Induction Motor Fundamentals

Slip is everything. The stator builds a field that rotates at synchronous speed; the rotor chases it and must never catch it — only the lag (slip) induces rotor current, and only rotor current makes torque. Drive the machine below: trace the torque–speed curve, see why starting inrush is ~6× rated with almost no torque to show for it, watch torque collapse as V² when voltage sags, and see what a V/f drive actually changes.

Machine
NEMA rotor design

Poles

Supply
Applied voltage
Supply frequency
V/f drive

Hold V/f: volts scale with hertz below 60 Hz (constant flux); above 60 Hz volts cap at the slider setting — field weakening.

Load
Load type
Load magnitude

100 % = rated shaft torque (1.0 pu). Fan torque is referenced to 60 Hz synchronous speed; constant-power torque is limited to 2.5× at low speed.

Torque–Speed Curve
—
Motor torque T(s) Load torque Breakdown torque ✛ Operating point
Stator Current vs Speed
Stator current I₁(s) Locked-rotor current Rated current (1 pu) ✛ Operating point
Readout — at the operating point

The Physics

The rotating field. Three-phase currents in the stator build a magnetic field that rotates at synchronous speed. The rotor only feels a changing field — and so only carries induced current — when it turns slower than the field. That fractional lag is the slip, and the rotor conductors see a frequency of s·f:

ns = 120·f / p  ·  s = (ns − n) / ns  ·  frotor = s·f

Torque needs slip. At exactly synchronous speed there is no relative motion, no induced rotor current, no torque — the curve pins to zero at ns. Thévenin-reducing the stator (Vth, Rth, Xth) gives the classic single-cage torque expression:

T = 3·Vth²·(R₂′/s) / ( ωs·[ (Rth + R₂′/s)² + (Xth + X₂′)² ] )

Torque ∝ V². Voltage appears only as Vth², so the whole curve — breakdown torque included — scales with the square of the applied voltage. An 80 % sag leaves 64 % of the torque; a 50 % reduced-voltage start leaves just 25 %. That is the entire trade in soft-starting: every volt you give up to tame inrush costs you double in torque.

Why locked-rotor current is huge but torque isn't. At standstill s = 1, so the rotor conductors see full line frequency and rotor reactance dominates rotor resistance (X₂′ ≫ R₂′/s). Only the leakage impedances limit the current — roughly 1/(X₁+X₂′) ≈ 5–6 pu — but the rotor circuit is nearly pure reactance: terrible rotor power factor, so almost none of that enormous current makes torque. As the rotor accelerates, s·f falls, the rotor turns resistive, and current drops only in the last stretch before full speed. This is why starting duty is thermally brutal.

Slip is loss. The air-gap power splits in fixed proportions — the slip fraction never reaches the shaft; it is dissipated in the rotor conductors:

Pairgap : Protor loss : Pmech  =  1 : s : (1 − s)

NEMA designs = a rotor-resistance dial. Design A (low R₂′) runs tight slip and high efficiency but makes the least starting torque. Design B is the general-purpose compromise. Design D (high R₂′) shifts the torque peak all the way to standstill — huge breakaway torque for punch presses, cranes and hoists — but pays for it with 5–13 % running slip, i.e. permanent rotor heating. Same breakdown torque in all three: R₂′ moves where the peak sits, not how tall it is.

⚡ Deep bars & V/f drives. Real Design B rotors cheat with deep or double-cage bars: at start the rotor sees 60 Hz, skin effect crowds current into the bar top (high R — Design-D-like punch), and at running slip the whole bar conducts (low R — Design-A-like efficiency). Our single-cage model can't do that, which is why its locked-rotor torque looks modest. A V/f drive sidesteps the problem entirely: holding V/f keeps flux constant, so the whole torque curve simply slides along the speed axis with its peak intact — the motor starts at a few Hz with rated torque and a fraction of the inrush.