Induction motor

Two three-phase induction motors.

An induction or asynchronous motor is a type of AC motor where power is supplied to the rotor by means of electromagnetic induction. These motors are widely used in industrial drives, particularly polyphase induction motors, because they are robust and have no brushes. Their speed can be controlled with a variable frequency drive.

History

The idea of a rotating magnetic field was developed by François Arago in 1824, and first implemented by Walter Baily. Based on this, practical induction motors were independently invented by Nikola Tesla in 1883 and Galileo Ferraris in 1885. According to his 1915 autobiography Tesla conceived the rotating magnetic field in 1882 and used it to invent the first induction motor in 1883; Ferraris developed the idea in 1885. In 1888, Ferraris published his research to the Royal Academy of Sciences in Turin, where he detailed the foundations of motor operation; Tesla, in the same year, was granted U.S. patent 381,968 for his motor. The induction motor with a cage was invented by Mikhail Dolivo-Dobrovolsky a year later.

Operation and comparison to synchronous motors

A 3-phase power supply provides a rotating magnetic field in an induction motor.

In a synchronous AC motor, the rotating magnetic field of the stator imposes a torque on the magnetic field of the rotor, causing it to rotate steadily. It is called synchronous because at steady state, the speed of the rotor matches the speed of the rotating magnetic field in the stator. By contrast, an induction motor has a current induced in the rotor; to do this, stator windings are arranged so that when energised with a polyphase supply they create a rotating magnetic field that induces current in the rotor conductors. These currents interact with the rotating magnetic field, causing rotational motion of the rotor.

For these currents to be induced, the speed of the physical rotor must be lower than that of the stator's rotating magnetic field ($n_{s}$), or the magnetic field would not be moving relative to the rotor conductors and no currents would be induced. If this happens while the motor is operating, the rotor slightly slows down, and consequently a current is induced again. The ratio between the speed of the magnetic field as seen by the rotor (slip speed) and the speed of the stator's rotating field is unitless and it is called slip. For this reason, induction motors are sometimes referred to as asynchronous motors. An induction motor can be used as induction generator, or it can be unrolled to form the linear induction motor which can directly generate linear motion.

Synchronous speed

To understand the behaviour of induction motors, it is helpful to understand their distinction from a synchronous motor. A synchronous motor always runs at a shaft rotation frequency that is an integer fraction of the supply frequency; the synchronous speed of an induction motor is the same. It can be shown that $n_{s}$ in rpm is determined by

$n_{s}={120\times {f} \over {p}}$

where f is the frequency of the AC supply in Hz and p is the number of magnetic poles per phase. Some texts refer to the number of pole pairs per phase; a 6 pole motor would have 3 pole pairs. In this case, P, the number of pole pairs, takes the place of p in the equation.

Slip

Typical torque curve as a function of slip.

The slip s is a ratio relative to the synchronous speed and is defined as

$s={\Bigl (}{\frac {n_{s}-n_{r}}{n_{s}}}{\Bigr )}$

where $n_{r}$ is the rotor rotation speed in rpm.

Construction

Typical winding pattern for a 3 phase, 4 pole motor (phases here are labelled U, V, W). Note the interleaving of the pole windings and the resulting quadrupole field.

Squirrel cages were invented by Mikhail Dolivo-Dobrovolsky.

The stator of an induction motor consists of poles carrying supply current to induce a magnetic field that penetrates the rotor. To optimize the distribution of the magnetic field, the windings are distributed in slots around the stator, with the magnetic field having the same number of north and south poles. Induction motors are most commonly run on single-phase or three-phase power, but two-phase motors exist; in theory, induction motors can have any number of phases. Many single-phase motors having two windings and a capacitor can be viewed as two-phase motors, since the capacitor generates a second power phase 90 degrees from the single-phase supply and feeds it to a separate motor winding. Single-phase power is more widely available in residential buildings, but cannot produce a rotating field in the motor, so they must incorporate some kind of starting mechanism to produce a rotating field. There are three types of rotor: squirrel cage rotors made up of skewed (to reduce noise) bars of copper or aluminum that span the length of the rotor, slip ring rotors with windings connected to slip rings replacing the bars of the squirrel cage, and solid core rotors made from mild steel.

Speed control

Typical torque curves for different line frequencies. By varying the line frequency with an inverter, induction motors can be kept on the stable part of the torque curve above the peak over a wide range of rotation speeds. However, the inverters can be expensive, and fixed line frequencies and other start up schemes are often employed instead.

The theoretical unloaded speed (with slip approaching zero) of the induction motor is controlled by the number of pole pairs and the frequency of the supply voltage.

When driven from a fixed line frequency, loading the motor reduces the rotation speed. When used in this way, induction motors are usually run so that in operation the shaft rotation speed is kept above the peak torque point; then the motor will tend to run at reasonably constant speed. Below this point, the speed tends to be unstable and the motor may stall or run at reduced shaft speed, depending on the nature of the mechanical load.

Before the development of semiconductor power electronics, it was difficult to vary the frequency, and induction motors were mainly used in fixed speed applications. However, many older DC motors have now been replaced with induction motors and accompanying inverters in industrial applications.

Equivalent circuit

The equivalent circuit of an induction motor.

The equivalent circuit of an induction motor has the equivalent resistance of the stator on the left, consisting of the copper and core resistance in series, as $R_{s}$. During operation, the stator induces reactance, represented by the inductor $X_{s}$. $X_{r}$ represents the effect of the rotor passing through the stator's magnetic field. The effective resistance of the rotor, $R_{r}$, is composed of the equivalent value of the machine's power and the ohmic resistance of the stator windings and squirrel cage.

The induction motor equivalent circuit when idle is approximately $R_{s}+X_{s}$, which is mostly reactive. Induction motors generally have a poor power factor, which can be improved by a compensation network.

The idle current draw is often near the rated current, due to the copper and core losses existing without load. In these conditions, this is usually more than half the power loss at the rated load. If the torque against the motor spindle is increased, the active current in the rotor increases by $R_{r}$. Due to the construction of the induction motor, the two resistances induce magnetic flux, in contrast to synchronous machines where it is induced only by the reactive current in the stator windings.

The current produces a voltage drop in the cage factor of $R_{r}$ and a slightly higher one in the stator windings. Hence, the losses increase faster in the rotor than in the stator. $R_{s}$ and the copper factor of $R_{r}$ both cause $I^{2}R$ losses, meaning the efficiency improves with increasing load and reduces with temperature.

$X_{s}$ gets smaller with smaller frequency and must be reduced by the delivered drive voltage. Thus, $R_{s} \over X_{s}+R_{s}$ increases engine power losses. In continuous operation, this is an approximation because a nominal torque generated by the cooling of the rotor and stator is not included in the calculation. Above the rated speed or frequency, induction motors are more effective at higher voltages. Today, $R_{s}$ and $R_{r}$ are measured automatically and thus can be used on a motor to automatically configure itself and thus protect it from overload. Holding torques and speeds close to zero can be achieved with vector controls. There can be problems with cooling here, since the fan is usually mounted on the rotor.

Starting

Main article: Motor controller

Torque curves for 4 types of asynchronous induction motors:
A) Single-phase motor
B) Polyphase squirrel cage motor
C) Polyphase squirrel cage deep bar motor
D) Polyphase double squirrel cage motor

A single phase induction motor is not self starting. Hence it is necessary to provide a starting circuit to start up a single phase induction motor. A single phase induction motor rotates either way; the starting circuit determines rotational direction.

The four methods of starting an induction motor are direct on-line, reactor, auto-transformer and star-delta. Unlike a wound-rotor motor, the rotor circuit is inacessible and it is not feasible to introduce extra resistance for starting or speed control.

For small single-phase shaded-pole motor of a few watts, starting is done by a shaded pole, with a turn of copper wire around part of the pole. The current induced in this turn lags behind the the supply current, creating a delayed magnetic field around the shaded part of the pole face. This imparts sufficient rotational character to start the motor. These motors are typically used in applications such as desk fans and record players, as the starting torque is very low and efficiency is not a problem.

Larger single phase motors have a second stator winding fed with out-of-phase current; such currents may be created by feeding the winding through a capacitor or having it have different values of inductance and resistance from the main winding. In some designs, the second winding is disconnected once the motor is up to speed, usually either by a centrifugal switch acting on weights on the motor shaft or a thermistor which heats up and increases its resistance, reducing the current through the second winding to an insignificant level. Other designs keep the second winding on when running, improving torque.

Polyphase motors have rotor bars shaped to give different speed/torque characteristics. The current distribution within the rotor bars varies depending on the frequency of the inducted current. At standstill, the rotor current is the same frequency as the stator current, and tends to travel at the outermost parts of the squirrel-cage rotor bars. As the rotor accelerates, the slip frequency declines, and current tends to travel deeper within the squirrel cage bars. Polyphase motors can generate torque from standstill, so no extra mechanism is required to initiate rotation. The different bar shapes can give usefully different speed/torque characteristics as well as some control over the inrush current at startup.

Linear induction motor

Main article: linear induction motor

A linear induction motor (LIM) is an AC asynchronous linear motor that works by the same general principles as other induction motors but which has been designed to directly produce motion in a straight line.

Linear motors frequently run on a 3 phase power supply.

Their uses include magnetic levitation, linear propulsion, and linear actuators. They have also been used for pumping liquid metals.

Sources

• Henri Boy de la Tour (1906). The induction motor: its theory and design, set forth by a practical method of calculation. Translated Cyprien Odilon Mailloux. McGraw Pub. Co.
• Benjamin Franklin Bailey (1911). The induction motor. McGraw-Hill.
• Bernhard Arthur Behrend (1901). The induction motor: A short treatise on its theory and design, with numerous experimental data and diagrams. Electrical world and engineer.

External links

• A drawing of an induction motor
• Template:It Rotating magnetic fields: interactive
• Construct your squirrelcage electromotor using povray