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

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.
Then

N_{P} =\frac {2k}{(1 + 2m) sin^{2}  \phi}\left( m +\sqrt {m^{2} + (1 + 2m) sin^{2} \phi}   \right)                   (13.11)

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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