## 613 Radial ball bearings

The essential elements of the multiball bearing is the inner externally grooved and the outer intern ally grooved ring races (tracks). Lodged between these inner and outer members are a number of balls which roll between the grooved tracks when relative angular motion of the rings takes place (Fig. 6.3(a)). A fourth important component which is not subjected to radial load is the ball cage or retainer whose function is to space the balls apart so that each ball takes its share of load as it passes from the loaded to the unloaded side of the bearing. The cage prevents the balls piling up and rubbing together on the unloaded bearing side.

Contact area The area of ball to track groove contact will, to some extent, determine the load carrying capacity of the bearing. Therefore, if both ball and track groove profiles more or less conform, the bearing load capacity increases. Most radial ball bearings have circular grooves ground in the inner and outer ring members, their radii being 2-4% greater than the ball radius so that ball to track contact, friction, lubrication and cooling can be controlled (Fig. 6.3(a)). An unloaded bearing produces a ball to track point contact, but as the load is increased, it changes to an elliptical contact area (Fig. 6.3(a)). The outer ring contact area will be larger than that of the inner ring since the track curvature of the outer ring is in effect concave and that of the inner ring is convex.

Bearing failure The inner ring face is subjected to a lesser number of effective stress cycles per revolution of the shaft than the corresponding outer ring race, but the maximum stress developed at the inner race because of the smaller ball contact area as opposed to the outer race tends to be more critical in producing earlier fatigue in the inner race than that at the outer race.

Lubrication Single and double row ball bearings can be externally lubricated or they may be prepacked with grease and enclosed with side covers to prevent the grease escaping from within and at the same time stopping dust entering the bearing between the track ways and balls.

6.1.4 Relative movement of radial ball bearing elements (Fig. 6.3(b))

The relative movements of the races, ball and cage may be analysed as follows:

Consider a ball of radius rb revolving Nb rev/min without slip between an inner rotating race of radius ri and outer stationary race of radius ro (Fig. 6.3(b)). Let the cage attached to the balls be at a pitch circle radius rp and revolving at Nc rev/min.

Linear speed of ball = 2^rbNb(m/s)

Linear speed of inner race = 2^riNi(m/s) Linear speed of cage = 2^rpNc(m/s)

Pitch circle radius rp

'p - 2 But the linear speed of the cage is also half the speed of the inner race

Hence Linear speed of cage = ^riNi(m/s)

If no slip takes place,

Linear speed of ball = Linear speed of inner race

Linear speed of cage

Half inner speed of inner race

Hence

rp 2

Example A single row radial ball bearing has an inner and outer race diameter of 50 and 70 mm respectively.

If the outer race is held stationary and the inner race rotates at 1200 rev/min, determine the following information:

(a) The number of times the balls rotate for one revolution of the inner race.

(b) The number of times the balls rotate for them to roll round the outer race once.

(c) The angular speed of balls.

(d) The angular speed of cage.

Assuming no slip,

Number of Ball _ Inner race ball rotations circumference = circumference

Number of ball rotations, 2-xrb = 2^ri

.'. Number of ball revolutions

"T

5 revolutions

(b) Number of Ball Outer race ball rotations circumference = circumference

Number of ball rotations, 2^rb = 2^ro

.'. Number of rotations o o

2^rb rb

= = 7 revolutions

Cage angular speed Nc

=25x1200 = 6000 rev/min ri + ro _ 25 + 35 2 = 2 30 mm r±

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