Two shafts connected by circular spiral gears are 500 mm apart. The speed ratio is 3 and the angle between the shafts is 60°. The normal circular pitch is 20 mm. The spiral angles for the driving and driven gears are equal. Find (a) number of teeth on each gear, (b) exact centre distance, and

Question

Two shafts connected by circular spiral gears are 500 mm apart. The speed ratio is 3 and the angle between the shafts is 60°. The normal circular pitch is 20 mm. The spiral angles for the driving and driven gears are equal. Find (a) number of teeth on each gear, (b) exact centre distance, and (c) efficiency of the drive. Take friction angle equal to 6°.

Accepted Answer

Given: [latex] C=500 mm , i=3, \Sigma=60^{\circ}, ho_{n}=20 mm , \phi=6^{\circ} [/latex].

[latex] \beta_{1}=\beta_{2}=\frac{\Sigma}{2}=\frac{60}{2}=30^{\circ} [/latex].

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

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

[latex] 500=14.7 z_{1} [/latex].

or [latex] z_{1}=34 [/latex].

[latex] z_{2}=34 imes 3=102 [/latex].

Exact centre distance, [latex] C=\left(\frac{20 imes 34}{2 \pi} ight)\left[\frac{1}{\cos 30^{\circ}}+\frac{3}{\cos 30^{\circ}} ight]=499.87 mm [/latex].

Efficiency of the drive, [latex] \eta=\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 30^{\circ}}{\cos \left(30^{\circ}-6^{\circ} ight) \cos 30^{\circ}} [/latex].

[latex] =88.56 \% [/latex].

Question 14.38: Two shafts connected by circular spiral gears are 500 mm apa...

Related Answered Questions