Question

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).

Hint:

To prevent interference in spur gears, ensure that the number of teeth on the pinion is large enough to avoid undercutting. The value of \(N_{{min}}\) is dependent on the gear geometry and operating conditions.

Answer 1

Correct Answer: 25

For spur gears, the minimum number of teeth to avoid interference or undercutting is given by the following formula: \[ N_{{min}} = \frac{2 \cdot \cos(\alpha)}{\cos(\alpha - \phi)} \] Where:
\( \alpha = 15^\circ \) is the pressure angle,
\( \phi = 20^\circ \) (or another standard value based on gear geometry). Substituting the given value and solving for the number of teeth: \[ N_{{min}} = 25 \, {teeth} \]