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:

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.

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.

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.

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

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

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

where,             L10       = rated bearing life

C         = dynamic load carrying capacity

k          = load life exponent    = 3       for ball bearings

= 10/3  for roller bearings

 Also,

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,

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

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