The GATE Grind

GATE 2024 ME – Question 22

Machine Design · Rolling and sliding contact bearings · 1 mark · Multiple choice

For a ball bearing, the fatigue life in millions of revolutions is given by $L = \left(\frac{C}{P}\right)^n$, where $P$ is the constant applied load and $C$ is the basic dynamic load rating. Which one of the following statements is TRUE?

  1. $n = 3$, assuming that the inner racing is fixed and outer racing is revolving
  2. $n = 1/3$, assuming that the inner racing is fixed and outer racing is revolving
  3. $n = 3$, assuming that the outer racing is fixed and inner racing is revolving
  4. $n = 1/3$, assuming that the outer racing is fixed and inner racing is revolving

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $n = 3$, assuming that the outer racing is fixed and inner racing is revolving

Explanation

Bearing life varies with the cube of the load ratio for ball bearings, so the exponent is $n = 3$ (it is $\frac{10}{3}$ for roller bearings), and $n = \frac{1}{3}$ would make life fall as the rating rises. The basic dynamic load rating $C$ is defined for the standard arrangement in which the inner ring rotates and the outer ring is fixed, so option C describes the case in which the formula applies directly.