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### Tilting Pad Thrust Plate Bearing Design Equation and Calculator

Tilting Pad Thrust Plate Bearing Design Equation and Calculator:

Each bearing section is wedge shaped, as shown at the right below, for the purposes of design calculation, it is considered to be a rectangle with a length b equal to the circumferential length along the pitch line of the section being considered and a width a equal to the difference in the external and internal radii,

Related: Tilting Pad 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

Table p

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

External diameter formula:

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

Where:

W = applied load, pounds
Kg = fraction of circumference occupied by pads; usually, 0.8
p = unit load, see Table p

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, estimated

i = ( B Kg ) / a = nearest even number

i as the nearest even number to that calculated.

Length of bearing pad given in inches

b = ( B Kg ) / i

Operating number

O = ( 1.45 x 10-7 Z2 U ) / ( 5 p b z)

Where, Z2 = viscosity of oil at outlet temperature (inlet temperature assumed temperatur rise through the bearing).

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

Minimum film thickness given in mils inches - hmin = α b

α = dimensionless film thickness is found from Film Thickness Factor Chart

In general, this value should be 0.001 inch for small bearings and 0.002 inch for larger and high-speed bearings.

Coefficient of friction, f found from Coefficient of Friction Chart

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

Pf = ( f W U ) / 33,000

Actual oil flow, given in gpm

Q = 0.0591 α i a b U

Δt = ( 0.0217 f p ) / ( α c )

Where:

c = specific heat of oil in Btu/gal/°F

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