017.

[22] V. Badescu, “Two classes of sub-optimal shapes for one-dimensional slider bearings with couples stress lubricants,” Applied Mathematical Modelling, vol. 81, pp. 887-909, 2020.

[23] T. Cyraic, B.N. Hanumagowda, M. Umeshaiah, V. Kumar, J. Chohan, R. Kumar, et al., “Performance of rough secant slider bearing lubricated with couple stress fluid in the presence of magnetic field,” Modern Physics Letters B, vol. 38, no. 19, pp. 2450140-2450143, 2023.

[24] V. Jyothi, B. N. Hanumagowda, A. Verma, “Analysis of pressure load-carrying capacity and squeezing time on magnetohydrodynamic couple stress fluid flow between sphere and flat plate with slip velocity,” International journal of Modern physics B, vol. 38, no. 26, pp. 2450349-2450350, 2023.

[25] R. Vinutha, B. N. Hanumagowda, K. R. Vasanth, “Effect of magnetic field and slip velocity on the performance of bearings lubricated by couple stress fluid on long cylinder and infinte plate- A theoretical analysis,” Modern Physics Letters B, vol. 38, no. 30, pp. 2450176-2450259, 2024.

[26] U. Devani, J. Patil, S. Bilal, B. N. Hanumagowda, V. B. Trimbak, J. Tawade, et al., “Study of MHD on porous flat and curved circular plate lubricated with couple stress fluid- a slip velocity model,” Results in Engineering, vol. 24, pp. 102914-1-12, 2024.

[27] J. R. Lin, L. M. Chu, W. L. Liaw, “Effects of non-Newtonian couple stresses on the dynamic characteristics of wide Rayleigh step slider bearings,” Journal of Marine Science and Technology, vol. 20, no. 5, pp. 547-553, 2012.

[28] N. B. Naduvinamani, A. Angadi, “Surface roughness influence on the dynamic performance of Rayleigh step bearing lubricated with couplestress fluid,” in Proceeding of the Natinoal Academy of Sciences, India Section. A - Physical Sciences, vol. 94, pp. 235-247, 2024.

[29] N. B. Naduvinamani, R. Ganachari, “Double-layered porous Rayleigh step slider bearings lubricated with couplestress fluids,” Indian Journal of Science and Technology, vol. 15, no. 28, pp. 1389-1398, 2022.

[30] N. B. Naduvinamani, S. T. Fathima, P. S. Hiremath, “Hydrodynamic lubrication of rough slider bearings with couple stress fluids,” Tribology International, vol. 36, no. 12, pp. 949-959, 2003.

[31] N. B. Naduvinamani, A. Siddangouda, “Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couple stress fluids,” Tribology International, vol. 40, no. 5, pp. 780-793, 2007.

[32] M. Barik, S. R. Mishra, G. C. Dash, “Effect of sinusoidal magnetic field on a rough porous hyperbolic slider bearing with ferrofluid lubrication and slip velocity,” Tribology – Materials, Surfaces and Interfaces, vol. 10, no. 3, pp. 131-137, 2016.

[33] J. R. Patel, G. M. Deheri, “A study of thin film lubrication at nanoscale for a ferrofluid based infinitely long rough porous slider bearing,” Facta Universitatis Series: Mechanical Engineering, vol. 14, no. 1, pp. 89-99, 2016.

[34] D. A. Patel, M. Joshi, D. B. Patel, “Design of porous step bearing by considering different ferro fluid lubrication flow models,” Journal of Manufacturing Engineering, vol. 16, no. 4, pp. 108-114, 2021.

[35] T. Ariman, M. A. Turk, N. D. Sylvester, “Microcontinuum fluid mechanics-A review,” International Journal of Engineering Science, vol. 11, no. 8, pp. 905-930, 1973.

[36] T. Ariman, M. A. Turk, N. D. Sylvester, “Applications of microcontinuum fluid mechanics,” International Journal of Engineering Science, vol. 12, no. 6, pp. 273-293, 1974.

[37] V. K. Stokes, “Couple stresses in fluids,” Physics of Fluids, vol. 9, pp. 1709-1715, 1966.

[38] V. K. Stokes, “Effects of couple stresses in fluids on hydromagnetic channel flows,” Physics of Fluids, vol. 11, pp. 1131-1133, 1968.

[39] V. K. Stokes, “Effects of couple stresses in fluids on the creeping flow past a sphere,” Physics of Fluids, vol. 14, pp. 1580-1582, 1971.

[40] A. Cameron. Basic Lubrication Theory. 1st Ed. London: Longman, 1971.

[41] J. L. Neuringer, R. E. Rosensweig, “Ferrohydrodynamics,” Physics of Fluids, vol. 7, no.12, pp. 1927-1937, 1964.

[42] B. L. Prajapati, “On certain theoretical studies in hydrodynamic and electro-magneto hydrodynamic lubrication,” Ph.D. Thesis, Sardar Patel University, India, 1995.

[43] M. V. Bhat. Lubrication with Magnetic fluid. 1st Ed. India: Team Spirit (India) Pvt. Ltd., 2003.