Chapter 13: Rolling-Element Bearings

Covered in this class:
•13.1 - 13.3
•13.4 (Figures only)
•Tables 13.6 and 13.8
•13.9 Most importantly

Bearing types:

• Ball bearings

– Deep groove (Conrad)

– Angular contact

– Thrust

Bearing types

• Cylindrical roller bearings

• Tapered roller bearings

• Spherical roller bearings

Characteristics of Ball Bearings

Table 13.1 Characteristics of representative radial ball bearings

Table 13.2 Characteristics of representative angular-contact ball
bearings

Table 13.3 Characteristics of representative thrust ball bearings

Table 13.4 Characteristics of representative cylindrical roller
bearings

Table 13.5 Characteristics of representative spherical roller bearings

Read Example 13.1 Selection of bearing types

Preloading for stiffness

Figure 13.17 Angular-contact
bearings in back-to-back
arrangement, shown (a)
individually as manufactured
and (b) as mounted with preload.

Ball Bearings, important dimensions

Text Reference: Figure 13.1, page 550

Outside
diameter

Inside
diameter

b

w

Width

Outer race

Inner race

Important skills

Figure 13.20

Typical fatigue

spall.

Text Reference: Figure 13.20, page 586

• How to predict fatigue failure: use empirical

formulae.

• Select bearing type

• Select bearing size

• Predict bearing life

(failure is usually due to
fatigue)

Fatigue Life

Figure 13.21 Distribution of
bearing fatigue failures.

Text Reference: Figure 13.21, page 580

• For a lower load, the number of cycles to cause

10% failure (L

10

) will be higher.

10% of the bearings fail at 0.2 million cycles

60% of the bearings
fail at 1 million cycles

Predicting fatigue life

k

m

P

C

L













=

10

• Life in millions of cycles is (Eq. 13.84)

Table 13.6 for deep groove ball
Table 13.7 for cylindrical roller

3.0 for deep groove ball
3.3 for cylindrical roller

P = X P

r

+ Y P

a

(Eq.13.86)

Table 13.9 for deep groove ball
Table 13.10 for thrust bearings

X and Y depend on P

a

/C

0

Single Row Deep Groove Ball Bearings,

Table 13.6

Pr incipal Dim ensions

Basic load ratings

Allowable

load lim it

Speed ratings

Abutment and fillet

Dim ensions

d

b

d

a

b

w

dynam ic

C

static

C

0

w

all

grease

oil

D

b,min

D

a,ma x

r

a,max

m m
in

m m

in

m m

in

N

lbf

rpm

m m

in

m m

in

m m

in

2.5
0.0984

8

0.3150

2.8

0.1102

319

71.7

106

23.8

4

0.899

67000

80000

3.7

0.146

6.8

0.268

0.1

0.004

5
0.1969

11

0.4331

3

0.1181

637
143

255

57.3

11

2.47

53000

63000

6.2

0.244

9.8

0.386

0.1

0.004

19

0.7480

6

0.2362

1720

387

620
139

26

5.85

36000

43000

7

0.276

17

0.669

0.3

0.012

7
0.2756

14

0.5512

3.5

0.1378

956
215

400

89.9

17

3.82

45000

53000

8.2

0.323

12.8

0.504

0.1

0.004

10
0.3937

19

0.7480

5

0.1969

1380

310

585
132

25

5.62

36000

43000

12

0.472

17

0.669

0.3

0.012

26

1.0236

8

0.3150

4620
1040

1960

441

83

18.7

30000

36000

12

0.472

24

0.945

0.3

0.012

35

1.3780

11

0.4331

8060
1810

3400

764

143

32.1

20000

26000

14

0.551

31

1.220

0.6

0.024

15
0.5906

24

0.9449

5

0.1969

1560

351

800
180

34

7.64

28000

34000

17

0.669

22

0.866

0.3

0.012

28

1.1024

7

0.2756

4030

906

2040

459

85

19.1

24000

30000

17

0.669

26

1.024

0.3

0.012

32

1.2598

8

0.3150

5590
1260

2850

641

120

27.0

22000

28000

17

0.669

30

1.181

0.3

0.012

32

1.2598

9

0.3543

5590
1260

2850

641

120

27.0

22000

28000

17

0.669

30

1.181

0.3

0.012

35

1.3780

11

0.4331

7800
1750

3750

843

160

36.0

19000

24000

19

0.748

31

1.220

0.6

0.024

42

1.6535

13

0.5118

11400

2560

5400
1210

228

51.3

17000

20000

20

0.787

37

1.457

1

0.039

Note: See additional Data in SKF Folder on CD.

Text Reference: Table 13.6, page 578

Capacity Formulas for Radial and Angular Bearings

Table 13.9

Bearing type

e

Single row bearings

Double row bearings

Pa/Pr<e

Pa/Pr>e

Pa/Pr<e

Pa/Pr>e

X

Y

X

Y

X

Y

X

Y

Deep groove
ball bearings

P

a

/C

0

=0.025

P

a

/C

0

=0.04

P

a

/C

0

=0.07

P

a

/C

0

=0.13

P

a

/C

0

=0.25

P

a

/C

0

=0.50

0.22
0.24
0.27
0.31
0.37
0.44

1
1
1
1
1
1

0
0
0
0
0
0

0.56
0.56
0.56
0.56
0.56
0.56

2.0
1.8
1.6
1.4
1.2

1

Angular contact
ball bearings

β

=20°

β

=25°

β

=30°

β

=35°

β

=40°

β

=45°

0.57
0.68
0.80
0.95
1.14
1.33

1
1
1
1
1
1

0
0
0
0
0
0

0.43
0.41
0.39
0.37
0.35
0.33

1

0.87
0.76
0.66
0.57
0.50

1
1
1
1
1
1

1.09
0.92
0.78
0.66
0.55
0.47

0.70
0.67
0.63
0.60
0.57
0.54

1.63
1.41
1.24
1.07
0.93
0.81

Self-aligning
ball bearings

1.5 x

tan

β

1

0.42 x

cot

β

0.65

0.65 x

cot

β

Spherical roller
bearings

1.5 x

tan

β

1

0.45 x

cot

β

0.67

0.67 x

cot

β

Tapered roller
bearings

1.5 x

tan

β

1

0

0.40

0.40 x

cot

β

1

0.42 x

cot

β

0.67

0.67 x

cot

β

Table 13.9 Capacity formulas for rectangular and elliptical conjunctions for radial and
angular bearings.

Text Reference: Table 13.9, page 592

Life in hours

• The resulting life is L

10

, meaning the number of cycles when 10% of the bearings

fail.

•

L

10

means Survival rate S = 0.9.

(L

50

means S = 0.5, etc)

• Life in hours is

b

N

L

L

60

)

cycles

million

in

(

10

)

hours

in

(

10

6

10

=

(13.85)

N

b

= rotational speed (in rpm)

Example 13.8 p 595

Life other than L

10

Figure 13.23 Typical Weibull
plot of bearing fatigue failures.

Text Reference: Figure 13.23, page 590

results in the number of cycles that causes

10% failure (L

10

).

k

m

P

C

L













=

10

• To predict the

number of cycles
that causes x%
failure (L

x

), use the

Weibull plot.

• See Example 13.9.

Effect of contact angle (optional)

Figure 13.6

Text Reference: Figure 13.6, page 555

Shoulder height

• Contact angle

β

determines the radial and
thrust factors in

P = X P

r

+ Y P

a

(Eq.13.86)

• To estimate

β

,

see

subsection 13.4.1.3.

Radial and Thrust Factors

Bearing Type

Single

Row

Double

Row

X

0

Y

0

X

0

Y

0

Radial deep-groove ball

0.6

0.5

0.6

0.5

Radial angular-contact
ball

β

=20°

0.5

0.42

1

0.84

β

=25°

0.5

0.38

1

0.76

β

=30°

0.5

0.33

1

0.66

β

=35°

0.5

0.29

1

0.58

β

=40°

0.5

0.26

1

0.52

Radial self-aligning ball

0.5

0.22cot

β

1

0.44cot

β

Radial spherical roller

0.5

0.22cot

β

1

0.44cot

β

Radial tapered roller

0.5

0.22cot

β

1

0.44cot

β

Table 13.8 Radial factor X

0

and thrust factor Y

0

for statically stressed radial

bearings.

Text Reference: Table 13.8, page 580

Radial and Thrust Factors

Bearing type

e

Single acting

Double acting

P

a

/P

r

>e

P

a

/P

r

<e

P

a

/P

r

>e

X

Y

X

Y

X

Y

Thrust
ball

β

=45°

β

=60°

β

=75°

1.25
2.17
4.67

0.66
0.92
1.66

1
1
1

1.18
1.90
3.89

0.59
0.55
0.52

0.66
0.92
1.66

1
1
1

Spherical roller
thrust

1.5tan

β

tan

β

1

1.5tan

β

0.67

tan

β

1

Tapered roller

1.5tan

β

tan

β

1

1.5tan

β

0.67

tan

β

1

Table 13.10 Radial factor X and thrust factor Y for thrust bearings.

Text Reference: Table 13.10, page 592

Fatigue Life vs. Film Parameter

Figure 13.24 Group fatigue
life L

10

as function of

dimensionless film
parameter. [From Tallian
(1967)]

Text Reference: Figure 13.24, page 594