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Chapter 15: Problem 17

For a gear having an outside diameter of \(3.000\) in., full-depth involute gear teeth with a diametral pitch of 20 , and a \(20^{\circ}\) pressure angle, find the pitch diameter of the gear, the circular pitch, the addendum, the dedendum, and the number of gear teeth.

Short Answer

Expert verified
The pitch diameter of the gear, the circular pitch, the addendum, the dedendum, and the number of gear teeth can be derived using specific formulas related to gear geometry. Considering the outside diameter of 3in, a diametral pitch of 20, and a 20-degree pressure angle, the above steps can guide in acquiring these parameters.

Step by step solution

01

Calculate the Pitch Diameter

The pitch diameter can be calculated using the formula: \( P_D = \frac{O_D - 2A}{cos(P_A)} \). Where: \(P_D\) is pitch diameter, \(O_D\) is outside diameter, \(A\) is addendum and \(P_A\) is pressure angle. Plugging in the given values, \(O_D = 3in\), \(A = \frac{1}{diametral pitch} = \frac{1}{20} = 0.05in\) and \(P_A = 20^{\circ}\), we get the pitch diameter.
02

Calculate the Circular Pitch

Circular pitch is given by the formula: \( CP = \frac{\pi}{diametral pitch}\). We plug in \(\pi\) and diametral pitch of 20, to find the circular pitch value.
03

Find the addendum

The addendum is already given as it's \(1 / diametral pitch \). Here, it's 0.05in.
04

Calculate the dedendum

The dedendum can be calculated as \(1.157 / diametral pitch\). Substituting diametral pitch of 20, we get the dedendum value.
05

Find the number of teeth

The number of teeth is given by \(N = pitch diameter * diametral pitch\). Substituting the values, we get the number of teeth on the gear.

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Most popular questions from this chapter

A gear speed reducer with a 10 to 1 speed reduction ratio has an output torque of \(50 \mathrm{lb}\) - in. at an output speed of \(100 \mathrm{rpm}\). The required input torque is \(6 \mathrm{lb}\). in. and the input speed is \(1000 \mathrm{rpm}\). Determine the efficiency of the speed reducer. Once the reducer reaches a steady state temperature, what happens to the energy lost by the reducer?

A 17-tooth pinion meshes with an 84-tooth gear. The full-depth involute gear teeth have a \(20^{\circ}\) pressure angle and a diametral pitch of 32 . Determine the arc of approach, arc of recess, arc of action, base pitch, and the contact ratio. Also calculate the addendum, dedendum, circular pitch, tooth thickness, and the base diameter for the pinion and gear. If the center distance is increased by \(0.125 \mathrm{in}\)., what are the new values for the contact ratio and the pressure angle?

A two-stage gear reducer using identical pinion and gear sets for the high- speed and low-speed stages (similar to Figure P15.23) is to be used between a 10-hp, 2700-rpm motor and a 300-rpm load. The center distance is to be 8 in. The motor involves "light shock" and the driven machine "moderate shock." The shafts and their mountings correspond to ordinary good industrial practice, but not to "high-precision" industrial practice. Design the gears for a life of \(10^{7}\) cycles with \(99 \%\) reliability and a safety factor of 1.2. Determine an appropriate combination of diametral pitch, face width, level of manufacturing precision, and material.

Two gears with a module of \(2 \mathrm{~mm}\) are mounted at a center distance of \(130 \mathrm{~mm}\) in a 4: 1 ratio reduction gearset. Find the number of teeth in each gear.

A pair of standard \(20^{\circ}\) spur gears with 10 -in. center distance has a velocity ratio of 4.0. The pinion has 20 teeth. (a) Determine \(P, p\), and \(P_{b}\). (b) Begin a full-size layout showing partial pitch circles, partial base circles, pressure angle, addendum, and dedendum. Label each of these on your drawing. (c) Show on your drawing the interference-limiting maximum addendum radii, \(r_{\text {ag,max }}\), and \(r_{\text {ap, max }}\). Scale their numerical values from the drawing. Will interference be encountered with teeth of standard proportions? (d) Measure on the drawing the length of the path of contact for standard tooth proportions and, from this, compute the contact ratio.
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