Question

The life of the ball bearing of 10KN is 8000hours. its life in hours,if the load is increased to 20KN, keeping all other conditions the same, is​

Answer 1

Given:

The life of the ball bearing of 10 kN is 8000 hours.

To Find:

Find life of bearing at load of 20 kN.

Solution:

$\mathbf{Initial \ Load\ (P_{1})= 10 \ kN}$

$\mathbf{Final \ Load\ (P_{2})= 20 \ kN}$

$\mathbf{Initial \ Life\ (L_{1})= 8000 \ Hours}$

$\mathbf{Final \ Life\ (L_{2})= ?}$

We know as load on bearing increase its life will decrease:

We know the relation between life and load for ball bearing, which are given below:

$\mathbf{\dfrac{L_{2}}{L_{1}}=\left (\dfrac{P_{1}}{P_{2}} \right )^{3}}$

On putting respective value in above equation:

$\mathbf{\dfrac{L_{2}}{8000}=\left (\dfrac{10}{20} \right )^{3}}$

$\mathbf{\dfrac{L_{2}}{8000}=\left (\dfrac{1}{2} \right )^{3}}$

$\mathbf{\dfrac{L_{2}}{8000}=\dfrac{1}{8}}$

On simplify:

$\mathbf{L_{2}= 1000 \ Hours}$

Means life of bearing at load of 20 kN is 1000 Hours.