Handbook of Mechanical Engineering Calculations ar Episode 3 Part 2 pps

22.1

FIGURE 1 Shaft and 6-spoked bearing system hav￾ing three rotor masses. (Product Engineering.)

SECTION 22

BEARING DESIGN AND

SELECTION

Determining Stresses, Loading, Bending

Moments, and Spring Rate in Spoked

Bearing Supports 22.1

Hydrodynamic Equations for Bearing

Design Calculations 22.6

Graphic Computation of Bearing Loads

on Geared Shafts 22.13

Shaft Bearing Load Analysis Using Polar

Diagrams 22.17

Journal Bearing Frictional Horsepower

Loss During Operation 22.21

Journal Bearing Operation Analysis

22.22

Bearing Type Selection of a Known

Load 22.23

Shaft Bearing Length and Heat

Generation 22.28

Roller-Bearing Operating-Life Analysis

22.31

Roller-Bearing Capacity Requirements

22.32

Radial Load Rating for Rolling Bearings

22.32

Roller-Bearing Capacity and Reliability

22.34

Porous-Metal Bearing Capacity and

Friction 22.35

Hydrostatic Thrust Bearing Analysis

22.37

Hydrostatic Journal Bearing Analysis

22.39

Hydrostatic Multidirection Bearing

Analysis 22.42

Load Capacity of Gas Bearings 22.46

DETERMINING STRESSES, LOADING, BENDING

MOMENTS, AND SPRING RATE IN SPOKED

BEARING SUPPORTS

Spoked bearing supports are used in gas turbines, large air-cooling fans, electric￾motor casings slotted for air circulation, and a variety of other applications. For the

shaft and 6-spoked bearing system in Fig. 1 having three rotor masses and these

parameters and symbols,

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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS

22.2 DESIGN ENGINEERING

SI values

P
10,000 lb (at either bearing) 4 IS
25 in 4 IR
0.3 in2 A
7 in (for ring also) 6 E
E
10 10 psi S R

L
10 in

R
12 in

CR
0.40 in

(44,480 N)

(1040.6 cm4

)

(12.5 cm4

)

(45.2 cm2

)

(68,900 MPa)

(25.4 cm)

(30.5 cm)

(8.9 cm)

(1.02 cm)

Symbols SI values

A
spoke cross-section area, in2 (cm2

)

CS
distance, neutral axis to extreme fiber (of spoke), in (cm)

CR
distance, neutral axis to extreme fiber (of ring), in (cm)

ER , ES
elasticity moduli (ring and spoke), psi (kPa)

RR1
axial loading in inclined spokes, lb; ( for upper two,  for lower

two)

(N)

FR2
axial loading in vertical spokes, lb; ( for top,  for bottom) (N)

FT
tangential load at OD of inclined spokes, lb; (clockwise on left side,

counterclockwise on right side)

(N)

IR
outer-ring moment of inertia about neutral axis pependicular to plane

of support, in4

(cm4

)

IS
spoke moment of inertia about neutral axis perpendicular to plane of

support, in4

(cm4

)

k
spring rate with respect to outer shell, lb/in (N/cm)

L
spoke length, in (cm)

M
max bending moment (6-spoked support) in outer ring at OD of

vertical spokes, in-lb; ( at inner-fiber upper point and outer-fiber

lower point)

max bending moment at OD of all spokes in 4-spoked support

(Nm)

P
bearing radial-load, lb (N)

R
ring radius, in (cm)

T
axial loading in outer ring at OD of vertical spokes in 6-spoked

support; all spokes in 4-spoked support ( at upper points, at

lower points)

lb (N)

denotes tension

 denotes compression

find (a) the maximum bending moment in the outer ring of the support, (b) the

axial loading in the outer ring, (c) the total stress in the outer ring at the top vertical

spoke, Fig. 2, (d) the total axial loading in one of the inclined spokes, (e) the

bending moment in the spoke at the hub, and (f) the spring rate of the spoked

bearing support. Use the free-body diagram, Fig. 3, to analyze this bearing support.

Calculation Procedure:

1. Find the maximum bending moment in the outer ring of the 6-spoke bearing

support

Use the relation

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BEARING DESIGN AND SELECTION

BEARING DESIGN AND SELECTION 22.3

FIGURE 2 Typical 6-spoke bearing support having the mount

load at the top for an aircraft gas turbine; in a stationary plant, mount

load would be at the bottom of the support. (Product Engineering.)

3 I E S S R



abscissae parameter, Fig. 4 ILE R R

where the symbols are as shown above. Substituting, we find the parameter
144,

from:

3 25 12 1


0.3 10 1

Using the M curve in Fig. 4 for a parameter value of 144 gives

100M
1.45 PR

Solving for M, we have

1.45 PR 1.45(10,000)(12) M


1740 in/lb (196.6 Nm) 100 100

2. Determine the axial loading in the outer ring at the outside diameter (OD)

Find T, the axial loading from Fig. 4 for the 144 parameter as

10T
1.55 P

Substituting,

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BEARING DESIGN AND SELECTION

22.4 DESIGN ENGINEERING

FIGURE 3 Free-body diagram for 6- and 4-spoke bearing

supports. (Product Engineering.)

1.55P (1.55)(10,000) T


1550 lb (6894 N) 10 10

3. Compute the total stress in the outer ring at the top vertical spoke

Use the relation

T (0.4) 1550 M 2 (C /I )
1740
2320 220
2540 lb/in (17501 kPa) R R A (0.3) 7

4. Find the total axial loading in one of the inclined spokes

Using the FR1 curve in Fig. 4 for the same parameter, 144,

10F 0.82 P (0.82)(10,000) R1
0.82 F


820 lb (3647 N) R1 P 10 10

Also,

10F (1.47)(P) (1.47)(10,000) T
1.47 F


1470 lb (6539 N) T P 10 10

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BEARING DESIGN AND SELECTION