Question

A ball bearing subjected to a radial load of 3000 N is expected to have a life of 40 million revolutions with a reliability of 95%. If the desired reliability is 50%, the life of the bearing in millions of revolutions

Answer 1

$P_e=F_r=3000N$

$\text{For, R = 0.95,}{L}_{95}=\text{40 million revolutions}$

$R=0.5,L_{50}=P$

$\text{We know that}$

$\frac{L}{L_{90}}={\left(\frac{ln\left(1/R\right)}{ln\left(1/R_{90}\right)}\right)}^{1/1.17}$

$\frac{L_{50}}{L_{95}}={\left(\frac{ln\left(1/0.5\right)}{ln\left(1/0.95\right)}\right)}^{1/1.17}$

$L_{50}=40\times {\left(\frac{ln2}{ln\left(1/0.95\right)}\right)}^{1/1.17}$

$L_{50}=370.27\text{million revolutions}$