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Water Lubricated Bearings

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Book cover Green Tribology

Part of the book series: Green Energy and Technology ((GREEN))

Abstract

The increasing ecological awareness and stringent requirements for environmental protection have led to the development of water lubricated bearings in many applications where oil was used as the lubricant. The chapter details the theoretical analysis to determine both the static and dynamic characteristics, including the stability (using both the linearised perturbation method and the nonlinear transient analysis) of multiple axial groove water lubricated bearings. Experimental measurements and computational fluid dynamics (CFD) simulations by the Tribology research group at Queensland University of Technology, Australia and Manipal Institute of Technology, India, have highlighted a significant gap in the understanding of the flow phenomena and pressure conditions within the lubricating fluid.

An attempt has been made to present a CFD approach to model fluid flow in the bearing with three equi-spaced axial grooves and supplied with water from one end of the bearing. Details of the experimental method used to measure the film pressure in the bearing are outlined. The lubricant is subjected to a velocity induced flow (as the shaft rotates) and a pressure-induced flow (as the water is forced from one end of the bearing to the other). Results are presented for the circumferential and axial pressure distribution in the bearing clearance for different loads, speeds and supply pressures. The axial pressure profile along the axial groove located in the loaded part of the bearing is measured. The theoretical analysis shows that smaller the groove angle better will be the load-carrying capacity and stability of these bearings. Results are compared with experimentally measured pressure distributions.

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Abbreviations

C :

Radial clearance (m)

D :

Diameter of the bearing (m)

D rr D ΦΦ D rΦ D Φr :

Damping coefficients

\( \bar{D}_{rr}\,\bar{D}_{\phi \phi }\,\bar{D}_{r\phi }\,\bar{D}_{\phi r} \) :

Non-dimensional damping coefficient, \( \bar{D}_{ij} = \frac{{D_{ij} C\omega }}{{LDp_{s} }} \)

e :

Eccentricity (m)

F :

Friction force (N); Non-dimensional friction \( \bar{F} = \frac{F}{{2LCp_{s} }} \)

F r , \( \bar{F}_{r} \):

Dynamic force along radial direction, \( \bar{F}_{r} = \frac{{F_{r} }}{{2LCp_{s} }} \)

F ϕ, \( \bar{F}_{\phi } \) :

Dynamic force along \( {\phi } \) direction, \( \bar{F}_{\phi } = \frac{{F_{\phi } C^{2} }}{\eta \omega R} \)

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

Local film thickness (m), \( \bar{h} = \frac{h}{c} = 1 + \varepsilon \cos \theta \)

K rr K ΦΦ K rΦ K Φr :

Stiffness coefficients

\( \bar{K}_{rr} \bar{K}_{\phi \phi } \bar{K}_{r\phi } \bar{K}_{\phi r} \) :

Non-dimensional stiffness coefficient, \( \bar{K}_{ij} = \frac{{K_{ij} C\omega }}{{LDp_{s} }} \)

L :

Length of the bearing (m)

L cav :

Dimensionless width of analytical bubble

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

Mass parameter (kg), \( \bar{M} = \frac{{MC\omega^{2} }}{{LDp_{s} }} \)

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

Film pressure (N/m2), \( \bar{p} = p/p_{s} \)

p s :

Supply pressure (N/m2)

\( \bar{p}_{1} ,\bar{p}_{2} \) :

Perturbed pressures

q p :

Flow on pressure side

q cav :

Flow in cavitation zone

q t :

Flow due to boundary movement

Q :

Volume Flow rate (m3/sec); Non-dimensional volume flow rate \( \bar{Q} = \frac{2Q\eta L}{{C^{3} p_{s} D}} \)

R :

Radius of the bearing (m)

t :

Time (s)

U :

Journal peripheral speed, ωR (m/s)

W :

Steady state load capacity (N)

\( \bar{W} \) :

Non-dimensional load capacity, \( \bar{W} = W/LDp_{s} \)

W r,t :

Components of load along and perpendicular to the line of centres (N)

\( \bar{W}_{r} ,\bar{W}_{t} \) :

Non-dimensional load capacity, \( \bar{W}_{r,t} = W_{r,t} /LDp_{s} \)

ε:

Eccentricity ratio, e/C

ε1 Φ1 :

Perturbation parameters

η:

Coefficient of absolute viscosity of lubricant (Ns/m2)

θ, \( \bar{z} \) :

Non-dimensional co-ordinates, \( \theta = \frac{x}{R},\bar{z} = z/L, \) θ measured from line of centre

\( \theta^{*} \) :

Co-ordinate in the circumferential direction measured from centre of the groove

θ1θ2 :

Angular coordinates at which the film cavitates and reforms, respectively

\( \lambda \) :

Whirl ratio, \( \lambda \) = ω p /ω

τ:

Non-dimensional time, τ = ωp t

θ:

Filling gap coefficient

\( \Uplambda \) :

Bearing number \( \Uplambda = 6 \)ηω/[ps(C/R)2]

Φ:

Attitude angle (rad)

Ψ:

Assumed attitude angle

ω:

Journal rotational speed (rad/s)

ω p :

Frequency of journal vibration (rad/sec)

( )0 :

Steady state value

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, Manipal Institute of Technology, Manipal University, Manipal, 576104, India

    R. Pai

  2. School of Engineering Systems, Queensland University of Technology, G.P.O. Box 2434, Brisbane, 4001, Australia

    D. J. Hargreaves

Authors
  1. R. Pai
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  2. D. J. Hargreaves
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Correspondence to R. Pai .

Editor information

Editors and Affiliations

  1. , Department of Mechanical Engineering, University of Wisconsin-Milwaukee, North Cramer Street 3200, Milwaukee, 53211-0413, Wisconsin, USA

    Michael Nosonovsky

  2. Nanoprobe Lab. for Bio- & Nanotechnology, Biomimetics (NLB²), Ohio State University, West 19th Avenue 201, Columbus, 43210-1142, Ohio, USA

    Bharat Bhushan

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Pai, R., Hargreaves, D.J. (2012). Water Lubricated Bearings. In: Nosonovsky, M., Bhushan, B. (eds) Green Tribology. Green Energy and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23681-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-23681-5_13

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