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 L10 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 (L10) 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:

281.png

where,             L10       = rated life of the bearing (life corresponding to 90% reliability)

                        L          = life of the bearing corresponding to x % reliability

R90       = reliability of 90% (0.9)

Rx         = 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 (C0) 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,

282.png

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

Self-aligning

C0

C

C0

C

C0

C

C0

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

283.png

28.5          Load Life Relationship

Relationship between bearing life, dynamic load carrying capacity and equivalent dynamic load, is given by,

284.png

where,             L10       = 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,

 

284.png

where,             L10h      = 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:

  1. Determine radial and axial forces (Fr and Fa respectively) acting on the shaft.
  2. Calculate the diameter of the shaft.
  3. Select suitable type of the bearing from manufacturer’s catalogue.

Following guidelines can be used for selecting ball bearings:

Type of Ball Bearing

Fa/ Fr

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, C0. 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 Fa and Fr, and value of C0 of selected bearing. Refer table 28.2 for deep groove ball bearings.
6. Calculate equivalent dynamic load of the bearing,

285.png
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.

286.png
9.Dynamic load carrying capacity of the selected bearing should be greater than the required value calculated above, i.e.

287.png

If , choose higher series of the bearings from the catalogue and repeat the procedure from Step 3.

 

References

  1. Design of Machine Elements by VB Bhandari
  2. Analysis and Design of Machine Elements by V.K. Jadon
  3. Machine Design by R.S. Khurmi
  4. Design of Machine Elements by C.S. Sharma & K. Purohit
  5. 5.      SKF General Catalogue
Last modified: Monday, 24 March 2014, 9:20 AM