# Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the ex

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Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.

1. 6 kN
2. 44 kN
3. 54000 kN
4. 60000 kN

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Correct Answer - Option 2 : 44 kN

Concept:

The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.

${\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}}$

L10 = Rated bearing life (in million revolutions)

P = Load acting in bearing.

k = 3 for ball bearing and k = 10/3 for the roller bearing.

The relation between life in million revolutions and life in hours is given by:

$L_{10}=\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}$

where, L10h = rated bearing life in hours and N = speed of rotation in rpm.

Calculation:

Given:

N = 1500 rpm, P = 6 kN, L10h = 8100 hours, roller bearing k = 10/3

We know that;

${\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \times {10^6}{\rm\;{revolution}}$ and;

$L_{10}=\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}$

Combining both equations:

$\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}= {\left( {\frac{{\rm{C}}}{{\rm{6}}}} \right)^{{\frac{10}{3}}}}$

$\frac{8100\;\times \;1500 \;\times \;60}{10^6}= {\left( {\frac{{\rm{C}}}{{\rm{6}}}} \right)^{{\frac{10}{3}}}}$

C = 43.34 kN