Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses

Kihuga Daniel; Kinyanjui Mathew; Kimathi Mark

doi:doi:10.11648/j.ajam.20140204.14

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Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses

Kihuga Daniel, Kinyanjui Mathew, Kimathi Mark

Published in American Journal of Applied Mathematics (Volume 2, Issue 4)

Received: 2 August 2014 Accepted: 18 August 2014 Published: 30 August 2014

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Abstract

The performance of finite elastohydrodynamic journal bearings lubricated by ferrofluids with couple stresses has been studied. We derive a Reynolds equation that takes into account magneto elastohydrodynamics, by using the continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, the modified Reynolds equation. The modified Reynolds equation obtained is solved numerically by the finite difference technique since it is highly non-linear. The numerical scheme used is implemented in MATLAB so as to obtain the approximate solutions. The pressure distributions are obtained and the solutions obtained represented in graphs. It is clear from the results that the pressure increases with the increase in magnetism and the couple stress.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 4)
DOI	10.11648/j.ajam.20140204.14
Page(s)	135-140
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Journal Bearing, Reynolds Equation, Magneto-Elasto-Hydrodynamic Lubrication, Couple Stresses

References

[1]	Abdo, H. S. M. (2009). Thermal effects on hydrodynamic journal bearing lubricated by magnetic fluids with couple stresses.
[2]	Bujurke N. M. & Naduvinamani N. B., (1990). The lubrication of lightly loaded cylinders in combined rolling, sliding and normal with couple stress fluid, Int. Journal Mech. Science.
[3]	Cowley, m. D., & Rosensweig, r. E. (April 1967). The interfacial stability of ferromagnetic fluid. Journal of fluid mech, 671-688.
[4]	Govidaraj, R. & Satishkumar V. M. (2012). Design of journal bearing test rig, Sweden blekinge Tekniska Hogskola.
[5]	Mokhiamer U. M., Crosby W. A. &El-Gamal H. A., (1999). A study of a journal bearing lubricated by fluids with couple stress considering the elasticity of the liner wear.
[6]	Nada, g. S. (2002). Static and dynamic characteristics of magnetized journal bearings lubricated with ferrofluid. PhD thesis in mechanical engineering, faculty of engineering. Cairo, Egypt: Cairo University.
[7]	Nada, g. S., & Osman, t. A. (2007). Static performance of finite hydrodynamic journal bearings lubricated by magnetic fluids with couple stresses. Tribology letters, 261-268.
[8]	Naduvinamani N. B., Hiremat P. S. & Gurubasavaraj G. (2002). Effects of surface roughness on the static characteristics of rotor bearing with couple stress fluid, Comput Struct.
[9]	Osman T. A., (1999). Static characteristics of hydrodynamic magnetic bearings working by Non-Newtonian Ferrofluid, Journal of Engineering and Applied science, Cairo University, 521-536
[10]	Osman T. A., Nada G. S. & Safar Z. S., (2003). Different magnetic models in the design of hydrodynamic journal bearings lubricated with Non-Newtonian Ferrofluid, Tribology letters, 211-223
[11]	Stokes, V. K. (1966). Couple stresses in fluids. Phys. Fluids, 1709–1715
[12]	Saynatjoki, M, and Holmberg K., (1982) Magnetic fluids in sealing and lubrication–a state of art review. Finland: Technical Research Center of Finland.

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APA Style

Kihuga Daniel, Kinyanjui Mathew, Kimathi Mark. (2014). Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. American Journal of Applied Mathematics, 2(4), 135-140. https://doi.org/10.11648/j.ajam.20140204.14

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ACS Style

Kihuga Daniel; Kinyanjui Mathew; Kimathi Mark. Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. Am. J. Appl. Math. 2014, 2(4), 135-140. doi: 10.11648/j.ajam.20140204.14

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AMA Style

Kihuga Daniel, Kinyanjui Mathew, Kimathi Mark. Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. Am J Appl Math. 2014;2(4):135-140. doi: 10.11648/j.ajam.20140204.14

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@article{10.11648/j.ajam.20140204.14,
  author = {Kihuga Daniel and Kinyanjui Mathew and Kimathi Mark},
  title = {Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {4},
  pages = {135-140},
  doi = {10.11648/j.ajam.20140204.14},
  url = {https://doi.org/10.11648/j.ajam.20140204.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140204.14},
  abstract = {The performance of finite elastohydrodynamic journal bearings lubricated by ferrofluids with couple stresses has been studied. We derive a Reynolds equation that takes into account magneto elastohydrodynamics, by using the continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, the modified Reynolds equation. The modified Reynolds equation obtained is solved numerically by the finite difference technique since it is highly non-linear. The numerical scheme used is implemented in MATLAB so as to obtain the approximate solutions. The pressure distributions are obtained and the solutions obtained represented in graphs. It is clear from the results that the pressure increases with the increase in magnetism and the couple stress.},
 year = {2014}
}

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TY  - JOUR
T1  - Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses
AU  - Kihuga Daniel
AU  - Kinyanjui Mathew
AU  - Kimathi Mark
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140204.14
DO  - 10.11648/j.ajam.20140204.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 135
EP  - 140
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140204.14
AB  - The performance of finite elastohydrodynamic journal bearings lubricated by ferrofluids with couple stresses has been studied. We derive a Reynolds equation that takes into account magneto elastohydrodynamics, by using the continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, the modified Reynolds equation. The modified Reynolds equation obtained is solved numerically by the finite difference technique since it is highly non-linear. The numerical scheme used is implemented in MATLAB so as to obtain the approximate solutions. The pressure distributions are obtained and the solutions obtained represented in graphs. It is clear from the results that the pressure increases with the increase in magnetism and the couple stress.
VL  - 2
IS  - 4
ER  -

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Author Information

Kihuga Daniel

Pure and Applied Mathematics Department, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Kinyanjui Mathew

Pure and Applied Mathematics Department, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Kimathi Mark

Pure and Applied Mathematics Department, Technical University of Kenya, T. U. K, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Kihuga Daniel, Kinyanjui Mathew, Kimathi Mark. (2014). Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. American Journal of Applied Mathematics, 2(4), 135-140. https://doi.org/10.11648/j.ajam.20140204.14

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ACS Style

Kihuga Daniel; Kinyanjui Mathew; Kimathi Mark. Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. Am. J. Appl. Math. 2014, 2(4), 135-140. doi: 10.11648/j.ajam.20140204.14

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AMA Style

Kihuga Daniel, Kinyanjui Mathew, Kimathi Mark. Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses. Am J Appl Math. 2014;2(4):135-140. doi: 10.11648/j.ajam.20140204.14

Copy | Download

@article{10.11648/j.ajam.20140204.14,
  author = {Kihuga Daniel and Kinyanjui Mathew and Kimathi Mark},
  title = {Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {4},
  pages = {135-140},
  doi = {10.11648/j.ajam.20140204.14},
  url = {https://doi.org/10.11648/j.ajam.20140204.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140204.14},
  abstract = {The performance of finite elastohydrodynamic journal bearings lubricated by ferrofluids with couple stresses has been studied. We derive a Reynolds equation that takes into account magneto elastohydrodynamics, by using the continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, the modified Reynolds equation. The modified Reynolds equation obtained is solved numerically by the finite difference technique since it is highly non-linear. The numerical scheme used is implemented in MATLAB so as to obtain the approximate solutions. The pressure distributions are obtained and the solutions obtained represented in graphs. It is clear from the results that the pressure increases with the increase in magnetism and the couple stress.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Investigation of Pressure Distributions for a Finite Elastohydrodynamic Journal Bearing Lubricated by Ferro Fluids with Couple Stresses
AU  - Kihuga Daniel
AU  - Kinyanjui Mathew
AU  - Kimathi Mark
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140204.14
DO  - 10.11648/j.ajam.20140204.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 135
EP  - 140
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140204.14
AB  - The performance of finite elastohydrodynamic journal bearings lubricated by ferrofluids with couple stresses has been studied. We derive a Reynolds equation that takes into account magneto elastohydrodynamics, by using the continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, the modified Reynolds equation. The modified Reynolds equation obtained is solved numerically by the finite difference technique since it is highly non-linear. The numerical scheme used is implemented in MATLAB so as to obtain the approximate solutions. The pressure distributions are obtained and the solutions obtained represented in graphs. It is clear from the results that the pressure increases with the increase in magnetism and the couple stress.
VL  - 2
IS  - 4
ER  -

Copy | Download