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Study of Longitudinal Roughness on Hydromagnetic Squeeze Film Between Conducting Rotating Circular Plates

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Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1057))

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Abstract

This investigation addresses the problem of squeeze film with electrical conduction between longitudinally rough surfaces and electrical lubricant in the existence of a transverse magnetic field for rotating circular plates. The surfaces are taken to be longitudinally rough in nature. In view of Christensen and Tonder’s stochastic averaging method, the arbitrary irregularity of the bearing surfaces is modeled by a stochastic arbitrary inconstant with non-zero variance, skewness, and mean. The Reynolds’ type equation for the distribution of pressure is stochastically averaged with regards to the arbitrary roughness constraint. A solution for SF pressure is obtained by using suitable Reynolds’ type BC, which is further used to calculate the LBC. Based on the results obtained, the bearing is generally suffering due to longitudinal roughness. On the whole, the hydromagnetic effect characterized by the Hartmann number produces an increase in LCC as compared to the classical NL case. However, in the case of (−ve) roughness (skewed) in particular, the condition can be retrieved to some extent when (−ve) variance occurs by selecting the appropriate plate conductivity and standard deviation.

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Abbreviations

r :

Radial coordinate

a :

Plate’s radius

\(\dot{h}\) :

Velocity of squeeze film

B 0 :

Transverse magnetic field applied between the plates

h 0 :

Initial film thickness

h :

Lubricant film thickness

s :

Electrical conductivity of the lubricant

μ :

Viscosity

M :

= \(B_{ 0} h\left( {\frac{s}{\mu }} \right)^{ 1 / 2}\) = Hartmann number

\(h_{ 0}^{{\prime }}\) :

Lower plate’s width surface

\(h_{ 1}^{{\prime }}\) :

Upper plate’s width surface

s 0 :

Lower surface’s electrical conductivity

s 1 :

Upper surface’s electrical conductivity

ϕ0(h):

= \(\frac{{s_{ 0} h_{ 0}^{{\prime }} }}{sh}\) = Lower surface’s electrical permeability

ϕ1(h):

 = \(\frac{{s_{ 1} h_{ 1}^{{\prime }} }}{sh}\) = Upper surface’s electrical permeability

ρ :

Density of lubricant

Ωu:

Upper plate’s angular velocity

Ωl:

Lower plate’s angular velocity

Ωr:

Ωu − Ωl

Ωf:

Ωl/Ωu—Rotation ratio

S :

 = \(- \frac{{h^{ 3} \rho \,\Omega _{u}^{ 2} }}{{\mu \dot{h}}}\) = rotational inertia in non-dimensional form

p :

Pressure of Lubricant

w :

Load-carrying capacity

σ*:

Non-dimensional standard deviation (σ/h)

α*:

Dimensionless variance (α/h)

ε*:

Dimensionless skewness (ε/h3)

P :

Dimensionless pressure

W :

Dimensionless load-carrying capacity

LCC:

Load-carrying capacity

LBC:

Load-bearing capacity

MHD:

Magnetohydrodynamic

HL:

Hydrodynamic lubrication

HSF:

Hydromagnetic squeeze film

MF:

Magnetic fluid

BC:

Boundary conditions.

References

  1. Andharia, P.I., Deheri, G.M.: Effect of longitudinal surface roughness on the behaviour of squeeze film in a spherical bearing. Int. J. Appl. Mech. Eng. 6(4), 885–897 (2001)

    MATH  Google Scholar 

  2. Andharia, P.I., Deheri, G.M.: Longitudinal roughness effect on magnetic fluid based squeeze film between conical plates. Ind. Lubr. Tribol. 62(5), 285–291 (2010)

    Article  Google Scholar 

  3. Andharia, P.I., Deheri, G.M.: Performance of magnetic fluid based squeeze film between longitudinally rough elliptical plates. ISRN Tribol. ID482604, 6 (2013)

    Google Scholar 

  4. Andharia, P.I., Gupta, J.L., Deheri, G.M.: Effect of longitudinal surface roughness on hydrodynamic lubrication of a slider bearings. In: Proceeding of The Tenth International Conference on surface modification Technologies, pp. 872–880 (1997)

    Google Scholar 

  5. Andharia, P.I., Gupta, J.L., Deheri, G.M.: Effect of transverse surface roughness on the behaviour of squeeze film in spherical bearing. J. Appl. Mech. Eng. 4, 19–24 (1999)

    Google Scholar 

  6. Berthe, D., Godet, M.A.: A more general form of Reynolds’ equation—application of rough surfaces. Wear 27, 345–357 (1973)

    Article  Google Scholar 

  7. Bhat, M.V.: Lubrication with a Magnetic Fluid. Team Spirit, India, Pvt. Ltd. (2003)

    Google Scholar 

  8. Burton, R.A.: Effect of two-dimensional sinusoidal roughness on the load support characteristics of a lubricant film. Trans. ASME J. Basic Eng. 85, 258–264 (1963)

    Article  Google Scholar 

  9. Chou, T.L., Lai, J.W., Lin, J.R.: Magneto-hydrodynamic squeeze film characteristics between a sphere and a plane surface. J. Mar. Sci. Technol. 11(3), 174–178 (2003)

    Google Scholar 

  10. Christensen, H., Tonder, K.C.: Tribology of rough surfaces: a stochastic model of mixed lubrication. SINTEF, Report no. 18/70, 21 (1970)

    Google Scholar 

  11. Christensen, H., Tonder, K.C.: Tribology of rough surfaces: parametric study and comparison of lubrication models. SINTEF, Report no 22/69, 18 (1969)

    Google Scholar 

  12. Christensen, H., Tonder, K.C.: Tribology of rough surfaces: stochastic models of hydrodynamic lubrication. SINTEF, Report No. 10/69, 18 (1969)

    Google Scholar 

  13. Davis, M.G.: the generation of pressure between rough lubricated moving deformable surfaces. Lubr. Eng. 19, 246 (1963)

    Google Scholar 

  14. Elco, R.A., Huges, W.E.: Magnetohydrodynamic pressurization in liquid metal lubrication. Wear 5, 198–207 (1992)

    Article  Google Scholar 

  15. Gupta, J.L., Deheri, G.M.: Effect of roughness on the behaviour of squeeze film in a spherical bearing. Tribol. Trans. 39, 99–102 (1996)

    Article  Google Scholar 

  16. Kuzma, D.C., Maki, E.M., Donnelly, R.J.: The magnehydrodynamic squeeze films. J. Fluid Mech. 19, 395–400 (1964)

    Article  Google Scholar 

  17. Kuzma, D.C.: Magnetohydrodynamic squeeze films. J. Basic Eng. Trans. ASME 86, 441–444 (1964)

    Article  Google Scholar 

  18. Lin, J.R.: Longitudinal surface roughness effects in magnetic fluid lubricated journal bearing. J. Mar. Sci. Technol. 24(4), 711–716 (2016)

    Google Scholar 

  19. Patel, H., Deheri, G.M., Patel, R.M.: Magnetic fluid based squeeze film between porous rotating rough circular plates. Ind. Lubr. Tribol. 61(3), 140–145 (2009)

    Article  Google Scholar 

  20. Patel, K.C., Gupta, J.L.: Behaviour of hydromagnetic squeeze film between porous plates. Wear 56, 327–339 (1979)

    Article  Google Scholar 

  21. Prajapati, B.L.: On the certain theoretical studies in hydrodynamic and electromagnet hydrodynamic lubrication. Ph.D. Thesis, S. P. university, Vallabh Vidyanagar (1995)

    Google Scholar 

  22. Prakash, J., Vij, S.K.: Load carrying capacity and time height relation for squeeze film between porous plates. Wear, 24, 309–332 (1973)

    Article  Google Scholar 

  23. Shimpi, M.E., Deheri, G.M.: Combine effect of bearing deformation and longitudinal roughness on the performance of a ferrofluid based squeeze film together with velocity slip in truncated conical plates. Imperial J. Interdisc. Res. 2(8), 1423–1430 (2016)

    Google Scholar 

  24. Shukla, J.B., Prasad, R.: Hydromagnetic squeeze films between two conducting surfaces. Transection ASME. J. Basic Eng. 87, 818–822 (1965)

    Article  Google Scholar 

  25. Ting, L.L.: Engagement behavior of lubricated porous annular disks part I: squeeze film phase, surface roughness and elastic deformation effects. Wear 34, 159–182 (1975)

    Article  Google Scholar 

  26. Tonder, K.C.: Surface distributed waviness and roughness. In: The Firdst World Conference in Industrial Tribology, New Delhi, A3, 128 (1972)

    Google Scholar 

  27. Tzeng, S.T., Saibel, E.: Surface roughness effect on slider bearing lubrication. Transection ASME. J. Lubr. Technol. 10, 334–338 (1967)

    Google Scholar 

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Acknowledgements

Comments and constructive suggestions for improving the overall quality of this article have been acknowledged.

Author information

Authors and Affiliations

  1. Mathematics Department, H. N. G. U, Patan, Gujarat, 384265, India

    Jatinkumar V. Adeshara & M. B. Prajapati

  2. Mathematics Department, S. P. U, Vallabh Vidyanagar, Gujarat, 388120, India

    G. M. Deheri

  3. 15 Badrinath, Society, Ghodasar, Ahmedabad, Gujarat, 380050, India

    R. M. Patel

Authors
  1. Jatinkumar V. Adeshara
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  2. M. B. Prajapati
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  3. G. M. Deheri
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  4. R. M. Patel
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Corresponding author

Correspondence to R. M. Patel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, India

    Kedar Nath Das

  2. Department of Mathematics, South Asian University, New Delhi, Delhi, India

    Jagdish Chand Bansal

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  4. Department of Mathematics, Faculty of Science, Liverpool Hope University, Liverpool, UK

    Atulya K. Nagar

  5. School of Electrical Engineering, VIT University, Vellore, Tamil Nadu, India

    Ponnambalam Pathipooranam

  6. School of Electrical Engineering, VIT University, Vellore, Tamil Nadu, India

    Rani Chinnappa Naidu

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Adeshara, J.V., Prajapati, M.B., Deheri, G.M., Patel, R.M. (2020). Study of Longitudinal Roughness on Hydromagnetic Squeeze Film Between Conducting Rotating Circular Plates. In: Das, K., Bansal, J., Deep, K., Nagar, A., Pathipooranam, P., Naidu, R. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 1057. Springer, Singapore. https://doi.org/10.1007/978-981-15-0184-5_20

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