Page 325 - Analysis and Design of Machine Elements

Rolling Contact Bearings
If F + S > S , the shaft has tendency to move to the left. The left bearing will be 303
2
a
1
squeezed while the right bearing will be relaxed. That is, for the left bearing, the shaft
together with the inner ring will press against the rolling elements and the outer ring,
while for the right bearing, the shaft and the inner ring will be pulled apart from the
outer ring. This will cause the separation of the inner and outer ring and reduces load
′
carrying area, which is not allowed. An appended thrust load S will generated in the
1
left bearing to establish a force equilibrium condition. Therefore, we have
′
S + S = F + S
1 1 a 2
The axial load each bearing carries will then be
{
′
A = S + S = F + S 2 (11.9)
1
1
a
1
′
A = S + S − F = S 2
1
2
a
1
Similarly, if F + S < S , the shaft has tendency to move right. There will be an addi-
a 2 1
′
tional thrust load S on the right bearing, which makes
2
S = F + S + S ′
1 a 2 2
The axial load of each bearing will then be
{
A = S 1 (11.10)
1
′
A = S + S = S − F
2 2 2 1 a
In summary, angular contact bearings often operate under the combination of radial
and axial loads. The axial load that an angular contact bearing can carry depends on the
bearing mounting direction, the magnitudes of induced thrust loads and the direction
and magnitude of external axial load. The procedure for determining axial loads on a
bearing is summarized as follows:
1. Determine the magnitude and direction of external axial load F and induced thrust
a
loads S ,S ;
1
2
2. According to the force equilibrium principle, judge the moving tendency of the shaft,
decide which bearing is relaxed and which one is squeezed
3. The axial load on the relaxed bearing is the induced thrust load itself, while the axial
load on the squeezed bearing is equal to the algebraic sum of the induced thrust load
at the relaxed bearing and the external axial load.
Readers can use a similar procedure to analyse axial load in the back to back mounted
bearings in Figure 11.9b.
11.2.3 Stress Analysis
Figure 11.10a shows selected points of a, b, c on the inner ring, outer ring and a rolling
element, respectively. As the rolling contact bearing is in operation, contact stresses gen-
erate between the contact surfaces of rolling elements and raceways each time a rolling
element passes through the loading zone. Considering the angular velocity of bearing
components discussed in Section 11.2.1, as well as load distributions in Figures 11.7 and
11.8, the stress variation at points of a, b and c is illustrated in Figure 11.10b. When the
number of repeated stress cycles accumulates and eventually exceeds the fatigue limit
of material, fatigue ensues.