A Shaft Rotating at Constant Speed is Subjected to Variable Load

PROBLEM

A shaft rotating at constant speed is subjected to variable load. The bearings supporting the shaft are subjected to a stationary equivalent radial load of 3kN for 10% of the time, 2kN for 20% of the time, 1kN for 30% of the time, and no load for the remaining time of the cycle. If the total life expected for the bearing is 20 x 106 revolutions at 95% reliability, calculate dynamic load rotating of the ball bearing. (b=1.17 , k=3 for ball bearings)

ANSWER

Dynamic loads

W1 = 3kN = 3 × 10N

W2 = 2kN = 2 × 10N

W3 = 1kN = 1 × 10N

Number of revolutions

n= 0.1n

n= 0.2n

n= 0.3n

n= [1- (0.1+0.2+0.3)]n = 0.4n

Life of the bearing corresponding to the reliability of 95% L90 =  20 × 10rev

Life of the bearing corresponding to the reliability of 90% L90 = ?

b = 1.17

Equivalent dynamic loads

So, the dynamic load rating,