I am designing a 12lb hobby robot with a 1000Kv BLDC motor at 14.8V nominal voltage and stall torque of 30A. How do I solve for the torque constant. I have seen equations where Kt(torque constant) = 1/Kv. And also equations where Kt = 30/pi(Kv). Which is the most accurate equation? Thank you,
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2\$\begingroup\$ Kt = 1/Kv. If you are using SI units throughout. (As it must be : Torque * Speed = power = Voltage * Current). The other equation differs only in a constant factor : therefore it is equally accurate, if you can figure out which system of units it is in. \$\endgroup\$– user16324Nov 9, 2020 at 14:57
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2\$\begingroup\$ A word of caution on Kv. These equations work when Kv is measured correctly, which means that the actual back EMF is measured when the motor is being rotated by an external force. Sometimes people measure it other ways, such as by running the motor no-load with an ESC. In this method you divide no load speed in RPM/Battery voltage. That may be useful but it is not correct for calculating torque. \$\endgroup\$– user57037Nov 9, 2020 at 18:08
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The equation for the torque constant of a BLDC motor: \$K_{\tau} = \frac{60}{2{\pi}K_{v(RPM)}} = \frac{1}{K_{v(SI)}} \$, where \$K_{\tau}\$ is the torque constant in \$\frac{N \cdot m}{A}\$, and \$K_v\$ is the speed constant, in either rpm or rad/s.
The speed constant given to you is almost certainly in rpm, not rad/s, so you would use the first equation with the unit conversion factor. You can verify the speed constant with an encoder/resolver, another motor, and an oscilloscope. Spin the test motor up to a constant velocity using the other motor (applying a constant voltage/duty cycle to the drive motor likely sufficient). Measure the induced backemf voltage from test motor with your oscilloscope, and the steady-state velocity of the test motor with the encoder/sensor (or by using frequency detection on your oscilloscope and scaling it based on the number of pole pairs). The steady state speed divided by the induced backemf will be the the Kv value of the motor (and will likely be more accurate than the one provided by the motor manufacturer/seller).
EDIT: The answer above is guilty of a common misconception regarding the measurement of the motor torque constant. The Kv rating commonly provided by motor sellers is obtained with this method, but it differs from the true value by a factor of \$ \sqrt{2}\$ for Wye wound motors, and \$ \sqrt{\frac{2}{3}} \$ for delta wound motors. See this video for further details.
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\$\begingroup\$ Kv should be measured with no current flowing in the windings. \$\endgroup\$ Nov 9, 2020 at 18:10
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\$\begingroup\$ i've obtained Kv with this method and compared the calculated Kt result against the one published in the motor datasheet, and they're consistent \$\endgroup\$– OcanathNov 9, 2020 at 18:15
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\$\begingroup\$ That is because the motor manufacturers use the same process as you. \$\endgroup\$ Nov 9, 2020 at 18:19
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\$\begingroup\$ so you're suggesting that a superior method for obtaining Kv might be to spin the motor to a constant velocity using, say, another motor, and measure the induced backemf no load? \$\endgroup\$– OcanathNov 9, 2020 at 18:21
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\$\begingroup\$ Yeah. Just to avoid the voltage drop in the winding due to no load current. \$\endgroup\$ Nov 9, 2020 at 18:23