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Numerical analysis of steady-state performance of misaligned journal bearings with turbulent effect

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Abstract

A theoretical analysis has been carried out to investigate into the effect of turbulence and journal misalignment on the steady-state characteristics of hydrodynamic journal bearings lubricated with micropolar fluid. The governing non-dimensional Reynolds equation applicable to turbulent micropolar lubrication has been solved numerically to obtain the film pressure distribution which was then used to determine the load carrying capacity, attitude angle, misalignment moment, end flow rate and frictional parameter. The turbulent shear coefficients have been computed by using the turbulent model proposed by Ng and Pan. The results suggest that the effect of turbulence is to increase the load carrying capacity and misalignment moment of the misaligned journal bearings, and this effect is more pronounced for micropolar fluid as compared to Newtonian fluid.

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Abbreviations

C :

Radial clearance, m

C z :

Constant parameter of turbulent shear coefficient for axial flow

D :

Journal diameter, m

D m :

Degree of misalignment, \( D_{m} = {{\xi_{e} } \mathord{\left/ {\vphantom {{\xi_{e} } {\xi_{m} }}} \right. \kern-0pt} {\xi_{m} }} \)

e 0,ɛ 0 :

Steady-state eccentricity ratio at the mid plane of the bearing, \( \varepsilon_{0} = {{e_{0} } \mathord{\left/ {\vphantom {{e_{0} } C}} \right. \kern-0pt} C} \)

e′, ɛ′:

Magnitude of projection of the axis of misaligned journal onto the mid plane of the bearing, \( \varepsilon^{\prime } = {{e^{\prime } } \mathord{\left/ {\vphantom {{e^{\prime } } C}} \right. \kern-0pt} C} \)

\( e_{\hbox{max} }^{\prime } ,\varepsilon_{\hbox{max} }^{\prime } \) :

Maximum possible value of e′ and ε′ respectively, \( \varepsilon_{\hbox{max} }^{\prime } = e_{\hbox{max} }^{\prime } /C \)

f(R/C):

Frictional parameter, \( f(R/C) = {{\overline{F} } \mathord{\left/ {\vphantom {{\overline{F} } {\overline{W} }}} \right. \kern-0pt} {\overline{W} }} \)

F :

Frictional force, N

\( \overline{F} \) :

Non-dimensional frictional force, \( \overline{F} = {{FC^{2} } \mathord{\left/ {\vphantom {{FC^{2} } {\mu\Omega ^{2} R^{3} L}}} \right. \kern-0pt} {\mu\Omega ^{2} R^{3} L}} \)

h, \( \overline{h} \) :

Film thickness, \( \overline{h} = {h \mathord{\left/ {\vphantom {h C}} \right. \kern-0pt} C} \)

h cav, \( \bar{h}_{\text{cav}} \) :

Film thickness at the point of cavitation, \( \bar{h}_{\text{cav}} = {{h_{\text{cav}} } \mathord{\left/ {\vphantom {{h_{\text{cav}} } C}} \right. \kern-0pt} C} \)

\( k_{\theta } , { }k_{{\bar{z}}} \) :

Turbulent shear coefficients in circumferential and axial directions, respectively

l m :

Non-dimensional characteristics length of micropolar fluid, lm = C/Λ

L :

Bearing length, m

M, \( \overline{M} \) :

Resultant misalignment moment, \( \overline{M} = {{MC^{3} } \mathord{\left/ {\vphantom {{MC^{3} } {\mu R^{3} L}}} \right. \kern-0pt} {\mu R^{3} L}} \)

M i, \( \overline{M}_{i} \) :

Misalignment moment, \( \overline{M}_{i} = {{M_{i} C^{3} } \mathord{\left/ {\vphantom {{M_{i} C^{3} } {\mu R^{3} L}}} \right. \kern-0pt} {\mu R^{3} L}} \), i = r- and \( \phi \)- for radial and transverse directions, respectively

N :

Coupling number

p, \( \bar{p} \) :

Steady-state film pressure in the film region, \( \bar{p} = {{pC^{2} } \mathord{\left/ {\vphantom {{pC^{2} } {\mu\Omega R^{2} }}} \right. \kern-0pt} {\mu\Omega R^{2} }} \)

Q i, \( \bar{Q}_{i} \) :

Steady-state end flow rate, \( \bar{Q}_{i} = {{Q_{i} L} \mathord{\left/ {\vphantom {{Q_{i} L} {C\Omega R^{3} }}} \right. \kern-0pt} {C\Omega R^{3} }} \), i = Rear end, front end and z

R :

Radius of the journal, m

\( Re \) :

Mean or average Reynolds number defined by radial clearance, C,\( Re = {{\rho\Omega RC} \mathord{\left/ {\vphantom {{\rho\Omega RC} \mu }} \right. \kern-0pt} \mu } \)

U :

Velocity of journal, U = ΩR, m/s

W, \( \bar{W} \) :

Steady-state load in bearing, \( \bar{W} = {{WC^{2} } \mathord{\left/ {\vphantom {{WC^{2} } {\mu\Omega ^{2} R^{3} L}}} \right. \kern-0pt} {\mu\Omega ^{2} R^{3} L}} \)

W i, \( \bar{W}_{i} \) :

Steady-state load in bearing, \( \bar{W}_{i} = {{W_{i} C^{2} } \mathord{\left/ {\vphantom {{W_{i} C^{2} } {\mu\Omega ^{2} R^{3} L}}} \right. \kern-0pt} {\mu\Omega ^{2} R^{3} L}} \), i = r- and \( \phi \)- for radial and transverse directions respectively

x :

Cartesian coordinate axis in the circumferential direction, x = Rθ, m

z, \( \bar{z} \) :

Cartesian coordinate axis along the bearing axis, \( \bar{z} \, = \, {{ 2z} \mathord{\left/ {\vphantom {{ 2z} L}} \right. \kern-0pt} L} \)

β m :

Misalignment Angle

\( \phi_{0} \) :

Steady-state attitude angle, rad

\( \Phi _{{\theta ,\bar{z}}} \) :

Non-dimensional micropolar fluid functions along circumferential and axial directions

Ω:

Angular velocity of journal, rad/s

θ :

Circumferential coordinate, rad

ξ e :

Misalignment ratio at either bearing ends, ξe = βmL/2C

ξ m :

Maximum possible value of ξe

ψ :

Angle between the projection of the journal rear centre line onto the mid plane of the bearing and the eccentricity vector

References

  1. Constantinescu VN (1962) Analysis of bearings operating in turbulent regime. ASME J Basic Eng 84:139–151

    Article  Google Scholar 

  2. Constantinescu VN, Galetuse S (1965) On the determination of friction forces in turbulent lubrication. ASLE Trans 8:367–380

    Article  Google Scholar 

  3. Ng CW, Pan CHT (1965) A linearized turbulent lubrication theory. ASME J Basic Eng 87:675–688

    Article  Google Scholar 

  4. Taylor CM, Dawson D (1974) Turbulent lubrication theory- application to design. ASME J Lubr Technol 96:36–46

    Article  Google Scholar 

  5. Eringen A (1966) Theory of micropolar fluids. J Math Mech 16:1–18

    MathSciNet  Google Scholar 

  6. Allen S, Kline K (1971) Lubrication theory of micropolar fluids. J Appl Mech 38:646–650

    Article  Google Scholar 

  7. Prakash J, Sinha P (1975) Lubrication theory of micropolar fluids and its application to a journal bearing. Int J Eng Sci 13:217–232

    Article  Google Scholar 

  8. Sukhla JB, Isa M (1975) Generalised Reynolds equation for micropolar lubricants and its application to optimum one-dimensional slider bearings; effects of solid particle additives in solution. J Mech Eng Sci 17:280–284

    Article  Google Scholar 

  9. Zaheeruddin Kh, Isa M (1978) Micropolar fluid lubrication of one-dimensional journal bearings. Wear 50:211–220

    Article  Google Scholar 

  10. Tipei N (1979) Lubrication with micropolar fluids and its application to short bearings. ASME J Lubr Technol 101:356–363

    Article  Google Scholar 

  11. Khonsari MM, Brewe DE (1989) On the performance of finite journal bearing lubricated with micropolar fluid. Tribol Trans 32:155–160

    Article  Google Scholar 

  12. Safar ZS, El-Kotb MM, Mokhtar DM (1989) Analysis of misaligned journal bearing operating in turbulent regime. ASME J Tribol 111:215–219

    Article  Google Scholar 

  13. Osman TA (2001) Misalignment effect on the static characteristics of magnetized journal bearing lubricated with ferrofluid. Tribol Lett 11:195–203

    Article  Google Scholar 

  14. Das S, Guha SK, Chattopadhyay AK (2002) On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids. Tribol Int 35:246–255

    Article  Google Scholar 

  15. Shenoy BS, Pai R (2011) Effect of turbulence on the static performance of a misaligned externally adjustable fluid film bearing lubricated with coupled stress fluids. Tribol Int 44:1774–1781

    Article  Google Scholar 

  16. Sun J, Zhu X, Zhang L, Wang X, Wang C, Wang H, Zhao X (2014) Effect of surface roughness, viscosity-pressure relationship and elastic deformation on lubrication performance of misaligned journal bearings. Ind Lubr Tribol 66:337–345

    Article  Google Scholar 

  17. Xu G, Zhou J, Geng H, Lu M, Yang L, Yu L (2015) Research on the static and dynamic characteristics of misaligned journal bearing considering the turbulent and thermohydrodynamic effects. J Tribol. https://doi.org/10.1115/1.4029333

    Article  Google Scholar 

  18. Nikolakopoulos PG, Papadopoulos CA (2008) A study of friction in worn misaligned journal bearings under severe hydrodynamic lubrication. Tribol Int 41:461–472

    Article  Google Scholar 

  19. Zhang X, Yin Z, Jiang D, Gao G, Wang Y, Wang X (2016) Load carrying capacity of misaligned hydrodynamic water-lubricated plain journal bearings with rigid bush materials. Tribol Int. https://doi.org/10.1016/j.triboint.2016.02.038

    Article  Google Scholar 

  20. Lv F, Ta N, Rao Z (2017) Analysis of equivalent supporting point location and carrying capacity of misaligned journal bearing. Tribol Int. https://doi.org/10.1016/j.triboint.2017.06.034

    Article  Google Scholar 

  21. Faralli M, Belfiore NP (2006) Steady-state analysis of worn spherical bearing operating in turbulent regime with non-Newtonian lubricants. In: International conference on tribology, AITC–AIT, Parma, Italy

  22. Das S, Guha SK (2013) On the steady-state performance characteristics of finite hydrodynamic journal bearing under micropolar lubrication with turbulent effect. Int J Mech Ind Sci Eng 7:65–73

    Google Scholar 

  23. Elsharkawy AA (2004) Effects of misalignment on the performance of finite journal bearings lubricated with couple stress fluids. Int J Comput Appl Technol 21:137–146

    Article  Google Scholar 

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Acknowledgement

The authors are grateful to Mechanical Engineering Department of Indian Institute of Science and Technology, Shibpur for the continuous encouragement and cooperation in executing this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology, Shibpur P.O. Botanic Garden, Howrah, West Bengal, 711103, India

    Subrata Das & Sisir K. Guha

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  1. Subrata Das
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Correspondence to Subrata Das.

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Technical Editor: Cezar Negrao, PhD.

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Das, S., Guha, S.K. Numerical analysis of steady-state performance of misaligned journal bearings with turbulent effect. J Braz. Soc. Mech. Sci. Eng. 41, 81 (2019). https://doi.org/10.1007/s40430-019-1583-4

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