Electric Motors

ELECTRIC MOTORS

U.S. Patent 381968: Mode and plan of operating electric motors by progressive shifting; Field

Magnet; Armature; Electrical conversion; Economical; Transmission of energy; Simple

construction; Easier construction; Rotating magnetic field principles.

circa 1890.

Born

10 July 1856

Smiljan

,

Austrian Empire

a

(

Croatian Military Frontier

)

Died

7 January 1943 (aged 86)

New York City, New York, USA

Residence

Austria-Hungary

a

France

United States of America

Citizenship

Austro-Hungarian

a

_{(1856–1891)}

American

(1891–1943)

Nationality

Serbian

Fields

Mechanical

and

electrical

engineering

Institutions

Edison Machine Works

Manufacturing

Westinghouse Electric &

Manufacturing Co.

Notable

awards

Edison Medal

(1916)

Elliott Cresson Medal

(1893)

John Scott Medal

(1934)

Signature

Notes

a

_{Austrian Empire}

_{(1804–1867) reorganized and}

renamed into the

Austro-Hungarian Monarchy

(1867–1918) in 1867

Nikola Tesla's AC

dynamo

used to generate AC which is used to transport

electricity

across great

distances. It is contained in

U.S. Patent 390,721

.

AC motor

An AC motor is an electric motor that is driven by an alternating current. It consists of two basic parts, an outside stationary stator (there are examples such as some of the Papst motors that have the stator on the

inside and the rotor on the outside to increase the inertia and cooling, they were common on high quality tape and film machines where speed stability is important) having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor attached to the output shaft that is given a torque by the rotating field.

There are two types of AC motors, depending on the type of rotor used (not including eddy current motors also AC/DC mechanically commutated machines which are speed dependant on voltage and winding connection). The first is the synchronous motor, which rotates exactly at the supply frequency or a

submultiple of the supply frequency. The magnetic field on the rotor is either generated by current delivered through slip rings or by a permanent magnet.

The second type is the induction motor, which runs slightly slower than the supply frequency. The magnetic field on the rotor of this motor is created by an induced current.

History

In 1882 Nikola Tesla identified the rotating magnetic induction field principle[1][2] _{used in alternators and} pioneered the use of this rotating and inducting electromagnetic field force to generate torque in rotating machines. He exploited this principle in the design of a poly-phase induction motor in 1883. In 1885, Galileo Ferraris independently researched the concept. In 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

Introduction of Tesla's motor in 1888 initiated what is sometimes referred to as the Second Industrial

Revolution, making possible both the efficient generation and long distance distribution of electrical energy

using the alternating current transmission system, also of Tesla's invention (1888).[3] _{Before widespread use} of Tesla's principle of poly-phase induction for rotating machines, all motors operated by continually passing a conductor through a stationary magnetic field (as in homopolar motor).

Initially Tesla suggested that the commutators from a machine could be removed and the device could operate on a rotary field of electromagnetic force. Professor Poeschel, his teacher, stated that would be akin to building a perpetual motion machine. This was because Tesla's teacher had only understood one half of Tesla's ideas. Professor Poeschel had realized that the induced rotating magnetic field would start the rotor of the motor spinning, but he did not see that the counter electromotive force generated would gradually bring the machine to a stop.[4] _{Tesla would later obtain U.S. Patent 0,416,194, Electric Motor (December} 1889), which resembles the motor seen in many of Tesla's photos. This classic alternating current electro-magnetic motor was an induction motor.

Michail Osipovich Dolivo-Dobrovolsky later invented a three-phase "cage-rotor" in 1890. This type of motor is now used for the vast majority of commercial applications.

Squirrel-cage rotors

Most common AC motors use the squirrel cage rotor, which will be found in virtually all domestic and light industrial alternating current motors. The squirrel cage refers to the rotating exercise cage for pet animals. The motor takes its name from the shape of its rotor "windings"- a ring at either end of the rotor, with bars connecting the rings use cast copper to reduce the resistance in the rotor.running the length of the rotor. It is typically cast aluminum or copper poured between the iron laminates of the rotor, and usually only the end rings will be visible. The vast majority of the rotor currents will flow through the bars rather than the higher-resistance and usually varnished laminates. Very low voltages at very high currents are typical in the bars and end rings; high efficiency motors will often

In operation, the squirrel cage motor may be viewed as a transformer with a rotating secondary. When the rotor is not rotating in sync with the magnetic field, large rotor currents are induced; the large rotor currents magnetize the rotor and interact with the stator's magnetic fields to bring the rotor almost into

synchronization with the stator's field. An unloaded squirrel cage motor at rated no-load speed will consume electrical power only to maintain rotor speed against friction and resistance losses. As the mechanical load increases, so will the electrical load - the electrical load is inherently related to the mechanical load. This is

similar to a transformer, where the primary's electrical load is related to the secondary's electrical load. This is why a squirrel cage blower motor may cause household lights to dim upon starting, but doesn't dim the lights on startup when its fan belt (and therefore mechanical load) is removed. Furthermore, a stalled squirrel cage motor (overloaded or with a jammed shaft) will consume current limited only by circuit resistance as it attempts to start. Unless something else limits the current (or cuts it off completely) overheating and destruction of the winding insulation is the likely outcome.

To prevent the currents induced in the squirrel cage from superimposing itself back onto the supply, the squirrel cage is generally constructed with a prime number of bars, or at least a small multiple of a prime number (rarely more than 2). There is an optimum number of bars in any design, and increasing the number of bars beyond that point merely serves to increase the losses of the motor particularly when starting.

Virtually every washing machine, dishwasher, standalone fan, record player, etc. uses some variant of a squirrel cage motor.

Squirrel-cage rotor

Squirrel cage rotor

A squirrel cage rotor is the rotating part used in the most common form of AC induction motor. An electric motor with a squirrel cage rotor is termed a squirrel cage motor.

Structure

Diagram of the squirrel-cage (showing only three laminations)

In overall shape, it is a cylinder mounted on a shaft. Internally it contains longitudinal conductive bars (usually made of aluminum or copper) set into grooves and connected together at both ends by shorting

rings forming a cage-like shape. The name is derived from the similarity between this rings-and-bars winding and a squirrel cage (or, as it is commonly known, a hamster wheel).

The core of the rotor is built with stacks of electrical steel laminations. Figure 3 shows three of many laminations used.

Theory

Stator and rotor laminations

The field windings in the stator of an induction motor set up a rotating magnetic field around the rotor. The relative motion between this field and the rotation of the rotor induces electric current in the conductive bars. In turn these currents lengthwise in the conductors react with the magnetic field of the motor to produce force acting at a tangent orthogonal to the rotor, resulting in torque to turn the shaft. In effect the rotor is carried around with the magnetic field but at a slightly slower rate of rotation. The difference in speed is called slip and increases with load.

The conductors are often skewed slightly along the length of the rotor to reduce noise and smooth out torque fluctuations that might result at some speeds due to interactions with the pole pieces of the stator. The number of bars on the squirrel cage determines to what extent the induced currents are fed back to the stator coils and hence the current through them. The constructions that offer the least feedback employ prime numbers of bars.

The iron core serves to carry the magnetic field across the motor. In structure and material it is designed to minimize losses. The thin laminations, separated by varnish insulation, reduce stray circulating currents that would result in eddy current loss. The material is a low carbon but high silicon iron with several times the resistivity of pure iron, further reducing eddy-current loss. The low carbon content makes it a magnetically soft material with low hysteresis loss.

The same basic design is used for both single-phase and three-phase motors over a wide range of sizes. Rotors for three-phase will have variations in the depth and shape of bars to suit the design classification.

Practical Demonstration

To demonstrate how the cage rotor works, the stator of a single-phase motor and a copper pipe (as rotor) may be used. If adequate ac power is applied to the stator, an alternating magnetic field revolves around the stator. If the copper pipe is inserted inside the stator, there will be an induced current in the pipe, and this current produces another magnetic field. The interaction of the stator revolving field and rotor induced field produce a torque and thus rotation.

Use in synchronous motors

Synchronous motors must use other types of rotors although they may employ a squirrel cage winding to allow them to reach near-synchronous speed while starting. Once operating at synchronous speed, the magnetic field is rotating at the same speed as the rotor, so no current will be induced into the squirrel cage windings and they will have no further effect on the operation of the synchronous motor.

Induction generators

Three phase squirrel cage induction motors can also be used as generators. For this to work the motor must either be connected to a grid supply or an arrangement of capacitors. If the motor is run as a self exciting induction generator (SEIG) the capacitors can either be connected in a delta or c2c arrangement. The c2c method is for producing a single phase output and the delta method is for a three phase output. For the motor to work as a generator instead of a motor the rotor must be spun just faster than its nameplate speed, this will cause the motor to generate power after building up its residual magnetism.

Calecon Effect

If the rotor of a squirrel runs at the true synchronous speed, the flux in the rotor at any given place on the rotor would not change, and no current would be created in the squirrel cage. For this reason, ordinary squirrel-cage motors run at some tens of rpm slower than synchronous speed, even at no load. Because the rotating field (or equivalent pulsating field) actually or effectively rotates faster than the rotor, it could be said to slip past the surface of the rotor. The difference between synchronous speed and actual speed is called slip, and loading the motor increases the amount of slip as the motor slows down slightly.

Two-phase AC servo motors

A typical two-phase AC servo-motor has a squirrel cage rotor and a field consisting of two windings:

1. a constant-voltage (AC) main winding.

2. a control-voltage (AC) winding in quadrature (i.e., 90 degrees phase shifted) with the main

winding so as to produce a rotating magnetic field. Reversing phase makes the motor reverse.

An AC servo amplifier, a linear power amplifier, feeds the control winding. The electrical resistance of the rotor is made high intentionally so that the speed/torque curve is fairly linear. Two-phase servo motors are inherently high-speed, low-torque devices, heavily geared down to drive the load.

Single-phase AC induction motors

Three-phase motors produce a rotating magnetic field. However, when only single-phase power is available, the rotating magnetic field must be produced using other means. Several methods are commonly used:

Shaded-pole motor

A common single-phase motor is the shaded-pole motor and is used in devices requiring low starting torque, such as electric fans or the drain pump of washing machines and dishwashers or in other small household appliances. In this motor, small single-turn copper "shading coils" create the moving magnetic field. Part of each pole is encircled by a copper coil or strap; the induced current in the strap opposes the change of flux through the coil. This causes a time lag in the flux passing through the shading coil, so that the maximum field intensity moves across the pole face on each cycle. This produces a low level rotating magnetic field which is large enough to turn both the rotor and its attached load. As the rotor picks up speed the torque builds up to its full level as the principal magnetic field is rotating relative to the rotating rotor.

A reversible shaded-pole motor was made by Barber-Colman several decades ago. It had a single field coil, and two principal poles, each split halfway to create two pairs of poles. Each of these four "half-poles" carried a coil, and the coils of diagonally-opposite half-poles were connected to a pair of terminals. One terminal of each pair was common, so only three terminals were needed in all.

The motor would not start with the terminals open; connecting the common to one other made the motor run one way, and connecting common to the other made it run the other way. These motors were used in industrial and scientific devices.

An unusual, adjustable-speed, low-torque shaded-pole motor could be found in traffic-light and

advertising-lighting controllers. The pole faces were parallel and relatively close to each other, with the disc centred between them, something like the disc in a watthour meter. Each pole face was split, and had a shading coil on one part; the shading coils were on the parts that faced each other. Both shading coils were probably closer to the main coil; they could have both been farther away, without affecting the operating principle, just the direction of rotation.

Applying AC to the coil created a field that progressed in the gap between the poles. The plane of the stator core was approximately tangential to an imaginary circle on the disc, so the travelling magnetic field dragged the disc and made it rotate.

The stator was mounted on a pivot so it could be positioned for the desired speed and then clamped in position. Keeping in mind that the effective speed of the travelling magnetic field in the gap was constant, placing the poles nearer to the centre of the disc made it run relatively faster, and toward the edge, slower. It is possible that these motors are still in use in some older installations.

Split-phase induction motor

Another common single-phase AC motor is the split-phase induction motor,[5] _{commonly used in major} appliances such as washing machines and clothes dryers. Compared to the shaded pole motor, these motors can generally provide much greater starting torque by using a special startup winding in conjunction with a centrifugal switch.

In the split-phase motor, the startup winding is designed with a higher resistance than the running winding. This creates an LR circuit which slightly shifts the phase of the current in the startup winding. When the motor is starting, the startup winding is connected to the power source via a set of spring-loaded contacts pressed upon by the stationary centrifugal switch. The starting winding is wound with fewer turns of smaller wire than the main winding, so it has a lower inductance (L) and higher resistance (R). The lower L/R ratio creates a small phase shift, not more than about 30 degrees, between the flux due to the main winding and the flux of the starting winding. The starting direction of rotation may be reversed simply by exchanging the connections of the startup winding relative to the running winding.

The phase of the magnetic field in this startup winding is shifted from the phase of the mains power, allowing the creation of a moving magnetic field which starts the motor. Once the motor reaches near design operating speed, the centrifugal switch activates, opening the contacts and disconnecting the startup winding from the power source. The motor then operates solely on the running winding. The starting winding must be disconnected since it would increase the losses in the motor.

Schematic of a capacitor start motor.

A capacitor start motor is a split-phase induction motor with a starting capacitor inserted in series with the startup winding, creating an LC circuit which is capable of a much greater phase shift (and so, a much greater starting torque). The capacitor naturally adds expense to such motors.

Resistance start motor

A resistance start motor is a split-phase induction motor with a starter inserted in series with the startup winding, creating capacitance. This added starter provides assistance in the starting and initial direction of rotation.

Permanent-split capacitor motor

Another variation is the permanent-split capacitor (PSC) motor (also known as a capacitor start and run motor).[6] _{This motor operates similarly to the capacitor-start motor described above, but there is no} centrifugal starting switch,[6] _{and what correspond to the start windings (second windings) are permanently} connected to the power source (through a capacitor), along with the run windings.[6] _{PSC motors are} frequently used in air handlers, blowers, and fans (including ceiling fans) and other cases where a variable speed is desired.

A capacitor ranging from 3 to 25 microfarads is connected in series with the "start" windings and remains in the circuit during the run cycle.[6] _{The "start" windings and run windings are identical in this motor,}[6] _and reverse motion can be achieved by reversing the wiring of the 2 windings,[6] _{with the capacitor connected to} the other windings as "start" windings. By changing taps on the running winding but keeping the load constant, the motor can be made to run at different speeds. Also, provided all 6 winding connections are available separately, a 3 phase motor can be converted to a capacitor start and run motor by commoning two of the windings and connecting the third via a capacitor to act as a start winding.

Wound rotors

An alternate design, called the wound rotor, is used when variable speed is required. In this case, the rotor has the same number of poles as the stator and the windings are made of wire, connected to slip rings on the shaft. Carbon brushes connect the slip rings to an external controller such as a variable resistor that allows changing the motor's slip rate. In certain high-power variable speed wound-rotor drives, the slip-frequency energy is captured, rectified and returned to the power supply through an inverter. With bidirectionally controlled power, the wound-rotor becomes an active participant in the energy conversion process with the wound-rotor doubly-fed configuration showing twice the power density.

Compared to squirrel cage rotors and without considering brushless wound-rotor doubly-fed technology,

wound rotor motors are expensive and require maintenance of the slip rings and brushes, but they were the standard form for variable speed control before the advent of compact power electronic devices.

motors are becoming less common.

Several methods of starting a polyphase motor are used. Where the large inrush current and high starting torque can be permitted, the motor can be started across the line, by applying full line voltage to the terminals (direct-on-line, DOL). Where it is necessary to limit the starting inrush current (where the motor is large compared with the short-circuit capacity of the supply), reduced voltage starting using either series inductors, an autotransformer, thyristors, or other devices are used. A technique sometimes used is (star-delta, YΔ) starting, where the motor coils are initially connected in star for acceleration of the load, then switched to delta when the load is up to speed. This technique is more common in Europe than in North America. Transistorized drives can directly vary the applied voltage as required by the starting

characteristics of the motor and load.

This type of motor is becoming more common in traction applications such as locomotives, where it is known as the asynchronous traction motor.

The speed of the AC motor is determined primarily by the frequency of the AC supply and the number of poles in the stator winding, according to the relation:

N

s = 120F / p

where

N

s

= Synchronous speed, in revolutions per minute

F = AC power frequency

p = Number of poles per phase winding

Actual RPM for an induction motor will be less than this calculated synchronous speed by an amount known as slip, that increases with the torque produced. With no load, the speed will be very close to synchronous. When loaded, standard motors have between 2-3% slip, special motors may have up to 7% slip, and a class of motors known as torque motors are rated to operate at 100% slip (0 RPM/full stall).

The slip of the AC motor is calculated by:

S = (N

s − Nr) / Ns

where

N

r

= Rotational speed, in revolutions per minute.

S = Normalised Slip, 0 to 1.

As an example, a typical four-pole motor running on 60 Hz might have a nameplate rating of 1725 RPM at full load, while its calculated speed is 1800 RPM.

The speed in this type of motor has traditionally been altered by having additional sets of coils or poles in the motor that can be switched on and off to change the speed of magnetic field rotation. However, developments in power electronics mean that the frequency of the power supply can also now be varied to provide a smoother control of the motor speed.

If connections to the rotor coils of a three-phase motor are taken out on slip-rings and fed a separate field current to create a continuous magnetic field (or if the rotor consists of a permanent magnet), the result is called a synchronous motor because the rotor will rotate synchronously with the rotating magnetic field produced by the polyphase electrical supply.

The synchronous motor can also be used as an alternator.

Nowadays, synchronous motors are frequently driven by transistorized variable-frequency drives. This greatly eases the problem of starting the massive rotor of a large synchronous motor. They may also be started as induction motors using a squirrel-cage winding that shares the common rotor: once the motor reaches synchronous speed, no current is induced in the squirrel-cage winding so it has little effect on the synchronous operation of the motor, aside from stabilizing the motor speed on load changes.

Synchronous motors are occasionally used as traction motors; the TGV may be the best-known example of such use.

One use for this type of motor is its use in a power factor correction scheme. They are referred to as

synchronous condensers. This exploits a feature of the machine where it consumes power at a leading power factor when its rotor is over excited. It thus appears to the supply to be a capacitor, and could thus be used to correct the lagging power factor that is usually presented to the electric supply by inductive loads. The excitation is adjusted until a near unity power factor is obtained (often automatically). Machines used for this purpose are easily identified as they have no shaft extensions. Synchronous motors are valued in any case because their power factor is much better than that of induction motors, making them preferred for very high power applications.

Some of the largest AC motors are pumped-storage hydroelectricity generators that are operated as synchronous motors to pump water to a reservoir at a higher elevation for later use to generate electricity using the same machinery. Six 350-megawatt generators are installed in the Bath County Pumped Storage Station in Virginia, USA. When pumping, each unit can produce 563,400 horsepower (420 megawatts).[7]

Universal motors and series wound motors

AC motors can also have brushes. The universal motor is widely used in small home appliances and power tools.

Repulsion motor

Repulsion motors are wound-rotor single-phase AC motors that are similar to universal motors. In a repulsion motor, the armature brushes are shorted together rather than connected in series with the field. By transformer action ,the stator induces currents in the rotor, which create torque by repulsion instead of attraction as in other motors. Several types of repulsion motors have been manufactured, but the

repulsion-start induction-run (RS-IR) motor has been used most frequently. The RS-IR motor has a centrifugal switch

that shorts all segments of the commutator so that the motor operates as an induction motor once it has been accelerated to full speed. Some of these motors also lift the brushes out of contact with the

commutator once the commutator is shorted. RS-IR motors have been used to provide high starting torque per ampere under conditions of cold operating temperatures and poor source voltage regulation. Few repulsion motors of any type are sold as of 2005.

Other types of motors

Single-phase AC synchronous motors

idea; see "Hysteresis synchronous motors" below).

If a conventional squirrel-cage rotor has flats ground on it to create salient poles and increase reluctance, it will start conventionally, but will run synchronously, although it can provide only a modest torque at synchronous speed. This is known as a reluctance motor.

Because inertia makes it difficult to instantly accelerate the rotor from stopped to synchronous speed, these motors normally require some sort of special feature to get started. Some include a squirrel-cage structure to bring the rotor close to synchronous speed. Various other designs use a small induction motor (which may share the same field coils and rotor as the synchronous motor) or a very light rotor with a one-way mechanism (to ensure that the rotor starts in the "forward" direction). In the latter instance, applying AC power creates chaotic (or seemingly chaotic) jumping movement back and forth; such a motor will always start, but lacking the anti-reversal mechanism, the direction it runs is unpredictable. The Hammond organ tone generator used a non-self-starting synchronous motor (until comparatively recently), and had an auxiliary conventional shaded-pole starting motor. A spring-loaded auxiliary manual starting switch connected power to this second motor for a few seconds.

Hysteresis synchronous motors

These motors are relatively costly, and are used where exact speed (assuming an exact-frequency AC source) as well as rotation with a very small amount of fast variations in speed (called 'flutter" in audio recordings) is essential. Applications included tape recorder capstan drives (the motor shaft could be the capstan). Their distinguishing feature is their rotor, which is a smooth cylinder of a magnetic alloy that stays magnetized, but can be demagnetized fairly easily as well as re-magnetized with poles in a new location. Hysteresis refers to how the magnetic flux in the metal lags behind the external magnetizing force; for instance, to demagnetize such a material, one could apply a magnetizing field of opposite polarity to that which originally magnetized the material.

These motors have a stator like those of capacitor-run squirrel-cage induction motors. On startup, when slip decreases sufficiently, the rotor becomes magnetized by the stator's field, and the poles stay in place. The motor then runs at synchronous speed as if the rotor were a permanent magnet. When stopped and re-started, the poles are likely to form at different locations.

For a given design, torque at synchronous speed is only relatively modest, and the motor can run at below synchronous speed.

Electronically commutated motors

Such motors have an external rotor with a cup-shaped housing and a radially magnetized permanent magnet connected in the cup-shaped housing. An interior stator is positioned in the cup-shaped housing. The interior stator has a laminated core having grooves. Windings are provided within the grooves. The windings have first end turns proximal to a bottom of the cup-shaped housing and second end turns positioned distal to the bottom. The first and second end turns electrically connect the windings to one another. The permanent magnet has an end face rom the bottom of the cup-shaped housing. At least one galvano-magnetic rotor position sensor is arranged opposite the end face of the permanent magnet so as to be located within a magnetic leakage of the permanent magnet and within a magnetic leakage of the interior stator. The at least one rotor position sensor is designed to control current within at least a portion of the windings. A magnetic leakage flux concentrator is arranged at the interior stator at the second end turns at a side of the second end turns facing away from the laminated core and positioned at least within an angular area of the interior stator in which the at (?-someone got distracted)

ECM motors are increasingly being found in forced-air furnaces and HVAC systems to save on electricity costs as modern HVAC systems are running their fans for longer periods of time (duty cycle).[8] _{The cost} effectiveness of using ECM motors in HVAC systems is questionable, given that the repair (replacement) costs are likely to equal or exceed the savings realized by using such a motor.

Watthour-meter motors

These are essentially two-phase induction motors with permanent magnets that retard rotor speed, so their speed is quite accurately proportional to wattage of the power passing through the meter. The rotor is an aluminium-alloy disc, and currents induced into it react with the field from the stator.

The stator is composed of three coils that are arranged facing the disc surface, with the magnetic circuit completed by a C-shaped core of permeable iron. One phase of the motor is produced by a coil with many turns located above the disc surface. This upper coil has a relatively high inductance, and is connected in parallel with the load. The magnetic field produced in this coil lags the applied (line/mains) voltage by almost 90 degrees. The other phase of the motor is produced by a pair of coils with very few turns of heavy-gauge wire, and hence quite-low inductance. These coils, located on the underside of the disc surface, are wired in series with the load, and produce magnetic fields in-phase with the load current.

Because the two lower coils are wound anti-parallel, and are each located equidistant from the upper coil, an azimuthally traveling magnetic flux is created across the disc surface. This traveling flux exerts an average torque on the disc proportional to the product of the power factor; RMS current, and voltage. It follows that the rotation of the magnetically-braked disc is in effect an analogue integration the real RMS power

delivered to the load. The mechanical dial on the meter then simply reads off a numerical value proportional to the total number of revolutions of the disc, and thus the total energy delivered to the load.

Slow-speed synchronous timing motors

Representative are low-torque synchronous motors with a multi-pole hollow cylindrical magnet (internal poles) surrounding the stator structure. An aluminum cup supports the magnet. The stator has one coil, coaxial with the shaft. At each end of the coil are a pair of circular plates with rectangular teeth on their edges, formed so they are parallel with the shaft. They are the stator poles. One of the pair of discs distributes the coil's flux directly, while the other receives flux that has passed through a common shading coil. The poles are rather narrow, and between the poles leading from one end of the coil are an identical set leading from the other end. In all, this creates a repeating sequence of four poles, unshaded alternating with shaded, that creates a circumferential traveling field to which the rotor's magnetic poles rapidly synchronize. Some stepping motors have a similar structure.

When considering starting criteria, we must determine how often the motor will be started, once a week, once a day, once an hour. The reason we are concerned with the frequency of starting is the high starting current.

Common induction motors have locked rotor starting currents of up to six times their nameplate current. At locked rotor conditions, during starting, the effect of heat on stator windings equals 6 squared, or 36 times, the heating effect under rated load. A motor can sustain locked rotor currents only briefly, for about 10 to 15 seconds. Thereafter, damage results to the motor's windings

Slow acceleration or jogging increases motor temperature in the same manner. For applications involving slow acceleration or jogging, excessive heat input must be offset with idle periods for motor cooling. If the motor is subjected to slow or repeated starts without resting, high starting current is present in the windings until the motor exceeds breakdown torque, and stalls.

Starting Torque

Starting a motor involves special torque characteristic

considerations, including locked rotor or starting

torque, pull-up torque, and breakdown torque. The

motor must have sufficient starting and pull-up torque

to bring the driven machine to operating speed,

otherwise the motor will stall and this can eventually

damage the motor.

Acceleration Restrictions

Some applications require a motor to accelerate the driven load to normal operating speed within in a certain time frame. The longer a motor takes to accelerate, the higher the temperature rise in the motor. The larger the load, the longer is the acceleration time. A motor's ability to accelerate a driven load influences both the safety and performance factors of an operation.

Use this chart as a guide to maximum allowable acceleration times:

Electrical Supply System

Motors require the correct phase, voltage, and frequency from an electrical supply system. The system must also have sufficient capacity, or current carrying capability, to start and operate the motor. Motor

nameplates include all this information.

Motors operate satisfactorily on voltage that is within 10 percent, or frequency within 5 percent, of the optimal value listed on the motor nameplate. There is a risk of motor damage if the combined total voltage and frequency variation of a power supply exceeds 10 percent.

NEMA rated motors can be satisfactorily operated up to a combination voltage and frequency variation of 10 percent, assuming that the frequency variation itself does not exceed 5 percent.

Phase

Motors operate on either single or three phase electrical power. Single phase motors may operate on one phase of a three phase power supply with a compatible voltage rating. Many power suppliers do not allow large single phase motors to be connected to their lines. This is because a single phase motor larger than 10

horsepower started on a three phase source often causes voltage flicker problems.

One advantage of three phase motors is that they cause little or no voltage flicker on starting. Three phase motors cost less and last longer than comparably sized single phase motors.

One disadvantage of three phase power is that it often entails line extension charges upon installation. Operation of a three phase motor on a single phase power source results in permanent damage to the motor.

This is a diagram that may be helpful in understanding how single and three phase power commonly appear.

Physical Environmental Considerations

Motors must be rated to withstand the physical and environmental conditions their operation subjects them to. The selection of the proper enclosure is vital to the successful safe operation of a motor. Motor

performance and life can be significantly impacted by using a motor enclosure inappropriate for the application. An examination of the operating conditions of the motor environment will determine the most appropriate enclosure along with attention to applicable codes and standards.

The NEMA frame size of the motor you select depends upon the horsepower and speed you require. After choosing the motor, check the dimensions of that frame size to see if it fits in the space available.

If the standard motor does not fit, determine whether it is most economical to change the driven machine, use a different standard motor, or adapt the standard motor by using a mechanical modification or

accessory.

Ambient Temperature

NEMA rates most motors for exposure to ambient temperatures ranging from 32 to 104 degrees F (0 to 40 degrees C). If the motor has water cooling capabilities, NEMA ratings range from 50 to 104 degrees F (10 to 40 degrees C). Standard NEMA maximum ambient temperature is 104 degrees F.

Altitude

NEMA bases temperature rise ratings on operation altitudes of 3,300 feet (1,000 meters) or less. NEMA considers any altitude up to 3,300 feet equivalent to sea level. NEMA also assumes a maximum ambient temperature of 104 degrees F (40 degrees C) within these parameters.

When a motor operates at high altitude, de-rating is necessary since lower air density does not cool motors as well as high density air. Motors with Class B or F insulation systems and temperature rise in accordance with NEMA operate satisfactorily at altitudes above 3,300 feet; as long as ambient temperature remains lower than 104 degrees F (40 degrees C).

Rigid Mounting Surfaces

A motor's mounting surface must be rigid, and motor drives must accord with NEMA specifications. Furthermore, supplemental enclosures and structural accessories cannot noticeably interfere with motor ventilation. If a motor does not meet these provisions, the acquisition of a specialized motor, more suited to unconventional installation, is necessary.

Duty cycle:

Continuous steady-running loads over long periods are demonstrated by fans and blowers. On the other hand, electric motors installed in machines with flywheels may have wide variations in running loads. Often, electric motors use flywheels to supply the energy to do the work, and the electric motor does nothing but restore lost energy to the flywheel. Therefore, choosing the proper electric motor also depends on whether the load is steady, varies, follows a repetitive cycle of variation, or has pulsating torque or shocks.

For example, electric motors that run continuously in fans and blowers for hours or days may be selected on the basis of continuous load. But electric motors located in devices like automatically controlled compressors and pumps start a number of times per hour. And electric motors in some machine tools start and stop

many times per minute.

Duty cycle is a fixed repetitive load pattern over a given period of time which is expressed as the ratio of on-time to cycle period. When operating cycle is such that electric motors operate at idle or a reduced load for more than 25% of the time, duty cycle becomes a factor in sizing electric motors. Also, energy required to start electric motors (that is, accelerating the inertia of the electric motor as well as the driven load) is much higher than for steady-state operation, so frequent starting could overheat the electric motor.

For most electric motors (except squirrel-cage electric motors during acceleration and plugging) current is almost directly proportional to developed torque. At constant speed, torque is proportional to horsepower. For accelerating loads and overloads on electric motors that have considerable droop, equivalent horsepower is used as the load factor. The next step in sizing the electric motor is to examine the electric motor's performance curves to see if the electric motor has enough starting torque to overcome machine static friction, to accelerate the load to full running speed, and to handle maximum overload.

Electric Motors - Service factors:

A change in NEMA standards for electric motor service factors and temperature rise has been brought about because of better insulation used on electric motors. For instance, a 1.15 service factor -- once standard for all open electric motors -- is no longer standard for electric motors above 200 hp.

Increases in electric motor temperature are measured by the resistance method in the temperature rise table. Electric motors feature a nameplate temperature rise, which is always expressed for the maximum allowable load. That is, if the electric motor has a service factor greater than unity, the nameplate

temperature rise is expressed for the overload. Two Class-B insulated electric motors having 1.15 and 1.25 service factors will, therefore, each be rated for a 90°C rise. But the second electric motor will have to be larger than the first in order to dissipate the additional heat it generates at 125% load.

Electric motors feature a service factor, which indicates how much over the nameplate rating any given electric motor can be driven without overheating. NEMA Standard MGI-143 defines service factor of an ac motor as "...a multiplier which, when applied to the rated horsepower, indicates a permissible horsepower loading which may be carried under the conditions specified for the service factor..." In other words, multiplying the electric motor's nameplate horsepower by the service factor tells how much electric motors can be overloaded without overheating. Generally, electric motor service factors:

Handle a known overload, which is occasional.

Provide a factor of safety where the environment or service condition is not well defined, especially for general-purpose electric motors.

Obtain cooler-than-normal electric motor operation at rated load, thus lengthening insulation life.

Electric Motors - Efficiency:

Small universal electric motors have an efficiency of about 30%, while 95% efficiencies are common for three-phase machines. In less-efficient electric motors, the amount of power wasted can be reduced by more careful application and improved electric motor design.

Electric motor's feature an efficiency level, which also depends on actual electric motor load versus rated load, being greatest near rated load and falling off rapidly for under and overload conditions.

Mechanical requirements of a Driven Load:

A motor must produce enough torque to accelerate from a standstill to operating speed, and supply

enough power for all possible demands without exceeding its design limits. Selecting the right motor for

the application is not always a simple task.

In this section we examine the characteristics of driving the load, and see how important each part is in

properly specifying a motor.

Pulse-width modulation

An example of PWM in an AC motor drive: the phase-to-phase voltage (blue) is modulated as a series of

pulses that results in a sine-like flux density waveform (red) in the magnetic circuit of the motor. The

smoothness of the resultant waveform can be controlled by the width and number of modulated

impulses (per given cycle)

Pulse-width modulation (PWM) is a commonly used technique for controlling power to an electrical device, made practical by modern electronic power switches. The average value of voltage (and current) fed to the load is controlled by turning the switch between supply and load on and off at a fast pace. The longer the switch is on compared to the off periods, the higher the power supplied to the load is.

The PWM switching frequency has to be much faster than what would affect the load, which is to say the device that uses the power. Typically switchings have to be done several times a minute in an electric stove,

120 Hz in a lamp dimmer, from few kilohertz (kHz) to tens of kHz for a motor drive and well into the tens or hundreds of kHz in audio amplifiers and computer power supplies.

The term duty cycle describes the proportion of on time to the regular interval or period of time; a low duty cycle corresponds to low power, because the power is off for most of the time. Duty cycle is expressed in percent, 100% being fully on.

The main advantage of PWM is that power loss in the switching devices is very low. When a switch is off there is practically no current, and when it is on, there is almost no voltage drop across the switch. Power loss, being the product of voltage and current, is thus in both cases close to zero. PWM works also well with digital controls, which, because of their on/off nature, can easily set the needed duty cycle.

PWM has also been used in certain communication systems where its duty cycle has been used to convey information over a communications channel.

History

In the past, when only partial power was needed (such as for a sewing machine motor), a rheostat (located in the sewing machine's foot pedal) connected in series with the motor adjusted the amount of current flowing through the motor, but also wasted power as heat in the resistor element. It was an inefficient scheme, but tolerable because the total power was low. This was one of several methods of controlling power. There were others—some still in use—such as variable autotransformers, including the trademarked Autrastat for theatrical lighting; and the Variac, for general AC power adjustment. These were quite efficient, but also relatively costly.

For about a century, some variable-speed electric motors have had decent efficiency, but they were somewhat more complex than constant-speed motors, and sometimes required bulky external electrical apparatus, such as a bank of variable power resistors or rotating converter such as Ward Leonard drive . However, in addition to motor drives for fans, pumps and robotic servos, there was a great need for compact and low cost means for applying adjustable power for many devices, such as electric stoves and lamp dimmers.

One of early applications of PWM was in the Sinclair X10, a 10 W audio amplifier available in kit form in the 1960s. At around the same time PWM started to be used in AC motor control [1]

[edit] Principle

Fig. 1: a pulse wave, showing the definitions of

y

min

,

y

max

and D.

Pulse-width modulation uses a rectangular pulse wave whose pulse width is modulated resulting in the variation of the average value of the waveform. If we consider a pulse waveform

f(t)

with a low value

y

min

, a high value

y

_max

and a duty cycle D (see figure 1), the average value of the waveform is given by:

As

f(t)

is a pulse wave, its value is

y

_max

for and

y

_min

for . The above expression then becomes:

This latter expression can be fairly simplified in many cases where

y

_min

= 0

as . From this, it is obvious that the average value of the signal ( ) is directly dependent on the duty cycle D.

Fig. 2: A simple method to generate the PWM pulse train corresponding to a given signal is the

intersective PWM: the signal (here the green sinewave) is compared with a sawtooth waveform (blue).

When the latter is less than the former, the PWM signal (magenta) is in high state (1). Otherwise it is in

the low state (0).

The simplest way to generate a PWM signal is the intersective method, which requires only a sawtooth or a triangle waveform (easily generated using a simple oscillator) and a comparator. When the value of the reference signal (the green sine wave in figure 2) is more than the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state.

Delta

In the use of delta modulation for PWM control, the output signal is integrated, and the result is compared with limits, which correspond to a reference signal offset by a constant. Every time the integral of the output signal reaches one of the limits, the PWM signal changes state.

Fig. 3 : Principle of the delta PWM. The output signal (blue) is compared with the limits (green). These

limits correspond to the reference signal (red), offset by a given value. Every time the output signal

reaches one of the limits, the PWM signal changes state.

Delta-sigma

In delta-sigma modulation as a PWM control method, the output signal is subtracted from a reference signal to form an error signal. This error is integrated, and when the integral of the error exceeds the limits, the output changes state.

Fig. 4 : Principle of the sigma-delta PWM. The top green waveform is the reference signal, on which the

output signal (PWM, in the middle plot) is subtracted to form the error signal (blue, in top plot). This

error is integrated (bottom plot), and when the integral of the error exceeds the limits (red lines), the

output changes state.

Space vector modulation

Space vector modulation is a PWM control algorithm for multi-phase AC generation, in which the reference signal is sampled regularly; after each sample, non-zero active switching vectors adjacent to the reference vector and one or more of the zero switching vectors are selected for the appropriate fraction of the sampling period in order to synthesize the reference signal as the average of the used vectors.

Direct torque control (DTC)

Direct torque control is a method used to control AC motors. It is closely related with the delta modulation (see above). Motor torque and magnetic flux are estimated and these are controlled to stay within their hysteresis bands by turning on new combination of the device's semiconductor switches each time either of the signal tries to deviate out of the band.

Time proportioning

Many digital circuits can generate PWM signals (e.g. many microcontrollers have PWM outputs). They normally use a counter that increments periodically (it is connected directly or indirectly to the clock of the circuit) and is reset at the end of every period of the PWM. When the counter value is more than the reference value, the PWM output changes state from high to low (or low to high).[2] _{This technique is} referred to as time proportioning, particularly as time-proportioning control[3] _{– which proportion of a} fixed cycle time is spent in the high state.

The incremented and periodically reset counter is the discrete version of the intersecting method's sawtooth. The analog comparator of the intersecting method becomes a simple integer comparison between the current counter value and the digital (possibly digitized) reference value. The duty cycle can only be varied in discrete steps, as a function of the counter resolution. However, a high-resolution counter can provide quite satisfactory performance.

Types

Fig. 5 : Three types of PWM signals (blue): leading edge modulation (top), trailing edge modulation

(middle) and centered pulses (both edges are modulated, bottom). The green lines are the sawtooth

waveform (first and second cases) and a triangle waveform (third case) used to generate the PWM

waveforms using the intersective method.

Four types of pulse-width modulation (PWM) are possible:[dubious – discuss]

1. The pulse center may be fixed in the center of the time window and both edges of the pulse

moved to compress or expand the width.

2. The lead edge can be held at the lead edge of the window and the tail edge modulated.

3. The tail edge can be fixed and the lead edge modulated.

4. The pulse repetition frequency can be varied by the signal, and the pulse width can be constant.

However, this method has a more-restricted range of average output than the other three.

Spectrum

The resulting spectra (of the three cases) are similar, and each contains a dc component, a base sideband containing the modulating signal and phase modulated carriers at each harmonic of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a

sinx / x

envelope (sinc function) and extend to infinity.

On the contrary, the delta modulation is a random process that produces continuous spectrum without distinct harmonics.

Applications

Telecommunications

In telecommunications, the widths of the pulses correspond to specific data values encoded at one end and decoded at the other.

Pulses of various lengths (the information itself) will be sent at regular intervals (the carrier frequency of the modulation).

_ _ _ _ _ _ _ _

| | | | | | | | | | | | | | | |

Clock | | | | | | | | | | | | | | | |

__| |____| |____| |____| |____| |____| |____| |____| |____

_ __ ____ ____ _

PWM Signal | | | | | | | | | |

| | | | | | | | | |

_________| |____| |___| |________| |_| |___________

Data 0 1 2 4 0 4 1 0

The inclusion of a clock signal is not necessary, as the leading edge of the data signal can be used as the clock if a small offset is added to the data value in order to avoid a data value with a zero length pulse.

_ __ ___ _____ _ _____ __ _

| | | | | | | | | | | | | | | |

PWM Signal | | | | | | | | | | | | | | | |

__| |____| |___| |__| |_| |____| |_| |___| |_____

Data 0 1 2 4 0 4 1 0

Power delivery

PWM can be used to adjust the total amount of power delivered to a load without losses normally incurred when a power transfer is limited by resistive means. The drawback are the pulsations defined by the duty cycle, switching frequency and properties of the load. With a sufficiently high switching frequency and, when necessary, using additional passive electronic filters the pulse train can be smoothed and average analog waveform recovered.

High frequency PWM power control systems are easily realisable with semiconductor switches. As has been already stated above almost no power is dissipated by the switch in either on or off state. However, during the transitions between on and off states both voltage and current are non-zero and thus considerable power is dissipated in the switches. Luckily, the change of state between fully on and fully off is quite rapid (typically less than 100 nanoseconds) relative to typical on or off times, and so the average power

dissipation is quite low compared to the power being delivered even when high switching frequencies are used.

Modern semiconductor switches such as MOSFETs or Insulated-gate bipolar transistors (IGBTs) are quite ideal components. Thus high efficiency controllers can be built. Typically frequency converters used to control AC motors have efficiency that is better than 98 %. Switching power supplies have lower efficiency due to low output voltage levels (often even less than 2 V for microprocessors are needed) but still more than 70-80 % efficiency can be achieved.

Variable-speed fan controllers for computers usually use PWM, as it is far more efficient when compared to a potentiometer or rheostat. (Neither of the latter is practical to operate electronically; they would require a small drive motor.)

Light dimmers for home use employ a specific type of PWM control. Home use light dimmers typically include electronic circuitry which suppresses current flow during defined portions of each cycle of the AC line voltage. Adjusting the brightness of light emitted by a light source is then merely a matter of setting at what voltage (or phase) in the AC halfcycle the dimmer begins to provide electrical current to the light source (e.g. by using an electronic switch such as a triac). In this case the PWM duty cycle is the ratio of the conduction time to the duration of the half AC cycle defined by the frequency of the AC line voltage (50 Hz or 60 Hz depending on the country).

These rather simple types of dimmers can be effectively used with inert (or relatively slow reacting) light sources such as incandescent lamps, for example, for which the additional modulation in supplied electrical energy which is caused by the dimmer causes only negligible additional fluctuations in the emitted light. Some other types of light sources such as light-emitting diodes (LEDs), however, turn on and off extremely rapidly and would perceivably flicker if supplied with low frequency drive voltages. Perceivable flicker effects from such rapid response light sources can be reduced by increasing the PWM frequency. If the light fluctuations are sufficiently rapid, the human visual system can no longer resolve them and the eye perceives the time average intensity without flicker (see flicker fusion threshold).

In electric cookers, continuously-variable power is applied to the heating elements such as the hob or the grill using a device known as a Simmerstat. This consists of a thermal oscillator running at approximately two cycles per minute and the mechanism varies the duty cycle according to the knob setting. The thermal time constant of the heating elements is several minutes, so that the temperature fluctuations are too small to matter in practice.

Voltage regulation

PWM is also used in efficient voltage regulators. By switching voltage to the load with the appropriate duty cycle, the output will approximate a voltage at the desired level. The switching noise is usually filtered with an inductor and a capacitor.

One method measures the output voltage. When it is lower than the desired voltage, it turns on the switch. When the output voltage is above the desired voltage, it turns off the switch.

Audio effects and amplification

PWM is sometimes used in sound (music) synthesis, in particular subtractive synthesis, as it gives a sound effect similar to chorus or slightly detuned oscillators played together. (In fact, PWM is equivalent to the difference of two sawtooth waves. [1]) The ratio between the high and low level is typically modulated with a low frequency oscillator, or LFO. In addition, varying the duty cycle of a pulse waveform in a subtractive-synthesis instrument creates useful timbral variations. Some synthesizers have a duty-cycle trimmer for their square-wave outputs, and that trimmer can be set by ear; the 50% point was distinctive, because even-numbered harmonics essentially disappear at 50%.

A new class of audio amplifiers based on the PWM principle is becoming popular. Called "Class-D amplifiers", these amplifiers produce a PWM equivalent of the analog input signal which is fed to the loudspeaker via a suitable filter network to block the carrier and recover the original audio. These amplifiers are characterized by very good efficiency figures (≥ 90%) and compact size/light weight for large power outputs. For a few decades, industrial and military PWM amplifiers have been in common use, often for driving servo motors. They offer very good efficiency, commonly well above 90%. Field-gradient coils in MRI machines are driven by relatively-high-power PWM amplifiers.

Historically, a crude form of PWM has been used to play back PCM digital sound on the PC speaker, which is driven by only two voltage levels, typically 0 V and 5 V. By carefully timing the duration of the pulses, and by relying on the speaker's physical filtering properties (limited frequency response, self-inductance, etc.) it was possible to obtain an approximate playback of mono PCM samples, although at a very low quality, and with greatly varying results between implementations.

In more recent times, the Direct Stream Digital sound encoding method was introduced, which uses a generalized form of pulse-width modulation called pulse density modulation, at a high enough sampling rate (typically in the order of MHz) to cover the whole acoustic frequencies range with sufficient fidelity. This method is used in the SACD format, and reproduction of the encoded audio signal is essentially similar to the method used in class-D amplifiers.

References

1. Schönung, A.; Stemmler, H. (August 1964). "Geregelter Drehstrom-Umkehrantrieb mit

gesteuertem Umrichter nach dem Unterschwingungsverfahren". BBC Mitteilungen (Brown

Boveri et Cie) 51 (8/9): 555–577.

2.

www.netrino.com – Introduction to Pulse Width Modulation (PWM)

3. Fundamentals of HVAC Control Systems, by Robert McDowall,

p. 21

Three-phase induction motors

An induction motor or asynchronous motor is a type of alternating current motor where power is supplied to the rotor by means of electromagnetic induction.[1]

An electric motor turns because of magnetic force exerted between a stationary electromagnet called the stator and a rotating electromagnet called the rotor. Different types of electric motors are distinguished by how electric current is supplied to the moving rotor. In a DC motor and a slip-ring AC motor, current is provided to the rotor directly through sliding electrical contacts called commutators and slip rings. In an induction motor, by contrast, the current is induced in the rotor without contacts by the magnetic field of the stator, through electromagnetic induction. An induction motor is sometimes called a rotating transformer because the stator (stationary part) is essentially the primary side of the transformer and the rotor (rotating part) is the secondary side. Unlike the normal transformer which changes the current by using time varying flux, induction motors use rotating magnetic fields to transform the voltage. The current in the primary side creates an electromagnetic field which interacts with the electromagnetic field of the secondary side to produce a resultant torque, thereby transforming the electrical energy into mechanical energy. Induction motors are widely used, especially polyphase induction motors, which are frequently used in industrial drives.

Induction motors are now the preferred choice for industrial motors due to their rugged construction, absence of brushes (which are required in most DC motors) and—thanks to modern power electronics—the ability to control the speed of the motor.

History

The first induction motors were realized by Galileo Ferraris in 1885 in Italy. In 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin (later, in the same year, Nikola Tesla gained U.S. Patent 381,968) where he exposed the theoretical foundations for understanding the way the motor operates.[2] _{The induction motor with a cage was invented by Mikhail Dolivo-Dobrovolsky about a year later.}

Principle of operation and comparison to synchronous

motors

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

The basic difference between an induction motor and a synchronous AC motor is that in the latter a current is supplied into the rotor (usually DC) which in turn creates a (circular uniform) magnetic field around the rotor. The rotating magnetic field of the stator will impose an electromagnetic torque on the still magnetic field of the rotor causing it to move (about a shaft) and rotation of the rotor is produced. It is called synchronous because at steady state the speed of the rotor is the same as the speed of the rotating magnetic field in the stator.

By way of contrast, the induction motor does not have any direct supply onto the rotor; instead, a

secondary current is induced in the rotor. To achieve this, stator windings are arranged around the rotor so that when energised with a polyphase supply they create a rotating magnetic field pattern which sweeps past the rotor. This changing magnetic field pattern induces current in the rotor conductors. These currents interact with the rotating magnetic field created by the stator and in effect causes a rotational motion on the rotor.

However, for these currents to be induced, the speed of the physical rotor must be less than the speed of the rotating magnetic field in the stator or else the magnetic field will not be moving relative to the rotor conductors and no currents will be induced. If by some chance this happens, the rotor typically slows slightly until a current is re-induced and then the rotor continues as before. This difference between the speed of the rotor and speed of the rotating magnetic field in the stator is called slip. It is unitless and is the ratio between the relative speed of the magnetic field as seen by the rotor (the slip speed) to the speed of the rotating stator field. Due to this, an induction motor is sometimes referred to as an asynchronous machine.

AC Induction Motor

where

n = Revolutions per minute (rpm) f = AC power frequency (hertz)

p = Number of poles per phase (an even number) Slip is calculated using:

where s is the slip. The rotor speed is:

Synchronous Motor

A synchronous motor always runs at synchronous speed with 0% slip. The speed of a synchronous motor is determined by the following formula:

where v is the speed of the rotor (in rpm), f is the frequency of the AC supply (in Hz) and p is the number of magnetic poles.[3]

For example, a 6 pole motor operating on 60 Hz power would have a speed of:

Note on the use of p - some texts refer to number of pole pairs per phase instead of number of poles per phase. For example a 6 pole motor, operating on 60 Hz power, would have 3 pole pairs. The equation of synchronous speed then becomes:

with

P

being the number of pole pairs. For

P = 3

and :

Construction

The stator consists of wound 'poles' that carry the supply current to induce a magnetic field that penetrates the rotor. In a very simple motor, there would be a single projecting piece of the stator (a salient pole) for each pole, with windings around it; in fact, to optimize the distribution of the magnetic field, the windings are distributed in many slots located around the stator, but the magnetic field still has the same number of north-south alternations. The number of 'poles' can vary between motor types but the poles are always in pairs (i.e. 2, 4, 6, etc.).

Induction motors are most commonly built to run on single-phase or three-phase power, but two-phase motors also exist. In theory, two-phase and more than three phase induction motors are possible; many single-phase motors having two windings and requiring a capacitor can actually 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 ( the field merely oscillates back and forth), so single-phase induction motors must incorporate some kind of starting mechanism to produce a rotating field. They would, using the simplified analogy of salient poles, have one salient pole per pole number; a four-pole motor would have four salient poles. Three-phase motors have three salient poles per pole number, so a four-pole motor would have twelve salient poles. This allows the motor to produce a rotating field, allowing the motor to start with no extra equipment and run more efficiently than a similar single-phase motor.