Question

A ball bearing has a life of 380 million revolution under an equivalent radial load of 12 kN with 80% reliability. What will be the rated life of bearing, if load is doubled?

• A. 47.5 MR
• B. 25 MR
• C. 37.70 MR
• D. 19.84 MR

Answer 1

The correct option is B 25 MR

Given, $(L_{80}{)}_1=380MR$

$(P_c{)}_1=12kN$

We know that, $\because \frac{L_{80}}{L_{90}}={\left[\frac{ln\left(1/0.8\right)}{ln\left(1/0.9\right)}\right]}^{1/1.17}$

$L_{80}=1.90L_{90}$

$(L_{90}{)}_1=\frac{(L_{80}{)}_1}{1.90}=\frac{380}{1.90}=200MR$

Rated life of bearing is bearing life with 90% reliability

$L_{90}\alpha {\left(\frac{1}{P_c}\right)}^3$

$\frac{(L_{90}{)}_1}{(L_{90}{)}_2}={\left[\frac{(P_c{)}_2}{(P_c{)}_1}\right]}^3$

$\because (P_c{)}_2=2(P_c{)}_1$

$\frac{(L_{90}{)}_1}{(L_{90}{)}_2}=(2{)}^3$

$(L_{90}{)}_2=\frac{200}{8}=25MR$