Induction Motors: Slip, Torque-Speed Characteristics and

An induction motor is industry's workhorse — a rugged AC motor whose rotor spins slightly slower than the stator's rotating magnetic field, with no brushes, no commutator and no electrical connection to the rotor. Currents are induced in the rotor by the relative motion, which gives the motor its name.

Induction motors matter because they consume an estimated 70% of industrial electricity: pumps, fans, compressors, conveyors and lifts. They are cheap, tough and nearly maintenance-free — and slip plus the torque-speed curve are essential for selecting and starting them.

Key Concepts

• Synchronous speed (Ns): the stator field's speed, Ns = 120f/P rpm (f in Hz, P poles).
• Slip (s): the rotor's fractional lag — s = (Ns − N)/Ns; typically 2–5% at full load.
• Rotor frequency: f2 = s·f — only a few hertz at running slip.
• Squirrel-cage rotor: bars shorted by end rings — simple, rugged, the common industrial type.
• Slip-ring rotor: windings brought out through slip rings so external resistance can raise starting torque and control speed.
• Pull-out torque: the peak of the torque-speed curve, typically 2–3 times full-load torque; beyond it the motor stalls.
• Starting current: direct-on-line starting draws 5–7 times rated current.

Formulas

Ns = 120f/P rpm; s = (Ns − N)/Ns. Power flow across the air gap Pg: rotor copper loss = s·Pg, mechanical power Pm = (1 − s)·Pg — slip is literally the fraction of air-gap power burned as rotor heat. Torque T = Pm/ωr newton-metres (ωr in rad/s). Maximum torque occurs at slip sm = R2/X2. Torque rises with slip, peaks, then falls: T ∝ s·V1²·R2/(R2² + (s·X2)²). Starting methods (star-delta, autotransformer, soft starter) cut the inrush; adding rotor resistance shifts the curve so maximum torque appears at start. Assumes balanced sinusoidal supply and linear magnetics.

Worked Example

A 4-pole, 50 Hz, 15 kW motor runs at 1470 rpm full load. Ns = 120 × 50/4 = 1500 rpm; s = (1500 − 1470)/1500 = 0.02. Rotor frequency f2 = 0.02 × 50 = 1 Hz. With 0.6 kW rotational losses, Pm = 15.6 kW; air-gap power Pg = 15.6/0.98 = 15.92 kW; rotor copper loss = 0.02 × 15.92 = 0.318 kW. Torque T = 15600/(2π × 1470/60) = 15600/153.94 = 101.3 N·m. At start (s = 1) it draws about 6 × rated current — roughly 168 A for a 28 A motor — which is why a star-delta starter cuts starting current to about one-third.

Common Misconceptions

• "The rotor spins at synchronous speed." It cannot — at zero slip no flux cuts the rotor, no current is induced, and torque is zero. The small lag is what makes it work.
• "Any slip means a fault." Small slip (2–5%) is normal and necessary. Only excessive slip from overload or low voltage signals trouble.
• "Speed can't be controlled." Variable-frequency drives change f, shifting Ns and the whole torque curve smoothly — the standard modern method.

Real-World Applications

Squirrel-cage motors run water pumps, fans, air-conditioner compressors and conveyor belts. Slip-ring motors start heavy crushers and hoists. VFD-driven motors give precise speed control in elevators and HVAC systems, and submersible motors lift water from borewells.

The induction motor turns slip — a tiny lag behind the rotating field — into torque: a little slip for efficient running, a lot of slip (tamed by starters) to get moving.