Two spiral gears in mesh have the following data:
Angle of friction = 6°
Normal circular pitch = 20 mm
Shaft angle = 55°
Speed ratio = 3
Approximate centre distance = 400 mm
Spiral angle of pinion = 25°
Determine (a) the exact centre distance, (b) the number of teeth in each wheel, and (c) the efficiency
of the drive.

Question

Accepted Answer

[latex] ext { Given: } \quad \phi=6^{\circ}, p_{n}=20 mm , \Sigma=55^{\circ}, i=3, C \cong 400 mm , \beta_{1}=25^{\circ} [/latex].

[latex] C=\left(\frac{z_{1} p_{n}}{2 \pi} ight)\left[\frac{1}{\cos \beta_{1}}+\frac{i}{\cos \beta_{2}} ight] [/latex].

[latex] 400=\left(\frac{z_{1} imes 20}{2 \pi} ight)\left[\frac{1}{\cos 25^{\circ}}+\frac{3}{\cos 30^{\circ}} ight] [/latex].

[latex] z_{1}=27.51 \approx 28 [/latex].

[latex] z_{2}=84 [/latex].

Exact centre distance, [latex] C=\left(\frac{z_{1} p_{n}}{2 \pi} ight)\left[\frac{1}{\cos \beta_{1}}+\frac{i}{\cos \beta_{2}} ight] [/latex].

[latex] =\left(\frac{28 imes 20}{2 \pi} ight)\left[\frac{1}{\cos 25^{\circ}}+\frac{3}{\cos 30^{\circ}} ight] [/latex].

[latex] =407.08 mm [/latex].

Efficiency of drive, [latex] =\frac{\cos \left(\beta_{2}+\phi ight) \cos \beta_{1}}{\cos \left(\beta_{1}-\phi ight) \cos \beta_{2}} [/latex].

[latex] =\frac{\cos \left(30^{\circ}+6^{\circ} ight) \cos 25^{\circ}}{\cos \left(25^{\circ}-6^{\circ} ight) \cos 30^{\circ}} [/latex].

[latex] =81.54 \% [/latex].

Question 14.39: Two spiral gears in mesh have the following data: Angle of f...

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