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Chapter 13: Problem 47

A 2-start wormset has \(L=2.00 \mathrm{in}, C=9.00 \mathrm{in}, m_{G}=20\), and the angle between the shafts is \(90^{\circ}\). Find the pitch diameters of the worm and worm gear, the lead angle, and the axial pitch.

Short Answer

Expert verified
The pitch diameters of the worm and the worm gear are 1.273 inches and 16.727 inches respectively. The lead angle is 1.01 radian or 57.8 degrees, and the axial pitch is 2.00 inches.

Step by step solution

01

Calculate the Lead (P1)

First, the lead (P1) is obtained. Using the formula \[ P1 = 2脳L \], the result is P1 = 2脳2.00 = 4.00 inches.
02

Calculate the Pitch Diameter of the Worm (d1)

Secondly, use the resulting lead to find the pitch diameter of the worm using the equation \[ d1 = P1梅蟺 \]. Hence, d1 = 4.00 梅 3.1416 = 1.273 inches.
03

Calculate the Pitch Diameter of the Gear (d2)

Thirdly figures out the pitch diameter of the gear using the result of the worm pitch diameter. Use \[ d2 = 2脳C - d1 \] equation to find d2. Therefore, d2 = 2脳9.00 - 1.273 = 16.727 inches.
04

Calculate the Lead Angle (位)

Next, compute the lead angle with the formula above as in Step 4: \[位 = arctan(P1梅(蟺脳d1))\]. Hence, 位 = arctan(4.00 梅 (3.1416 脳 1.273)) = 1.01 (in radian) or 57.8 degrees (in degrees).
05

Calculate Axial Pitch

Finally, figure out the axial pitch using the equation \[Axial pitch = P1梅Number of starts\], and because the number of start is already given as 2, the axial pitch would be 2.00 inches.

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Most popular questions from this chapter

A \(90^{\circ}\) straight-bevel gearset is needed to give a \(4.5: 1\) reduction. Determine the pitch cone angles, pitch diameters, and gear forces if the \(20^{\circ}\)-pressure-angle pinion has 18 teeth of \(p_{d}=5\), and the transmitted power is \(7460 \mathrm{~W}\) at 800 pinion rpm.

A \(25^{\circ}\)-pressure-angle, \(20^{\circ}\)-helix-angle, 43-tooth helical gear has a diametral pitch \(p_{d}=8\). Find the pitch diameter, addendum, dedendum, outside diameter, normal, transverse, and axial pitch.

A 1 -start wormset has \(d=2.00\) in, \(p_{x}=0.25 \mathrm{in}, m_{G}=40\). Find the lead, lead angle, worm gear diameter, and center distance. Will it self- lock? The input speed is \(1100 \mathrm{rpm}\).

A \(90^{\circ}\) straight bevel gearset is needed to give a \(6: 1\) reduction. Determine the pitch cone angles, pitch diameters, and gear forces if the \(20^{\circ}\) pressure angle pinion has 20 teeth of \(p_{d}=8\), and the transmitted power is \(3 \mathrm{~kW}\) at 900 pinion rpm.

A 3-start wormset has \(d=60 \mathrm{~mm}, p_{x}=12 \mathrm{~mm}, m_{G}=60\). Find the lead, lead angle, worm gear diameter, and center distance. Will it self-lock? The input speed is \(2500 \mathrm{rpm}\).
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