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### Tapered Land Thrust Bearing Design Equation and Calculator

Tapered Land Thrust Plate Bearing Design Equation and Calculator:

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Tapered Thrust Plate Bearing

 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

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

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

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

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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