GATE 2023 ME – Question 29
Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio $|\omega_2|/|\omega_1| = 1/4$, have their centers 30 mm apart. The number of teeth on the driver (gear 1) is _______.
(Answer in integer)
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Correct answer: 96
Explanation
For meshing gears the pitch diameter is $d = N/P$ with the same diametral pitch $P$. The centre distance is $\frac{d_1 + d_2}{2} = \frac{N_1 + N_2}{2P} = 30$, so $N_1 + N_2 = 2 \times 8 \times 30 = 480$. The speed ratio gives $\frac{\omega_2}{\omega_1} = \frac{N_1}{N_2} = \frac{1}{4}$, so $N_2 = 4N_1$. Then $5N_1 = 480$ and $N_1 = 96$.