### International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

###### Lubrication of Rough Short Bearing on Shliomis Model by Ferrofluid Considering Viscosity Variation Effect

Alpha College of Engineering and Technology, Gujarat Technological University, Kalol, 382721, Gujarat, India.

A. R. Patel
Vishwakarma Government Engineering College, Gujarat Technological University, Ahmedabad, 382424, Gujarat, India.

G. M. Deheri
Department of Mathematics, Sardar Patel University, Vallabh Vidhyanagar, 388120, Gujarat, India.

Received on January 16, 2019
;
Accepted on May 01, 2019

Abstract

This study aims to explore the impact caused by change in viscosity and the roughness of a bearing surface on a ferrofluid lubrication of Shliomis model for short bearing. Based on this model and the Tipei (1962) model, a new resultant Reynolds equation has been found that shows thermal variation. The Christensen and Tonder models have been taken to derive the transverse roughness stochastically. An assumed mean has been taken for the probability density function with a non-zero value. This value is assigned to a random variable that measures the bearing’s surface roughness. This creates a more realistic situation that can have a lot of field applications. The model defines the problem mathematically while defining boundary conditions. It also uses the Simpson’s method to derive a conclusion. The results thus obtained are discussed in terms of pressure distribution and load bearing capacity. The graphical results obtained suggest that in the presence of magnetization, there is a significant enhance in the load bearing capacity. This positive effect can easily nullify the negative impact of the thermal effect. The short bearing approximation shown here is an example of the probable applications. Ferrofluids in the presence of magnetic fields significantly enhance the performance of a short bearing.

Keywords- Ferrofluid, Thermal variation, Load carrying capacity.

Citation

Munshi, M. M., Patel, A. R., & Deheri, G. M. (2019). Lubrication of Rough Short Bearing on Shliomis Model by Ferrofluid Considering Viscosity Variation Effect. International Journal of Mathematical, Engineering and Management Sciences, 4(4), 982-997. https://dx.doi.org/10.33889/IJMEMS.2019.4.4-078.

Conflict of Interest

The authors confirm that there is no conflict of interest to publish the paper in the journal.

Acknowledgements

The authors acknowledge with regards the constructive comments, fruitful suggestions and remarks of the reviewer/Editor, leading to an overhauling of the materials presented in the paper, necessitating the introduction of a few more references.

References

Basu, S.K., Sengupta, S.N., & Ahuja, B.B. (2005). Fundamentals of tribology. Prentice‐Hall of India private limited, New Delhi, India.

Bhat, M.V. (2003). Lubrication with a magnetic fluid. Team spirit Pvt. Ltd., India.

Christensen, H., & Tonder, K. (1971). The hydrodynamic lubrication of rough bearing surfaces of finite width. Journal of Lubrication Technology, 93(3), 324-329.

Christensen, H., & Tonder, K.C. (1969a). Tribology of rough surfaces: stochastic models of hydrodynamic lubrication. SINTEF Report 10/69.

Christensen, H., & Tonder, K.C. (1969b). Tribology of rough surfaces: parametric study and comparison of lubrication model. SINTEF Report 22/69.

Deheri, G.M., & Patel, J.R. (2011). Effect of surface roughness on the performance of a magnetic fluid based short bearing. Mathematics Today, 27, 10-23.

Deheri, G.M., Patel, J.R., & Patel, N.D. (2016). Shliomis model based ferrofluid lubrication of a rough porous convex pad slider bearing. Tribology in Industry, 38(1), 46-65.

Freeman, P. (1962). Lubrication and friction. Chap.2, Pitman, London.

Gokul Raj, P., Esakki, B., & Ganesan, S. (2019). Evaluation of mechanical strength characteristics of double ducted unmanned amphibious aerial vehicle using finite element analysis. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 420-431.

Gupta A., Yadav, V., Sawant, V.A., & Agarwal, R. (2019). Development of design charts considering the effect of backfill inclination and wall inclination on the seismic active pressure for c-ϕ soil. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 409-419.

Hamrock, B.J. (1994). Fundamentals of fluid film lubrication. McGraw-Hill, New York.

Huang, W., & Wang, X. (2016). Ferrofluids lubrication: a status report. Lubrication Science, 28, 3-26.

Khamari, B.K., Gunji, B., Karak, S.K., & Biswal, B.B. (2019). Variation of microstructural and mechanical properties with respect to polarity in shielded metal arc welding of mild steel. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 521-530.

Kumar, V.B., Suneetha, P.A., & Prasad, K.R. (2013). Lubrication of journal bearing consider in thermal effect in two-layer fluid considering cavitation. International Journal of Advanced Engineering Technology, 4(4), 82-85.

Lin, J.R. (2016). Longitudinal surface roughness effects in magnetic fluid lubricated journal bearings. Journal of Marine Science and Technology, 24(4), 711-716.

Lin, J.R., Li, P.J., & Hung, T.C. (2013a). Effects of non-newtonian ferrofluids on the performance characteristics of long journal bearings. Fluid Dynamics & Materials Processing, 9(4), 419-434.

Lin, J.R., Li, P.J., & Hung, T.C. (2013b). Lubrication performances of short journal bearings operating with non-Newtonian ferrofluids. Z. Naturforsch., 68, 249-254.

Majumdar, B.C. (2008). Introduction to tribology of bearings. S. Chand and Comp. Ltd., New Delhi, India.

Munshi, M.M., Patel, A.R., & Deheri, G.M. (2017). Effect of slip velocity on a magnetic fluid based squeeze film in rotating transversely rough curved porous circular plates. Industrial Engineering Letters, 7(8), 28-42.

Naduvinamani, N.B., Apparao, S., Kadadi, A.K., & Biradar, S.N. (2014). Combined effect of viscosity variation and surface roughness on the squeeze film lubrication of journal bearings with micropolar fluids. Tribology Online, 9(4), 175-183.

Patel, J.R., & Deheri, G.M. (2013a). A comparison of porous structures on the performance of a magnetic fluid based rough short bearing. Tribology in Industry, 35(3), 177-189.

Patel, J.R., Deheri, G.M., & Patel, P.A. (2018). Ferro-fluid lubrication of journal bearing with thermal effects. Mathematics Today, 34(A), 92-99.

Patel, N.S., Vakharia, D.P., Deheri, G.M., & Patel, H.C. (2017). Experimental performance analysis of ferrofluid based hydrodynamic journal bearing with different combination of materials. Wear, 376-377, Part B, 1877-1884.

Patel, R.M., Deheri, G.M., & Vadher, P.A. (2010a). Performance of a magnetic fluid-based short bearing. Acta Polytechnica Hungarica, 7(3), 63-78.

Patel, R.M., Deheri, G.M., & Vadher, P.A. (2010b). Magnetic fluid based short bearing and roughness effect. Journal of Science, 1(1), 102-107.

Patel, R.M., Deheri, G.M., & Vadher, P.A. (2015). Hydromagnetic short bearings. Journal of Mechanical Engineering and Technology, 7(2), 19-32.

Patel, R.U., & Deheri, G.M. (2013b). Effect of slip velocity on the performance of a short bearing lubricated with a magnetic fluid. Acta Polytechnica, 53(6), 890-894.

Prajapati, B.L. (1994). Magnetic fluid-based porous inclined slider bearing with velocity slip. Prajna, 73-78.

Ramadevi, B., Ramana Reddy, J.V., & Sugunamma, V. (2018). Influence of thermodiffusion on time dependent casson fluid flow past a wavy surface. International Journal of Mathematical, Engineering and Management Sciences, 3(4), 472-490.

Reddy, S.C.N., Reddy, G.J.C., & Prasad, K.R.K. (2012). Effects of viscosity variation due to additives on squeeze film characteristics of long partial journal bearing: couple stress fluid model. International Journal of Mathematical Archive, 3(8), 2858-2868.

Shimpi, M.E., & Deheri, G.M. (2010). Magnetic fluid based rough short bearing. Journal of the Balkan Tribological Association, 16(4), 484-497.

Shimpi, M.E., & Deheri, G.M. (2012). Effect of deformation in magnetic fluid based transversely rough short bearing. Tribology-Materials Surfaces & Interfaces, 6(1), 20-24.

Shliomis, M.I. (1974). Magnetic fluids. Soviet Physics Uspekhi, 17(2), 153-169.

Siddangouda, A., Biradar, T.V., & Naduvinamani, N.B. (2013). Combined effects of surface roughness and viscosity variation due to additives on long journal bearing. Tribology–Materials, Surfaces & Interfaces, 7(1), 21-35.

Singh, U.P., Medhavi, A., Gupta, R.S., & Bhatt, S.S. (2018). Theoretical study of heat transfer on peristaltic transport of non-newtonian fluid flowing in a channel: Rabinowitsch fluid model. International Journal of Mathematical, Engineering and Management Sciences, 3(4), 450-471.

Sinha, P., Singh, C., & Prasad, K.R. (1981). Effect of viscosity variation due to lubricant additives in journal bearings. Wear, 66(2), 175-188.

Tipei, N. (1962). Theory of lubrication: with applications to liquid-and gas-film lubrication. Stanford University Press.

Vashi, Y.D., Patel, R.M., & Deheri, G.M. (2018). Ferrofluid based squeeze film lubrication between rough stepped plates with couple stress effect. Journal of Applied Fluid Mechanics, 11(3), 597-612.

Verma, P.D.S. (1986). Magnetic fluid-based squeeze films. International Journal of Engineering Sciences, 24(3), 395-401.