Question

A ball bearing is operated on a work cycle consisting of three parts: a radial load of 3000 N at 1440 rpm for one quarter cycle, a radial load of 5000 N at 720 rpm for one half of cycle and a radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of the bearing is 10,000 hrs. The dynamic load cayying capacity of the bearing is

• A. 11, 000 N
• B. 33,000 N
• C. 55,000 N
  
• D. 22,000

Answer 1

The correct option is B 33,000 N

$\begin{array}{cccc}\text{P(N)}& \text{Element time (min)}& \text{speed (rpm)}& \text{Revolution N In element time}\\ \text{3000}& \text{0.25}& \text{1440}& \text{360}\\ \text{5000}& \text{0.5}& \text{720}& \text{360}\\ \text{2500}& \text{0.25}& \text{14.40}& \text{360}\\ \text{Total}& \text{1}& & \text{1080}\end{array}$

$\text{Equivalent load,}$

$P_e=\sqrt[3]{3\frac{360({3000}^3+{5000}^3+{2500}^3)}{1080}}$

$P_e=3823.01N$

$L_{90}=10000\text{hr}$

$L_{90}=10000\times 60\times 1080$

$=648\text{million revolutions}$

$L_{90}={\left(\frac{C}{P_e}\right)}^3\text{million revolutions}$

$C=[648\times (3823.01{)}^3{]}^{1/3}$

$C=33000N$