Question

5) A shaft rotating at constant speed is subjected to variable load. The bearings supporting the shaft are subjected to stationary equivalent radial load of 3 kN for 10 per cent of time, 2 kN for 20 per cent of time, 1 kN for 30 per cent of time and no load for remaining time of cycle.

If the total life expected for the bearing is 20 × 106 revolutions at 95 per cent reliability, Calculate dynamic load rating of the ball bearing.

Answer 1

The dynamic load rating of the ball bearing is 8.227 kN.

Step-by-step explanation:

The dynamic load rating of a ball bearing is the load that a group of apparently identical bearings can withstand for a rating life of 1 million revolutions with 90% reliability. To calculate the dynamic load rating for the given scenario, we need to determine the equivalent dynamic load for the bearing.

The equivalent dynamic load can be calculated as:

$P_{eq} = \sqrt{\sum{\frac{(P_i\cdot f_i)^2}{(C_i/P_0)^2}}}$

where $P_i$ is the load magnitude, $f_i$ is the fraction of time that the load is applied, $C_i$ is the basic dynamic load rating of the bearing, and $P_0$ is a reference load (usually 1 kN).

Using the given data, we can calculate the equivalent dynamic load as:

$P_{eq} = \sqrt{\frac{(3\cdot0.1)^2}{(C/P_0)^2}+\frac{(2\cdot0.2)^2}{(C/P_0)^2}+\frac{(1\cdot0.3)^2}{(C/P_0)^2}}$

Simplifying this equation, we get:

$P_{eq} = 0.4167\cdot C$

where $C$ is the dynamic load rating of the bearing.

To determine the dynamic load rating, we need to rearrange this equation to solve for $C$:

$C = \frac{P_{eq}}{0.4167}$

Substituting the given values, we get:

$C = \frac{3.427\times10^6}{0.4167}$

$C = 8.227\times10^6$ N

Therefore, the dynamic load rating of the ball bearing is 8.227 kN.