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Tapered Land Thrust Bearing Design Equation and Calculator

Machine Design Applications
Bearing Engineering and Design

Tapered Land Thrust Plate Bearing Design Equation and Calculator:

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Tapered Thrust Plate Bearing

Tapered Thrust Plate Bearing

Basic Element of thrust bearing

Preview: Tapered Land Thrust Plate Bearing Design Calculator

Thrust Bearing Typical Loads
Surface
Loads
Lbs/in2
Max Loads
Lbs/in2
Parallel surface
< 75
< 150
Step Surface
200
500
Tapered Land Surface
200
500
Tilting Pad Surface
200
500

Reproduced with permission from Wilcock and Booser, Bearing Design and Applications, McGraw-Hill Book Co., Copyright © 1957.


General Design Parameters: Usually, the taper extends to only 80 per cent of the pad length with the remainder being flat, thus: b2 = 0.8b and b1 = 0.2b.


External diameter formula:

D2 = ( ( 4 W ) / ( ( π Kg Pa ) + D12 )1/2

Where:

W = applied load, pounds
Kg = fraction of circumference occupied by pads; usually, 0.8
Pa = bearing unit load, psi

 


Radial pad width , given in inches

a = (1/2) ( D2 - D1 )


Pitch line circumference , given in inches

B = π (D1 - D2 ) / 2


Number of bearing pads, assume oil groove s.

i = B / ( a + s ) = nearest even number

i as the nearest even number to that calculated.


Length of bearing pad given in inches

b = ( B - i s ) / i


Taper values, δ1 and δ2 derived from Taper Table T

Pad Size
(inches)
Taper
(inch)
a x b
δ1 = h2 − h1
(at ID)
δ2 = h2 − h1
(at OD)
0.5 x 0.5
0.0025
0.0015
1.0 x 1.0
0.005
0.003
3.0 x 3.0
0.007
0.004
7 x 7
0.009
0.006

Table T


Bearing unit load, actual given in psi

p = W / ( i a b )


Pitch line velocity, given in fpm

U = ( B N ) / 12

where, N - rpm


Oil leakage factor

YL = b / [ 1 + ( π2 b2 / ( 12 a 2 ) ) ]

or can be estimated from:

Oil leakage factor table
Oil leakage factor table


Film thickness factor

K = ( 5.75 x 106 p ) / ( U YL Z )


Minimum film thickness given in mils inches - h should be 0.001 inch for small bearings and 0.002 inch for larger and high-speed bearings.

Use K value and the selected taper values δ1 and δ2, h is found

Chart h
Chart h


Friction power loss (HP), derived from table using film thickness h

Pf = 8.79 x 10-13 i a b J U2 Z

coefficient J can be obtained from the following table.

Chart J
Chart J


Required oil flow, given in gpm at temperature rise Δt

Q = ( 42.4 Pf ) / ( c Δt )

Where:

c = specific heat of oil in Btu/gal/°F
Δt = 50 °F typical maximum


Shape factor

Ys = ( 8 a b ) / ( D22 - D21 )


YG Oil flow factor using Ys and D1 / D2

Oil flow factor , YG vs diameter ratio D1/D2
Table YG
Oil flow factor , YG vs diameter ratio D1/D2


Actual oil film flow

Qf = ( 8.9 x 10-4 i δ2 D32 N Yg Y2s ) / ( D2 - D1 )


Notation:

a = radial width of pad, inches
b = circumferential length of pad at pitch line, inches
b2 = pad step length
B = circumference of pitch circle, inches
c = specific heat of oil, Btu/gal/°F
D = diameter, inches
e = depth of step, inch
f = coefficient of friction
g = depth of 45° chamfer, inches
h = film thickness, inch
i = number of pads
J = power loss coefficient
K = film thickness factor
Kg = fraction of circumference occupied by the pads; usually, 0.8
l = length of chamfer, inches
M = horsepower per square inch
N = revolutions per minute
O = operating number
p = bearing unit load, psi
ps = oil-supply pressure, psi
Pf = friction horsepower
Q = total flow, gpm
Qc = required flow per chamfer, gpm
Qoc = uncorrected required flow per chamfer, gpm
QF = film flow, gpm
s = oil-groove width
∆t = temperature rise, °F
U = velocity, feet per minute
V = effective width-to-length ratio for one pad
W = applied load, pounds
Yg = oil-flow factor
Yl = leakage factor
YS = shape factor
Z = viscosity, centipoises
α = dimensionless film-thickness factor
δ = taper
ξ = kinetic energy correction factor

References:

  • Machinery's Handbook, 29th Edition
  • Understanding Journal Bearings, Malcolm E. Leader, P.E. Applied Machinery Dynamics Co.
  • Theory and Practice of Lubrication for Engineers by Dudley D. Fuller, Wiley and Sons, 1984, ISBN 0- 471-04703-1
  • Bearing Design and Application by Donald F. Wilcock and E. Richard Booser, McGraw Hill, 1957, 195, LC number 56-9641
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