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Tapered Land Thrust Bearing Design Equation and Calculator
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Tapered Thrust Plate Bearing
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Thrust Bearing Typical Loads 

Surface 
Loads Lbs/in^{2} 
Max Loads Lbs/in^{2} 
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, McGrawHill 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:
D_{2} = ( ( 4 W ) / ( ( π K_{g} P_{a} ) + D_{1}^{2} )^{1/2}
Where:
W = applied load, pounds
K_{g} = fraction of circumference occupied by pads; usually, 0.8
P_{a} = bearing unit load, psi
Radial pad width , given in inches
a = (1/2) ( D_{2}  D_{1} )
Pitch line circumference , given in inches
B = π (D_{1}  D_{2} ) / 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, δ_{1} and δ_{2} derived from Taper Table T
Pad Size (inches) 
Taper (inch) 

a x b 
δ_{1} = h_{2} − h_{1} (at ID) 
δ_{2} = h_{2} − h_{1} (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
Y_{L} = b / [ 1 + ( π^{2} b^{2} / ( 12 a ^{2} ) ) ]
or can be estimated from:
Oil leakage factor table
Film thickness factor
K = ( 5.75 x 10^{6} p ) / ( U Y_{L} Z )
Minimum film thickness given in mils inches  h should be 0.001 inch for small bearings and 0.002 inch for larger and highspeed bearings.
Use K value and the selected taper values δ1 and δ2, h is found
Chart h
Friction power loss (HP), derived from table using film thickness h
P_{f} = 8.79 x 10^{13} i a b J U^{2} Z
coefficient J can be obtained from the following table.
Chart J
Required oil flow, given in gpm at temperature rise Δt
Q = ( 42.4 P_{f} ) / ( c Δt )
Where:
c = specific heat of oil in Btu/gal/°F
Δt = 50 °F typical maximum
Shape factor
Y_{s} = ( 8 a b ) / ( D^{2}_{2}  D^{2}_{1} )
Y_{G} Oil flow factor using Y_{s} and D_{1} / D_{2}
Table YG
Oil flow factor , Y_{G} vs diameter ratio D_{1}/D_{2}
Actual oil film flow
Q_{f} = ( 8.9 x 10^{4} i δ_{2} D^{3}_{2} N Y_{g} Y^{2}_{s} ) / ( D_{2}  D_{1} )
Notation:
a = radial width of pad, inches
b = circumferential length of pad at pitch line, inches
b_{2} = 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
K_{g} = 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
p_{s} = oilsupply pressure, psi
P_{f} = friction horsepower
Q = total flow, gpm
Q_{c} = required flow per chamfer, gpm
Q^{o}_{c} = uncorrected required flow per chamfer, gpm
Q_{F} = film flow, gpm
s = oilgroove width
∆t = temperature rise, °F
U = velocity, feet per minute
V = effective widthtolength ratio for one pad
W = applied load, pounds
Y_{g} = oilflow factor
Y_{l} = leakage factor
Y_{S} = shape factor
Z = viscosity, centipoises
α = dimensionless filmthickness 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 471047031
 Bearing Design and Application by Donald F. Wilcock and E. Richard Booser, McGraw Hill, 1957, 195, LC number 569641
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