Concept explainers
A 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1120 rev/min, and drives a gear at a speed of 544 rev/min. Find the number of teeth on the gear and the theoretical center-to-center distance.
The number of teeth on the gear.
The theoretical center to-center distance.
Answer to Problem 1P
The number of teeth on the gear is
The theoretical center to-center distance is
Explanation of Solution
Write the expression for the diametrical pitch for the pinion.
Here, the number of teeth on pinion is
Write the expression of velocity ratio in terms of the number tooth.
Here, the rotational speed of the gear is
Write the relation between number of tooth on pinion and gear and diameters of the pinion and gear.
Here, the pitch circle diameter of the gear is
Write the expression for the centre distance between gear and pinion.
Conclusion:
Substitute
Substitute
Thus, the number of teeth on the gear is
Substitute
Substitute
Thus, the centre distance is
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