## Is power, torque and RPM a linear relationship?

Hi I have a problem dealing with rpm power and torque.

I have a motor powering a gearbox which has a 20:1 ratio.

The power and rpm are not an issue so i have not looked at those figures but the motor produces 240Nm of torque. Since it is a 20:1 gearbox, i have assumed the torque is 20 times greater with the rpm being 20 times slower? Is this correct?

From there the power is transferred through a number of gears. Can I follow the same method above and assume the torque multiplies each time buy the gear ratio?

I.e. the gearbox shaft is connected to a 110mm shaft connected to a 600mm gear, therefore is the torque at the outer surface of the gear is equal to (240nm*20)*(600/110) = 26181.8Nm of torque?

Thank you.Hi I have a problem dealing with rpm power and torque.

I have a motor powering a gearbox which has a 20:1 ratio.

The power and rpm are not an issue so i have not looked at those figures but the motor produces 240Nm of torque. Since it is a 20:1 gearbox, i have assumed the torque is 20 times greater with the rpm being 20 times slower? Is this correct?

From there the power is transferred through a number of gears. Can I follow the same method above and assume the torque multiplies each time buy the gear ratio?

I.e. the gearbox shaft is connected to a 110mm shaft connected to a 600mm gear, therefore is the torque at the outer surface of the gear is equal to (240nm*20)*(600/110) = 26181.8Nm of torque?

Thank you.