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
bw
Width
Outer race
Inner race
Outside
diameter
Inside
diameter
Text Reference: Figure 13.1, page 550
Important skills
• Select bearing type
• Select bearing size
• Predict bearing life
(failure is usually due to
fatigue)
Figure 13.20
Typical fatigue
spall.
• How to predict fatigue failure: use empirical
formulae.
Text Reference: Figure 13.20, page 586
Fatigue Life
60% of the bearings
fail at 1 million cycles
Figure 13.21 Distribution of
bearing fatigue failures.
10% of the bearings fail at 0.2 million cycles
• For a lower load, the number of cycles to cause
Text Reference: Figure 13.21, page 580
10% failure (L10) will be higher.
Predicting fatigue life
• Life in millions of cycles is (Eq. 13.84)
Table 13.6 for deep groove ball
Table 13.7 for cylindrical roller
mk
C 
L10 =  
P 
3.0 for deep groove ball
3.3 for cylindrical roller
P = X Pr + Y Pa (Eq.13.86)
Table 13.9 for deep groove ball
Table 13.10 for thrust bearings
X and Y depend on Pa/C0
Single Row Deep Groove Ball Bearings, Table 13.6
Principal Dimensions
db
mm
in
2.5
0.0984
5
0.1969
7
0.2756
10
0.3937
15
0.5906
da
mm
in
8
0.3150
11
0.4331
19
0.7480
14
0.5512
19
0.7480
26
1.0236
35
1.3780
24
0.9449
28
1.1024
32
1.2598
32
1.2598
35
1.3780
42
1.6535
bw
mm
in
2.8
0.1102
3
0.1181
6
0.2362
3.5
0.1378
5
0.1969
8
0.3150
11
0.4331
5
0.1969
7
0.2756
8
0.3150
9
0.3543
11
0.4331
13
0.5118
Basic load ratings
dynamic
C
N
lbf
319
71.7
637
143
1720
387
956
215
1380
310
4620
1040
8060
1810
1560
351
4030
906
5590
1260
5590
1260
7800
1750
11400
2560
static
C0
Allowable
load limit
Speed ratings
grease
w all
rpm
106
23.8
255
57.3
620
139
400
89.9
585
132
1960
441
3400
764
800
180
2040
459
2850
641
2850
641
3750
843
5400
1210
4
0.899
11
2.47
26
5.85
17
3.82
25
5.62
83
18.7
143
32.1
34
7.64
85
19.1
120
27.0
120
27.0
160
36.0
228
51.3
Note: See additional Data in SKF Folder on CD.
67000
Abutment and fillet
Dimensions
oil
80000
53000
63000
36000
43000
45000
53000
36000
43000
30000
36000
20000
26000
28000
34000
24000
30000
22000
28000
22000
28000
19000
24000
17000
20000
Db,min
mm
in
3.7
0.146
6.2
0.244
7
0.276
8.2
0.323
12
0.472
12
0.472
14
0.551
17
0.669
17
0.669
17
0.669
17
0.669
19
0.748
20
0.787
D a,ma x
mm
in
6.8
0.268
9.8
0.386
17
0.669
12.8
0.504
17
0.669
24
0.945
31
1.220
22
0.866
26
1.024
30
1.181
30
1.181
31
1.220
37
1.457
Text Reference: Table 13.6, page 578
r a,max
mm
in
0.1
0.004
0.1
0.004
0.3
0.012
0.1
0.004
0.3
0.012
0.3
0.012
0.6
0.024
0.3
0.012
0.3
0.012
0.3
0.012
0.3
0.012
0.6
0.024
1
0.039
Capacity Formulas for Radial and Angular Bearings
Table 13.9
Bearing type
e
Single row bearings
Pa/Pr<e
Deep groove
ball bearings
Angular contact
ball bearings
Pa/C0=0.025
Pa/C0=0.04
Pa/C0=0.07
Pa/C0=0.13
Pa/C0=0.25
Pa/C0=0.50
β=20°
β =25°
β =30°
β =35°
β =40°
β =45°
Self-aligning
ball bearings
Spherical roller
bearings
Tapered roller
bearings
0.22
0.24
0.27
0.31
0.37
0.44
0.57
0.68
0.80
0.95
1.14
1.33
1.5 x
tanβ
1.5 x
tanβ
1.5 x
tanβ
X
1
1
1
1
1
1
1
1
1
1
1
1
Y
0
0
0
0
0
0
0
0
0
0
0
0
Double row bearings
Pa/Pr>e
X
0.56
0.56
0.56
0.56
0.56
0.56
0.43
0.41
0.39
0.37
0.35
0.33
Y
2.0
1.8
1.6
1.4
1.2
1
1
0.87
0.76
0.66
0.57
0.50
Pa/Pr<e
X
Y
X
Y
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
1
0.42 x
cotβ
0.45 x
cotβ
0.42 x
cotβ
0.65
0.65 x
cotβ
0.67 x
cotβ
0.67 x
cotβ
1
1
0
0.40
0.40 x
cotβ
Pa/Pr>e
1
0.67
0.67
Table 13.9 Capacity formulas for rectangular and elliptical conjunctions for radial and
Text Reference: Table 13.9, page 592
angular bearings.
Life in hours
• Life in hours is
L10 (in hours) =
10 6 L10 (in million cycles)
60 N b
(13.85)
Nb = rotational speed (in rpm)
• The resulting life is L10, meaning the number of cycles when 10% of the bearings
fail.
• L10 means Survival rate S = 0.9. (L50 means S = 0.5, etc)
Example 13.8 p 595
Life other than L10
mk
C 
L10 =  
P 
results in the number of cycles that causes
10% failure (L10).
• To predict the
number of cycles
that causes x%
failure (Lx), use the
Weibull plot.
• See Example 13.9.
Figure 13.23 Typical Weibull
plot of bearing fatigue failures.
Text Reference: Figure 13.23, page 590
Effect of contact angle (optional)
• Contact angle β
determines the radial and
thrust factors in
P = X Pr + Y Pa (Eq.13.86)
• To estimate β,see
subsection 13.4.1.3.
Figure 13.6
Shoulder height
Text Reference: Figure 13.6, page 555
Radial and Thrust Factors
Bearing Type
Radial deep-groove ball
Radial angular-contact
ball
Radial self-aligning ball
Radial spherical roller
Radial tapered roller
β=20°
β=25°
β=30°
β=35°
β=40°
Single
Row
X0
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Y0
0.5
0.42
Double
Row
X0
0.6
1
Y0
0.5
0.84
0.38
0.33
0.29
0.26
0.22cotβ
0.22cotβ
0.22cotβ
1
1
1
1
1
1
1
0.76
0.66
0.58
0.52
0.44cotβ
0.44cotβ
0.44cotβ
Table 13.8 Radial factor X0 and thrust factor Y0 for statically stressed radial
bearings.
Text Reference: Table 13.8, page 580
Radial and Thrust Factors
Bearing type
e
Single acting
Thrust
ball
β=45°
β=60°
β=75°
Spherical roller
thrust
1.25
2.17
4.67
1.5tanβ
Pa/Pr>e
X
Y
1
0.66
1
0.92
1
1.66
tanβ
1
Pa/Pr<e
X
Y
0.59
1.18
0.55
1.90
0.52
3.89
1.5tanβ 0.67
Pa/Pr>e
X
Y
1
0.66
1
0.92
1
1.66
tanβ
1
Tapered roller
1.5tanβ
tanβ
1.5tanβ
tanβ
1
Double acting
0.67
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 L10 as function of
dimensionless film
parameter. [From Tallian
(1967)]
Text Reference: Figure 13.24, page 594