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I created a simple electric motor following Khan Academy's tutorial, and now I am trying to figure out how I can find the torque from it (which should be quite small).

Here is an image of the setup from Khan Academy. I made something pretty similar.

enter image description here

Since I have yet to begin post-secondary education, I want to figure the torque of a simple electric motor (something similar to a Johnson motor) without using any math that requires calculus and beyond. I want to know if this is possible?

I do not know the magnetic field of my simple motor so I found this paper and I am using this formula that I found from it. The formula is also mentioned here, but the derivation seems to require integrals, which I have yet to learn.

enter image description here

I am trying to combine this equation with another I found online for finding the force of a motor which is

F = ILB (once again from Khan Academy)

whilst using

T = F (force) * r (radius), (from a textbook on motors, so I think I can use it)

To do a substitution to derive an equation for torque, listed below: enter image description here

If the formula works, then I believe that I can find the torque of the simple motor as I know the current of my motor, the voltage, the radius (and hence the length, using 2πr, I believe? Please correct me if I'm wrong), and the number of loops (N).

I got the information about the voltage and the current from a DC supply box, so I'm pretty sure its the right information, right?

Please let me know if there is something incorrect in my logic.

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    \$\begingroup\$ The easiest way is to mechancially measure the torque of the motor. Mount the motor so as it twists it pulls on a calibrated newton meter or similar at a known distance, that will give you the torque. You then vary the load and speed of the motor across its range. If you want to calculate it, you need to know the currents, votlages, disatances, resistances and magnets used, and that gets complicated. \$\endgroup\$
    – Puffafish
    Commented Aug 31, 2023 at 8:25
  • \$\begingroup\$ I created the motor a while back (and it is now disassembled) so I am wondering if there are other ways to find the torque? Or would you suggest for me to recreate the motor? I am wondering if I can use a broad assumption that my electric motor is x % efficient and work from there via calculations. \$\endgroup\$
    – WChan
    Commented Aug 31, 2023 at 8:53

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Torque is not a constant for a motor: it varies (a lot) with speed and other factors. Let's consider simplest value: stalling torque -- which is the rotational force it generates while being prevented from turning.

Your calculations omit the efficiency of the motor, which obviously is one of the most important aspects of a motor. You can easily see that the magnetic force generated depends on more than just radius and how much electricity is going in; one of the most important factors is the gap size between the magnetic parts and the exact orientation of the magnetic fields. It also depends on, for example, how much energy is being converted to heat by resistance.

Consider measuring the torque in the most basic way from its definition: torque is force (in newtons) x lever length (in metres).

You can do this by attaching small weights, determining the weight which just stops the motor turning. Or equivalently, by pushing down on a small digital scales (converting to newtons if it is calibrated in grammes or whatever units of mass.)

enter image description here
View along axis of motor

Obviously, there are inaccuracies in any measurement, but this will be sufficient to distinguish, say, a motor with twice as many turns or the effect of varying the voltage on the motor or the strength of the magnets.

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  • \$\begingroup\$ I created the motor a while back (and it is now disassembled) so I am wondering if there are other ways to find the torque? Or would you suggest for me to recreate the motor? I am wondering if I can use a broad assumption that my electric motor is x % efficient and work from there via calculations. \$\endgroup\$
    – WChan
    Commented Aug 31, 2023 at 8:47
  • \$\begingroup\$ I found this link (simplemotor.com/calculations) which allows me to calculate it based on some assumptions. \$\endgroup\$
    – WChan
    Commented Aug 31, 2023 at 8:52
  • \$\begingroup\$ You can work out the theoretical maximum torque, but there really is no substitute for measuring it. That link says "Now you can calculate the torque for this load at this speed assuming that you know efficiency of the motor." But you don't know the efficiency of the motor: you would be simply guessing. Is it 1%? 0.001%? This is engineering: Recreate the motor and measure. You'll first be astounded at how low the efficiency is. Then you'll be astounded by how efficient commercial motors are. \$\endgroup\$
    – jonathanjo
    Commented Aug 31, 2023 at 8:56
  • \$\begingroup\$ I thought about this some more and what you said made sense. So, if I were to try attaching weights, I don't know if it would be possible because the simple motor (check the picture above) does not really have a place to add a load. It's quite flimsy as well, as the single copper wire acting as the commutator is quite pliable. Or maybe I am just being shortsighted? What do you think? I might have to modify the design, but I am not too sure where to start. \$\endgroup\$
    – WChan
    Commented Aug 31, 2023 at 14:21

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