Machine Design Databook Episode 3 part 2 ppsx

The difference in temperature (
T) of the bearing

and of the cooling medium can be found from the

equation

The difference between the bearing-wall temperature

tb and the ambient temperature ta, for three main

types of lubrication by oil bath, by an oil ring, and

by waste pack or drop feed

BEARING CAP

The bearing cap thickness

Hd ¼ ð
T þ 18Þ

2

427k ðLdÞ

Customary Metric ð23-80cÞ

where Hd in kcal/s, ðLdÞ in m2

,
T in 8C values of

k are as given inside parentheses under

Eq. (23-80a) for US customary system units

and values of k for customary metric units

also given under Eqs. (23-80a) and (23-80b)

ð
T þ 18Þ

2 ¼ K0

Pv SI ðMetricÞ ð23-81Þ

where P in N/m2 (kgf/mm2

), v in m/s, and
T in K

(8C)

K 0 ¼ 0.475 (4:75 106

) for bearings of light construc￾tion located in still air

¼ 0.273 (2:7 106

) for bearings of heavy con￾struction and well ventilated

¼ 0.165 (1:65 106

) for General Electric Com￾pany’s well-ventilated bearing

Refer to Fig. 23-46 for tb
ta ’

t0
tb

2

hc ¼

ffiffiffiffiffiffiffiffiffiffi

3Wa

2L

r

ð23-82Þ

Particular Formula

0

0

1

2

3

4

10 20 30 40 50 60 70

0

1

3

5

7

9

11

13

15

17

19

21

80 90

Well ventilated

Average

Thin shell not attached to

radiating mass

(a)

FIGURE 23-45 The rate of heat dissipated from a journal bearing.

(b) Temperature rise (tb ta) k(tb ta), ft-ibf/min/in2/ F

1000

900

800

700

600

500

400

300

200

100

0

0 20 40 60 80 100 120 140 160

3

2

1

1 - Thin shell not attached to

large radiating mass

3 - Well ventilated bearing

2 - Average industrial

bearing, unventilated

DESIGN OF BEARINGS AND TRIBOLOGY 23.55

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DESIGN OF BEARINGS AND TRIBOLOGY

The deflection of the cap

The thickness of cap from Eq. (23-71)

EXTERNAL PRESSURIZED BEARING OR

HYDROSTATIC BEARING: JOURNAL

BEARING (Fig. 23-47)

The pressure in the lower pool of quadrant 1

(Fig. 23-47)

y ¼ Wa3

4ELh3

c

ð23-83Þ

hc ¼ 0:63a 3

ffiffiffiffiffiffiffiffiffi

W

ELy s

ð23-84Þ

where the deflection should be limited to 0.025 mm

(0.001 in)

P1 ¼ K1Po ð23-85aÞ

where

K1 ¼ 1

1 þ

4

Po

P0
1

4 þ 2:121" þ 1:93"2
0:589"3

ð23-85bÞ

Particular Formula

FIGURE 23-46 Relation between oil film temperature and

bearing wall temperature.

Temperature rise of wall above

ambient tb ta, C

0 10 20 30 40

70

60

50

40

30

20

10

0

Oil film temperature rise above ambient, to ta, C

Drop

feed

Still air Moving air

Oil

ring

Still air Moving air

Oil

bath

Still air

Moving air

23.56 CHAPTER TWENTY-THREE

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DESIGN OF BEARINGS AND TRIBOLOGY

The pressure in the upper pool of quadrant 3 (Fig.

23-47)

The pressure in the left pool of quadrant 2 (Fig. 23-47)

The pressure in the right pool of quadrant 4 (Fig.

23-47)

The flow of lubricant through the lower quadrant 1 of

the bearing from the manifold

P3 ¼ K3Po ð23-86aÞ

where

K3 ¼ 1

1 þ

4

Po

P0
1

4 þ 2:121" þ 1:93"2 þ 0:589"3

ð23-86bÞ

P2 ¼ K2Po ð23-87aÞ

where

K2 ¼ 1

8

P0

Po

ð6:283 þ 3:425"2

Þ ð23-87bÞ

P4 ¼ K4Po ð23-88aÞ

where

K4 ¼ 1

8

P0

Po

ð6:283 þ 3:425"2

Þ ð23-88bÞ

Q1 ¼ 3

d4

P1

96l1

CPF1 ð23-89aÞ

where

CPF1 ¼

4
2:121" þ 1:93"2
0:589"3 ð23-89bÞ

Particular Formula

b

w

h e

1

(a)

(b)

(c)

3

2

Oil

inlet

Hydraulic resistance Oil inlet hole

Oil

pocket

Constant pressure oil manifold

4 e

t

1

L

l

1 3 l

1

l

1

Ps

hmin

hmax

d

FIGURE 23-47 (a) and (b) schematic diagram of a full cylindrical hydrostatic bearing; (c) oil pressure distribution along the

bearing. [Shaw and Macks10]

DESIGN OF BEARINGS AND TRIBOLOGY 23.57

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DESIGN OF BEARINGS AND TRIBOLOGY

The flow of lubricant through the left quadrant 2 of

the bearing from the manifold

The flow of lubricant through the upper quadrant 3 of

the bearing from the manifold

The flow of lubricant through the right quadrant 4 of

the bearing from the manifold

The total flow of lubricant through quadrant of the

bearing from the manifold assuming P2 ¼ P4 ¼ P0

(good approximation)

The flow factor in Eq. (23-81b)

The external load on the hydrostatic journal bearing

The load factor

The pressure ratio connecting the dimensions of the

bearing and its external resistances

Q2 ¼ 3

d4

P2

768l1

CPF2 ð23-90aÞ

where

CPF2 ¼ 6:283 þ 3:425"2 ð23-90bÞ

Q3 ¼ 3

d4

P3

48l1

CPF3 ð23-91aÞ

where

CPF3 ¼

4 þ 2:121" þ 1:93"2 þ 0:589"3 ð23-91bÞ

Q4 ¼ 3

d4

P4

768l1

CPF4 ð23-92aÞ

where

CPF4 ¼ CPF2 ¼ 6:283 þ 3:425"2 ð23-92bÞ

Q ¼ Q1 þ Q2 þ Q3 þ Q4 ð23-93aÞ

Q ¼ 3

d4

Po

48l1

G ð23-93bÞ

where G ¼ flow factor given by Eq. (23-94)

G ¼ CPF1K1 þ 1

8 ðCPF2K2 þ CPF4K4Þ þ CPF3K3

¼ CPF1K1 þ 1

4 CPF2K2 þ CPF3K3 ð23-94Þ

since K2 ¼ K4 and CPF2 ¼ CPF4

W ¼ ðP1
P3Þ

A þ

A0

2

¼ Po

A þ

A0

2

FPFW

ð23-95Þ

where FPFW ¼ load factor given by Eq. (23-95)

FPFW ¼ K1
K3 ð23-96Þ

Po

P0 ¼ 1 þ 6

d

dc

c

dc

3 lc

l1

ð23-97Þ

Particular Formula

23.58 CHAPTER TWENTY-THREE

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DESIGN OF BEARINGS AND TRIBOLOGY