GATE 2025 ME – Question 59
A pair of spur gears is required to maintain a velocity ratio of 1:2. The module of the gears is 10 mm and the addendum is 10 mm. If the operating pressure angle is 15°, the minimum number of teeth required on the pinion to ensure NO interference/undercutting is ____ (answer in integer).
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Correct answer: 49
Explanation
The gear has twice as many teeth as the pinion, so the gear ratio is $G = 2$. The addendum is 1 module. The minimum number of teeth on the pinion to avoid interference is $T = \frac{2a_w}{\sqrt{1 + \frac{1}{G}\left(\frac{1}{G} + 2\right)\sin^2\phi} - 1}$ with $a_w = 1$ and $\phi = 15°$. This gives $\frac{2}{\sqrt{1 + 0.5 \times 2.5 \times 0.06699} - 1} = \frac{2}{0.04101} = 48.8$, which rounds up to 49 teeth.