Set the supply voltage, armature resistance, torque/back-EMF constants and operating current to compute torque, speed, output power and efficiency in real time. Switch tabs to see torque-speed curves, power vs efficiency, and motor-type comparisons.
The torque constant Kt and back-EMF constant Ke are entered separately, but aren't they the same number in theory?
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Sharp catch! In an ideal DC motor, Kt (Nm/A) and Ke (V·s/rad) are numerically equal — it follows from energy conservation between electrical (V·I) and mechanical (T·ω) power. Real motors show slight differences because of iron loss, copper loss and friction, but for design calculations engineers usually assume Kt = Ke.
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What kind of motor do EVs use? Can I see it in the simulator?
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Tesla and the Nissan Leaf both rely on PMSMs because of >95% efficiency and excellent regenerative braking. The Model 3's rear motor is rated about 250 kW with peak torque around 420 Nm and 18,000 rpm. This tool defaults to small-motor parameters, but pushing voltage and Kt up gives you a feel for EV-class machines too.
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Why is the torque-speed curve a falling straight line?
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From V = IaRa + Keω we get Ia = (V − Keω)/Ra, and torque T = KtIa, so T is linear in ω. Stall (ω=0) gives the maximum torque, and zero load (T=0) gives the no-load speed; the line connects those two points. The actual operating point is set by where this line crosses the load curve.
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Induction motors have "slip", but PMSMs don't — why?
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In an induction motor the rotor torque comes from the speed difference (slip) between rotor and rotating stator field. Zero slip means no induced rotor current and zero torque, so there must always be some slip. A PMSM has permanent magnets locked to the stator field, so it spins at exactly synchronous speed with no slip — but it needs careful vector control to avoid losing sync.
Frequently Asked Questions
Q1. How do I increase a motor's torque?
Increase the current (T = Kt·I), increase the magnetic flux (higher Kt via more turns or stronger magnets), or use multiple motors in parallel. Higher current means more I²R copper loss, so cooling matters.
Q2. What does adding a gearbox do?
A gear ratio n multiplies output torque by n and divides speed by n: T_out = T_motor × n × η_gear. Many robots and power tools spin a small high-speed motor and use gearing to amplify torque.
Q3. What's the difference between continuous and peak rating?
Continuous rating is the safe steady-state load (S1 duty). Peak rating is for short bursts (seconds) at typically 2–5× continuous. Servo motors use peak torque only for acceleration; the steady operation must stay within continuous.
Q4. How does regenerative braking work?
The motor runs as a generator, converting kinetic energy back into electrical energy that recharges the battery. Both PMSMs and induction motors can do this; EVs typically recover 70–80% of decel energy. Mathematically it's just the operating point with reversed torque.
Real-World Applications
Automotive industry: EV traction motor designers use simplified equivalent circuits like this to size torque and speed envelopes before running detailed FEA in JMAG or Maxwell.
Education and research: Universities use real-time torque-speed plots to teach motor fundamentals; researchers use efficiency maps to study control strategies for PMSMs.
CAE workflow: A first-pass equivalent-circuit calculation sets boundary conditions for detailed 3D electromagnetic FEA, shortening the design cycle.
Common Misconceptions
"Motor torque is strictly proportional to current" is only true at low current. Magnetic saturation and armature reaction reduce Kt at high current. "Lower induction-motor slip is always better" is also wrong — at zero slip the motor cannot produce torque; the efficiency peak typically sits near 1–5% slip. And in inverter-fed PMSMs raising voltage doesn't always increase output: above base speed the controller enters field-weakening, where output torque actually drops.