A helical gear has a transverse diametral pitch of 12, a transverse pressure angle of 14(1/2)°, 28 teeth, a face width of 1.25 in, and a helix angle of 30°. Compute the transverse circular pitch, normal circular pitch, normal diametral pitch, axial pitch, pitch diameter, and the normal pressure

Question

A helical gear has a transverse diametral pitch of 12, a transverse pressure angle of 14(1/2)°, 28 teeth, a face width of 1.25 in, and a helix angle of 30°. Compute the transverse circular pitch, normal circular pitch, normal diametral pitch, axial pitch, pitch diameter, and the normal pressure angle. Compute the number of axial pitches in the face width.

Accepted Answer

Transverse Circular Pitch
Use Equation (8-12):
[latex]p_{t}=\pi / P_{d}=\pi / 12=0.262 \mathrm{in}[/latex]
Normal Circular Pitch
Use Equation (8-13):
[latex]p_{n}=p_{t} \cos \psi=(0.262) \cos (30)=0.227 ext { in }[/latex]
Normal Diametral Pitch
Use Equation (8-16)
[latex]P_{ ext {nd }}=P_{d}/ \cos \psi=12 / \cos (30)=13.856[/latex]
Axial Pitch
Use Equation (8-14):
[latex]p_{x}=p_{t} / an \psi=0.262 / an (30)=0.453 ext { in }[/latex]
Pitch Diameter
Use Equation (8-15):
[latex]D=N / P_{d}=28 / 12=2.333 ext { in }[/latex]
Normal Pressure Angle
Use Equation (8-11):
[latex]\begin{gathered}\phi_{n}= an ^{-1}\left( an \phi_{t} \cos \psi ight) \\phi_{n}= an ^{-1}\left[ an \left(14 \frac{1}{2} ight) \cos (30) ight]=12.62^{\circ}\end{gathered}[/latex]
Number of Axial Pitches in the Face Width
[latex]F / p_{x}=1.25 / 0.453=2.76 ext { pitches }[/latex]
Since this is greater than 2.0, there will be full helical action.

Q. 8.2

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