Two shafts inclined at an angle of 65° and with a least distance between them of 175 mm are to be connected by spiral gears of normal circular pitch 15 mm to give a reduction ratio 3:1. Find suitable diameters and number of teeth. Determine also the efficiency of the drive if the spiral angles are

Question

Two shafts inclined at an angle of 65° and with a least distance between them of 175 mm are to be connected by spiral gears of normal circular pitch 15 mm to give a reduction ratio 3:1. Find suitable diameters and number of teeth. Determine also the efficiency of the drive if the spiral angles are determined by the condition of maximum efficiency. The angle of firction is 7°.

Accepted Answer

[latex] ext { Given: } \quad \Sigma=65^{\circ}, C=175 mm , p_{n}=15 mm , i=3, \phi=7^{\circ} [/latex].

[latex] ext { For maximum efficiency, } \beta_{1}=0.5(\Sigma+\phi)=0.5(65+7)=36^{\circ}, \beta_{2}=29^{\circ} [/latex].

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

[latex] 175=\left[z_{1} imes 15 /(2 \pi)\left[1 / \cos 36^{\circ}+3 / \cos 29^{\circ} ight] ight. [/latex].

[latex] z_{1}=15.7 \cong 16 [/latex].

[latex] z_{2}=48 [/latex].

Maximum efficiency [latex] =[1+\cos (\Sigma+\phi)] /[1+\cos (\Sigma-\phi)] [/latex].

[latex] =\left(1+\cos 72^{\circ} ight) /\left(1-\cos 58^{\circ} ight)=85.56 \% [/latex].

Question 14.40: Two shafts inclined at an angle of 65° and with a least dist...

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