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Chapter 12: Problem 45

A \(25^{\circ}\) pressure angle, 32 -tooth spur gear has a diametral pitch of 4 . Find the pitch diameter, addendum, dedendum, outside diameter, and circular pitch.

Short Answer

Expert verified
The pitch diameter is 8 inches, the addendum is 0.25 inches, the dedendum is 0.28925 inches, the outside diameter is 8.5 inch, and the circular pitch is 0.785 inches.

Step by step solution

01

Calculate for Pitch Diameter

The pitch diameter of a spur gear can be determined by the formula \(D_p = \frac{N}{P}\), where \(N\) is the number of teeth and \(P\) is the diametral pitch. Substituting the given values, the equation becomes \(D_p = \frac{32}{4} = 8\) inches.
02

Calculate for Addendum

The addendum (height of the tooth above the pitch circle) can be calculated as the inverse of the diametral pitch. Therefore, the addendum \(a = \frac{1}{P} = \frac{1}{4} = 0.25\) inches.
03

Calculate for Dedendum

The dedendum (depth of the tooth below the pitch circle) is 1.157 times the addendum. Therefore, the dedendum \(d = 1.157 \times a = 1.157 \times 0.25 = 0.28925\) inches.
04

Calculate for Outside Diameter

The outside diameter \(D_o\) is given by the equation \(D_o = D_p + 2 \times a = 8 + 2 \times 0.25 = 8.5\) inches.
05

Calculate for Circular Pitch

The circular pitch (distance from one tooth to the next on the pitch circle) can be found by the formula: \(CP = \frac{\pi}{P} = \frac{\pi}{4} = 0.785\) inches.

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Most popular questions from this chapter

A \(20^{\circ}\)-pressure-angle, 27-tooth spur gear has a diametral pitch \(p_{d}=5\). Find the pitch dia. addendum, dedendum, outside dia, and circular pitch.

A \(20^{\circ}\) pressure angle, 23-tooth spur gear has a diametral pitch of 6. Find the pitch diameter, addendum, dedendum, outside diameter, and circular pitch.

The pinion of an external gearset has pitch radius \(r_{p}=40 \mathrm{~mm}\) and the gear has pitch radius \(r_{g}=160 \mathrm{~mm}\). If the pinion is the input member of the set, determine the velocity ratio, the torque ratio, and the gear ratio of the set.

A pinion having 20 teeth and a diametral pitch of 8 (in-1) is in mesh with a rack. If the pinion rotates one revolution, how far will the rack move?

The pinion of an internal gearset has pitch radius \(r_{p}=30 \mathrm{~mm}\) and the gear has pitch radius \(r_{g}=150 \mathrm{~mm}\). If the pinion is the input member of the set, determine the velocity ratio, the torque ratio, and the gear ratio of the set.
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