A pair of helical gears having 30 and 48 teeth and a 23° helix angle transmits power between parallel shafts. The module in the normal plane is 3 mm, and the pressure angle in this plane in 20°. Determine (a) the module in the plane of rotation, (b) pitch diameters, (c) centre distance, (d) circular

Question

A pair of helical gears having 30 and 48 teeth and a 23° helix angle transmits power between parallel shafts. The module in the normal plane is 3 mm, and the pressure angle in this plane in 20°. Determine (a) the module in the plane of rotation, (b) pitch diameters, (c) centre distance, (d) circular pitch in the normal plane, and (e) circular pitch in the plane of rotation.

Accepted Answer

Given: [latex] z_{1}=30, z_{2}=48, m_{n}=3 mm , \alpha_{n}=20^{\circ}, \beta=23^{\circ} [/latex].

(a) [latex] m_{t}=m_{n} / \cos \beta=3 / \cos 23^{\circ}=3.259 mm [/latex].

(b) [latex] d_{1}=z_{1} m_{n} / \cos ^{3} \beta=30 imes 3 / \cos ^{3} 23^{\circ}=115.4 mm [/latex].

[latex] d_{2}=z_{2} m_{n} / \cos ^{3} \beta=48 imes 3 / \cos ^{3} 23^{\circ}=184.64 mm [/latex].

(c) [latex] C=0.5 m _{t}\left(z_{1}+z_{2} ight)=0.5 imes 3.259(30+48)=127.1 mm [/latex].

(d) [latex] p_{n}=\pi m_{n}=\pi imes 3=11.42 mm [/latex].

(e) [latex] p_{t}=\pi m_{t}=\pi imes 3.259=10.238 mm [/latex].

Question 14.34: A pair of helical gears having 30 and 48 teeth and a 23° hel...

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