A pair of helical gears for parallel shafts are to be cut with a three-module hob. The helix angle is to be 20° and the centre distance between 153 and 159 mm. The angular velocity ratio is to approach 2:1 as closely as possible. Calculate the circular pitch and the module in the plane of rotation. Determine the number of teeth, pitch diameters, and the centre distance to satisfy the above conditions.
Question 14.32: A pair of helical gears for parallel shafts are to be cut wi...
\text { Given: } m_{n}=3 mm , \beta=20^{\circ}, C =153-159 mm , i \approx 2 .
m_{t}=m_{n} / \cos \beta=3 / \cos 20^{\circ}=3.19 mm .
p_{t}=\pi m_{t}=\pi \times 3.19=10 mm .
\text { For parallel helical gears, } \beta_{1}=\beta_{2} .
z_{2} / z_{1}=2 .
C=0.5 m_{t}\left(z_{1}+z_{2}\right)=0.5 z_{1} m_{t}(1+2)=1.5 \times 3.19 \times z_{1}=4.875 z_{1} .
\text { For } z_{1}=32, C=153.12 mm \text {, so that } z_{2}=64 .
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