A double reduction gear train is required to drive a load at approximately 400rpm from a motor running at 3000rpm. A standard compound gear is to be used, made up of two gears of 20 and 50 teeth fixed on a common shaft. Calculate the number of teeth required on the output gear.

Question

A double reduction gear train is required to drive a load at approximately 400rpm from a motor running at 3000rpm.  A standard compound gear is to be used, made up of two gears of 20 and 50 teeth fixed on a common shaft. Calculate the number of teeth required on the output gear.

BlackTom AI · Accepted Answer

We need to determine the output gear tooth count for a two-stage compound gear reduction from a motor at 3000 rpm down to about 400 rpm.

First, identify the gear train arrangement. The standard compound gear is made up of two gears (20 and 50 teeth) fixed on a common shaft. The motor gear (Ti teeth) meshes with the 20-tooth gear on the intermediate shaft, and the 50-tooth gear on that same intermediate shaft meshes with the output gear (T_o teeth).

Compute the overall speed ratio. For a single mesh, the speed ratio is inverse to the tooth count of the driving gear. For the first stage:
- intermediate shaft speed = (Ti / 20) × input speed (since the 20-tooth gear on the intermediate shaft is driven by a Ti-tooth motor gear)
For the second stage:
- output speed = (50 / T_o) × intermediate speed (the 50-tooth gear on the same shaft drives the output gear with T_o teeth)
Therefore, overall speed ratio = (Ti / 20) × (50 / T_o).

Set up the target ratio from input to output. Desired output speed / input speed = 400 rpm / 3000 rpm = 0.1333...
Thus: (Ti / 20) × (50 / T_o) = 0.1333...

Assuming the motor gear on the input side has Ti = 20 teeth (a common simple pairing where the motor gear size matches the first driven gear), substitute Ti = 20:
(20 / 20) × (50 / T_o) = 0.1333...
1 × (50 / T_o) = 0.1333...
T_o = 50 / 0.1333... ≈ 375 teeth.

Conclusion (based on the stated assumption Ti = 20): the output gear should have approximately 375 teeth to achieve the desired 400 rpm from 3000 rpm using the given compound gear arrangement.

If a different motor gear tooth count Ti is used, the required output gear teeth T_o would adjust accordingly according to T_o = 50 × Ti / (20 × 0.1333...).

INU1127 (24/25) Mechanical Drives - Quiz 1

A double reduction gear train is required to drive a load at approximately 400rpm from a motor running at 3000rpm. A standard compound gear is to be used, made up of two gears of 20 and 50 teeth fixed on a common shaft. Calculate the number of teeth required on the output gear.

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