Braking, Cogging and Crawling

A mechanical brake converts kinetic energy into heat in a friction lining that wears. Electrical braking makes the machine itself produce a torque opposing rotation, so the stored energy is dissipated in the rotor circuit or returned to the supply. Three methods are used with induction motors.

Interchanging any two stator leads reverses the direction of the rotating field. The rotor, still turning forward at speed \(N\), now moves against the field, so its slip relative to the new field is

• The rotor frequency jumps to almost \(2f\); rotor EMF is nearly twice its standstill value, and the current is higher than the starting current.

• The braking torque is modest because \(R_2'/s\) is small compared with the reactance at this slip; slip-ring motors insert external rotor resistance to raise it and limit current.

• The supply must be disconnected the moment the speed reaches zero — otherwise the motor accelerates in reverse. A zero-speed (plugging) switch on the shaft does this.

The stator is disconnected from the AC supply and a DC current is passed through two of its phases. This sets up a stationary magnetic field. The rotating rotor cuts this field, EMF and current are induced, and the resulting torque opposes motion.

• Relative to the stationary field the "slip" is simply the per-unit speed, so the braking torque falls to zero as the rotor stops — the motor cannot reverse.

• Braking torque is controlled by the DC current magnitude; the kinetic energy is dissipated in the rotor.

• It is smooth and widely used in machine tools, hoists and textile drives; it needs a rectifier and a contactor sequence.

When an overhauling load (a descending crane hook, a train going downhill) drives the rotor above synchronous speed, the slip becomes negative and the machine acts as an induction generator (Chapter 70), returning power to the supply.

The stator MMF is not a pure sinusoid in space: a three-phase winding also produces space harmonics of order \(h = 6k \pm 1\) (5th, 7th, 11th, 13th …). Each harmonic field rotates at \(N_s/h\) — the 5th backward and the 7th forward.

• The 7th harmonic produces its own small induction-motor torque curve, with its synchronous speed at \(N_s/7\).

• The total torque–speed curve therefore has a dip near \(N_s/7\). If the load torque exceeds the torque in this dip, the motor accelerates only to about \(N_s/7\) and runs there stably — it crawls.

• The 5th harmonic, rotating backward, produces a braking torque that deepens the dip at low speed.

Remedies: chorded (short-pitched) and distributed stator windings that suppress the 5th and 7th harmonics, and skewing of the rotor bars (Chapter 57).

If the number of stator slots \(S_1\) equals the number of rotor slots \(S_2\), or bears a simple ratio to it, the rotor teeth can align with the stator teeth in a position of minimum reluctance. The resulting alignment torque may be large enough that the motor refuses to start at all — this is cogging, or magnetic locking.

• Cogging is most likely at low voltage, when the main starting torque is weak.

• It is prevented by a suitable choice of slot numbers and by skewing the rotor slots by about one slot pitch.

• Plugging: \(s = 2 - s_\text{run}\); fast, very lossy, must be cut off at zero speed.

• DC injection: stationary field; torque vanishes at standstill; energy dissipated in rotor.

• Regeneration: \(s < 0\); returns energy but needs speed above \(N_s\).

• Crawling occurs near \(N_s/7\) because of the 7th space harmonic; cogging occurs when slot numbers are equal or badly related.

1. P69.1 A 6-pole, 50 Hz motor runs with 3 % slip and is plugged. Find the slip and rotor frequency immediately after plugging.

   Show answer

   \(s = 2 - 0.03 = 1.97\); \(f_r = 1.97 \times 50 = 98.5\) Hz.

2. P69.2 Find the probable crawling speed of an 8-pole, 60 Hz motor.

   Show answer

   \(N_s = 120(60)/8 = 900\) rev/min; \(N_\text{crawl} \approx 900/7 = 129\) rev/min.