The expected life of a ball bearing subjected to a load of 9800N and working at 1000 rpm is 3000 hrs. What is the expected life of the same bearing for a similar load of 4900N and speed of 2000 rpm?

Unchanged

12000 hrs

1500 hrs

6000 hrs
Solution:
From the FE Reference Handbook, \[C = PL^{\dfrac{1}{a}},\] where,
C = minimum required basic load rating
P = design radial load
L = design life (in millions of revolutions)
a = 3 for ball bearings, \(\dfrac{10}{3}\) for roller bearings
\[\begin{aligned}
\dfrac{L_1}{L_2} &= \left[\dfrac{P_2}{P_1}\right]\\
\dfrac{1000 \times 60 \times 3000}{2000 \times 60 \times t_2} &= \left[\dfrac{4900}{9800}\right]\\
t_2 &= 12000\ \mathrm{hrs}\end{aligned}\] Ans: B