Question

I'm having problems on my homework with this one, so I threw some random numbers in my equation to follow your solution steps. Please help solve:

A speed reducing gearbox is typically required to reduce the speed of rotation of a drive from an electric motor shaft that has an initial rpm of 3,450rpm motor speed to the outshaft speed. The outshaft speed is 21rpm.

The given horsepower is as well 21 horsepower.

Please help me through the steps of designing a speed-reducing spur gearbox with these specifications.

Minimum teeth should not be less then 17 and not more then 150.

The Output shaft speed tolerance has to be within plus or minus 3% of the ideal output speed.

I know we typically start with finding the gear ratio, and gear size. Can you please walk me through this problem?

Answer 1

for designing the gear box for speed reduction we don't need power of the motor it is just the additional data available, do not get confused.

The formula written here is also proved below

Since nothing is mentioned regarding number of gears to be used or number of stages to be taken I have proceeded with minimum possible stages for the given limitation on gear teeth, you can also take as many as 6 stages or anything else for that matter. Because of the tolerance provided for output speed I could get integer values for Individual speed ratios but to get the output speed close to ideal that is 21RPM we can increase the teeth on driven gears( even numbered teeth) from the above calculated values.

for example to get exactly 21 RPM as output we can design as 20 teeth on 1st and 82.14 teeth on 2nd and keeping all other same, but fractional teeth is not possible so let us say 82 teeth then the output speed that can be obtained is 21.036RPM

Similarly for any particular output speed we can increase the no. of teeth on driven gear (even numbered) from the above values and obtain required values.