Construction and Types of Induction Motors

With the universal adoption of the AC system for the distribution of electrical energy for light and power, the field of application of AC motors has widened considerably.

As regards the principle of operation, AC motors can be classified into:

• Synchronous motors — which run at exactly the speed of the rotating field, treated in Part 5.

• Asynchronous motors, or induction motors — which must run at a speed different from that of the field in order to develop torque at all.

The induction motor itself is of two kinds, distinguished entirely by the construction of the rotor:

As a general rule, conversion of electrical power into mechanical power takes place in the rotating part of an electric motor.

• In DC motors, the electric power is conducted directly to the armature — the rotating part — through brushes and a commutator. A DC motor may therefore be called a conduction motor.

• In AC motors, the rotor does not receive electric power by conduction but by induction, in exactly the same way as a two-winding transformer receives its power from the primary. Such motors are therefore known as induction motors.

Of all the AC motors, the polyphase induction motor is the one most extensively used for industrial drives of every kind. Chapters 58 to 64 develop its behaviour; this chapter builds the machine.

The stator is essentially identical in both types of machine.

The winding is distributed over several slots per pole per phase rather than concentrated in one, which improves the waveform and uses the iron more evenly — at the cost of a small reduction in EMF measured by the distribution factor.

The cage rotor is the simplest rotating structure in all of electrical engineering, and about 90 % of induction motors in service use it.

• A laminated cylindrical core with slots near the surface, usually semi-closed or fully closed.

• Each slot holds one uninsulated bar of copper, aluminium or an alloy. No insulation is needed because the induced rotor EMF is very small and the bars are all at nearly the same potential.

• The bars are permanently short-circuited at both ends by heavy end rings of the same material, brazed or, in small machines, cast integrally with the bars.

• There are no brushes, no slip rings and no external connections. The rotor circuit is entirely self-contained.

• The rotor carries a proper three-phase winding of insulated conductors, distributed in slots exactly like the stator winding and wound for the same number of poles.

• The three phases are usually star connected, and the three free ends are brought out to three slip rings mounted on the shaft.

• Carbon brushes bearing on the slip rings connect the rotor circuit to an external three-phase variable resistance.

• Once the machine is running, the external resistance is cut out and the slip rings are short-circuited. Many machines then lift the brushes to reduce wear.

The price is real: slip rings and brushes to maintain, a more expensive rotor, and lower reliability. A slip-ring motor is bought only when its starting behaviour is genuinely needed — increasingly it is displaced by a cage motor with a variable-frequency drive.

The number of rotor slots cannot be chosen freely. Certain combinations with the stator slot number cause the machine to misbehave badly, and the rules that avoid them are among the most practical results in machine design.

Cage rotor bars are almost never parallel to the shaft. They are set at a slight angle — skewed — usually by about one stator slot pitch over the length of the core.

The cost is a slight reduction in the induced rotor EMF, since the bar no longer lies wholly under one point of the flux wave. This is measured by the skew factor:

where \(\alpha\) is the skew angle in electrical radians. Example 57.5 shows how small the penalty is.

The last two deserve emphasis because they shape so much of Part 4. The air gap makes the magnetising current far larger than in a transformer of the same rating — often 30 to 50 % of full-load current rather than 2 to 6 % — and that is the whole reason for the induction motor's characteristic lagging power factor.

• AC motors are synchronous or asynchronous (induction); induction motors are cage or wound rotor.

• An induction motor is a rotating transformer: the rotor receives power by induction, not conduction, and the rotor EMF is at frequency \(sf\).

• The machine must slip — at synchronous speed there is no relative motion, no rotor EMF and no torque.

• The stator is a laminated slotted core carrying a distributed three-phase winding; the pole number fixes \(N_s = 120f/P\).

• Distribution costs EMF — \(k_d = \sin(q\beta/2)/(q\sin(\beta/2))\), about 0.96 for \(q=3\) — but improves the waveform.

• The cage rotor is uninsulated bars short-circuited by end rings, with no external connection. The end ring carries \(I_b/[2\sin(\pi p/S_2)]\), typically over twice the bar current.

• The wound rotor brings a three-phase winding out to slip rings so that external resistance can raise starting torque and control speed.

• Rotor slots must satisfy \(S_2 \ne S_1\) and \(S_2 - S_1 \ne \pm P, \pm2P, \pm3P, \pm5P\), to avoid cogging and crawling.

• Skewing by one slot pitch costs about 0.5 % of EMF and removes cogging, harmonic torques and much noise.

• Cage motors win on cost, robustness and maintenance; wound rotors win only on starting torque and rotor-side speed control.

For nameplate problems, find the synchronous speed just above the running speed — that fixes the pole number at once.

1. P57.1 A three-phase induction motor runs at 960 rev/min from a 50 Hz supply. Find the number of poles, the slip and the rotor frequency.

   Show answer

   The synchronous speed just above 960 is 1000, so

   \[P = \frac{120(50)}{1000} = 6\ \text{poles}\]

   \[s = \frac{1000 - 960}{1000} = 0.0400 = 4.00\,\%\]

   \[f_r = (0.04)(50) = 2.00~\mathrm{Hz}\]

2. P57.2 An 8-pole, 50 Hz motor has a full-load slip of 3 %. Find the synchronous and full-load speeds.

   Show answer

   \[N_s = \frac{120(50)}{8} = 750~\mathrm{rev/min}\]

   \[N = (1 - s)N_s = (0.97)(750) = 727.5~\mathrm{rev/min}\]

3. P57.3 A 6-pole, three-phase stator has 54 slots. Find \(q\), the slot angle and the distribution factor.

   Show answer

   \[q = \frac{54}{(6)(3)} = 3, \qquad \frac{S_1}{P} = 9, \qquad \beta = \frac{180^{\circ}}{9} = 20^{\circ}\]

   \[k_d = \frac{\sin30^{\circ}}{3\sin10^{\circ}} = 0.9598\]

   The same as Example 57.2, since \(q\) and \(\beta\) are the same.

4. P57.4 A 6-pole cage rotor has 44 bars each carrying 250 A. Find the end-ring current.

   Show answer

   \[p = 3, \qquad \frac{\pi p}{S_2} = \frac{3\pi}{44} = 0.21420~\mathrm{rad} = 12.27^{\circ}\]

   \[I_e = \frac{250}{2\sin12.27^{\circ}} = \frac{250}{(2)(0.21257)} = 588.0~\mathrm{A}\]

   A factor of 2.35 — again over twice the bar current.

5. P57.5 A 4-pole machine has 48 stator slots. List the forbidden rotor slot numbers between 30 and 66.

   Show answer

   \[S_2 = 48 \quad (=S_1), \qquad 44,\ 52 \quad (\pm P), \qquad 40,\ 56 \quad (\pm2P)\]

   \[36,\ 60 \quad (\pm3P), \qquad 28,\ 68 \quad (\pm5P)\]

   The full forbidden set is \(\left\{28, 36, 40, 44, 48, 52, 56, 60, 68\right\}\), of which \(\left\{36, 40, 44, 48, 52, 56, 60\right\}\) lie in the range 30 to 66 — the values 28 and 68 fall just outside it.

   A good choice would therefore be 38, 42, 46, 50, 54, 58 or 62. Note that \(\pm5P = \pm20\), not \(\pm16\) — it is easy to lose count of the multiples, so it is worth writing each one out.

6. P57.6 An 8-pole machine with 48 stator slots has its bars skewed by one stator slot pitch. Find the skew factor and compare with a 4-pole machine of the same slot count.

   Show answer

   \[\text{slot pitch} = \frac{360^{\circ}}{48} = 7.50^{\circ}\ \text{mechanical}\]

   8 poles (\(p = 4\)):

   \[\alpha = (7.50)(4) = 30.00^{\circ} = 0.52360~\mathrm{rad}, \quad k_s = \frac{\sin15^{\circ}}{0.26180} = 0.98862\]

   4 poles (\(p = 2\)):

   \[\alpha = 15.00^{\circ} = 0.26180~\mathrm{rad}, \quad k_s = \frac{\sin7.5^{\circ}}{0.13090} = 0.99714\]

   The same physical skew costs 1.14 % on 8 poles but only 0.29 % on 4 — four times as much, since the penalty depends on the electrical angle.

7. P57.7 Explain why an induction motor is called a rotating transformer, and why it cannot run at synchronous speed.

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   Rotating transformer. In a DC motor the armature receives power by conduction, through brushes and commutator. In an induction motor the rotor receives no conducted power at all — the stator sets up a rotating field, and the rotor conductors have EMF induced in them exactly as a transformer secondary does. The stator is the primary, the rotor the secondary, and the only difference from Part 3 is that this secondary is free to turn.

   Why it cannot reach synchronous speed. Torque requires rotor current, rotor current requires rotor EMF, and rotor EMF requires the rotor conductors to cut the rotating field.

   \[N = N_s \quad\Longrightarrow\quad \text{relative speed} = 0 \quad\Longrightarrow\quad E_r = 0 \quad\Longrightarrow\quad I_r = 0 \quad\Longrightarrow\quad T = 0\]

   The machine would produce no torque at all and could not even overcome its own friction. It must therefore always run a little below synchronous speed — hence "asynchronous", and hence the slip as the fundamental variable of Part 4.

8. P57.8 Why is the end-ring current larger than the bar current, and what follows for the design?

   Show answer

   Each end ring collects current from many bars, but those bar currents are not in phase — they are distributed around the rotor following the pole pattern. The ring current is therefore a phasor sum of the contributions, giving

   \[I_e = \frac{I_b}{2\sin\left(\pi p/S_2\right)}\]

   For a 4-pole rotor with 30 bars this is \(2.40\,I_b\).

   Design consequences. The rings must be of much heavier cross-section than the bars — plainly visible on any cage rotor. Their \(I^{2}R\) loss produces no torque whatever, so it is pure waste and the rings are made generously large in efficient designs.

   Note that the factor depends on the design: fewer poles make it worse. A 2-pole rotor with the same 30 bars gives \(\pi/30 = 6^{\circ}\) and a factor of 4.78.

9. P57.9 Explain cogging and crawling, and how each is prevented.

   Show answer

   Cogging (magnetic locking). If the rotor and stator have equal slot numbers, every rotor slot faces a stator slot simultaneously. The reluctance is then minimum at that alignment, and the resulting reluctance torque locks the rotor magnetically. The motor refuses to start at all, however much current it draws.

   Crawling. The stator MMF is not a pure sine wave — it contains space harmonics, chiefly the fifth and seventh. Each harmonic produces its own rotating field with its own synchronous speed, one seventh of the fundamental for the seventh harmonic. If the harmonic torque is strong enough, the motor runs stably at that low speed and will not accelerate past it.

   Prevention:

   • Choose \(S_2 \ne S_1\), and avoid \(S_2 - S_1 = \pm P, \pm2P, \pm3P, \pm5P\).

   • Skew the rotor bars, so that no bar can align with a stator slot along its whole length.

   • Use a distributed and short-pitched stator winding to suppress the harmonics at source.

10. P57.10 When is a slip-ring motor worth its extra cost?

    Show answer

    Only when its starting behaviour is genuinely needed. External rotor resistance moves the point of maximum torque towards standstill, giving

    • High starting torque with low starting current — up to maximum torque at rest.

    • Smooth acceleration of a high-inertia load, with resistance cut out in steps.

    • Some speed control, at the cost of efficiency.

    The price is slip rings and brushes to maintain, a costlier rotor, lower reliability and slightly lower efficiency.

    Typical applications are therefore cranes, hoists, crushers and mills — loads that must be started under full torque or that have large inertia.

    The modern qualification: a cage motor with a variable-frequency drive now gives better starting torque and far better speed control than rotor resistance ever could, and without the maintenance. New slip-ring installations are consequently rare.