Question 13.4: A gearbox is needed to provide an exact 30:1 increase in spe...

Shigley’s Mechanical Engineering Design [EXP-6591]

A gearbox is needed to provide an exact 30:1 increase in speed, while minimizing the overall gearbox size. Specify appropriate teeth numbers.

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The previous example demonstrated the difficulty with finding integer numbers of teeth to provide an exact ratio. In order to obtain integers, factor the overall ratio into two integer stages.

e = 30 = (6)(5)

$N_2/N_3=6$ and $N_4/N_5=5$

With two equations and four unknown numbers of teeth, two free choices are available. Choose $N_3$ and $N_5$ to be as small as possible without interference. Assuming a 20° pressure angle, Eq. (13–11) gives the minimum as 16.

$N_P=\frac{2k}{(1+2m)\sin ^2\phi }(m+\sqrt{m^2+(1+2m)\sin ^2\phi } )$ (13.11)

Then

$N_2$ = 6 $N_3$ = 6(16) = 96

$N_4$ = 5 $N_5$ = 5(16) = 80

The overall train value is then exact.

e = (96/16) (80/16) = (6)(5) = 30

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