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Each button recomputes the steady-state model for the current settings.
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How to use
The motor switches itself on a moment after reset. Press Guided tour for a narrated slow-motion explanation, pick a preset (fan, heavy load, stall, voltage sag, star start, wound rotor, drive at 15 Hz, other pole counts), or change any slider. Space pauses, R resets, Switch ON / OFF controls the supply. Red and blue arcs show the rotating N and S poles of the stator field; windings A (red), B (yellow) and C (blue) glow with their phase current; the orange glow in the rotor bars is the induced current; green arrows are the force on each bar. The needle bar below the section shows the speed against the synchronous speed (green tick). Tick Slip stroboscope to see the rotor drift slowly backwards relative to the field.
The science
Rotating field. Three stator windings placed 120 degrees apart in space carry currents 120 degrees apart in time, ia = I sin(wt), ib = I sin(wt - 120 deg), ic = I sin(wt + 120 deg). Their combined flux density is a wave travelling round the air gap, B(a, t) = B0 cos(p/2 * a - w t), that turns at the synchronous speed
n_s = 120 f / p (rpm), w_s = 2 pi f / (p/2) (rad/s)
Slip and induction. The rotor turns at n a little slower than the field. Relative to the rotor the field sweeps by at n_s - n, so each short-circuited bar sees a changing flux (Faraday) and carries a current at the slip frequency
s = (n_s - n) / n_s, f_rotor = s f
The bar current lags its emf by atan(s X2 / R2). The force on each bar is F = i L x B; the sum over the bars is the torque. At s = 0 there is no relative motion, no current and no torque, which is why an induction motor cannot reach synchronous speed.
Equivalent circuit (per phase, referred to the stator). R1, X1 stator winding, Xm magnetising branch, R2'/s, X2' rotor branch. With the current I2' in the rotor branch
P_gap = 3 I2'^2 R2'/s, P_cu2 = s P_gap, P_mech = (1 - s) P_gap, T = P_gap / w_s
Thevenin reduction of the stator side gives a closed-form torque and the breakdown (pull-out) point:
T(s) = 3 Vth^2 (R2'/s) / ( w_s [ (Rth + R2'/s)^2 + (Xth + X2')^2 ] )
s_max = R2' / sqrt(Rth^2 + (Xth + X2')^2), T_max = 3 Vth^2 / ( 2 w_s [ Rth + sqrt(Rth^2 + (Xth + X2')^2) ] )
Torque scales with V^2 (voltage sag halves the breakdown torque at 70 % voltage), and the position of the peak scales with the rotor resistance R2' but its height does not (the wound-rotor starter resistor experiment). A variable-frequency drive keeps V/f constant to keep the flux, and so the breakdown torque, roughly constant.
Mechanical model. J dw/dt = T_e(s) - T_load(w) - T_friction, with a fan load T = T0 (w/w0)^2 or a constant torque. The load and friction values are typical, not those of a specific machine.
Honest simplifications. (1) The electrical side is quasi-static (a steady-state phasor model): the fast switching transient of the first few supply cycles and the oscillating torque at start are not shown. (2) No iron (core) loss, no magnetic saturation (Xm is constant), no skin effect in the bars (R2 does not change with slip), no harmonics. (3) Parameters are textbook-class values for a 3 kW, 400 V, 50 Hz, 4-pole machine, not measurements of a real motor. (4) The cut-away shows a 4-pole winding layout; the pole-count selector changes the physics and the glowing field pattern. (5) In the 3D view bar-current and force arrows are a visual encoding of the model, scaled to the locked-rotor current.
Checks run in the page. T-circuit torque against the Thevenin closed form; breakdown torque and slip against a numerical scan; the energy balance P_in = P_cu1 + P_cu2 + P_mech; the angular speed of the space vector of three phase currents against 2 pi f; and an integrated start-up against the algebraic operating point.