Speed Reduction, Torque, high Rpms's?

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MountainDew
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hello, i am unsure if someone will be able to help me with this?

If you have a motor running at say 3000 rpm's, and the torque "needed" is more than the motor has to offer. Can you do a gear reduction to get more torque, and gain "all or most" of the lost rpm's back after reduction is made?

or maybe get more torque and more rpm's?
 
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If I understand the question correctly, the answer is 'no'. You could use gear reduction to increase the torque, then use another transmission after your high-torque load to output a high-speed/low-torque rotation. You could not, however, increase the speed of your load while maintaining extra torque.
 
The motor has a certain available power at any point on it's operating curve. The torque provided by a motor at a given speed is a function of it's construction and the components used to drive the motor, not what it is connected to.
 
In other words, if you gear-down the motor, you reduce the rmp and increase the torque, keeping the power the same. If you try to drive the motor faster (with higher voltage or frequency depending on the type of motor), you risk burning it out.