Parametric Characterization of Load Capacity of Infinitely Wide Parabolic Slider Bearing with Couple Stress Fluids
A mathematical model for the hydrodynamic
lubrication of parabolic slider bearings with couple stress lubricants
is presented. A numerical solution for the mathematical model using
finite element scheme is obtained using three nodes isoparametric
quadratic elements. Stiffness integrals obtained from the weak form
of the governing equations were solved using Gauss Quadrature to
obtain a finite number of stiffness matrices. The global system of
equations was obtained for the bearing and solved using Gauss Seidel
iterative scheme. The converged pressure solution was used to obtain
the load capacity of the bearing. Parametric studies were carried out
and it was shown that the effect of couple stresses and profile
parameter are to increase the load carrying capacity of the parabolic
slider bearing. Numerical experiments reveal that the magnitude of
the profile parameter at which maximum load is obtained increases
with decrease in couple stress parameter. The results are presented in
graphical form.
[1] L.H. Berlins, C.E.Goodyer and P.K.Jimack,, "High Order Discontinuous
Galerkin Method for Elastohydrodynamic Lubrication Line Contact
Problems", Communications in Numerical Methods in Engineering, Vol.
9, Issue 18, pp 1 - 7,2000.
[2] A.A. Ozalp, and H.Umur, "Optimum surface profile deign and
performance evaluation of inclined slider bearings", Current Science,
Vol. 90, Issue 11, pp 1480 - 1491 ,2006.
[3] H.Bayrakceken. and M.Yurusoy, "Comparison of pressure distribution
in inclined and Parabolic Slider Bearing", Mathematical and
Computational applications, Vol. 11, Issue 1, pp 65-71,2006.
[4] C.J.Shah, and M.V.Bhat, "Lubrication of a porous Exponential Slider
bearing by Ferrofluid with slip velocity", Turkish Journal of Engineering
Environmental Science, Vol. 27, pp 183 - 187.2003.
[5] M.Yurusoy, "A study of pressure distribution of a slider bearing
lubricated with Powel - Eyring fluid" Turkish J.Eng.Env Sci, Vol 27.,
pp 299-304(2003)
[6] N.M.Bujurke and B.R.Kudenati, "Multigrid solution of modified
Reynolds- Equation incorporating poroelasticity and Couple Stress",
Journal of porous media, Vol. 10, issue 2, pp 125 - 136, 2007.
[7] C.J. Shah, and M.V.Bhat, "Effect of slip velocity in a porous secant
shaped slider bearing with a ferrofluid lubricant", Fizika A - 12, pp 1 -
8, 2003.
[8] J.R.Lin and M.L.Yu, "Steady State performance of parabolic slider
bearings with a couple stress fluid", Journal of Marine Science and
Technology, Vol 12, Issue 4, pp 239 - 246 ,2004.
[9] V.K. Stokes, "Couple stresses in fluids "Phys Fluids, Vol. 9, pp 1709 -
1715, 1966.
[10] J.R.Lin, "Effects of Couple Stress on the Lubrication of Finite Journal
Bearing", Wear, Vol. 206, pp 171 - 178, 1997.
[11] B.P.Mitidierri, "Advanced Modeling of Elastohydrodynamic
Lubrication", Doctoral Thesis, Tribology Section and thermo fluids
section, Department of Mechanical Engineering, Imperial College,
London, pp 19 2005.
[12] M.Senangi, B.C.Majumda, and A.S.Sekhar, "Elastohydrodynamically
lubricated ball bearings with couple stress fluids, Part 1: Steady state
analysis", Tribology transactions, Vol 48, issue 3, pp 404 - 414, 2005.
[13] R.Linj, "Squeeze film characteristics of finite journal bearings; couple
stress fluid model", Tribology International, Vol 31, issue 4, pp 201 -
207, 1998.
[14] A.A.Elsharkawy, "Effects of misalignment on the performance of finite
journal bearings lubricated with couple stress fluids", International
Journal of Computer Applications in Technology (IJCAT), Vol. 21, No.
3, 2004
[15] J.R.Lin, "Derivation of dynamic couple-stress Reynolds-s equation of
sliding-squeezing surfaces and numerical solution of plane inclined
slider bearings", Tribology International, Vol 36, issue 9, pp 679 - 685
2003.
[16] G.S.Nada and T.A.Osman,, "Static Performance of Finite Hydrodynamic
Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses",
Tribology letters, Vol 27, number 3,, pp 261 - 268, 2007
[17] F. Paulo, J.C Pimenta and A. Jorge, "Journal Bearings Subjected to
Dynamic loads: The Analytical Mobility Method", Mecanica
Experimental, Vol. 13, pp 115 - 127, 2006.
[18] J.R.Lin, "Optimal design of one dimensional porous slider bearing using
the Brinkman model", Tribology International, Vol. 34, issue 1, pp 57 -
64, 2001.
[19] B.V.R Kumar, P.S.Rao and P.Sinha, "A numerical study of performance
of a Slider bearing with heat conduction to the Pad, Finite Elements in
Analysis And Design, Vol. 37, issue 8, pp 581 - 585, 2001.
[20] C.C.Hwang, J.R.Lin and R.F.Yang," Lubrication of long Porous Slider
Bearings (use of Brinkman-extended Darcy Model)", JSME
International Journal (Series B), Vol.39, issue 1, pp 141 - 148. (1996).
[21] X. Ni, "Numerical Analysis of a Spiral Groove Dry Gas Seal Under slip
flow conditions", Proceeding of the seventeenth International offshore
and Polar Engineering Conference, 2007.
[1] L.H. Berlins, C.E.Goodyer and P.K.Jimack,, "High Order Discontinuous
Galerkin Method for Elastohydrodynamic Lubrication Line Contact
Problems", Communications in Numerical Methods in Engineering, Vol.
9, Issue 18, pp 1 - 7,2000.
[2] A.A. Ozalp, and H.Umur, "Optimum surface profile deign and
performance evaluation of inclined slider bearings", Current Science,
Vol. 90, Issue 11, pp 1480 - 1491 ,2006.
[3] H.Bayrakceken. and M.Yurusoy, "Comparison of pressure distribution
in inclined and Parabolic Slider Bearing", Mathematical and
Computational applications, Vol. 11, Issue 1, pp 65-71,2006.
[4] C.J.Shah, and M.V.Bhat, "Lubrication of a porous Exponential Slider
bearing by Ferrofluid with slip velocity", Turkish Journal of Engineering
Environmental Science, Vol. 27, pp 183 - 187.2003.
[5] M.Yurusoy, "A study of pressure distribution of a slider bearing
lubricated with Powel - Eyring fluid" Turkish J.Eng.Env Sci, Vol 27.,
pp 299-304(2003)
[6] N.M.Bujurke and B.R.Kudenati, "Multigrid solution of modified
Reynolds- Equation incorporating poroelasticity and Couple Stress",
Journal of porous media, Vol. 10, issue 2, pp 125 - 136, 2007.
[7] C.J. Shah, and M.V.Bhat, "Effect of slip velocity in a porous secant
shaped slider bearing with a ferrofluid lubricant", Fizika A - 12, pp 1 -
8, 2003.
[8] J.R.Lin and M.L.Yu, "Steady State performance of parabolic slider
bearings with a couple stress fluid", Journal of Marine Science and
Technology, Vol 12, Issue 4, pp 239 - 246 ,2004.
[9] V.K. Stokes, "Couple stresses in fluids "Phys Fluids, Vol. 9, pp 1709 -
1715, 1966.
[10] J.R.Lin, "Effects of Couple Stress on the Lubrication of Finite Journal
Bearing", Wear, Vol. 206, pp 171 - 178, 1997.
[11] B.P.Mitidierri, "Advanced Modeling of Elastohydrodynamic
Lubrication", Doctoral Thesis, Tribology Section and thermo fluids
section, Department of Mechanical Engineering, Imperial College,
London, pp 19 2005.
[12] M.Senangi, B.C.Majumda, and A.S.Sekhar, "Elastohydrodynamically
lubricated ball bearings with couple stress fluids, Part 1: Steady state
analysis", Tribology transactions, Vol 48, issue 3, pp 404 - 414, 2005.
[13] R.Linj, "Squeeze film characteristics of finite journal bearings; couple
stress fluid model", Tribology International, Vol 31, issue 4, pp 201 -
207, 1998.
[14] A.A.Elsharkawy, "Effects of misalignment on the performance of finite
journal bearings lubricated with couple stress fluids", International
Journal of Computer Applications in Technology (IJCAT), Vol. 21, No.
3, 2004
[15] J.R.Lin, "Derivation of dynamic couple-stress Reynolds-s equation of
sliding-squeezing surfaces and numerical solution of plane inclined
slider bearings", Tribology International, Vol 36, issue 9, pp 679 - 685
2003.
[16] G.S.Nada and T.A.Osman,, "Static Performance of Finite Hydrodynamic
Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses",
Tribology letters, Vol 27, number 3,, pp 261 - 268, 2007
[17] F. Paulo, J.C Pimenta and A. Jorge, "Journal Bearings Subjected to
Dynamic loads: The Analytical Mobility Method", Mecanica
Experimental, Vol. 13, pp 115 - 127, 2006.
[18] J.R.Lin, "Optimal design of one dimensional porous slider bearing using
the Brinkman model", Tribology International, Vol. 34, issue 1, pp 57 -
64, 2001.
[19] B.V.R Kumar, P.S.Rao and P.Sinha, "A numerical study of performance
of a Slider bearing with heat conduction to the Pad, Finite Elements in
Analysis And Design, Vol. 37, issue 8, pp 581 - 585, 2001.
[20] C.C.Hwang, J.R.Lin and R.F.Yang," Lubrication of long Porous Slider
Bearings (use of Brinkman-extended Darcy Model)", JSME
International Journal (Series B), Vol.39, issue 1, pp 141 - 148. (1996).
[21] X. Ni, "Numerical Analysis of a Spiral Groove Dry Gas Seal Under slip
flow conditions", Proceeding of the seventeenth International offshore
and Polar Engineering Conference, 2007.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52969", author = "Oladeinde Mobolaji Humphrey and Akpobi John", title = "Parametric Characterization of Load Capacity of Infinitely Wide Parabolic Slider Bearing with Couple Stress Fluids", abstract = "A mathematical model for the hydrodynamic
lubrication of parabolic slider bearings with couple stress lubricants
is presented. A numerical solution for the mathematical model using
finite element scheme is obtained using three nodes isoparametric
quadratic elements. Stiffness integrals obtained from the weak form
of the governing equations were solved using Gauss Quadrature to
obtain a finite number of stiffness matrices. The global system of
equations was obtained for the bearing and solved using Gauss Seidel
iterative scheme. The converged pressure solution was used to obtain
the load capacity of the bearing. Parametric studies were carried out
and it was shown that the effect of couple stresses and profile
parameter are to increase the load carrying capacity of the parabolic
slider bearing. Numerical experiments reveal that the magnitude of
the profile parameter at which maximum load is obtained increases
with decrease in couple stress parameter. The results are presented in
graphical form.", keywords = "Finite element, numerical, parabolic slider.", volume = "3", number = "9", pages = "1050-5", }
