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Question 14.36: A crown bevel gears of 48 teeth and a module of 2 is driven ...

A crown bevel gears of 48 teeth and a module of 2 is driven by a 24-tooth pinion. Calculate the pitch angle of the pinion and the shaft angle.

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Given:    m=2 mm , z_{1}=24, z_{2}=48 .

i=z_{2} / z_{1}=48 / 24=2 .

d_{1}=m z_{1}=2 \times 24=48 mm , d_{2}=2 \times 48=96 mm .

L=0.5\left[d_{1}^{2}+d_{2}^{2}\right]^{0.5}=0.5\left(48^{2}+96^{2}\right)^{0.5}=53.66 mm .

\sin \delta_{1}=d_{1} /(2 L)=48 /(2 \times 53.66)=0.4472 .

\delta_{1}=26.56^{\circ} .

\tan \delta_{1}=\sin \Sigma /(\cos \delta+i) .

\tan 26.56^{\circ}=\sin \Sigma /(\cos \Sigma+2) .

0.5=\sin \Sigma /(\cos \Sigma+2) .

0.5 \cos \Sigma+1=\sin \Sigma .

\text { Both sides are equal, if } \Sigma=90^{\circ} .

\text { Hence shaft angle is } 90^{\circ} .

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