A KDE brushless DC motor has:

  • Kt = 0.0189 N*m/A (Kv = 505 rpm/V)
  • R = 7 mΩ
  • voltage range of about 30-60 VDC
  • Specsheet link

Assume the motor is

  • connected to 30 VDC input
  • ideal, sensored, six-step commutation speed controller
  • initially stationary (zero back-EMF)
  • perfectly cooled

Is the max torque of the motor equal to 81 N*m, or do I need a conversion factor for per-phase/line-to-line?

$$ T_{max} = k_{t}I_{max} = k_{t}\frac{V}{R}$$ $$ T_{max} = (0.0189 \frac{N \cdot m}{A}) \frac{30 V}{0.007 \Omega}$$ $$ T_{max} = 81 N\cdot m$$

I forgot to admit that the “max current” is outrageous to begin with. Without good cooling, the motor can melt at 10s of Amps, let alone 10s of thousands. I’m just curious if there are any other conversion factors needed for the torque calculation.

  • \$\begingroup\$ N*m ? Isn’t newton metre represented as N.m or N m ? \$\endgroup\$
    – Solar Mike
    Apr 30 '20 at 5:40
  • \$\begingroup\$ motor torque is proportional to the current, no additional conversion factors required :) \$\endgroup\$
    – Ocanath
    Apr 30 '20 at 6:18
  • \$\begingroup\$ @SolarMike It’s been clearer to use N*m in my problems, but N.m is certainly shorter. I’ll try it going forward \$\endgroup\$
    – techSultan
    Apr 30 '20 at 6:21
  • 2
    \$\begingroup\$ They specify a max current of 290 A, which given the 0.0189 Nm/A figure gives you 5.481 Nm. Don't forget that motors have several limits on their maximum current. One is winding temperature. Another is that a high enough winding current will demagnetise the motor, instantly giving you a permanent new torque constant of approaching 0 Nm/A, not so good. \$\endgroup\$
    – Neil_UK
    Apr 30 '20 at 7:43
  • 1
    \$\begingroup\$ @techSultan With a small permanent magnet brushed DC motor that would typically be started by just connecting it to the nominal voltage, you could always expect Imax at stall = V/Rmotor to be below Idemag. With a BLDC which is used with an ESC which can control the current, that is no longer the case. You can guarrantee Idemag is less than any max current they specify, whether continuous or peak. If it's not specified, then you're on your own. You could sacrifice one motor to test perhaps. My guess is that 2x nominal current may be safe, but it's not my motor or my money! \$\endgroup\$
    – Neil_UK
    Apr 30 '20 at 18:22

Technically speaking, if you could dump 4285A in that motor steady state at 30V without melting it to slag, then yes that is the stall torque you'd get.

Dumping 128,571 watts into that motor might have some amusing results, but the end result won't be an exciting 81 Nm of torque. Use the rated motor current from the spec sheet instead.

Also, it is useful to note that with an ideal sensorless six step controller, you won't even be able to get the rated stall torque. In a practical setting, you need a sensored BLDC driver for high torques at low (to zero) speeds.

  • \$\begingroup\$ Hot damn, thanks for catching my sensored/sensorless issue. I knew that. I’ve edited my question to ignore the outrageous current figures. Even their “rated” current is only for 3 min with excellent cooling. \$\endgroup\$
    – techSultan
    Apr 30 '20 at 6:17
  • \$\begingroup\$ I think this is off topic but... if you're looking for a stronger motor, you can easily find motors off the shelf that are wound for (significantly) more torque in that form factor, for less than a 10th of the price. BLDC motors are so simple, reliability isn't really a problem with the cheap ones, and in my experience the Kv value listed is generally pretty accurate (I think you know already you can get Kt from Kv). In my opinion, cheap BLDC motor + expensive controller is far better than expensive BLDC motor + cheap controller. \$\endgroup\$
    – Ocanath
    Apr 30 '20 at 6:31
  • \$\begingroup\$ thanks for additional comment. This was just a thought exercise. What high quality controllers would you pair with this motor in, say, a robotic application with precision torque control? \$\endgroup\$
    – techSultan
    Apr 30 '20 at 6:47
  • 1
    \$\begingroup\$ technically shopping advice, so idk if we'll get flagged. I personally build robots on the side, and I use my own FOC board that I designed for all of my motors (that has a really nice form factor, sits right on the motor shaft). If you don't want the technical overhead of making your own FOC board, ODrive is a good choice. \$\endgroup\$
    – Ocanath
    Apr 30 '20 at 6:52

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