Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
A deep-groove ball bearing carries a steady radial load of $F_r = 4.5\text{ kN}$ with zero axial load at a shaft speed of $N = 1200\text{ rpm}$. The basic dynamic load rating of the bearing is $C = 27.0\text{ kN}$. The $L_{10h}$ rating life of the bearing in operating hours is ________ (answer in integer).
Answer Key:
3000
Step-by-Step Solution & Explanation
1. Rating life in millions of revolutions for a ball bearing ($p = 3$):
$L_{10} = \left(\frac{C}{P}\right)^3 = \left(\frac{27.0}{4.5}\right)^3 = 6^3 = 216\text{ million revolutions}$
2. Life in operating hours ($L_{10h}$):
$L_{10h} = \frac{L_{10} \times 10^6}{60 \times N} = \frac{216 \times 10^6}{60 \times 1200} = \frac{216,000,000}{72,000} = 3000\text{ hours}$