Module 5: Motors, Actuators & FOC
4-wire resistance, wye/delta + tempco, Ke/Kt, FOC and current sensing.
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1conceptYou need to measure a motor phase resistance that is well under 1 Ω. Why is a 2-wire DMM reading unreliable, and what is the fix?
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At sub-ohm levels the test-lead and contact resistance (tenths of an ohm) is a large fraction of the reading, so 2-wire is not fine.
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Correct. A 4-wire Kelvin measurement forces current through one pair of leads and senses voltage with a separate pair right at the part, so lead/contact resistance drops out of the result.
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Changing the voltage range does not remove the series lead resistance from a 2-wire measurement.
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AC introduces inductive reactance in a motor winding and still includes lead resistance; it does not cancel the lead error.
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2calcA wye-connected (star) BLDC measures 1.0 Ω line-to-line. What is the per-phase resistance R_ph?
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1.0 Ω is the line-to-line value, which is two phases in series for a wye, not one phase.
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Correct. In wye, a line-to-line measurement is two phases in series: R_LL = 2·R_ph, so R_ph = 1.0 Ω / 2 = 0.5 Ω.
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2.0 Ω would be the line-to-line resistance for a 1.0 Ω per phase wye, the inverse of what is asked.
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0.67 Ω comes from the delta relation R_LL = (2/3)·R_ph; this motor is wye, so that formula does not apply.
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3calcA motor's phase resistance is 0.50 Ω at 20 °C. Copper has a temperature coefficient of about 0.0039 /°C. What is the phase resistance at 70 °C?
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Resistance rises with temperature for copper, so it cannot fall to 0.40 Ω.
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0.50 Ω ignores the 50 °C rise; copper resistance increases with temperature.
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Correct. ΔT = 50 °C, so R = 0.50·(1 + 0.0039×50) = 0.50·1.195 ≈ 0.60 Ω.
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0.75 Ω overshoots; that would need roughly a 0.010 /°C coefficient, not copper's ~0.0039 /°C.
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4conceptIn SI units, how do a motor's torque constant Kt (N·m/A) and back-EMF constant Ke (V·s/rad) relate?
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They are tied by energy conservation, not independent: measuring Ke gives you Kt.
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Correct. In consistent SI units Kt (N·m/A) and Ke (V·s/rad) are numerically equal; they are the same electromechanical coupling constant viewed from the torque side and the back-EMF side.
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There is no squaring relationship; the SI equality is linear (Kt ≈ Ke).
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The 2π factor appears only when mixing units like V/krpm; in proper SI (V·s/rad) the constants are equal, with no 2π.
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5scenarioYou are implementing field-oriented control (FOC) and the motor spins but produces little torque per amp. Which control setup is correct?
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Correct. Clarke takes the three phase currents abc to the stationary αβ frame, Park rotates αβ to the rotor dq frame; torque is produced by Iq, so you command Iq and drive Id toward zero to keep current aligned for maximum torque per amp.
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The transform names are swapped: Clarke is abc→αβ and Park is αβ→dq, and Iq (not Id) is the torque-producing current.
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Forcing Id high wastes current that produces no torque (and weakens/over-fluxes the field); only Iq should carry torque-producing current.
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Regulating raw αβ defeats FOC; the Park transform into dq is what lets you control torque (Iq) and flux (Id) as DC quantities.
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