CHAPTER 6
Rolling element bearings
Nomenclature
Generally, preferred SI units have been stated
a1
a2
a3
a23
aSKF
B
ci
C
Co
d
di
dm
D
DB
DF
DT
e
ISO
k
lo
L
L1
L10
L2
Lcat
Ld
Lna
Lnm
P
P1
P2
Pd
Pu
R
T
V
X
Y
α
life adjustment factor for reliability
life adjustment factor for material
life adjustment factor for operating conditions
combined life adjustment factor
SKF life modification factor
width (m)
ratio of internal diameter of hollow shaft to bore diameter
basic dynamic load rating (N)
basic static load rating (N)
bore diameter (m)
internal diameter of hollow shaft (m)
mean diameter (m)
outer diameter (m)
duplex back to back
duplex face to face
tandem
thrust to radial load ratio
International organisation for standardisation
constant
original length (m)
life (number of revolutions)
life at load P1 (number of revolutions)
rated life at the rated load (number of revolutions)
life at load P2 (number of revolutions)
catalogue rating (N)
design life (number of revolutions)
adjusted rating life (millions of revolutions)
rating life (at 100–n% reliability) in millions of revolutions
load (N)
load (N)
load (N)
design load (N)
fatigue load limit (N)
applied radial load (N)
thrust load (N)
rotating factor
radial factor
thrust factor
coefficient of expansion (K1)
Mechanical Design Engineering Handbook. https://doi.org/10.1016/B978-0-443-22077-7.00009-0
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199
200 Chapter 6
Δl
ΔT
ηc
κ
ν
ν1
change in length (m)
temperature rise (°C)
contamination factor
viscosity ratio
operating kinematic viscosity of the lubricant (m2/s)
rated kinematic viscosity depending on the bearing mean diameter and rotational speed (m2/s)
6.1 Introduction
The purpose of a bearing is to support a load, typically applied to a shaft, whilst allowing
relative motion between two components of a machine. The selection of bearing type was
introduced in Chapter 5 along with the design of boundary lubricated and hydrodynamically
lubricated journal bearings. In this chapter rolling element bearings, sometimes also known as
rolling contact or ball bearings, are considered with a specific focus on the selection of stock
items from original equipment manufacturers.
The term rolling element bearings or rolling contact bearings encompasses the wide variety of
bearings that use spherical balls or some form of roller between the stationary and moving
elements. A schematic for a deep groove ball bearing is given in Fig. 6.1 showing the principal
components for this type including the inner raceway, balls, the retainer ring used to separate
the rolling elements and retain them in position, and the outer raceway. Some of the principal
types of rolling element bearing are illustrated in Figs. 6.2–6.9. A typical application for a
bearing is to support a rotating shaft resisting a combination of radial and axial (or thrust) loads.
Some bearings are designed to carry only radial or only thrust loads. As can be seen in
Figs. 6.2–6.9 the form of rolling element used varies widely from spherical balls to cylinders,
Fig. 6.1
Schematic for a deep groove ball bearing showing some of the principal features and dimensions.
Rolling element bearings 201
Fig. 6.2
Deep groove ball bearing. Cutaway view presented to reveal the inner raceway, rolling elements,
retainer ring and outer raceway.
Fig. 6.3
Cylindrical roller bearing. Cutaway view presented to reveal the inner raceway, rolling elements,
retainer ring and outer raceway.
and conical sections. Owing to the common use of spherical balls in rolling element bearings,
the class of bearings is sometimes referred to as ball bearings, even though the rolling
element for the specific bearing concerned may not actually be a spherical ball. The terms ball
bearings for bearings with spherical rolling elements and roller bearings for bearings with
conical, cylindrical, needle and barrel rollers are in common use to enable the types of bearings
to be distinguished.
Selection of the type of bearing to be used for a given application can be aided by the
comparison charts, an example of which is given in Table 6.1. The majority of bearing
202 Chapter 6
Fig. 6.4
Needle rolling bearing.
Fig. 6.5
Taper roller bearing. Cutaway view presented to reveal the inner raceway, rolling elements, retainer
ring and outer raceway.
manufacturers such as FAG, INA, NSK, NTN, RBC, SKF and Timken produce comprehensive
online catalogues and associated design and technical guidance. The reader is advised to gain
access to this, typically, readily available information.
The comparative ratings shown in Table 6.1 can be justified for say radial load carrying
capacity; roller bearings are better than ball bearings because of their shape and the area over
which the load is spread. Thrust load capacity varies dramatically with design. The grooves in
the races of the deep groove ball bearing permit the transfer of moderate thrust in combination
with radial load. The angular contact bearing (Fig. 6.8) can be better than the single row
deep groove ball bearing at accommodating combined thrust and radial loads (Figs. 6.1 and 6.2)
Rolling element bearings 203
Fig. 6.6
Spherical roller bearing. Cutaway view presented to reveal the spherical form inner raceway, rolling
elements, retainer ring and outer raceway.
Fig. 6.7
Self-aligning ball bearing. Cutaway view presented to reveal the inner raceway, rolling elements,
retainer ring and outer raceway.
because the races, in the case of the angular contact bearing, are higher on one side
providing a more favourable load path. Cylindrical and needle bearings should not generally
be subjected to any thrust load.
6.2 Bearing life and selection
The theoretical region of contact between a spherical ball and a surface with a greater
radius is a point. In the case of practical materials experiencing a force, there will be some
deformation of the surfaces concerned and instead of point contact, the load on a rolling contact
bearing will be exerted on a very small area, as illustrated in Figs. 6.1 and 6.10. The resulting
204 Chapter 6
Fig. 6.8
Angular contact ball bearing. Cutaway view presented to reveal the inner raceway, rolling elements,
retainer ring and outer raceway.
Fig. 6.9
Thrust ball bearing. Cutaway view presented to reveal the rolling elements, retainer rings and
raceways.
Table 6.1 Merits of different rolling contact bearings.
Bearing type
Radial load capacity
Axial or thrust load
capacity
Misalignment capability
Single row deep groove ball
bearing
Double row deep groove ball
Angular contact
Cylindrical roller
Needle roller
Spherical roller
Tapered roller
Thrust ball bearing
Good
Fair
Fair
Excellent
Good
Excellent
Excellent
Excellent
Excellent
Poor
Good
Excellent
Poor
Poor
Fair/good
Excellent
Excellent
Fair
Poor
Fair
Poor
Excellent
Poor
Fair
Rolling element bearings 205
Fig. 6.10
Contact area for a ball bearing.
contact stresses are very high and can be of the order of 2000MPa. The combination of loading
and over-rolling in a rolling element bearing leads to stresses which eventually cause
significant loss of material, either due to wear or fatigue. Despite very strong steels (e.g. BS 970
534 A99, AISI 52100) bearings tend to have a finite life and will eventually fail due to fatigue,
the weakening of a material due to cyclic loading, and wear. Wear is a key issue in rolling
element bearings and debris arising from wear can lead to rapid degradation of bearing
performance and failure (see, for example, Sayles and Ioannides (1988), and El-Thalji and
Jantunen (2015)).
6.2.1 Simple bearing life equation
For two groups of apparently identical bearings tested under loads P1 and P2, the respective
lives L1 and L2 have been found empirically to be related by the life equation given in Eq. (6.1).
k
L1
P2
¼
(6.1)
L2
P1
206 Chapter 6
Where:
L1 ¼ life at load P1 (number of revolutions).
L2 ¼ life at load P2 (number of revolutions).
P1 ¼ load (N).
P2 ¼ load (N).
The exponent k in Eq. (6.1) is:
k ¼ 3 for ball bearings.
k ¼ 3.33 for cylindrical roller bearings.
The principal dimensions for rolling element bearings, such as the width, B, bore diameter, d,
and outer raceway diameter, D, have been standardised (see for example BS ISO 104:2015) and
bearings can be purchased as stock items from specialist manufacturers and suppliers. The
selection of a bearing from a supplier’s catalogue involves consideration of the bearing load
carrying capacity and the bearing geometry. For a given bearing the load carrying capacity
is given in terms of the basic dynamic load rating and the basic static load rating. Various
commonly used definitions for rolling element bearing life specification are outlined as follows
for basic dynamic load rating, life, fatigue and rated life.
The basic dynamic load rating, C, is the constant radial load which a rolling element
bearing can endure for 1 106 revolutions without evidence of the development of fatigue
in any of the bearing components in a standard test.
The life of a ball bearing, L, is the number of revolutions (or hours at some constant speed),
which the rolling element bearing runs before the development of fatigue in any of the
bearing components.
Fatigue occurs over a large number of cycles of loading. For a bearing this would mean a large
number of revolutions. Fatigue is a statistical phenomenon with considerable spread of the
actual life of a group of bearings of a given design.
The rated life is the standard means of reporting the results of many tests of bearings. It
represents the life that 90% of the bearings would achieve successfully at a rated load. The rated
life is referred to as the L10 life at the rated load. The rated life, L10, of a group of apparently
identical bearings is defined as the number of revolutions (or hours at some constant speed) that
90% of the group of bearings will complete before the first evidence of fatigue develops.
If in Eq. (6.1), P2 ] C and the corresponding life L2 ¼1106, then the life of a bearing L, with
basic dynamic load rating C with a load P is given by:
k
C
L¼
(6.2)
P
Rolling element bearings 207
Where:
L ¼ life (millions of revolutions).
C ¼ basic dynamic load rating (N).
P ¼ load (N).
When selecting a particular bearing from a manufacturer’s catalogue, it is useful to know the
required basic dynamic load rating C for a given load P and life L, which is given by:
ð1=kÞ
L
C¼P
106
(6.3)
Example 6.1
A straight cylindrical roller bearing operates with a load of 7.5kN. The required life is 8760h (24h
a day, 365 days a year) at 1000 rpm. What load rating should be used for selection from the
catalogue?
Solution
Using Eq. (6.3),
L
C¼P
106
1=k
1=3:33
8760 1000 60
¼ 7500
¼ 49:2 103 ¼ 49:2 kN
106
Example 6.2
A catalogue lists the basic dynamic load rating for a ball bearing to be 33,800N for a rated life of
1 million revolutions. Calculate the expected L10 life of the bearing if it were subjected to 15,000N
and determine the life in hours that this corresponds to if the speed of rotation is 2000 rpm.
Comment on the value obtained and its suitability for a machine.
Solution
Ccat ¼ 33,800N, Pd ¼ 15,000N, Lcat ¼106 (L10 life at load C), k¼3 (ball). Using Eq. (6.2), the
basic rating life is given by:
L ¼ 106
33800 3
¼ 11:44 106 revolutions ð¼ L10 life at 15000 NÞ
15000
If the rotational speed is 2000rpm, L¼11.44106/(200060)¼ 95h operation. This is not very
long and illustrates the need to use a bearing with a high basic dynamic load rating.
An outline procedure for bearing selection is shown in Fig. 6.11.
208 Chapter 6
Fig. 6.11
Outline procedure for the selection of a rolling element bearing.
Eqs. (6.1)–(6.3) have been traditionally used to model the life of a bearing. However, the life of
practical rolling element bearings in service depends on a series of factors that include
lubrication, contamination, misalignment, installation and environmental conditions as well as
the quality of manufacture and design. ISO 281:1990/Amd 2:2000/BS ISO 281:2007 provides a
modified life equation to be used as a supplement to the basic rating life. The modified life
equation is presented in Section 6.2.2. The modified life equation can result in predicted lives
that can be an order of magnitude greater than the standard life equation, Eq. (6.1) or (6.3),
depending, of course, on the various parameters for the application concerned.
Rolling element bearings 209
The basic static load rating, Co, is the load the bearing can withstand without any permanent
deformation of any component. If this load is exceeded it is likely the bearing races will be
indented by the rolling elements (called Brinelling). Subsequently, the operation of the
bearing would be noisy, impact loads on the indented area would produce rapid wear and
progressive failure of the bearing could ensue. Unintentional damage to bearings can occur for
machines during transportation. If a rotor is unsecured it can vibrate and although not
rotating the loads are transferred through the small areas of contact between the bearing
elements and raceways. If these loads are above the basic static load rating, Brinelling can take
place. As an example, the drum in a washing machine is often locked in place for transportation
purposes, with wedges to separate the rolling elements from one or both of the raceways.
Loads on bearings often vary with time and may not be entirely radial. An example is the thrust
bearing illustrated in Fig. 6.12 from the Rolls-Royce Trent series of engines (see Fig. 6.13).
This bearing has to take a substantial thrust load as well as a radial load. In addition, and
somewhat unusually for a bearing both inner and outer raceways rotate. This is because
Rolls-Royce plc use a three-spool technology for some of their engines (see Rolls-Royce the Jet
Engine, 2015) in order to operate the turbine and compressor stages at optimum speeds. The
combined effects of radial and thrust loads can be accommodated in the life equation by an
equivalent load.
The equivalent load, P, is defined as the constant radial load which if applied to a bearing
would give the same life as that which the bearing would attain under the actual conditions of
load and rotation. When both radial and thrust loads are exerted on a bearing the equivalent
load is the constant radial load that would produce the same rated life for the bearing as the
combined loading.
Normally, the equivalent load, P, is given by:
P ¼ VXR + YT
Fig. 6.12
Thrust bearing from the Rolls-Royce Trent series of engines.
(6.4)
210 Chapter 6
Fig. 6.13
The Trent 800 engine illustrating three spools, each rotating at a different speed. Figure courtesy of RollsRoyce plc, # Rolls-Royce plc 2020, all rights reserved.
Where:
P ¼ equivalent load (N).
V ¼ 1.2 is recommended if the mounting rotates, V ¼ 1.0 if the shaft rotates.
X ¼ radial factor (given in bearing catalogues, see Table 6.2 for example data).
R ¼ applied radial load (N).
Y ¼ thrust factor (given in bearing catalogues, see Table 6.2 for example data).
T ¼ applied thrust load (N).
Table 6.2 Values for the radial and thrust factors for determining the equivalent load for deep
groove ball single bearings and bearing pairs arranged in tandem.
Normal clearance
C3 clearance
C4 clearance
T/C0
e
X
Y
e
X
Y
e
X
Y
0.025
0.04
0.07
0.13
0.25
0.5
0.22
0.24
0.27
0.31
0.37
0.44
0.56
0.56
0.56
0.56
0.56
0.56
2
1.8
1.6
1.4
1.2
1
0.31
0.33
0.36
0.41
0.46
0.54
0.46
0.46
0.46
0.46
0.46
0.46
1.75
1.62
1.46
1.3
1.14
1
0.4
0.42
0.44
0.48
0.53
0.56
0.44
0.44
0.44
0.44
0.44
0.44
1.42
1.36
1.27
1.16
1.05
1
C3 and C4 indicate increasing clearance between the rollers and casing and are generally used in hotter applications.
Data courtesy of SKF.
Rolling element bearings 211
The equivalent load can be taken as P¼R if the thrust to radial load ratio T/Re and as stated in
Eq. (6.4) if T/R > e, where e is the limiting value of T/R for the applicability of different
calculation factors.
6.2.2 Modified life equation
The basic rating life of a rolling element bearing for a specific application can deviate
significantly from the actual service life. Influencing factors include lubrication,
contamination, misalignment, installation and environmental conditions. Careful attention to
tolerancing and management of these factors in a rolling element bearing can result in
significantly improved performance. To account for the arising variation in bearing life an
adjusted rating life equation can be used, taking the form:
k
C
Lna ¼ a1 a2 a3
(6.5)
P
Where:
Lna ¼ adjusted rating life.
a1 ¼ the life adjustment factor for reliability.
a2 ¼ a materials factor.
a3 ¼ the operating conditions factor.
With improved lubrication, better materials have no significant benefit, and a2 and a3 are often
combined.
k
C
Lna ¼ a1 a23
(6.6)
P
ISO 281:2007 gives provision for a modification to the basic rating life accounting for
lubrication, contamination conditions and the fatigue limit of the material. The standard also
makes provision for a specific manufacturer to recommend how to calculate the life
modification factor. In the case of SKF, for example, the factor aSKF is used, and the equation
for SKF rating life is given by
k
C
Lnm ¼ a1 aSKF
(6.7)
P
Where:
Lnm ¼ rating life (at 100–n% reliability) in millions of revolutions.
a1 ¼ the life adjustment factor for reliability.
aSKF ¼ SKF life modification factor.
212 Chapter 6
Table 6.3 Modified life equation factors.
Reliability %
Failure probability n%
SKF rating life Lnm
a1
90
95
96
97
98
99
10
5
4
3
2
1
L10m
L5m
L4m
L3m
L2m
L1m
1
0.62
0.53
0.44
0.33
0.21
Values of a1 are given in Table 6.3. Values for the life modification factor can be found from
tables provided by the specific manufacturer in catalogues, on-line or using an on-line tool
where the user inputs data for the fatigue load limit ratio, the lubrication condition and the
contamination level. The approach requires calculation of the kinematic viscosity ratio,
Eq. (6.8), of the actual operating kinematic viscosity of the lubricant to the rated kinematic
viscosity depending on the mean diameter and the rotational speed.
κ¼
ν
ν1
(6.8)
Where:
κ ¼ viscosity ratio.
ν ¼ operating kinematic viscosity of the lubricant (m2/s).
ν1 ¼ rated kinematic viscosity depending on the bearing mean diameter and rotational
speed (m2/s).
A guideline for the contamination factor, ηc, as a function of condition and the bearing mean
diameter, dm ¼ 0.5(d+D), is given in Table 6.4. Tables for aSKF are provided as a function of the
viscosity ratio, κ, and the product of the contamination factor, ηc, and the fatigue load limit and load
ratio, Pu/P, i.e. ηcPu/P. The fatigue load limit, Pu, is the load below which fatigue will not occur.
Tables 6.5–6.7 give an overview of the information typically available in bearing
manufacturers’ catalogues for parameters such as principal dimensions, static and dynamic load
Table 6.4 Typical values for the contamination factor, ηc.
Condition
dm < 100 mm
dm ≥100 mm
Extreme cleanliness
High cleanliness
Normal cleanliness
Slight contamination
Typical contamination
Severe contamination
Very severe contamination
1
0.8–0.6
0.6–0.5
0.5–0.3
0.3–0.1
0.1–0
0
1
0.9–0.8
0.8–0.6
0.6–0.4
0.4–0.2
0.1–0
0
Table 6.5 Single row deep groove ball bearings.
Selected deep groove ball bearings
Single row
Reference
d (mm) D (mm) B (mm) C (kN) C0 (kN) Fatigue load limit, Pu (kN) speed (rpm) Limiting speed (rpm) Mass (kg)
Designation
4
5
7
8
9
10
10
15
15
17
17
17
19.05
19.05
20
20
20
20
20
22
604
638/5-2Z
607-Za
608a
609a
6200a
6300a
6202-2Za
6302a
6003a
6203a
6403
RLS 6
RMS 6
61,904
6004a
6204a
6304a
6404
62/22
12
11
19
22
24
30
35
35
42
35
40
62
47.625
50.8
37
42
47
52
72
50
4
5
6
7
7
9
11
11
13
10
12
17
14.287
17.462
9
12
14
15
19
14
0.806
0.637
2.34
3.45
3.9
5.4
8.52
8.06
11.9
6.37
9.95
22.9
12.7
15.9
6.37
9.95
13.5
16.8
30.7
14
0.28
0.255
0.95
1.37
1.66
2.36
3.4
3.75
5.4
3.25
4.75
10.8
6.55
7.8
3.65
5
6.55
7.8
15
7.65
0.012
0.011
0.04
0.057
0.071
0.1
0.143
0.16
0.228
0.137
0.2
0.455
0.28
0.335
0.156
0.212
0.28
0.335
0.64
0.325
120,000
120,000
85,000
75,000
70,000
56,000
50,000
43,000
38,000
45,000
38,000
28,000
30,000
28,000
43,000
38,000
32,000
30,000
24,000
30,000
75,000
60,000
53,000
48,000
43,000
34,000
32,000
22,000
24,000
28,000
24,000
18,000
20,000
19,000
26,000
24,000
20,000
19,000
15,000
19,000
0.002
0.002
0.007
0.012
0.014
0.032
0.053
0.045
0.082
0.039
0.065
0.27
0.11
0.14
0.038
0.069
0.11
0.14
0.4
0.12
Continued
Table 6.5
Single row deep groove ball bearings—cont’d
Reference
d (mm) D (mm) B (mm) C (kN) C0 (kN) Fatigue load limit, Pu (kN) speed (rpm) Limiting speed (rpm) Mass (kg)
Designation
22
22.225
22.225
25
25
25
25
25.4
25.4
28
28
30
30
30
30
30
35
35
35
35
40
40
40
40
40
45
45
45
45
50
50
50
50
63/22
RLS 7
RMS 7
61,805
16,005a
6205-2RSLa
6405
RLS 8
RMS 8
62/28
63/28
61,806
16,006a
6206a
6306-ZNR
6406
61,807
61,907
6007a
6207a
61,808
6008a
6208a
6308-Za
6408
61,909
6009a
6209a
6409
61,910
6010-Za
6210a
6310a
56
50.8
57.15
37
47
52
80
57.15
63.5
58
68
42
55
62
72
90
47
55
62
72
52
68
80
90
110
68
75
85
120
72
80
90
110
16
14.287
17.462
7
8
15
21
15.875
19.05
16
18
7
9
16
19
23
7
10
14
17
7
15
18
23
27
12
16
19
29
12
16
20
27
18.6
14
18.6
4.36
8.06
14.8
35.8
17.8
22.5
16.8
25.1
4.49
11.9
20.3
29.6
43.6
4.75
9.56
16.8
27
4.94
17.8
32.5
42.3
63.7
14
22.1
35.1
76.1
14.6
22.9
37.1
65
9.3
7.65
9.3
2.6
4.75
7.8
19.3
9.65
11.6
9.5
13.7
2.9
7.35
11.2
16
23.6
3.2
6.8
10.2
15.3
3.45
11.6
19
24
36.5
10.8
14.6
21.6
45
11.8
16
23.2
38
0.39
0.325
0.39
0.125
0.212
0.335
0.815
0.405
0.49
0.405
0.585
0.146
0.31
0.475
0.67
1
0.166
0.29
0.44
0.655
0.186
0.49
0.8
1.02
1.53
0.465
0.64
0.915
1.9
0.5
0.71
0.98
1.6
28,000
26,000
26,000
38,000
32,000
28,000
20,000
24,000
22,000
26,000
22,000
32,000
28,000
24,000
20,000
18,000
28,000
26,000
24,000
20,000
26,000
22,000
18,000
17,000
14,000
20,000
20,000
17,000
13,000
19,000
18,000
15,000
13,000
18,000
19,000
18,000
24,000
20,000
14,000
13,000
17,000
16,000
16,000
14,000
20,000
17,000
15,000
13,000
11,000
18,000
16,000
15,000
13,000
16,000
14,000
11,000
11,000
9000
13,000
12,000
11,000
8500
12,000
11,000
10,000
8500
0.18
0.12
0.18
0.022
0.06
0.13
0.53
0.17
0.23
0.18
0.29
0.027
0.085
0.2
0.35
0.74
0.03
0.08
0.16
0.29
0.034
0.19
0.37
0.63
1.25
0.14
0.25
0.41
1.55
0.14
0.26
0.46
1.05
50
55
55
55
55
60
60
60
60
60
65
65
65
65
70
70
70
70
75
75
75
75
80
80
80
80
80
85
85
85
90
90
90
90
100
100
100
130
72
90
100
120
78
85
95
95
110
85
100
100
120
90
110
125
150
110
115
130
160
100
125
140
170
200
130
150
180
140
160
190
225
125
140
150
31
9
18
21
29
10
13
11
18
22
10
18
11
23
10
20
24
35
12
20
25
37
10
14
26
39
48
22
28
41
16
30
43
54
13
20
24
87.1
9.04
29.6
46.2
74.1
11.9
16.5
20.8
30.7
55.3
12.4
31.9
22.5
58.5
12.4
39.7
63.7
111
28.6
41.6
68.9
119
13
35.1
72.8
130
163
52
87.1
140
43.6
101
151
186
19.9
42.3
63.7
52
8.8
21.2
29
45
11.4
14.3
15
23.2
36
12.7
25
16.6
40.5
13.2
31
45
68
27
33.5
49
76.5
15
31.5
55
86.5
125
43
64
96.5
39
73.5
108
150
24
41
54
2.2
0.375
0.9
1.25
1.9
0.49
0.6
0.735
0.98
1.53
0.54
1.06
0.83
1.73
0.56
1.32
1.9
2.75
1.14
1.43
2.04
3
0.64
1.32
2.2
3.25
4.5
1.76
2.5
3.55
1.56
2.8
3.8
5
0.95
1.63
2.04
12,000
19,000
16,000
14,000
12,000
17,000
16,000
15,000
15,000
13,000
16,000
14,000
14,000
12,000
15,000
13,000
11,000
9500
13,000
12,000
10,000
9000
13,000
11,000
9500
8500
7500
11,000
9000
8000
10,000
8500
7500
6700
10,000
9500
9500
7500
12,000
10,000
9000
8000
11,000
10,000
9500
9500
8000
10,000
9000
9000
7500
9000
8000
7000
6300
8000
7500
6700
5600
6300
7000
6000
5300
4800
6700
5600
5000
6300
5300
4800
4300
6300
6000
5600
1.9
0.083
0.39
0.61
1.35
0.11
0.2
0.28
0.42
0.78
0.13
0.44
0.3
0.99
0.14
0.6
1.05
2.5
0.38
0.64
1.2
3
0.15
0.6
1.4
3.6
8
0.89
1.8
4.25
0.85
2.15
4.9
11.5
0.31
0.83
1.25
6410
61,811
6011a
6211a
6311
61,812
61,912
16,012a
6012a
6212a
61,813
6013a
16,013a
6213a
61,814
6014a
6214a
6314a
16,115
6015a
6215a
6315a
61,816-2RZ
16,016a
6216a
6316a
6416
6017a
6217a
6317a
16,018a
6218a
6318a
6418
61,820
61,920
6020a
Continued
Table 6.5
Single row deep groove ball bearings—cont’d
Reference
d (mm) D (mm) B (mm) C (kN) C0 (kN) Fatigue load limit, Pu (kN) speed (rpm) Limiting speed (rpm) Mass (kg)
100
105
105
105
105
110
110
110
110
120
120
120
120
130
130
130
130
140
140
140
150
150
150
150
160
160
160
160
170
170
170
180
180
180
145
160
190
225
150
170
200
240
150
165
180
215
180
200
230
280
175
190
210
190
210
225
320
200
240
290
340
215
260
360
280
320
34
20
18
36
49
20
19
38
50
16
22
28
40
24
22
40
58
18
24
22
20
28
24
65
20
25
48
68
22
28
72
46
52
127
44.2
54
140
182
43.6
60.2
151
203
29.1
55.3
88.4
146
65
83.2
156
229
39
66.3
80.6
48.8
88.4
92.2
276
49.4
99.5
186
276
61.8
119
312
190
229
93
44
51
104
153
45
57
118
180
28
57
80
118
67
81.5
132
216
46.5
72
86.5
61
93
98
285
64
108
186
285
78
129
340
200
240
3.35
1.7
1.86
3.65
5.1
1.66
2.04
4
5.7
1.29
2.04
2.75
3.9
2.28
2.7
4.15
6.3
1.66
2.36
2.8
1.96
2.9
3.05
7.8
2
3.25
5.3
7.65
2.4
3.75
8.8
5.6
6.4
7500
9500
8500
7000
6300
9000
8000
6700
6000
8500
8000
7500
6300
7500
7000
5600
5000
7500
7000
6700
6700
6300
6000
4300
6300
5600
4500
4000
6000
5300
3800
4800
4000
4800
5600
5300
4500
4000
5600
5000
4300
3800
5300
5000
4800
4000
4500
4300
3600
4500
4500
5600
4000
4300
5300
3800
4000
4000
3600
3000
3800
3600
3200
3400
4000
3600
3.15
0.87
1.2
3.7
8.25
0.9
1.45
4.35
9.55
0.65
1.2
2.05
5.15
1.85
2.35
5.8
17.5
0.99
1.7
2.5
1.4
3.05
3.15
26
1.45
3.7
14.5
29
1.9
5
34.5
10.5
18.5
Designation
6220a
61,921
16,021a
6221a
6321
61,922
16,022a
6222a
6322
61,824
61,924
6024a
6224
61,926
16,026a
6226
6326 M
61,828
61,928 MA
16,028
61,830
61,930 MA
16,030
6330 M
61,832
16,032
6232
6332 M
61,834
16,034
6334 M
6036 M
6236 M
180
190
190
200
200
220
240
260
280
300
300
320
330
340
350
360
380
400
420
440
460
480
500
530
540
560
600
650
670
710
750
800
850
900
950
1000
1060
380
290
340
250
360
340
360
400
420
460
460
480
460
480
500
540
560
600
620
650
680
700
720
780
625
750
800
920
980
1000
1090
1150
1220
1280
1360
1420
1500
75
31
55
24
58
37
56
65
65
74
50
50
56
60
70
57
82
90
90
94
100
100
100
112
40
85
90
118
136
140
150
155
165
170
180
185
195
351
148
255
76.1
270
174
255
291
302
358
286
281
281
291
319
351
462
520
507
553
582
618
605
650
225
494
585
780
904
832
995
1010
1040
1140
1170
1350
1350
405
166
280
102
310
204
315
375
405
500
405
405
425
430
475
550
750
865
880
965
1060
1140
1140
1270
425
980
1220
1730
2040
1900
2360
2550
2700
3100
3250
3900
3900
10.4
4.55
7.35
2.9
7.8
5.2
7.8
8.8
9.3
10.8
8.8
8.65
9
9
9.8
11
14.6
16.3
16.3
17.6
19
20
19.6
20.8
7.5
16.3
19.6
26
30
27.5
33.5
34.5
35.5
39
40.5
47.5
46.5
3600
4800
3800
5000
3600
4000
3600
3200
3000
2800
2800
2600
2600
2600
2400
1800
2200
2000
2000
1900
1800
1700
1600
1500
1700
1500
1400
1200
1100
1100
950
900
800
750
700
630
600
3200
3000
3400
3200
3200
2400
3000
2800
2600
2400
2400
2200
2200
2200
2000
1400
1800
1700
1600
1500
1500
1400
1300
1200
1400
1200
1100
1000
900
900
800
750
670
630
560
530
500
42.5
7.9
23
2.7
28
11.5
19.5
29.5
31
44
32
34
30
36
46
49
67.5
87.5
91.5
105
120
125
135
185
14
105
125
250
345
335
485
535
630
720
860
930
1080
6336 M
16,038
6238 M
61,840
6240 M
16,044
6048 M
6052 M
6056 M
6060 M
16,060 MA
16,064 MA
306,728
306,890
306,674
16,072 MA
6076 M
6080 M
6084 M
6088 M
6092 MB
6096 MB
60/500 N1MAS
60/530 N1MAS
BB1B 362,692
619/560 MA
619/600 MA
306,708 D
60/670 N1MAS
306,704C
60/750 MA
60/800 N1MAS
306,493 AA
60/900 MB
60/950 MB
60/1000 MB
60/1060 MB
Continued
Table 6.5
Single row deep groove ball bearings—cont’d
Reference
d (mm) D (mm) B (mm) C (kN) C0 (kN) Fatigue load limit, Pu (kN) speed (rpm) Limiting speed (rpm) Mass (kg)
Designation
1120
1180
1250
1320
1400
1500
1600
1700
2000
2390
60/1120 MB
619/1180 MB
618/1250 MB
609/1320 MB
619/1400 MB
619/1500 MB
619/1600 MB
619/1700 MB
BB1B 363,270
BB1–8001
1580
1540
1500
1720
1820
1950
2060
2180
2200
2690
200
160
112
128
185
195
200
212
75
120
1460
1140
852
1210
1590
1720
1860
1990
936
1300
4400
3600
2750
4050
5500
6100
6950
7650
4500
6200
a
SKF Explorer bearing.
NB this table presents a selection only of the bearings available.
Data courtesy of SKF.
50
41.5
31.5
44
57
62
69.5
73.5
41.5
52
530
220
530
450
400
380
300
280
220
120
450
280
430
360
340
320
260
220
190
100
1250
775
385
830
1250
1500
1650
1950
290
975
Table 6.6 Single row cylindrical roller bearings.
Selected cylindrical roller bearings
Single row
d
(mm)
D
(mm)
B
(mm) C (kN) C0 (kN)
15
15
15
17
17
17
20
20
20
20
25
25
25
25
30
30
35
35
35
40
40
47
47
47
52
52
47
52
62
62
55
62
11
11
11
12
16
14
18
14
15
21
12
15
24
24
13
16
12.5
12.5
12.5
17.2
23.8
24.6
29.7
25.1
35.5
47.5
14.2
28.6
64
64
17.9
44
10.2
10.2
10.2
14.3
21.6
20.4
27.5
22
26
38
13.2
27
55
55
17.3
36.5
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
1.22
1.22
1.22
1.73
2.65
2.55
3.45
2.75
3.25
4.8
1.4
3.35
6.95
6.95
1.86
4.55
22,000
22,000
22,000
19,000
19,000
15,000
16,000
16,000
15,000
15,000
18,000
14,000
12,000
12,000
15,000
13,000
26,000
34,000
26,000
22,000
22,000
20,000
19,000
19,000
18,000
18,000
18,000
16,000
15,000
15,000
15,000
22,000
0.047
0.047
0.049
0.07
0.095
0.12
0.14
0.11
0.15
0.21
0.084
0.13
0.42
0.39
0.12
0.22
NU 202 ECP
NU 202 ECPHA
NJ 202 ECP
NJ 203 ECP
NJ 2203 ECP
N 303 ECP
NJ 2204 ECP
NJ 204 ECP
N 304 ECPa
NU 2304 ECPa
NU 1005
N 205 ECP
NJ 2305 ECMLa
NJ 2305 ECPa
NU 1006
NUP 206 ECMLa
Continued
Table 6.6
d
(mm)
D
(mm)
B
(mm) C (kN) C0 (kN)
30
30
35
35
35
35
40
40
40
40
45
45
45
45
50
50
50
50
55
55
55
55
60
60
60
60
65
65
65
65
72
72
62
72
80
100
68
80
90
110
75
85
100
120
80
90
110
130
90
100
120
120
95
110
130
150
100
120
140
160
19
27
14
17
31
25
15
23
33
27
16
19
36
29
16
23
27
31
18
25
43
29
18
28
46
35
26
23
48
37
58.5
83
35.8
56
106
76.5
25.1
81.5
129
96.8
44.6
69.5
160
106
30.8
90
127
130
57.2
96.5
232
156
37.4
146
260
168
105
122
285
183
48
75
38
48
98
69.5
26
75
120
90
52
64
153
102
34.5
88
112
127
69.5
95
232
143
44
153
265
173
146
118
290
190
Single row cylindrical roller bearings—cont’d
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
6.2
9.65
4.55
6.1
12.7
9
3
9.65
15.3
11.8
6.3
8.15
20
13.4
4
11.4
15
16.6
6.3
12.2
15.3
18.6
5.3
20
34.5
22
18.3
15.6
38
24
11,000
11,000
12,000
11,000
9500
8000
12,000
9500
8000
7000
9500
9000
7500
6700
10,000
8500
6700
6000
8000
7500
6000
6000
8000
6700
5600
5000
6300
6300
5300
4800
12,000
19,000
20,000
18,000
11,000
9500
18,000
11,000
9500
11,000
11,000
9500
13,000
7500
15,000
9000
8000
7000
8500
8000
11,000
11,000
13,000
7500
10,000
6000
7500
10,000
9500
5600
0.44
0.58
0.16
0.36
0.75
1.05
0.22
0.54
0.96
1.45
0.26
0.48
1.45
1.65
0.31
0.59
1.15
2
0.4
0.68
2.48
1.58
0.48
1.1
3.2
3.1
0.7
1.1
3.6
3.65
NU 306 ECMa
NJ 2306 ECMLa
NU 1007 ECMP
NUP 207 ECMLa
NUP 2307 ECPa
N 407
NU 1008 ML
NU 2208 ECPa
NJ 2308 ECJa
NJ 408 MA
NU 1009 ECP
NU 209 ECJa
NJ 2309 ECMLa
NU 409
NU 1010 ML
NUP 2210 ECNPa
NJ 310 ECPa
NU 410
NU 1011 ECP
NUB 211 ECJ
NJ 2311 ECMLa
NJ 311 ECMLa
NU 1012 ML
NU 2212 ECMa
NJ 2312 ECMLa
NJ 412
NJ 3013 ECP
NUP 213 ECMLa
NJ 2313 ECMLa
NJ 413
70
70
70
70
75
75
75
75
80
80
80
80
85
85
85
85
90
90
90
90
95
95
95
95
100
100
100
100
100
105
105
105
105
110
110
125
125
150
115
130
160
190
125
140
170
200
130
150
180
180
140
160
190
225
170
170
200
200
150
180
180
215
250
160
190
225
260
170
20
31
24
35
20
31
55
45
22
33
39
48
22
36
41
60
24
40
64
54
32
43
45
67
24
46
34
47
58
26
36
49
60
28
56.1
180
137
236
58.3
150
380
264
99
212
300
303
68.2
190
340
455
80.9
280
500
380
255
325
390
530
85.8
285
285
450
429
101
300
500
501
128
67.2
193
137
228
71
156
400
280
127
245
290
320
86.5
200
335
490
104
315
540
415
265
375
390
585
114
305
305
440
475
137
315
500
570
166
8
25.5
18
29
8.5
20.4
50
34
16.3
31
36
39
10.5
24.5
41.5
60
12.7
39
65.5
48
32.5
45.5
46.5
69.5
13.7
36.5
36.5
51
53
16
36.5
57
64
19.3
7000
6000
6000
4800
6700
5600
4500
4000
5600
5300
4300
3800
6000
4800
4000
4000
5600
4500
3800
3400
4300
4300
3600
3600
5000
4000
4000
3200
3000
4800
3800
3200
2800
4500
11,000
10,000
6300
5600
10,000
6000
5300
4800
9500
5600
7500
4500
6000
5300
4800
4800
8500
5000
6700
4000
4800
4800
4300
4300
5000
4500
4500
6000
3600
4800
6300
5600
3400
4500
0.8
1.7
1.15
2.85
0.74
1.35
5.1
6.9
1.1
2.1
4.7
7.45
1.05
2.05
4.9
7
1.35
3.15
8.8
10.5
2.85
3.85
6.25
9.75
1.45
3.75
3.45
9
14
1.85
4
8.9
19
2.3
NU 1014 ML
NJ 2214 ECMLa
NU 214 ECPa
NUP 314 ECMa
NU 1015 ML
NUB 215 ECJ
NUP 2315 ECPa
NJ 415
NJ 1016 ECML
NUP 2216 ECJa
NJ 316 ECMLa
NJ 416
NU 1017 M
NUB 217 ECJ
NUP 317 ECPa
NUP 2317 ECPa
NU 1018 ML
NU 2218 ECPa
NJ 2318 ECMLa
NU 418
NU 219 ECJa
NU 2219 ECMa
NUP 319 ECPa
NUP 2319 ECPa
NU 1020 M
NUB 220 ECJ
NU 220 ECJa
NJ 320 ECMLa
NU 420
NU 1021 M
NUP 221 ECMLa
NU 321 ECMLa
NU 421 M
NU 1022 M
Continued
Table 6.6
d
(mm)
D
(mm)
B
(mm) C (kN) C0 (kN)
110
110
110
120
120
120
120
127
130
130
130
130
140
140
140
140
150
150
150
150
160
160
160
160
170
170
170
180
180
200
240
280
180
215
260
260
254
200
230
230
280
210
250
300
300
225
270
270
320
240
290
340
340
260
310
360
320
380
53
50
65
28
58
55
86
50.8
33
40
64
58
33
42
62
102
35
45
73
65
48
80
114
68
54
86
72
86
75
335
530
532
134
520
610
915
484
165
415
610
720
179
450
780
1200
198
510
735
900
418
930
1250
1000
473
1060
952
1100
1020
365
540
585
183
630
620
1040
585
224
455
735
750
255
510
830
1430
290
600
930
965
670
1200
1730
1080
735
1430
1180
1430
1290
Single row cylindrical roller bearings—cont’d
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
42.5
61
64
20.8
72
69.5
116
65.5
25
51
83
81.5
28
57
88
150
31.5
64
100
100
72
129
176
112
41.5
140
116
146
125
3600
3000
2600
4000
3400
2800
2800
2800
3800
3200
3200
2400
3600
2800
2400
2400
3200
2600
2600
2200
2600
2400
2000
2000
2400
2400
1700
2200
1600
4000
3400
3200
6300
3600
5000
3200
3200
3800
5300
5300
4500
5300
3200
4300
3600
5000
4500
2800
3400
4000
3400
3200
3200
3600
3200
2200
2400
2200
5.2
11.2
20
2.5
9
15.1
24
12
3.8
7
12.2
19.4
4.05
8.6
23
37.5
4.85
11
18.5
27.7
7.9
25
53.5
32.5
11
30
38.5
31.5
45
NUB 222 ECJ
NUP 322 ECPa
NU 422
NJ 1024 ML
NUP 2224 ECJa
NJ 324 ECMLa
NU 2324 ECMa
CRM 40 AMB
NJ 1026 M
NUP 226 ECMLa
NUP 2226 ECMLa
NJ 326 ECMLa
NU 1028 ML
NU 228 ECJa
NJ 328 ECMLa
NUP 2328 ECMAa
NU 1030 ML
NUP 230 ECMLa
NU 2230 ECMa
NJ 330 ECMa
NU 2032 ECMA
NUP 2232 ECMAa
NJ 2332 ECMA
NUP 332 ECMAa
NU 2034 ECMA
NU 2234 ECMAa
N 334 ECM
NU 2236 ECMa
NU 336 ECM
180
190
190
190
190
200
200
200
200
220
220
220
220
240
240
240
240
260
260
260
260
280
280
280
280
300
300
300
300
320
320
320
320
440
290
340
400
400
250
310
360
420
300
340
400
460
300
360
440
500
400
440
480
540
420
460
500
580
380
460
540
620
440
480
540
580
95
46
92
132
78
30
51
128
80
48
56
108
145
28
56
120
155
104
144
80
102
82
146
80
175
48
95
140
185
56
95
176
150
1250
347
1220
1830
1140
183
380
1540
1230
457
495
1570
2380
201
523
1450
2600
1420
2090
1170
1940
1230
2290
1140
2700
473
1510
2090
4020
693
1450
3140
3190
1600
500
1600
2550
1500
345
570
2450
1630
830
735
2280
3450
365
800
2360
3650
2320
3450
1700
2700
2160
3900
1700
4300
980
2750
3450
5850
1200
265
5400
5000
150
53
160
236
143
32.5
58.5
236
150
83
73.5
212
310
32
78
224
320
232
310
156
236
204
335
153
365
88
255
300
480
110
245
450
415
1600
2600
2000
1500
1500
2800
2400
1600
1400
2400
2200
1600
1300
2400
2000
1500
1200
1500
1300
1400
1100
1400
1200
1400
1000
1700
1300
1200
950
1500
1200
1000
1000
2400
3800
3000
2600
2000
3600
2400
2400
2400
3600
3200
2400
2200
3600
2600
2200
2000
2400
2200
2000
1800
2200
2000
1900
1700
1700
2000
1800
1600
2000
1900
1700
1600
80
11
39
82.5
50
3.55
14.5
59
57.5
10
19
62.5
120
4.5
20
85
155
49.5
98
72
125
40
105
71.5
230
14
59.5
145
270
27
62.5
175
180
NUP 436 MA
NJ 1038 ML
NU 2238 ECMa
NU 2338 ECMA
NU 338 ECM
NJ 2840 ECMA
NU 1040 M
NU 3240 ECM
NU 340 ECMA
NU 2944 M2P
NJ 1044 MP
NU 2244 ECMA
NU 2344 ECMA
NUZ 1848 ECMA
NU 1048 MA
NJ 2248 MA
NU 2348 ECMA
NU 3052 ECMA
NU 3152 ECMA
NUP 252 MA
NU 352 ECMA
NU 2056 ECMA
NU 3156 EMA/HB1
NU 256 MA
NU 2356 MA
NU 2860 ECM
NU 2060 ECMA
NU 2260 MA
NU 2360 ECMA
NU 1964 ECMA
NU 2064 ECMA
NU 3164 ECMA
NU 2264 ECMA
Continued
Table 6.6
d
(mm)
D
(mm)
B
(mm) C (kN) C0 (kN)
340
340
340
340
340
340
350
360
360
360
360
360
380
380
380
400
400
400
400
420
420
420
420
440
440
440
440
460
460
460
420
460
460
520
580
620
480
540
540
600
650
750
480
560
680
500
540
600
600
520
560
620
700
540
600
650
720
580
680
760
35
72
56
82
190
165
85
106
82
192
170
224
40
135
175
46
65
118
148
75
65
90
224
60
118
122
226
56
100
240
212
809
682
1080
3190
2640
1060
1940
1100
3410
2920
5010
270
2380
3960
572
952
2200
2810
935
968
1420
4950
809
1980
2550
5120
825
1650
5280
400
1660
1200
1760
5700
4500
2160
3600
1830
5700
4900
8150
520
4750
6400
1180
1730
4750
5500
2240
1800
2450
9000
1900
4250
4900
9650
1700
2850
9650
Single row cylindrical roller bearings—cont’d
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
33.5
146
108
156
475
365
196
320
163
415
400
630
37.5
415
510
100
153
380
440
196
156
212
695
153
355
390
735
140
224
735
1500
1400
1400
1300
950
1000
1200
1100
1300
900
950
850
1300
1000
850
1300
1200
950
950
1100
1100
1100
750
1100
900
8500
700
1100
950
670
2000
1400
1900
1700
1600
1500
1300
1600
1600
1500
1400
1300
1300
1800
1300
1900
1600
1400
1400
1600
1500
1400
1300
1500
1100
1300
1200
1400
1200
1100
9.6
36
27.5
68
210
220
48
88.5
67.5
225
250
510
15.5
115
275
21.8
41
120
175
33
48
96
380
34
105
145
395
37
115
455
316,197
NU 2968 M
NU 1968 ECMA
NJ 1068 MA
NU 3168 ECMA
NU 2268 MA
612,129 A
NU 2072 ECMA
NU 1072 MA
NU 3172 ECMA
NU 2272 MA
NU 2372 ECMA
316,010 A
NU 3076 ECMP
NU 2276 ECMA
NJ 1880 MP
NU 1980 ECMA
NU 2080 ECMA
NU 3080 MA6
NJ 3884 MA
NJ 1984 ECMA
NU 1084 MA
NU 3184 ECMA/HB1
NU 2888 ECMA
NUP 3988 ECM
NU 2088 ECMA
NU 3188 ECMA/HB1
N 1892 M2P/HB3
NU 1092 MA
NU 3192 ECMA/HB1
460
480
480
480
480
500
500
500
500
500
530
530
530
530
560
560
560
560
600
600
600
600
630
630
630
640
670
670
670
710
710
710
720
830
600
600
700
790
620
670
720
830
920
650
710
780
870
680
750
820
1030
730
870
870
870
780
850
920
790
900
980
980
870
1030
1030
880
212
56
72
100
248
72
78
128
264
185
45
106
145
272
45
85
115
206
52
118
200
155
88
100
170
56
103
136
230
95
140
185
62
5120
765
1100
1680
5940
1170
1210
2920
6440
5280
418
2380
3740
7480
429
1650
2330
7210
468
2750
5390
4180
1570
2240
4730
605
2330
3740
6600
1940
4680
5940
704
8650
1630
2450
3000
10,800
2700
2360
5850
12,000
8500
900
5000
7350
14,600
950
3250
4250
11,200
1020
5100
11,000
8000
3900
4400
9500
1290
4750
6800
14,000
5000
8500
12,000
1560
655
120
200
232
800
204
193
430
880
620
62
415
550
1040
62
260
310
780
65.5
365
780
570
305
315
670
83
325
465
950
365
570
815
91.5
700
1000
1000
900
630
950
900
750
600
670
2200
850
670
560
2000
800
750
560
1800
700
600
600
750
700
560
1700
630
600
500
630
560
480
1400
1100
1300
1300
1200
1100
1300
1200
1100
1000
950
3400
1100
1000
950
3200
1000
1000
800
2400
900
900
900
950
900
850
2200
850
800
800
850
750
700
1900
530
39
47.5
130
500
50
79
180
595
585
30
120
255
660
32
110
210
805
41
245
415
325
100
165
400
56
195
350
600
130
415
540
74.5
NU 2292 MA
NU 1896 MA
NJ 2896 ECMA
NU 1096 MA
NU 3196 ECMA/HB1
NU 28/500 ECMA
NU 19/500 MA
NU 20/500 ECMA
NU 31/500 ECMA/HB1
NU 12/500 MA
315,835 A
NU 29/530 ECMA
NU 20/530 ECMA
NU 31/530 ECMA/HB1
BC1B 320,938/HB3
NU 19/560 ECMA
NU 10/560 MA
NU 12/560 MA
315,836
NU 10/600 MA
NU 30/600 ECMA/HA1
NU 20/600 ECMA
N 28/630 MB
NU 19/630 ECMA
NU 20/630 ECMA
315,837
NU 19/670 ECMA
NU 10/670 ECMA
NU 30/670 MA/342771
N 28/710 ECMB
NU 10/710 ECN2MA
NU 20/710 ECMA
315,799
Continued
Table 6.6
d
(mm)
D
(mm)
B
(mm) C (kN) C0 (kN)
750
750
750
800
800
800
820
820
850
850
850
900
900
900
950
950
1000
1000
1000
1030
1060
1120
1180
1250
1320
1400
1500
1700
1000
1090
1090
980
1150
1150
990
990
1030
1120
1120
1090
1090
1180
1150
1250
1220
1220
1320
1250
1400
1360
1540
1500
1720
1700
1820
2060
112
150
195
82
200
155
72
72
106
118
155
85
112
122
90
175
100
128
185
100
250
104
272
106
300
175
140
160
2700
4730
7040
1720
7040
5500
858
858
2120
3190
4680
1120
2700
4130
1340
5830
2640
3690
7040
1510
9130
1650
11,200
1720
13,200
6600
3300
7210
5600
8800
14,600
4150
14,600
10,600
1960
1960
6000
6950
11,200
2550
7200
8800
3100
14,000
6550
10,000
17,300
3450
24,000
3800
29,000
4150
34,000
18,300
8000
19,300
Single row cylindrical roller bearings—cont’d
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
365
585
980
280
950
695
112
112
405
440
720
156
490
560
190
880
400
620
1080
216
1460
224
1730
240
1960
1040
440
1040
560
430
430
530
400
480
1200
1200
500
480
480
1100
450
430
1000
400
400
400
360
320
260
220
200
220
220
220
200
160
700
670
670
700
630
630
1600
1600
670
600
600
1500
600
560
1300
530
530
530
480
380
320
280
260
280
320
280
260
200
255
490
635
145
715
560
100
100
190
330
430
145
235
380
170
745
265
350
700
225
1070
285
1400
330
1900
860
665
1150
319,166 A
NU 10/750 ECN2MA
NU 20/750 ECMA
NJ 18/800 ECMA
NU 20/800 ECMA
NU 10/800 ECMA/HB1
315,800 B
315,800
NU 28/850 MA
NU 19/850 ECMA/HA1
N 29/850 ECMB6
319,161
NU 28/900 MA/343017
NU 19/900 ECMA
315,869 A
NU 29/950 ECMA
NU 18/1000 MA/HB1
NF 28/1000 ECMP/HA1
NU 29/1000 ECFR
BC1B 319,579
NU 39/1060 ECKMA/HA1
316,201
N 39/1180 MB
315,913
N 39/1320 MB
N 28/1400 ECMP
319,301
NU 18/1700 ECMA/HB1
a
SKF Explorer bearing.
NB this table presents a selection only of the bearings available.
Data courtesy of SKF.
Table 6.7 Single row angular contact ball bearings.
Selected angular contact ball bearings
Single row
d
(mm)
D
(mm)
B
(mm)
C
(kN)
C0
(kN)
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
10
12
12
12
12
15
15
15
15
17
17
17
17
20
20
20
20
25
25
30
32
32
32
37
35
35
35
42
40
40
47
47
47
47
52
52
52
62
9
10
10
10
12
11
11
11
13
12
12
14
14
14
14
15
15
15
17
7.02
7.61
7.61
7.61
10.6
9.5
9.5
8.84
13
11
10.4
15.9
15.9
13.3
14.3
19
17.4
15.6
26.5
3.35
3.8
3.8
3.8
5
5.1
5.1
4.8
6.7
5.85
5.5
8.3
8.3
7.65
8.15
10
9.5
10
15.3
0.14
0.16
0.16
0.16
0.208
0.216
0.216
0.204
0.28
0.25
0.236
0.355
0.355
0.325
0.345
0.425
0.4
0.43
0.655
30,000
26,000
26,000
26,000
24,000
26,000
26,000
24,000
20,000
22,000
20,000
19,000
19,000
18,000
19,000
18,000
16,000
17,000
15,000
30,000
26,000
26,000
26,000
24,000
26,000
26,000
24,000
20,000
22,000
20,000
19,000
19,000
19,000
19,000
18,000
16,000
17,000
15,000
0.03
0.036
0.036
0.036
0.063
0.045
0.045
0.045
0.081
0.07
0.064
0.11
0.11
0.11
0.11
0.15
0.14
0.14
0.24
7200 BEP
7201 BECBP
7201 BEGAP
7201 BEP
7301 BEP
7202 BECBPa
7202 BEGAPa
7202 BEP
7302 BEP
7203 BECBMa
7203 BEP
7303 BEGAP
7303 BEP
7204 BECBM
7204 BECBPa
7304 BECBMa
7304 BEP
7205 BECBMa
7305 BECBMa
Continued
Table 6.7
Single row angular contact ball bearings—cont’d
d
(mm)
D
(mm)
B
(mm)
C
(kN)
C0
(kN)
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
25
25
30
30
30
30
35
35
35
35
40
40
40
40
45
45
45
45
47.625
50
50
50
50
50.8
55
55
55
55
60
60
60
60
62
80
62
72
72
90
72
80
80
100
80
80
90
110
85
85
100
120
114.3
90
90
110
130
114.3
100
100
120
140
110
110
130
150
17
21
16
19
19
23
17
21
21
25
18
18
23
27
19
19
25
29
26.988
20
20
27
31
26.988
21
21
29
33
22
22
31
35
24.2
39.7
24
35.5
32.5
47.5
31
41.5
39
60.5
36.4
34.5
50
70.2
37.7
38
61
85.2
83.2
39
40
74.1
95.6
83.2
48.8
49
85.2
111
57.2
61
104
119
14
23.6
15.6
21.2
19.3
29
20.8
26.5
24.5
38
26
24
32.5
45
28
28.5
40.5
55
58.5
30.5
31
51
64
58.5
38
40
60
76.5
45.5
50
76.5
86.5
0.6
1
0.655
0.9
0.815
1.22
0.88
1.14
1.04
1.6
1.1
1.02
1.37
1.9
1.2
1.22
1.73
2.36
2.28
1.29
1.32
2.2
2.7
2.28
1.63
1.66
2.55
3.25
1.93
2.12
3.2
3.55
14,000
11,000
14,000
13,000
12,000
10,000
12,000
11,000
10,000
8500
10,000
10,000
10,000
8000
9000
10,000
9000
7000
8000
8500
9000
7500
6300
8000
7500
8000
6700
6000
7000
7500
6700
5600
14,000
11,000
14,000
13,000
12,000
10,000
12,000
11,000
10,000
9000
10,000
10,000
10,000
8000
9000
10,000
9000
7500
8000
8500
9000
7500
6700
8000
7500
8000
6700
6300
7000
7500
6700
5600
0.23
0.61
0.19
0.37
0.33
0.85
0.3
0.49
0.45
1.1
0.38
0.39
0.61
1.4
0.43
0.44
0.82
1.8
1.25
0.47
0.51
1.13
2.25
1.2
0.62
0.66
1.48
2.75
0.83
0.85
1.71
3.3
7305 BEP
7405 BCBM
7206 BECAPa
7306 BECBMa
7306 BEP
7406 BM
7207 BECBMa
7307 BECBMa
7307 BEP
7407 BCBM
7208 BECBJ
7208 BEM
7308 BECAPa
7408 BCBM
7209 BECBJ
7209 BECBMa
7309 BECAPa
7409 BCBM
AMS 15 ABP
7210 BECBJ
7210 BECBMa
7310 BECBJ
7410 BM
AMS 16 ABP
7211 BECBJ
7211 BECBMa
7311 BECBJ
7411 BCBM
7212 BECBJ
7212 BECBMa
7312 BECAPa
7412 BCBM
65
65
65
65
70
70
70
70
75
75
75
80
80
80
80
85
85
85
85
90
90
90
90
95
95
95
100
100
100
105
105
110
110
120
120
120
130
120
120
140
160
125
125
150
180
130
160
190
140
170
170
200
150
150
180
210
160
160
190
225
170
200
250
180
215
265
190
225
200
240
180
215
260
230
23
23
33
37
24
24
35
42
25
37
45
26
39
39
48
28
28
41
52
30
30
43
54
32
45
55
34
47
60
36
49
38
50
28
40
55
40
66.3
69.5
108
130
71.5
75
127
159
73.5
132
168
85
143
143
178
95.6
102
156
190
108
108
166
216
129
168
251
135
216
276
148
203
153
225
87.1
165
238
186
54
57
80
96.5
60
64
98
127
65.5
104
140
75
118
118
153
83
90
132
166
96.5
96.5
146
200
118
150
245
122
208
275
137
193
143
224
93
163
250
193
2.28
2.45
3.35
3.8
2.5
2.7
3.9
4.8
2.7
4.15
5.1
3.05
4.5
4.5
5.5
3.25
3.55
4.9
5.85
3.65
3.65
5.3
6.7
4.4
5.2
7.8
4.4
6.95
8.65
4.8
6.4
4.9
7.2
3.2
5.3
7.65
6.1
6300
6700
5600
5000
6000
6300
5600
4500
6300
5300
4300
5600
5000
4500
4000
5000
5300
4800
3800
4500
4500
4500
3600
4800
3800
3400
4000
4000
3200
3800
3400
3600
3200
3800
3400
3000
3200
6300
6700
5600
5300
6000
6300
5600
4800
6300
5300
4500
5600
5000
4500
4300
5000
5300
4800
4000
4500
4800
4500
3800
4800
3800
3400
4300
4000
3200
4000
3600
3800
3400
4000
3600
3200
3400
1
1.1
2.35
3.85
1.1
1.1
2.55
5
1.29
3.26
6.85
1.59
4.03
3.7
8
1.9
1.83
4.74
10.3
2.34
2.41
5.53
11.5
2.95
6.41
13.5
3.61
8
15.5
4.18
9.12
4.95
10.7
2.4
5.89
13.8
6.76
7213 BECBJ
7213 BECBM
7313 BECBF
7413 BGAM
7214 BECBJ
7214 BECBPa
7314 BECAPa
7414 BCBM
7215 BECBM
7315 BECBMa
7415 BCBM
7216 BECBMa
7316 BECBMa
7316 BEGAY
7416 M
7217 BECBJ
7217 BECBPa
7317 BECBMa
7417 BACBMC
7218 BECBJ
7218 BECBM
7318 BECBMa
7418 CBM
7219 BECBMa
7319 BEGAF
7419 M
7220 BECBM
7320 BECBMa
7420 CBM
7221 BECBM
7321 BECBM
7222 BECBM
7322 BECBM
7024 BGM
7224 BM
7324 BGBM
7226 BCBM
Continued
Table 6.7
Single row angular contact ball bearings—cont’d
d
(mm)
D
(mm)
B
(mm)
C
(kN)
C0
(kN)
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
130
140
140
140
150
150
150
160
160
170
170
180
180
180
190
190
200
200
220
220
220
240
240
240
260
280
280
300
320
320
335
340
280
210
250
300
225
270
320
290
340
310
360
280
320
320
340
400
360
420
340
400
460
360
440
500
480
420
500
460
440
480
450
460
58
33
42
62
35
45
65
48
68
52
72
46
52
52
55
78
58
80
56
65
88
56
72
95
80
65
80
74
56
74
56
56
276
114
199
302
133
216
332
255
358
281
390
195
291
291
307
442
325
462
255
390
494
260
364
559
507
338
520
423
351
390
281
338
305
129
212
345
146
240
390
300
440
345
490
240
375
375
405
600
430
655
355
560
720
375
540
865
780
540
850
695
585
670
480
585
9
4.15
6.4
9.8
4.55
6.95
10.8
8.5
11.8
9.5
12.7
6.7
10
10
10.4
14.6
11
15.6
9
13.4
16.6
9.15
12.5
19
17.3
12.2
18.3
15.3
12.9
14
10.4
12.5
2800
3200
2800
2600
3000
2600
2400
2400
2200
2400
2000
2400
2200
2200
2000
1900
1800
1800
2000
1800
1600
1800
1600
1400
1400
1500
1400
1500
1500
1300
1400
1500
2800
3400
3000
2600
3200
2800
2400
2600
2400
2400
2200
2600
2400
2400
2200
1900
2000
1800
2000
1800
1700
1900
1700
1500
1500
1600
1400
1600
1600
1400
1400
1500
17.1
3.85
8.83
21.3
4.7
10.8
25
13.6
30.3
16.7
34.6
10
17.6
17.6
21.9
48.3
25
52.8
18
35.2
70
19
49
88.5
66
30
69.5
42.5
25.5
44.5
25.5
24
7326 BCBM
7028 BGM
7228 BCBM
7328 BCBM
7030 BGM
7230 BCBM
7330 BCBM
7232 BCBM
7332 BCBM
7234 BCBM
7334 BCBM
7036 BGM
7236 BCAM
7236 BCBM
7238 BCBM
7338 BCBM
7240 BCBM
7340 BCBM
7044 BGM
7244 BCBM
7344 BCBM
7048 BGM
7248 BCBM
7348 BCBM
7252 BM
7056 BGM
7256 BM
7060 AGM
71,964 AC
7064 BGM
466,952
71,968 ACMB
340
340
360
360
360
380
380
400
400
400
410
420
420
440
460
460
460
465
480
500
500
500
530
530
530
540
560
600
600
600
630
630
670
670
710
710
750
750
520
620
440
480
540
480
560
540
600
720
560
560
620
650
580
620
680
635
700
620
670
720
650
710
760
630
750
730
800
870
700
920
820
980
870
1030
920
1090
82
92
38
56
82
31
82
65
90
103
70
65
90
94
37
74
100
76
100
37
78
100
56
82
100
45
85
42
90
118
22
128
69
136
74
140
78
150
449
702
234
351
520
190
507
423
605
728
423
423
605
650
265
507
689
468
702
276
553
715
390
618
702
260
592
338
715
884
135
956
553
1170
605
1190
650
1300
815
1340
425
630
950
345
950
780
1180
1500
830
800
1180
1320
560
1040
1460
980
1530
620
1220
1600
900
1340
1600
600
1290
735
1730
2160
440
2450
1290
3100
1630
3250
1800
3650
16.6
26
9
13.2
19
8
18.6
15.6
22.4
26.5
16
16
22
24
10.4
19
25.5
17.6
26.5
11
21.2
27.5
15.6
23.6
27.5
10.6
22.8
14
27.5
34
7.2
37.5
22.4
45.5
24.5
46.5
26.5
52
1200
1100
1500
1400
1300
1300
1200
1200
950
900
1100
1200
1100
1000
1100
100
950
900
950
1000
950
900
950
850
750
850
800
800
750
700
750
560
700
560
630
560
600
530
1300
1100
1500
1500
1300
1400
1300
1300
1200
950
1100
1200
1100
1100
1100
1100
1000
950
1000
1000
1000
950
1000
900
800
900
850
850
800
750
750
700
750
600
670
600
630
560
61.5
125
12
28.5
62.5
13.5
65.5
42
89.5
190
49.5
44.5
95
100
24.5
58
120
70.5
125
27
78
130
39.5
92
150
21.5
105
38.5
125
230
11.5
270
77
340
93.5
370
110
445
7068 BGM
7268 BGM
71,872 ACM/P5
71,972 ACMB
7072 AGM
70,876 AMB
7076 AM
71,980 AM
307,238
7280 BM
468,431
71,984 AM
7084 AM
7088 AM
70,892 AM
71,992 ACM
7092 AM
307,352
7096 AM
708/500 AMB
719/500 AGMB
70/500 AM
718/530 AMB
719/530 ACM
307,368 B
BA1B 311,585
719/560 AMB
708/600 AGMB
719/600 ACM
70/600 AGMB
BA1B 311,712
70/630 AMB
718/670 ACMB
70/670 AMB
718/710 ACMB
70/710 AMB
718/750 ACMB
70/750 AMB
Continued
Table 6.7
Single row angular contact ball bearings—cont’d
d
(mm)
D
(mm)
B
(mm)
C
(kN)
C0
(kN)
Fatigue load limit
(kN)
Reference speed
(rpm)
Limiting speed
(rpm)
Mass
(kg)
Designation
762
800
800
850
850
900
900
950
1000
1000
1060
1120
1180
1250
1700
889
1130
1150
1030
1220
1030
1280
1360
1320
1420
1500
1580
1660
1750
1900
63.5
120
155
82
165
63
170
180
103
185
195
200
212
218
80
449
1080
1330
689
1530
416
1560
1630
832
1630
1680
1720
1740
1780
975
1270
3200
3800
1860
4650
1270
4900
5200
2450
5400
5700
5850
6200
6550
4550
18.6
44
52
29
61
17.3
63
65.5
34.5
67
71
71
73.5
76.5
45.5
560
450
480
500
450
450
400
380
340
360
320
300
280
240
160
600
480
500
530
480
480
430
400
360
380
340
320
280
260
170
58
395
500
140
595
90
665
805
370
890
1050
1150
1350
1600
310
BA1B 311,576
BA1B 311,745
70/800 AMB
718/850 AMB
70/850 AMB
BA1B 307,788
70/900 AMB
70/950 AMB
307,101C
70/1000 AMB
70/1060 AMB
70/1120 AMB
70/1180 AMB
70/1250 AMB
BA1B 307,756
a
SKF Explorer bearing.
NB this table presents a selection only of the bearings available.
Data courtesy of SKF.
Rolling element bearings 233
rating, fatigue load limit, reference and limiting speeds. The reference speed is indicates the
permissible speed of the bearing subject to a certain load and operating with a specific lubricant
viscosity. The final entry in each row provides a designation code for the specific bearing
concerned.
Example 6.3
A bearing is required to carry a radial load of 2.8kN and provide axial location for a shaft of 30
mm diameter rotating at 1500 rpm. An L10 life of 10,000 h is required.
(i) Select and specify an appropriate bearing using the standard bearing life equation (Eq. 6.3).
(ii) Determine the rating life using the modified life equation assuming a fatigue load limit of
670 N and an SKF life modification factor of 14. The desired reliability is 90%.
Solution
(i) Axial shaft location is required, so a deep groove ball bearing, which provides axial location
capability in both directions, would be suitable.
The total number of revolutions for the bearing life is given by.
10,000 1500 60 ¼ 900 million.
So L ¼ 900.
The load is purely radial so P ¼ 2800 N.
The required dynamic load rating of the bearing is given by.
C ¼ PL1/3 ¼ 2800 9001/3 ¼ 27,030 N 27 kN.
Reference to the deep groove bearing chart (Table 6.5) shows a suitable bearing could be
Designation 6306-ZNR
Bore diameter 30 mm
Outer diameter 72 mm
Width 19 mm
C ¼ 29,600 N
Co ¼ 16,000 N
Reference speed 20,000 rpm
Limiting speed 13,000 rpm
(ii) Normally it would be necessary to determine the viscosity ratio, κ, and ηcPu/P in order to
determine aSKF. In this case, the SKF life modification factor has been given. Nevertheless, the
steps are included below.
The viscosity ratio is given by κ ¼ 40/14 ¼ 2.86.
The contamination factor is that for normal cleanliness, ηc ¼ 0.6.
ηc
Pu
670
¼ 0:6 0:239 ¼ 0:14
¼ 0:6
2800
P
234 Chapter 6
From manufacturer’s tables, using κ and ηcPu/P, aSKF ¼ 14.
Hence from Eq. (6.7), for a desired reliability of 90%,
p
C
29, 600 3
Lnm ¼ a1 aSKF
¼ 1 14 ¼ 16540 million revolutions
P
2800
This high life suggests either very extended operation, much greater than the 900 million
revolutions calculated for the bearing life, or an opportunity for an alternative design that does
not require this quality of bearing installation.
Modelling of bearing performance is an on-going research topic and developments in capability
to more accurately model the physics continue to advance. Examples of such developments
include the use of deep learning (Mao et al., 2019) and hybrid prediction methods (Guo et al.,
2021) to predict remaining life. Multi-objective design optimisation (see Chapter 1) of various
forms of rolling bearings is considered by Gupta et al. (2007), Kalyan et al. (2020), Jat and
Tiwari (2020), Ahmad et al. (2022), the optimisation of angular contact bearings by Kim et al.
(2016) and Kang et al. (2019), and the use of genetic algorithms for ball bearings by Verma and
Tiwari (2021) and cylindrical bearings by Koneru et al. (2023).
6.3 Bearing installation
The practical use of rolling element bearings requires consideration of their installation as well
as correct selection. Bearing installation considerations include the bearing combination, the
mounting of the bearings and the provision of lubrication.
A typical application of rolling element bearings is the support of a rotating shaft. If the
operating temperature of the machine varies, the shaft length can expand relative to the casing
or mounting arrangement. An idea of the magnitude of the axial shaft growth can be
estimated by:
Δl ¼ lo αΔT
(6.9)
Where:
Δl ¼ change in length (m).
lo ¼ original length (m).
α ¼ coefficient of linear thermal expansion (°C1) of the shaft material.
ΔT ¼ temperature rise (°C).
For a gas turbine engine, the difference in temperature between the casing and the shaft can
readily be of the order of 50°C. If the original length of the steel shaft was 1.5 m, the growth of
the shaft would be
Δl ¼ lo αΔT ¼ 1:5 11 106 50 ¼ 8:25 104 m ¼ 0:825 mm
Rolling element bearings 235
This is a considerable axial movement within a machine and must be allowed for, if significant
loadings and resultant stresses, and possible contact between stationary and rotating
components are to be avoided. A typical solution to this kind of situation is to allow for a limited
axial movement on one bearing as illustrated in Figs. 6.14 and 6.15. Here one bearing has the
location of its inner and outer races ‘fixed’ relative to the shaft and housing by means of
shoulders and locking rings. The location of the other bearing is fixed only for the inner race. If
the shaft expands, the axial movement can be accommodated by limited sliding motion of the
outer race of the right-hand bearing within the housing bore. For this kind of arrangement, the
bearings are referred to as fixed and floating bearings. Similar movement is also possible for the
arrangement shown in Figs. 6.16 and 6.17. Here the right-hand bearing is a cylindrical roller
bearing and the axial location of the roller is not fixed and can move or float axially to the
limited extents of the race to take up any axial movement or expansion of the shaft.
Fig. 6.14
Schematic for a basic bearing mounting using two deep groove ball bearing for a rotating horizontal
shaft for moderate radial and axial loading.
Fig. 6.15
Basic bearing mounting using two deep groove ball bearings for a rotating horizontal shaft for
moderate radial and axial loading.
236 Chapter 6
Fig. 6.16
Schematic for a basic bearing mounting using a deep groove and a cylindrical roller bearing for
moderate radial loads at the ‘locating deep groove bearing’ and high radial load capacity at the
cylindrical roller bearing.
Fig. 6.17
Basic bearing mounting using a deep groove and a cylindrical roller bearing for moderate radial loads
at the ‘locating deep groove bearing’ and high radial load capacity at the cylindrical roller bearing.
Correct lubrication is essential in order to ensure the calculated life of the bearing is achieved.
Too much lubrication can result in increased levels of viscous dissipation of energy in the
bearings and resultant overheating of the lubricant and the bearing. Too little lubrication can
result in excessive wear and early failure. The form of lubrication depends on that required by the
bearing application. Grease lubrication is normally the easiest and requires injection of a specific
quantity of grease into the bearing and some method of dirt and dust exclusion (Lugt, 2009, 2013;
Morales-Espejel et al., 2014). Bearings can be purchased which are grease filled and sealed for
life. Oil lubrication can be supplied by means of partial submersion as shown in Figs. 6.18 and
6.19, a recirculation circuit as shown in Figs. 6.20 and 6.21 or oil spot lubrication. A recirculation
system typically consists of a cooler, an oil pump, a filter, oil jets, scavenge or collector holes and
a reservoir. Oil spot lubrication involves the application of very small quantities of lubricant
directly to the bearing by means of compressed air. Once again, the bearing manufacturers’
handbooks are a good source of information for lubricant supply rates and systems.
Rolling element bearings 237
Fig. 6.18
Schematic for partial submersion lubrication arrangement.
Fig. 6.19
Partial submersion lubrication arrangement.
A key issue with bearings is ensuring their effective operation in service. If a bearing fails then
the outage can be costly both in terms of loss of service and repair of any damage caused to the
equipment as well as replacement of the bearings. A series of diagnostics technologies based on
monitoring, for example, vibration and acoustics (see McFadden and Smith, 1984; Cong et al.,
2013; Tandon and Choudhury, 1999; Chacon et al., 2015; Xu et al., 2021; Liu et al., 2021;
Nirwan and Ramani, 2022; Peng et al., 2022; Wang et al., 2022; Hakim et al., 2023), as well as
associated data analysis methods have been developed (e.g. Yang et al., 2005, and Unal et al.,
2014; Wu et al., 2022).
6.3.1 Radial location
The load capacity for a bearing, as defined by test procedures, within catalogues and by the
basic dynamic rating, is based upon full support of the raceways at the inner and outer diameters
in the case of a radial bearing, and the rings and washers in the case of, for instance, a thrust or
238 Chapter 6
Fig. 6.20
Schematic illustrating a basic recirculation lubrication system.
Fig. 6.21
Recirculation lubrication system.
taper roller bearing. The mating bearing seats for a bearing must be manufactured with adequate
accuracy to provide the necessary support and prevent them from turning within their seats
under load. The surfaces should be uninterrupted without grooves or other such features.
Generally, an interference fit is required for one ring and loose fit for the other. Table 6.8
provides an indication of the type of fit for a given application and Tables 6.9 and 6.10 provide
recommended fits for the case of radial bearings with a solid steel shaft and housings
Rolling element bearings 239
Table 6.8 Recommended type of fit depending on operating conditions for radial bearings.
Operating conditions
Load condition
Rotating inner ring
Stationary outer ring
Constant load direction
Rotating load on inner
ring
Stationary load on outer
ring
Stationary load on inner
ring
Rotating load on outer
ring
Stationary load on inner
ring
Rotating load on outer
ring
Rotating load on inner
ring
Stationary load on outer
ring
Stationary inner ring
Rotating outer ring
Constant load direction
Rotating inner ring
Stationary outer ring
Load rotates with the inner
ring
Stationary inner ring
Rotating outer ring
Load rotates with the outer
ring
Example
application
Recommended fits
Belt drives
Interference fit for the inner
ring
Loose fit for the outer ring
Conveyer idlers
Loose fit for the inner ring
Wheel hub
bearings
Vibrating
applications
Motors
Interference fit for the outer
ring
Interference fit for the outer
ring
Loose fit for the inner ring
Gyratory crusher
Interference fit for the inner
ring
Loose fit for the outer ring
Merry-go-round
respectively. For housings manufactured from light alloys, the interference should be
tighter than those indicated in Table 6.10. An introduction to tolerancing and consideration
of shaft and hole fits is given in Chapter 19, Section 19.2.
If a bearing is mounted on a hollow cylindrical shaft of internal diameter di, it is generally
necessary to use a slightly higher interference fit than the equivalent sized solid shaft in order to
provide a similar surface pressure between the shaft and inner raceway bearing seat. The fit is
not normally appreciably affected until the ratio ci ¼ di/d 0.5. For values above this a
correction factor, normally available from bearing manufacturers, can be applied to the mean
probable interference based on a solid shaft application to provide the requisite interference for
the hollow shaft application.
6.3.2 Preload
An inherent characteristic associated with the fabrication and assembly of a rolling element
bearing is clearance between the rolling elements and raceways. The total distance through
which a bearing raceway can move relative to the other radially is called radial internal
clearance or axially is called axial internal clearance. Radial internal clearance is sometimes
referred to as radial play. It is important to distinguish between the internal clearance of a
bearing prior to mounting versus that of a mounted bearing that has reached its operational
conditions. The initial clearance of a bearing prior to mounting is likely to be greater than the
operational clearance due to the fits used and differences in thermal expansion between the
raceways and mountings.
Table 6.9 Recommended radial rolling element bearing fits for solid cylindrical steel shafts.
Shaft diameter (mm)
Load
conditions
Examples
Light Loads Electrical home appliances pumps, blowers, transport
Rotating
or variable
vehicles, precision machinery, machine tools
inner
loads
Ring load or
Direction of
Normal
General bearing applications, medium and large motors,
Load
Loads
turbines, pumps, engine main bearings, gears,
Indeterminate
woodworking machines
Heavy
Loads or
Shock
Loads
Axial loads only
Data from NSK.
Railway axleboxes, industrial vehicles, traction motors,
construction equipment, crushers
Ball
bearings
Cylindrical roller
bearings; Tapered
roller bearings
Spherical
roller
bearings
<18
18–100
100–200
–
<18
–
<40
40–140
140–200
–
–
–
–
–
–
18–100
100–140
140–200
200–280
–
–
–
–
–
–
–
<40
40–100
100–140
140–200
200–400
–
–
50–140
140–200
over 200
–
<40
40–65
65–100
100–140
140–280
280–500
over 500
50–100
100–140
140–200
200–500
All shaft diameters
Tolerance
of shaft
js5
js6(j6)
k6
m6
js5 or js6
(j5 or j6)
k5 or k6
m5 or m6
m6
n6
p6
r6
r7
n6
p6
r6
r7
js6 (j6)
Rolling element bearings 241
Table 6.10 Recommended radial rolling element bearing fits with cast iron and steel housings.
Load conditions
Solid or
split
housings
Rotating inner
ring load
Loads of all kinds
Normal or light loads
High temperature rise of inner
ring through shaft
Accurate running desirable
under normal or light loads
Solid
housing
Direction of
load
indeterminate
Rotating inner
ring load
Accurate running and high
rigidity desirable under variable
loads
Minimum noise is required
Examples
General bearing
applications, railway
axleboxes
Plummer blocks
Paper dryers
Grinding spindle rear ball
bearings
High speed centrifugal
compressor free bearings
Grinding spindle front ball
bearings
High speed centrifugal
compressor fixed bearings
Cylindrical roller bearings
for machine tool main
spindle
Electrical home appliances
Tolerances for
housing bores
H7
H8
G7
JS6 (J6)
K6
M6 or N6
H6
Data from NSK.
Preload of a bearing involves managing these clearances in order to improve the running
performance of the bearing. If a bearing in operation has radial play, then one raceway can
move radially and axially relative to another. This looseness results in wobble or runout.
Such motion is unacceptable in high precision machinery such as prime movers, pinion
bearings in automotive axles, machine tool spindles and high speed cordless and corded hand
tools. Preload to the raceways forces the rolling elements in contact with the raceways and
the establishment of a stable and defined contact angle such that the set of balls will rotate in
a uniform circumferential plane about the bearing axis. By preloading a bearing, the life,
noise and vibration can all be improved. Preload is an important consideration in high
precision and high speed application, particularly when high levels of positional accuracy are
required.
The clearances associated with the manufacture of a bearing can result in bearing noise, vibration
and compromised life. An axial preload to one of the raceways can be applied. This increases
the stiffness of the bearing, has benefits including increased rotational positional accuracy and
more precise shaft location, reduction or elimination of ball skidding, reduction of deflections,
reduction of noise and improved load sharing between bearings. The higher the preload, the higher
the bearing stiffness. However, if the preload is excessive this can result in reduced bearing life
and failure. If inadequate preload is applied, vibration and fretting can result.
242 Chapter 6
The calculation of the optimum preload for a bearing can be based on the theoretical
consideration of the optimum surface stress that arises from elastic deformation of the contact
areas between the rolling elements and raceways. In practical applications, preload parameters
can generally be obtained from the bearing manufacturers for the specific bearing concerned.
There are two principal approaches to preloading: solid preload and spring preload, as
illustrated in Figs. 6.22 and 6.23. Solid preload, also known as rigid or fixed-constraint preload,
can be achieved by locking both inner and outer raceway in position so that they cannot move
axially relative to each other, thus fixing the ‘as preloaded’ positions of the raceways. Such a
design, however, is likely to be subject to growth or shrinkage of components due to
temperature changes which can result in changes to the expected preload. In addition,
components can wear and the level of preload reduce as a result. Spring preload, also known as
constant pressure preload, can be applied to a bearing raceway using a coil spring, bevel spring
or wave spring washer, with the spring pressing the raceways together or apart, depending on
the requirement. The advantage of spring preload is stable loading with temperature changes.
However, this comes at the expense of increased machine complexity. In most applications, the
spring is configured to press against the non-rotating raceway.
Bearing manufacturers produce matched pairs of bearings, known as duplex bearings, with
built in preload, achieved by grinding the inner or outer ring faces with defined dimensions
known as the bearing offset. The bearing offset corresponds with the axial movement of the
raceway if a specific preload is applied. When a duplex bearing pair is assembled, the offset is
removed as the bearings are clamped together establishing the preload in the bearing set.
Preload can be applied in various configurations such as duplex face to face (DF), duplex back
to back (DB) and tandem (DT) as illustrated in Fig. 6.24. Duplex bearings exhibit increased
axial and radial rigidity. The stiffness of DB is higher than that associated with DF
configurations. DB and DF configurations can handle bi-directional thrust loads and DT
Fig. 6.22
Schematics illustrating solid and spring preload.
Fig. 6.23
Solid and spring preload.
Fig. 6.24
Duplex face to face (DF), duplex back to back (DB) and tandem (DT) preload configurations.
244 Chapter 6
bearings can take heavy unidirectional thrust loads. As a rule of thumb, a preloaded bearing pair
can handle axial loads up to three times the preload. Beyond this limit one of the bearings in the
set may become unloaded and the deflection will be that of a single bearing.
6.4 Conclusions
Bearings are used to support a load whilst allowing relative motion between two elements of a
machine. Typical applications are shafts where the shaft rotates relative to a housing but
bearings can also be used to facilitate linear relative motion for, say, machine slides. This
chapter has introduced the selection and specification of rolling element bearings.
An important consideration in a design involving rolling element bearings is to ensure that the
bearings have sufficient load capacity to accommodate the forces generated by thermal growth
and misalignment in addition to any functional loading. An alternative is to make sure the
bearing mounting configuration allows for displacements to occur without imposing significant
loads on the bearings. A typical configuration for bearing mounting is the use of a fixed and a
floating bearing, with all of the shoulders of the fixed bearing axially-constrained, while a
raceway or the rolling elements on the floating bearing are not axially-constrained.
Rolling element bearings are produced by specialist manufacturers and many types and sizes
are available as stock items. For further information on bearings the reader is recommended to
view specific manufacturers’ literature and the texts by Harris (2001), Harris and Kotzalas
(2006a,b) and Brandlein et al. (1999).
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Standards
ANSI/ABMA Standard 11-2014 (R2020). Load ratings and fatigue life for roller bearings.
ANSI/ABMA Standard 7-1995 (S2013). Shaft and housing fits for metric radial ball and roller bearings (except
tapered roller bearings) conforming to basic boundary plans.
ANSI/ABMA Standard 9-2015 (R2020). Load ratings and fatigue life for ball bearings.
BS 4231:1992, ISO 3448:1992. Classification for viscosity grades of industrial liquid lubricants.
BS ISO 10317:2008+A1:2013. Rolling bearings. Tapered roller bearings. Designation system.
246 Chapter 6
BS ISO 104:2015. Rolling bearings. Thrust bearings. Boundary dimensions, general plan.
BS ISO 113:2010. Rolling bearings. Plummer block housings. Boundary dimensions.
BS ISO 14728-1:2017. Rolling bearings. Linear motion rolling bearings. Dynamic load ratings and rating life.
BS ISO 14728-2:2017. Rolling bearings. Linear motion rolling bearings. Static load ratings.
BS ISO 15:2017. Rolling bearings. Radial bearings. Boundary dimensions, general plan.
BS ISO 15243:2017. Rolling bearings. Damages and failures. Terms, characteristics and causes.
BS ISO 281:2007. Rolling bearings. Dynamic load ratings and rating life.
BS ISO 2982-1:2013. Rolling bearings. Accessories. Dimensions for adapter sleeve assemblies and withdrawal
sleeves.
BS ISO 2982-2:2013. Rolling bearings. Accessories. Dimensions for locknuts and locking devices.
BS ISO 3290-1:2014. Rolling bearings. Balls. Steel balls.
BS ISO 355:2019. Rolling bearings. Tapered roller bearings. Boundary dimensions and series designations.
BS ISO 492:2023. Rolling bearings. Radial bearings. Geometrical product specifications (GPS) and tolerance
values.
BS ISO 5593:2023. Rolling bearings. Vocabulary.
BS ISO 76:2006+A1:2017. Rolling bearings. Static load ratings.
DD ISO/TS 16281:2008. Rolling bearings. Methods for calculating the modified reference rating life for universally
loaded bearings.
ISO 281:1990/Amd 2:2000. Rolling bearings—Dynamic load ratings and rating life—Amendment 2: Life
modification factor aXYZ.
PD ISO/TR 1281-1:2021. Rolling bearings. Explanatory notes on ISO 281. Basic dynamic load rating and basic
rating life.
PD ISO/TR 1281-2:2008. Rolling bearings. Explanatory notes on ISO 281. Modified rating life calculation, based on
a systems approach to fatigue stresses.
Web sites
At the time of going to press the world-wide-web contained useful information relating to
this chapter at the following sites
www.arb-bearings.com.
www.cooperbearings.com.
www.hb-bearings.com.
www.newindo.com.
www.nsk.com.
www.ntn.ca.
www.peerbearing.com.
www.rbcbearings.com.
www.schaeffler.de.
www.skf.com.
www.timken.com.
www.toyobearings.com.