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LESSON 28 SELECTION OF ANTIFRICTION BEARINGS
28.1 Rated Life of a Bearing
Life of a bearing is the number of revolutions or number of hours at constant speed that the bearing runs, before the first evidence of fatigue crack in the balls or races. But test data shows large variation in the lives of identical bearings, operating under similar conditions. Because of this reason, life of bearings is expressed in terms of statistical average life of a group of bearings.
Rated life of a group of apparently identical bearings is defined as the number of revolutions that 90 % of bearings will complete or exceed before the first evidence of fatigue crack. It is also known as minimum life and L_{10} life.
Reliability is the ratio of number of bearings that complete L million revolutions to the total number of bearings tested. Therefore, by definition, rated life (L_{10}) corresponds to 90% reliability of the bearing. Depending upon the type of application, bearings with reliability greater than 90% or less than 90% may also be required. Relation between bearing life and reliability is as follows:
where, L_{10} = rated life of the bearing (life corresponding to 90% reliability)
L = life of the bearing corresponding to x % reliability
R_{90} = reliability of 90% (0.9)
R_{x} = reliability of x %
Using this relation, for given rated life of bearing, life of bearing corresponding to a reliability of x % (L) can be calculated.
28.2 Static Load Carrying Capacity
Static load carrying capacity (C_{0}) of a bearing is defined as the static load corresponding to a total permanent deformation of balls and races, at the most heavily stressed point of contact, equal to 0.0001 of the ball diameter.
The bearing is subjected to some static load, when the shaft is stationary. This leads to plastic deformation in the balls and races. This deformation increases with increase in the static load. It has been established that a total permanent deformation of 0.0001 of ball diameter, at the most heavily stressed point of contact, can be tolerated without affecting operational properties of the bearing.
Different formulae have been developed for calculation of static load carrying capacity. However for selection of bearings, use of these formulae is not necessary; as the values of static load carrying capacity are directly given in manufacturer’s catalogue.
28.3 Dynamic Load Carrying Capacity
Dynamic load carrying capacity (C) is defined as the constant stationary radial load (in case of radial bearings) or constant axial load (in case of thrust bearings), which a group of apparently identical bearings, with stationary outer ring can endure for a rated life of one million revolutions with only 10 % failures.
Various relations have been developed for calculating dynamic load carrying capacity also, but again its value for different bearings is available in manufacturer’s catalogue. Table 28.1 gives basic dimensions and load capacities of different types of bearings.
28.4 Equivalent Bearing Load
In many applications, bearings are subjected to both radial and axial loads and are sometimes required to operate with stationary inner race and rotating outer race.
The equivalent dynamic load of a bearing is defined as the constant radial load in radial bearings or trust load in trust bearings, which if applied to the bearing, would give same life as attained by the bearing under actual conditions of loading. It is given by,
where, V = race rotation factor = 1 if inner race rotates
= 1.2 if outer race rotates
X = radial load factor
Y = thrust load factor
Values of X and Y are available in manufacturer’s catalogue. Table 28.2 gives values of X and Y for deep groove ball bearings.
Table 28.1 Dimensions & Load Carrying Capacities of Ball Bearings
Bearing No. 
Bore (mm) 
Outside Diameter (mm) 
Width (mm) 
Load Carrying Capacity (kN) 

Single Row Deep Groove 
Single Row Angular Contact 
Double Row Angular Contact 
Selfaligning 

C_{0} 
C 
C_{0} 
C 
C_{0} 
C 
C_{0} 
C 

6200 6300 
10 
30 35 
9 11 
2.24 3.60 
4 6.3 
  
  
4.55  
7.35  
1.8  
5.7  
6201 6301 
12 
32 37 
10 12 
3.00 4.30 
5.4 7.65 
  
  
5.6  
8.3  
2 3 
5.85 9.15 
6202 6302 
15 
35 42 
11 13 
3.55 5.20 
6.1 8.8 
3.75  
6.30  
5.6 9.3 
8.3 14 
2.16 3.35 
6 9.3 
6203 6303 6403 
17 
40 47 62 
12 14 17 
4.40 6.30 11.00 
7.5 10.6 18 
4.75 7.2  
7.8 11.6  
8.15 12.9  
11.6 19.3  
2.8 4.15  
7.65 11.2  
6204 6304 6404 
20 
47 52 72 
14 14 19 
6.55 7.65 15.60 
10 12.5 24 
6.55 8.3  
10.4 13.7  
11 14  
16 19.3  
3.9 5.5  
9.8 14  
6205 6305 6405 
25 
52 62 80 
15 17 21 
7.10 10.40 19.00 
11 16.6 28 
7.8 12.5  
11.6 19.3  
13.7 20  
17.3 26.5  
4.25 7.65  
9.8 19  
6206 6306 6406 
30 
62 72 90 
16 19 23 
10.00 14.60 23.20 
15.3 22 33.5 
11.2 17  
16 24.5  
20.4 27.5  
25 35.5  
5.6 10.2  
12 24.5  
6207 6307 6407 
35 
72 80 100 
17 21 25 
13.70 17.60 30.50 
20 26 43 
15.3 20.4  
21.2 28.5  
28 36  
34 45  
8 13.2  
17 30.5  
6208 6308 6408 
40 
80 90 110 
18 23 27 
16 22 37.5 
22.8 32 50 
19 25.5  
25 35.5  
32.5 45.5  
39 55  
9.15 16  
17.6 35.5  
6209 6309 6409 
45 
85 100 120 
19 25 29 
18.3 30 44 
25.5 41.5 60 
21.6 34  
28 45.5  
37.5 56  
41.5 67  
10.2 19.6  
18 42.5  
6210 6310 6410 
50 
90 110 130 
20 27 31 
21.2 35.5 50 
27.5 48 68 
23.6 40.5  
29 53  
43 73.5  
47.5 81.5  
10.8 24  
18 50  
6211 6311 6411 
55 
100 120 140 
21 29 33 
26 42.5 60 
34 56 78 
30 47.5  
36.5 62  
49 80  
53 88  
12.7 28.5  
20.8 58.5  
6212 6312 6412 
60 
110 130 150 
22 31 35 
32 48 67 
40.5 64 85 
36.5 55  
44 71  
63 96.5  
65.5 102  
16 33.5  
26.5 68  
6213 6313 6413 
65 
120 140 160 
23 33 37 
35.5 55 76.5 
44 72 93 
43 63  
50 80  
69.5 112  
69.5 118  
20.4 39  
34 75  
6214 6314 6414 
70 
125 150 180 
24 35 42 
39 63 102 
48 81.5 112 
47.5 73.5  
54 90  
71 129  
69.5 137  
21.6 45  
34.5 85  
6215 6315 6415 
75 
130 160 190 
25 37 45 
42.5 72 110 
52 90 120 
50 81.5  
56 98  
80 140  
76.5 143  
22.4 52  
34.5 95  
6216 6316 6416 
80 
140 170 200 
26 39 48 
45.5 80 120 
57 96.5 127 
57 91.5  
63 106  
96.5 160  
93 163  
25 58.5  
38 106  
6217 6317 6417 
85 
150 180 210 
28 41 52 
55 88 132 
65.5 104 134 
65.5 102  
71 114  
100 180  
106 180  
30 62  
45.5 110  
6218 6318 6418 
90 
160 190 225 
30 43 54 
63 98 146 
75 112 146 
76.5 114  
83 122  
127   
118   
36 69.5  
55 118  
Table 28.2 Values of Radial Load Factor (X) and Thrust Load Factor (Y) for Deep Groove Ball Bearings
28.5 Load Life Relationship
Relationship between bearing life, dynamic load carrying capacity and equivalent dynamic load, is given by,
where, L_{10} = rated bearing life
C = dynamic load carrying capacity
P = equivalent dynamic load
k = load life exponent = 3 for ball bearings
= 10/3 for roller bearings
Also,

where, L_{10h} = rated bearing life in hours
N = speed of rotation in r.p.m.
28.6 Selection of Bearings
Following steps are generally followed in selection of antifriction bearings:
 Determine radial and axial forces (F_{r} and F_{a} respectively) acting on the shaft.
 Calculate the diameter of the shaft.
 Select suitable type of the bearing from manufacturer’s catalogue.
Following guidelines can be used for selecting ball bearings:
Type of Ball Bearing 
F_{a}/ F_{r} 
Single Row Deep Groove 
0.5 – 0.8 
Double Row Deep Groove 
0.8 – 1.5 
Angular Contact 
1.5 – 2.0 
Self Aligned 
0.2 – 0.5 
Select the lowest series of the selected category, depending upon the shaft diameter. Note the value of static load carrying capacity, C_{0}. Refer table 28.1.
4. Select value of race rotation factor, V.
5. Determine values of radial and thrust load factors (X and Y) corresponding to the calculated values of F_{a} and F_{r}, and value of C_{0} of selected bearing. Refer table 28.2 for deep groove ball bearings.
6. Calculate equivalent dynamic load of the bearing,
7. Decide expected life of the bearing in millions of revolutions (L).
8. Calculate the required dynamic load carrying capacity for expected life, using load life relationship.
9.Dynamic load carrying capacity of the selected bearing should be greater than the required value calculated above, i.e.
If , choose higher series of the bearings from the catalogue and repeat the procedure from Step 3.
References
 Design of Machine Elements by VB Bhandari
 Analysis and Design of Machine Elements by V.K. Jadon
 Machine Design by R.S. Khurmi
 Design of Machine Elements by C.S. Sharma & K. Purohit
 5. SKF General Catalogue