Skip to main content
SpringerLink
Log in

Analytical–numerical modeling of journal bearings with non-Newtonian fluids and cavitation effects

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The search for better performance in internal combustion engines and machines which use hydrodynamic journal bearings has motivated recent studies in lubrication field, with the application of computational fluid dynamics. The present study deals with the dynamics of some non-Newtonian fluids in short journal bearings, using the Newtonian, Herschel-Bulkley, and Bingham models. The main objective is to compare fluid pressure distribution, cavitation occurrence, and performance parameters, such as load-carrying capacity, friction force, and side leakage rate. The bearing equations were solved in a MATLAB program, based on the Reynolds equations, with discretization by the finite volume method and a cyclic Tri-Diagonal Matrix Algorithm solver. In all performance parameters, the Herschel-Bulkley and Bingham non-Newtonian fluids showed advantages when compared to Newtonian fluid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

c :

radial clearance

D :

shaft diameter

e:

eccentricity

F :

cavitation index; friction force

h :

film thickness

H :

dimensionless film thickness

k :

consistency index

k n,s,e,w :

diffusion coefficients

L :

length

n :

direction normal to cavitation boundary

P :

pressure

q :

flow

R :

bearing radius

S :

source team

u, U :

velocity, x-direction

v,V :

velocity, y-direction

w,W :

velocity, w-direction

W :

bearing load

x;X :

x-coordinate; dimensionless term

y;Y :

y-coordinate; dimensionless term

z;Z :

z-coordinate; dimensionless term

β :

dimensionless parameter

ε:

eccentricity ratio

ϕ:

dimensionless dependent variable

\(\dot{\gamma }\) :

shear rate

μ:

viscosity

θ:

circumferential coordinate

ρ:

density

τ:

shear stress

ω:

angular velocity

ψ:

attitude angle

*:

dimensionless term

A:

atmospheric

C:

cavitation

E:

east boundary surface of control volume

E:

east nodal point

N:

north boundary surface of control volume

N:

north nodal point

P:

grid point of interest

S:

south boundary surface of control volume

S:

south nodal point

W:

west boundary surface of control volume

W:

west nodal point

x,y,z :

x,y,z-directions

0:

initial value

References

  1. Reynolds O (1886) On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil. Phil Trans Roy Soc (London) A 177:157–231

  2. Sommerfeld A (1904) The hydrodynamic theory of lubrication friction. Zs Math Phys 50, 1 and 2, 97–55

  3. Eckert M (2015) Fluid mechanics in Sommerfeld's School. Annu Rev Fluid Mech 47:1–20

  4. Jakobson B, Floberg L (1957) The finite journal bearing considering vaporization. Transactions of Chalmers UniversityTechnology, Goteborg, Sweden, vol 190, pp 1–119

  5. Raimondi AA, Boyd J (1958) A solution for the finite journal bearing and its application to analysis and design-Parts I, II, and III. Trans Am Soc Lubrication Eng 1(1):159–209

    Google Scholar 

  6. Elrod HG (1981) A cavitation Algorithm. J Lubrication Technol 103:350–354

    Article  Google Scholar 

  7. Brewe DE (1986) Theoretical modelling of the vapor cavitation in dynamically loaded journal bearings. ASME J Tribol Trans ASME 108:628–638

    Article  Google Scholar 

  8. Payvar P, Salant RF (1992) A computational method for cavitation in a wavy mechanical seal. ASME J Tribol Trans ASME., 114/199

  9. Fortier A (2004) Numerical simulation of hydrodynamic bearings with engineered slip/no-slip surfaces. Thesis of Masters of Science in Mechanical Engineering. Georgia Institute of Technology

  10. Braun MJ, Hannon WM (2010) Cavitation formation and modeling for fluid film bearings: a review. J Eng Tribol 224:839

  11. Dien IK, Elrod HG (1983) A generalized steady-state Reynolds equations for non-Newtonian fluids, with application to journal bearings. J Lubrication Technol Trans of ASME 105:385–390

    Article  Google Scholar 

  12. Sinhasan R, Goyal KC (1990) Elastohydrodynamic studies of circular journal bearings with Non-Newtonian Lubricants. Tribol Int 23(I.6):419–428

  13. Dorier C, Tichy J (1992) Behavior of a Bingham-like viscous fluid in lubrication flows. J Non-Newton Fluid Mech 45:291–310

    Article  Google Scholar 

  14. Garg HC, Kumar V, Sharda HB (2010) A comparative thermal analysis of slot-entry and hole-entry hybrid journal bearings lubricated with Non-Newtonian Lubricant. ASME J Tribol 132(4): (041701)

  15. Skelland AHP (1967) Non-Newtonian flow and heat transfer, 1st edn.Willey, New York, 469 p

  16. Gertzos KP, Nikolakopoulos PG, Papadopoulos CA (2008) CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant. Tribol Int 41:1190–1204

    Article  Google Scholar 

  17. Bird RB, Curtiss CF, Armstrong RC, Hassanger O (1987) Dynamics of polymeric liquids, vol 1 Fluid Mechanics and vol 2 Kinetic Theory, 2nd edn. A Wiley-Interscience Publication, New York, NY

  18. Tichy J (1991) Hydrodynamic lubrication theory for Bingham plastic flow model. J Rheol 35:477

    Article  Google Scholar 

  19. Waukesha Bearings Corporation http://www.waukbearing.com/en/technical-resources/bearing-damage-index/bearing-damage:-cavitation-erosion/

  20. Floberg L (1964) Cavitation in lubricating oil films. In cavitation in real liquids. GM Research Labs. Warren, Michigan, Elsevier Publishing Co., NewYork, pp 138–146

  21. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere. New York, 197p

  22. Patankar SV, Liu CH, Sparrow EM (1977) Fully developed flow and heat transfer in ducts having streamwise-periodic variation of cross-sectional area. ASME J Heat Transfer 99:180–186

    Article  Google Scholar 

  23. Thompson RL, Soares EJ (2016) Viscoplastic dimensionless numbers. J Non-Newtonian Fluid Mech 238:57–64

    Article  MathSciNet  Google Scholar 

  24. Reinhardt E, Lund JW (1975) The influence of fluid inertia on the dynamic properties of journal bearings. J Lubr Tecnol 97:159–165

    Article  Google Scholar 

  25. Kuzma DC (1967) Fluid inertia effects in squeeze films. Appl Sci Res 18:15–20

    Article  Google Scholar 

  26. Milne AA (1959) On the effect of lubricant inertia in the theory of hydrodynamic lubrication. J Basic Eng TRANS ASME D 81:239–244

    Article  Google Scholar 

  27. Kulinsky ES, Ostrach S (1967) Journal bearing velocity profiles for small eccentricity and moderate Reynolds numbers. J Appl Mech TRANS ASME E 89:16–27

    Article  Google Scholar 

  28. Dousti S, Allaire P, Dimond T, Cao J (2016) An extended Reynolds equation applicable to high reduced Reynolds number operation of journal bearings. Tribol Int 102:182–197

    Article  Google Scholar 

  29. Frêne J, Arghir M, Constantinescu V (2006) Combined thin film and Navier-Stokes analysis in high Reynolds number lubrication. Tribol Int 39:734–747

    Article  Google Scholar 

  30. Zhu H, Kim YD, Kee D (2005) Non-Newtonian fluids with A yield stress. J Non-Newtonian Fluid Mech 29:177–181

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UNESP – São Paulo State University, Guaratinguetá, SP, Brazil

    Fabrício Vieira Silva & Teófilo Miguel de Souza

  2. UERJ –FAT/DME – Rio de Janeiro State University, Resende, RJ, Brazil

    Maurício Araújo Zanardi

Authors
  1. Fabrício Vieira Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maurício Araújo Zanardi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Teófilo Miguel de Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabrício Vieira Silva.

Additional information

Technical Editor: Roney Leon Thompson.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Silva, F.V., Zanardi, M.A. & de Souza, T.M. Analytical–numerical modeling of journal bearings with non-Newtonian fluids and cavitation effects. J Braz. Soc. Mech. Sci. Eng. 43, 525 (2021). https://doi.org/10.1007/s40430-021-03238-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-021-03238-4

Keywords

Search

Navigation