Sanity check for max motor torque

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

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.

• N*m ? Isn’t newton metre represented as N.m or N m ? Apr 30 '20 at 5:40
• motor torque is proportional to the current, no additional conversion factors required :) Apr 30 '20 at 6:18
• @SolarMike It’s been clearer to use N*m in my problems, but N.m is certainly shorter. I’ll try it going forward Apr 30 '20 at 6:21
• 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. Apr 30 '20 at 7:43
• @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! Apr 30 '20 at 18:22