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Numerical study of the influence of the pivot position on the steady-state behavior of tilting-pad thrust bearings

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Abstract

The coordinates of the pivot pads variation of a hydrodynamic thrust bearing can result in hydrodynamic pressure field changes that forms on the surface of the pad with consequent changes in the values of the bearing performance parameters, such as power loss, load capacity and operating temperatures. The analysis was performed by computer simulation (FORTRAN), based on the numerical solution of the two-dimensional isoviscous Reynolds equation in polar coordinates by finite difference method. The simulated bearing was based on the dimensions of a KV 9 Kingsbury thrust bearing, existing on the tribology laboratory of the university. With the pivot position variation (radius r and angle θ), starting with a bearing with central pivot pads, as well as a bearing consisting of pads with pivot located in other positions, both in the radial direction and in the circumferential direction, was possible to verify some significant changes in the bearing performance parameters. It was found that the maximum load occurs in the case of pads with pivot located approximately 60% of the average circumferential length, but for a substantially longer than the average radius of radial position. On the other hand, the minimum power loss occurs due to friction in the bearings for pivoting the pads with about 67% of the average circumferential length thereof.

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Abbreviations

a :

Oil film thickness obtained with the inclination of r axes

A1, A2, A3, A4 and A5:

Coefficients from discretized Reynolds equation

b :

Oil film thickness obtained with the inclination of θ axes

c p :

Specific heat of lubricant

denom:

Term used in the denominator from A1, A2, A3, A4 and A5 coefficients

DIFR:

Difference between the previously and currently iteration of the radial pivot position

DIFTETA:

Difference between the previously and currently iteration of the angular pivot position

fT :

Temperature coefficient

F :

Dimensionless load capacity of a pad

F a :

Friction force

F 0 :

Dimensional load capacity of a pad

h :

Oil film thickness at any point over the pad surface

h 0 :

Dimensional oil film thickness

h p :

Oil film thickness at the pivot position

h rs :

Oil film thickness at the intersection of the trailing edge of the pad with the θ axes

H :

Dimensionless power loss in a pad

H 0 :

Dimensional power loss in a pad

H 1 and H 2 :

Dimensionless discrete components from dimensional power loss equation

i :

Discrete variable in the θ direction

j :

Discrete variable in the r direction

J :

Thermal equivalent of work (4186 J/kcal)

k :

Number of iterations

k 1 and k 2 :

Walther’s equation constants

K :

Ratio of the values of h rs and h p

L :

Pad width

m :

Number of points in the r direction

m p :

Number of intervals in the r direction

n :

Number of points in the θ direction

n p :

Number of intervals in the θ direction

N :

Rotational speed

p :

Dimensionless pressure

pn :

Dimensionless pressure in the current interaction

p 0 :

Dimensional pressure

P m :

Average pad pressure

q E :

Dimensionless component from inlet circumferential flow equation

\(q_{{R_{\text{e}} }}\) :

Dimensionless lateral flow in outer radius

\(q_{{R_{\text{i}} }}\) :

Dimensionless lateral flow in inner radius

q S :

Dimensionless component from outlet circumferential flow equation

q 0E :

Component in brackets from Eq. (26)

Q E :

Inlet oil flow rate

\(Q_{{LR_{\text{e}} }}\) :

Outer radius oil flow rate

\(Q_{{LR_{\text{i}} }}\) :

Inner radius oil flow rate

Q S :

Outlet oil flow rate

Q sup :

Lubricant supply flow rate

r :

Radial coordinate

r 0 :

Dimensional radius

r 0p :

Radial coordinate of pivot position and polar coordinate of the resultant force F 0

R e :

Outer radius of the pad

R i :

Inner radius of the pad

T e :

Lubricant inlet temperature in the pad

T ef :

Effective temperature

T m :

Lubricant average temperature

T mist :

Temperature of the mixture

T 0 :

Dimensional lubricant temperature in the pad

T s :

Lubricant outlet temperature in the pad

T sup :

Lubricant supply temperature

U :

Tangential velocity in the rotating collar

x :

Cartesian coordinate of the pivot position

x i :

Cartesian coordinate of the sector shaped infinitesimal element

x p :

Cartesian coordinate of the resultant force F 0

y :

Cartesian coordinate of the pivot position

y i :

Cartesian coordinate of the sector shaped infinitesimal element

y p :

Cartesian coordinate of the resultant force F 0

Z :

Number of pads

α r :

Angle of inclination around of θ axes

α θ :

Angle of inclination around of r axes

Δθ :

Pad angle divided by number of intervals in the θ direction

Δr :

Pad width divided by number of intervals in the r direction

ΔT :

Lubricant temperature rise in a pad

η :

Lubricant dynamic viscosity

θ :

Angular coordinate

θ 0 :

Pad angle

θ p :

Angular coordinate of pivot position and polar coordinate of the resultant force F 0

λ :

Coefficient from the coefficient of over-relaxation great equation

λ 0 :

Coefficient of over-relaxation great

ρ :

Lubricant density

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Authors and Affiliations

  1. Federal University of Itajubá-UNIFEI, Av.BPS, no 1303, Pinheirinho, Itajubá, Minas Gerais, 37500-903, Brazil

    Marcos Moura Galvão, Genésio José Menon & Vilmar Arthur Schwarz

Authors
  1. Marcos Moura Galvão
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  2. Genésio José Menon
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  3. Vilmar Arthur Schwarz
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Correspondence to Marcos Moura Galvão.

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Technical Editor: Fernando Antonio Forcellini.

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Galvão, M.M., Menon, G.J. & Schwarz, V.A. Numerical study of the influence of the pivot position on the steady-state behavior of tilting-pad thrust bearings. J Braz. Soc. Mech. Sci. Eng. 39, 3165–3180 (2017). https://doi.org/10.1007/s40430-017-0805-x

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  • DOI: https://doi.org/10.1007/s40430-017-0805-x

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