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 × 10³ N

W₂ = 2kN = 2 × 10³ N

W₃ = 1kN = 1 × 10³ N

Number of revolutions

n₁ = 0.1n

n₂ = 0.2n

n₃ = 0.3n

n₄ = [1- (0.1+0.2+0.3)]n = 0.4n

Life of the bearing corresponding to the reliability of 95% L₉₀ =  20 × 10⁶ rev

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

b = 1.17

Equivalent dynamic loads

So, the dynamic load rating,