## 10+ single-phase motors per home

You should know that single-phase motors are rarely rated above 5 kW. Fractional-kilowatt motors, most of which are single-phase, account for 80−90% of the total number of motors manufactured and for 20−30% of the total commercial value. A typical modern home may have 10 or more single-phase motors in its domestic electrical equipment.

That makes single-phase motors the most used motor types in the world. Let’s get into these types one by one.

## 1. Series motor

As the direction of rotation and of torque in a DC series motor are independent of the polarity of the supply, such a motor can operate on AC provided that all ferromagnetic parts of the magnetic circuit are laminated to minimize core loss.

### 1.1 Universal motor

In the fractional-kilowatt sizes the series motor has the advantage, since it is non-synchronous, of being able to run at speeds **up to 10 000 rev/min**. It is very well adapted to driving suction cleaners, drills, sewing machines and similar small-power rotary devices.

Its facility of operating on DC and AC is not now important, but is the origin of the term “**universal**“.

**“series” speed-torque characteristic**, the no-load speed being limited by mechanical losses. The power factor is between 0.7 and 0.9 (mainly the result of armature inductance), but this is of no significance in small ratings.

Typical characteristics for a motor for DC and 50 Hz supplies of the same nominal voltage are shown in Figure 1.

In all AC commutator motors the commutation conditions are more onerous than on DC because the coils undergoing commutation link the main alternating flux and have e.m.f.s induced of supply frequency. The e.m.f.s are offered a short-circuited path through the brushes and contribute to sparking at the commutator.

As the e.m.f.s are proportional to the main flux, the frequency and the number of turns per armature coil, these must be limited. A further limit on the current in a short-circuited coil is provided by high-resistance carbon brushes.

### 1.2 Compensated motor

Series AC commutator motors **up to 700±800 kW rating** are used in several European railway traction systems. For satisfactory commutation the frequency must be low, usually 16 2/3 Hz, and the voltage must also be low (400−500 V ), this being provided by a transformer mounted on the locomotive.

**in order to ensure a reasonable power factor**.

Motors of this type have been built, of limited output, for operation on modern 50 Hz traction systems but have now been superseded by rectifier- or thyristor-fed DC motors. See Figure 1a.

## 2. Repulsion motor

The repulsion motor is a form of series motor, **with the rotor energized inductively instead of conductively**. The commutator rotor winding is designed for a low working voltage. The brushes are joined by a short circuit and the brush axis is displaced from the axis of the one-phase stator winding (Figures 2, 3, and 4).

With non-reversing motors (Figure 2) a single stator winding suffices.

However, for reversing motors the stator has an additional winding, connected in one or other sense in series with the first winding to secure the required angle between the rotor and effective stator axes for the two directions of rotation, as in Figure 3.

A stator winding of N_{1} turns as in (a) can be resolved into two component windings respectively coaxial with and in quadrature with the axis of the rotor winding, and having respectively turns **N _{1} sinα** and

**N**. Windings (b) give the two axis windings directly, although here the turns can be designed for optimum effect.

_{1}cosα**the motor has a “series” characteristic**. When the motor is running, the direct and quadrature axis fluxes have a phase displacement approaching 90°, so producing a travelling-wave field of elliptical form which becomes nearly a uniform synchronously rotating field at speeds near the synchronous.

Near synchronous speed, therefore, the rotor core losses are small and the commutation conditions are good.

Small motors can readily be direct-switched for starting, with **2.5−3 times full-load current** and **3−4 times full-load torque**. The normal full-load operating speed is chosen near, or slightly below, synchronous speed in order to avoid excessive sparking at light load.

Repulsion motors are used where a high starting torque is required and where a three-phase supply is not available. For small lifts, hoists and compressors their rating **rarely exceeds about 5 kW**.

## 3. Induction motors

The one-phase induction motor is occasionally built for **outputs up to 5 kW**, but is normally made in ratings between 0.1 and 0.5 kW for domestic refrigerators, fans and small machine tools where a substantially constant speed is called for. The behavior of the motor may be studied by the rotating-field or the cross-field theory.

The former is simpler and gives a clearer physical concept.

### 3.1 Rotating-field theory

The pulsating m.m.f. of the stator winding is resolved into **two “rotating” m.m.f.s of constant and equal magnitude** revolving in opposite directions. These m.m.f.s are assumed to set up corresponding gap fluxes which, with the rotor at rest, are of equal magnitude and each equal to one-half the peak pulsating flux.

**component torque-speed curve marked “forward”**in Figure 5.

The **backward component b** gives the other torque component, and the net torque is the algebraic sum. At zero speed the component torques cancel so that the motor has no inherent starting torque, but if it is given a start in either direction a small torque in the same direction results and the machine runs up to near synchronous speed provided that the load torque can be overcome.

The component torques in Figure 5 are, in fact, modified by the rotor current. Compared with the three-phase induction motor, the one-phase version has a torque falling to zero at a speed slightly below synchronous, and the slip tends to be greater.

There is also a core loss in the rotor produced by the backward field, reducing the efficiency. Moreover, there is a double-frequency torque pulsation generated by the backward field that can give rise to noise.

The efficiency lies between about **40% for a 60 W motor** and about **70% for a 750 W motor**, the corresponding power factors being **0.45** and **0.65**, approximately.

The equivalent circuit of Figure 6 is based on the rotating-field theory, using parameters generally similar to those for the three-phase machine. The e.m.f.s **E _{f}** and

**E**are generated respectively by the forward and backward field components and are proportional thereto.

_{b}The respective component torques are proportional to **I _{2f}^{2} × r_{2 }/ 2s** and

**I**, the next torque being their difference.

_{2f}^{2}× r^{2}/ [2(2 − s)]### 3.2 Starting

To start a one-phase induction motor, means are provided to develop initially some form of travelling-wave field. The arrangements commonly adopted give rise to the terms “**shaded-pole**” and “**split-phase**“.

### 3.3 Shaded-pole motor

The stator has salient poles, with about one-third of each pole-shoe embraced by a shading coil. That flux which passes through the shading coil is delayed with respect to the flux in the main part of the pole, so that a crude shifting flux results.

The starting torque is limited, the efficiency is low (as there is a loss in the shading coil), **the power factor is 0.5−0.6** and the pull-out torque is **only 1−1.5 times full-load torque**.

Applications include **small fans of output not greatly exceeding 100 W**.

### 3.4 Resistance split-phase motor

The additional flux is provided by an auxiliary starting winding arranged spatially at 90°(electrical) to the main (running) winding. If the respective winding currents are **I _{m}** and

**I**with a relative phase angle

_{s}**α**, the torque is approximately proportional to

**I**.

_{m}I_{s}sinαAt starting, the main-winding current lags the applied voltage by **70−80°**. The starting winding, connected in parallel with the main winding, is designed with a high resistance or has a resistor in series so that **I _{s}** lags by

**30−40°**.

The effect of this resistance on the starting characteristic is shown in Figure 7(a). With given numbers of turns per winding and a given main-winding resistance, then for a specified supply voltage and frequency there is a particular value of starting-winding resistance for maximum starting torque.

The relation can be obtained from the phasor diagram. Figure 7(b), in which **V _{1}** is the supply voltage and

**I**at phase angle

_{m}**Φ**is the main-winding current. The locus of the starting-current phase I

_{m}_{s}with change in resistance is the semicircle of

**diameter OD**(which corresponds to zero resistance). The torque is proportional to

**I**and is a maximum for the greatest length of the line AC.

_{m}I_{s}sin(Φ_{m}− Φ_{s})From the geometry of the diagram it can be shown that for this condition **Φ _{s} = 1/2 Φ_{m}**.

Direct switching is usual. To reduce loss, the auxiliary winding is open-circuited as soon as the motor reaches running speed. The starting torque for small motors up to 250 W is 1.5−2 times full-load torque, and that for larger motors rather less, in each case with 4−6 times full-load current.

The operating efficiency is **55−65%** and the power factor **0.6−0.7**.

### 3.5 Capacitor split-phase motor

A greater phase difference (**Φ _{m} − Φ_{s}**) can be obtained if a series capacitor is substituted for the series resistor of the auxiliary winding. Maximum torque occurs for a capacitance such that the auxiliary current leads the main current by (1/2πα)/2.

**20−30 mF for a 100 W motor**to

**60−100 mF for a 750 W motor**. For economic reasons the capacitor is as small as is consistent with producing adequate starting torque, and some manufacturers quote alternative sizes for various levels of starting torque.

If the capacitor is left in circuit continuously (capacitor-run) the power factor is improved and the motor runs with less noise. Ideally, however, the value of capacitance for running should be about one-third of that for the best starting. If a single capacitor is used for both starting and running, the starting torque is 0.5−1 times full-load value and the power factor in running is near unity.

### 3.6 Repulsion-induction motor

Machines have been designed to combine the high starting torque capability of the repulsion motor with the constant-speed running characteristic of the induction motor.

#### 3.6.1 Repulsion-start motor

This motor has a stator winding like that of a repulsion motor and a lap commutator winding, with the addition of a device to short circuit the commutator sectors together by centrifugal action when the speed reaches about 75% of normal. The device may also release the brushes immediately thereafter.

Thus the commutator rotor winding becomes, in effect, **a short-circuited “induction”-type winding for running**.

Small motors direct-switched give 3−4 times full-load torque with about three times full-load current. Alower starting current is obtained by connecting a graded resistor in series with the stator winding.

#### 3.6.2 Repulsion-induction motor

The machine has a **repulsion-type stator winding** but the change from the repulsion-mode to the induction-mode operation is gradual as the machine runs up to speed. The rotor has two windings in slots resembling those of a double-cage induction motor. The outer slots carry a commutator winding with brushgear, the inner slots contain a low-resistance cage with cast aluminium bars and end-rings, and its deep setting endows it with a high inductance.

**tending to counterbalance the falling torque of the commutator winding**. At speeds above synchronous the cage torque reverses, giving a braking action which holds the no-load speed to a value only slightly above synchronous speed.

The commutation is better than that of a plain repulsion motor, and the motor is characterised by a good full-load power factor (e.g. 0.85−0.9 lagging).

With direct switching the starting torque is **2.5−3 times** and the current **3−3.5 times** full-load value.

**Source:** Electrical Engineer’s Reference Book by M. A. Laughton and D. J. Warne

Me gustó la información técnica, especializado en lo referente a motores eléctricos. Muy valioso para los técnicos e ingenieros.