GATE ME 2025 Set 1 — Question 59
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Interference & Undercutting
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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).
Correct answer
25 to 25
Solution
For a pinion meshing with a larger gear of gear ratio , interference is avoided when the addendum circle of the gear does not cut the line of action beyond the interference point of the pinion. This gives the minimum number of pinion teeth:where is the addendum in modules.Data: velocity ratio ; addendum mm module ; , .The number of teeth must be a whole number not less than this, so the pinion needs at least 25 teeth.(Using the formula with and swapped, which gives about 8.4, is the common mistake: that is the limit for the gear's teeth, not the pinion's.)Answer: 25
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