Tapered Land Thrust Bearing Design Equation and Calculator

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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:

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

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 K_g P_a ) + D₁² )^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) ( 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

Y_L = 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 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 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

P_f = 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 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 ) / ( D²₂ - D²₁ )

Y_G Oil flow factor using Y_s and D₁ / D₂

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

Actual oil film flow

Q_f = ( 8.9 x 10^-4 i δ₂ D³₂ N Y_g Y²_s ) / ( 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
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 = oil-supply 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 = 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
Y_g = oil-flow factor
Y_l = leakage factor
Y_S = 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