How do I determine the terminal voltages and currents that will be produced by turning a dc motor at a known angular velocity and a known torque? I know that for a dc motor, the load torque has a linear relationship with speed (negative slope) and with current (positive slope). But these relationships are for when a voltage and current are being applied. Do the same relationships hold when a torque and angular velocity are being applied?

  • \$\begingroup\$ You can apply a known torque, and the motor will accelerate until its torque is equal and opposite. Or you can use a machine with an abundance of torque to bring the motor to a a known angular velocity regardless of torque. But you don't get to specify both torque and angular velocity (unless you also control the load on the generator's output). \$\endgroup\$
    – user57037
    Feb 6, 2015 at 21:56
  • \$\begingroup\$ So this generator is going to be attached to a door, and on the swing of the door, the motor will turn and produce volts and amps at the output terminals. I don't understand why I wouldn't be able to specify both torque and speed if we know what force we are applying to the door and what speed it is moving at. \$\endgroup\$
    – Jucesanc
    Feb 8, 2015 at 6:26
  • \$\begingroup\$ I don't want to argue over a fine point. You may KNOW both the torque and the angular velocity. What I mean is that you can not leave the motor out of the calculation. You can apply a torque and measure the angular velocity. But if you pick both torque and angular velocity before hand, it will just be luck if they match. The motor gets to decide how fast to spin, based on applied torque. See what I mean? \$\endgroup\$
    – user57037
    Feb 8, 2015 at 7:58

2 Answers 2


There are four major (electrical) parameters that are used by engineers when selecting a brushed dc motor: The torque constant (Nm/A), the "back-emf" constant (V/(rad/s)), the armature resistance (ohms), and the armature inductance (H). Normally the inductance is low enough that it is ignored. By some fluke of units it turns out that in the SI system the newton-meter/amp is numerically equal to the "back-emf" which is simply the volts/(radian/second) of rotation. When a motor spins it generates a voltage which is called "back-emf". This happens even when you are using the motor to generate torque by applying a voltage. The result is the faster it turns, the less current flows until an equilibrium is reached. More here:


The result is you can estimate the voltage the motor will produce at a given rotational velocity (Volt/(radian/second)). However, the actual output of the motor is going to vary a ridiculous amount so it really can't be depended on. Your best bet is to find an appropriate dc-dc converter that takes the nominal voltage of the motor as the input and outputs your desired voltage.


Also don't forget about the armature resistance that will limit the total power available.


There is theory and there is practice. I have no doubts about Faraday's / Lenz's laws etc. but expecting a formula for every possible set up is asking too much.

I would suggest you go back to first principles, do a few experiments and plot a few graphs. From those results draw your relationships.

Here's the sort of set up I'm thinking of. The motor and the 'generator' would be the same type of device so you should expect what goes in to be similar in magnitude to what comes out.

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note: The 'known torque' is a tricky one as the torque will vary with speed (bearing friction and 'windage') together with any current extracted from the generator.

You would start by calibrating the drive motor without the generator attached, measuring voltage, current and speed with 'no load'

You could then repeat this with known loads (torque calculated from applied force to the rotating shaft) so you have the voltage,current,speed and torque characteristics of the driving system.

You should expect that increasing torque on the motor reduces the rotational speed (at a given input voltage) and increases current.

Now you can attach your 'generator'

Start with the output of the generator open circuit and plot the output voltage against input speed. (From the input measurements you can estimate the 'no-load' torque of the generator). This will give you the maximum voltage you can expect at a given speed.

I would expect to see a value of about 1V per 1000 rpm.

Repeat with different electrical load on the generator (Rload) and see what happens as you take power (draw current) from the system.

Measuring torque.

There are two basic methods, contacting and non-contacting.

Contacting methods usually involve some type of brake or rubbing contact with the rotating shaft with a variable weight or spring system to apply a force.

Non contacting methods either measure the am(you are measuring three variables so you can calculate the torque at any given speed).ount twisting in a drive shaft or have a means of applying force with no physical contact (e.g. magnetic field).

  • \$\begingroup\$ I tried a similar experiment to try to draw some relationships. I coupled these mpja.com/13VDC-700-RPM-Gearhead-Motor/productinfo/16392%20MD two dc motors together. I attached the driving motor to a variable dc power supply, and I had the driven motor attached to an oscilloscope so that I could see what kind of voltage I would get. Should I not use an oscilloscope? Also I tried putting a multimeter in series to get the current but I wasn't getting any readings. For angular velocity I simply counted the rpm for different values from the dc supply. These results were inconclusive. \$\endgroup\$
    – Jucesanc
    Feb 6, 2015 at 18:07

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