Skip to main content
SpringerLink
Log in

Effect of Elasticity on Capillary Compensated Flexible Multi-recess Hydrostatic Journal Bearing Operating with Micropolar Lubricant

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

This paper presents a theoretical study of the effects of bearing shell deformation upon the performance characteristics of a capillary compensated multi-recess hydrostatic journal bearing system operating with micropolar lubricant. The finite element method has been used to solve the modified Reynolds’ equation governing the micropolar lubricant flow in the bearing and the three dimensional elasticity equations governing the displacement field in the bearing shell. The elasto-hydrostatic performance characteristics of the bearing are presented for various values of micropolar parameters (l m and N 2) and for a wide range of the deformation coefficient \(\bar{C}_{d}\) which takes into account the flexibility of the bearing shell. The computed results indicate that the influence of the bearing shell flexibility is quite significant on the performance characteristics of recessed hydrostatic journal bearing system operating with micropolar lubricant.

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. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

a b :

Land width (m)

c :

Radial clearance (m)

D :

Journal diameter (m)

E b :

Modulus of elasticity (N/m−2)

F :

Fluid film reaction (N)

h :

Fluid film thickness (m)

l :

Characteristic length (m)

L :

Bearing length (m)

p :

Pressure (N m−2)

p s :

Supply Pressure (N m−2)

Q :

Bearing flow (m3 s−1)

r :

Radial coordinate

R J :

Journal radius (m)

t :

Time (s),

t h :

Shell thickness

W 0 :

External load (N)

X J , Z J :

Journal center coordinates

x, y :

Circumferential and axial coordinates (m)

z :

Coordinate across film thickness (m)

δ :

Elastic deformation

μ :

Dynamic viscosity (Pa. s)

ω J :

Journal speed (rps)

θ :

Angle of inter-recess land width (Fig. 1b)

Fig. 1
figure 1

a Four-pocket hydrostatic bearing Co-ordinate system b Bearing geometry

Full size image
\(\bar{a}_{b}\) :

\(a_{b} /L\); Land width ratio

\(\bar{A}^{e}\) :

Area of eth element

\(\bar{C}_{d}\) :

\(\left( {p_{s} \,t_{h} } \right)/\left( {E_{b} c} \right)\) Elastic deformation coefficient

\(\bar{C}_{s1}\) :

\(\frac{{3\pi \;a^{4} }}{{2c^{3} l_{cap} }}\)

\(\bar{C}_{s2}\) :

\(\frac{{\bar{C}_{s1} }}{12}\)

\(\bar{F}\) :

\(F\left( {1/p_{s} R_{J}^{2} } \right) ; Fluid film reaction\)

\(\bar{h}\) :

h/c

l m :

c/l

N :

\(\left( {k/\left( {2\mu + k} \right)} \right)^{1/2} ; Coupling number\)

\(\bar{p}\) :

p/p s

\(\bar{Q}\) :

\(\left( {\mu_{r} /c^{3} p_{s} } \right)Q\)

\(\bar{t}\) :

\(t\left( {c^{2} p_{s} /\mu_{r} R_{J}^{2} } \right)\)

\(\bar{t}_{h}\) :

\(\frac{{t_{h} }}{{R_{J} }}\)

\(\bar{u},\;\bar{v}\) :

\(\left( {u,v} \right)\left( {\mu_{r} R_{J} /c^{2} p_{s} } \right)\)

\(\bar{w}\) :

\(w\left( {\mu_{r} R_{J} /c^{2} p_{s} } \right)\left( {R_{J} /c} \right)\)

\(\bar{W}_{0}\) :

\(\left( {W_{o} /p_{s} R_{J}^{2} } \right)\)

\(\bar{X}_{J} ,\bar{Z}_{J}\) :

\(\left( {X_{J} ,Z_{J} } \right)/c\)

\(\bar{z}\) :

z/h

(α, β):

(x, y)/R J , Circumferential and axial coordinates (m)

\(\bar{\delta }\) :

\(\delta /c\)

ε :

e/c; Eccentricity ratio

λ :

L/D; Aspect ratio

\(\bar{\mu }\) :

\(\mu /\mu_{r}\)

\(\varOmega\) :

\(\omega_{J} \left( {\mu_{r} R_{J}^{2} /c^{2} p_{s} } \right); {\rm Speed\,parameter}\)

b :

Bearing

c :

Pocket

cap:

Capillary

J :

Journal

R :

Reference value

R :

Restrictor

s :

Supply condition

N i , N j :

Shape function matrices

[M]:

Mass matrix

\(\left\{ {\bar{p}} \right\}\) :

Pressure vector

\(\left\{ {\bar{Q}} \right\}\) :

Flow vector

\(\left\{ {\bar{R}_{xJ} } \right\},\;\left\{ {\bar{R}_{zJ} } \right\}\) :

Right hand side vectors due to journal velocity

\(\left\{ {\bar{R}_{H} } \right\}\) :

Column vector (hydrodynamic term)

References

  1. M.S. Khader, R.I. Vachon, Theoretical effects of solid particles in hydrostatic bearing lubricant. J. Lubr. Technol. Trans. ASME 95, 104–106 (1973)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  3. M. Balaram, Micropolar squeeze films. J. Lubr. Technol. Trans. ASME 97, 635–637 (1975)

    Article  Google Scholar 

  4. M.M. Khonsari, D.E. Brewe, On the performance of finite journal bearings lubricated with micropolar fluids. STLE Tribol. Trans. 32(2), 155–160 (1989)

    Article  Google Scholar 

  5. J.B. Sukhla, M. Isa, Externally pressurized optimum bearing with micropolar fluid as lubricant. Jpn. J. Appl. Phys. 14(2), 275–279 (1974)

    Google Scholar 

  6. T.W. Hung, C. Weng, C.K. Chen, Analysis of finite width journal bearings with micropolar fluids. Wear 123, 1–12 (1988)

    Article  Google Scholar 

  7. T.W. Hung, C. Weng, Dynamics characteristics of finite width journal bearings with micropolar fluids. Wear 141, 23–33 (1990)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. C. Singh, P. Sinha, The three-dimensional reynolds equation for micropolar fluid lubricated bearings. Wear 76(2), 199–209 (1982)

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. S. Das, S.K. Guha, A.K. Chattopadhyay, On the conical whirl instability of hydrodynamic journal bearings lubricated with micropolar fluids. Proc. Inst. Mech. Eng. Part-J. 215, 431–439 (2001)

    Article  Google Scholar 

  12. S. Das, S.K. Guha, A.K. Chattopadhyay, On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids. J. Tribol. Int. 35, 201–210 (2002)

    Article  Google Scholar 

  13. Xiao-Li Wang, Ke-Qin Zhu, A study of the lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing. Tribol. Int. 37, 481–490 (2004)

    Article  Google Scholar 

  14. Xiao-Li Wang, Ke-Qin Zhu, Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects. Tribol. Int. 39, 227–237 (2006)

    Article  Google Scholar 

  15. R. Sinhasan, S.C. Sharma, S.C. Jain, Performance characteristics of an externally pressurized capillary-compensated flexible journal bearing. Tribol. Int. 22(4), 283–293 (1989)

    Article  Google Scholar 

  16. R. Sinhasan, S.C. Sharma, S.C. Jain, Performance characteristics of a constant flow valve compensated multirecess flexible hydrostatic journal bearing. Wear 134, 335–356 (1989)

    Article  Google Scholar 

  17. R. Sinhasan, S.C. Sharma, S.C. Jain, Performance characteristics of externally pressurized orifice compensated flexible journal bearing. STLE Tribol. Trans. 34(3), 465–471 (1991)

    Article  Google Scholar 

  18. S.C. Sharma, R. Sinhasan, S.C. Jain, Performance characteristics of multirecess hydrostatic/hybrid flexible journal bearing with membrane type variable-flow restrictor as compensating elements. Wear 152, 279–300 (1992)

    Article  Google Scholar 

  19. S. Verma, V. Kumar, K.D. Gupta, Analysis of multirecess hydrostatic journal bearing operating with micropolar lubricant. J. Tribol. ASME. 131, 021103-1 (2009)

  20. S. Verma, K.D. Gupta, V. Kumar, Analysis of capillary compensated hole-entry hydrostatic/hybrid journal bearing operating with micropolar lubricant, IUTAM symposium, Indian Institute of Technology, Delhi, India March 23–26, (2009)

  21. E.R. Nicodemus, S.C. Sharma, Influence of wear on the performance of multirecess hydrostatic journal bearing operating with micropolar lubricant. J. Tribol. 132(2), 021703 (2010)

    Article  Google Scholar 

  22. E.R. Nicodemus, S.C. Sharma, Orifice compensated multirecess hydrostatic/hybrid journal bearing system of various geometric shapes of recess operating with micropolar lubricant. Tribol. Int. 44, 284–296 (2011)

    Article  Google Scholar 

  23. S. Verma, V. Kumar, K.D. Gupta, Analysis of capillary compensated hydrostatic journal bearing operating with micropolar lubricant. Ind. Lubr. Tribol. 63(3), 192–202 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Haryana, 131039, India

    Suresh Verma & Kapil Dev Gupta

  2. School of Engineering and Emerging Technologies, Baddi University of Emerging Science and Technology, Baddi, Himachal Pradesh, 173205, India

    Vijay Kumar

Authors
  1. Suresh Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vijay Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kapil Dev Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suresh Verma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Verma, S., Kumar, V. & Gupta, K.D. Effect of Elasticity on Capillary Compensated Flexible Multi-recess Hydrostatic Journal Bearing Operating with Micropolar Lubricant. J. Inst. Eng. India Ser. C 97, 11–23 (2016). https://doi.org/10.1007/s40032-015-0195-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-015-0195-8

Keywords

Search

Navigation