Question

Two identical ball bearings P and Q are operating at loads 15 kN and 45 kN respectively. The ratio of life bearing P to Q is

1. 81
2. 27
3. 9
4. 3

Answer 1

Correct Answer - Option 2 : 27

Concept:

Load-Life relationship of a Bearing:

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

L10 = Rated bearing life (in million revolutions), C = Dynamic load-carrying capacity, P = Load acting on the bearing

n = 3 for ball bearing and n = 10/3 for roller bearing.

Calculation:

Given:

PP = 15 kN, PQ = 45 kN, n = 3 (∵ ball bearing) and CP = CQ (∵ identical bearing).

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

\(\therefore \frac{{{L_P}}}{{{L_Q}}} = {\left( {\frac{{{P_Q}}}{{{P_P}}}} \right)^3} = {\left( {\frac{{45}}{{15}}} \right)^3} = 3^3 =27 \)