**Motor Action**
Michael Faraday showed that passing a current through a conductor freely suspended in a fixed magnetic field creates a force which causes the conductor to move through the field.

Conversely, if the conductor rather than the magnet is constrained then the magnet creating the field will move relative to the conductor.

More generally, the force created by the current, now known as the Lorentz force, acts between the current conductor and the magnetic field, or the magnet creating the field.

The magnitude of the force acting on the conductor is given by:

**F = BLI **

Where ** F** is the force on the conductor, **L** is the length of the conductor and **I** is the current flowing through the conductor

**Generator Action**
Faraday also showed that the converse is true - moving a conductor through a magnetic field, or moving the magnetic field relative to the conductor, causes a current to flow in the conductor.

The magnitude of the EMF generated in this way is given by:

**E = BLv **

Where **E** is the generator EMF (or back EMF in a motor) and **v** is the velocity of the conductor through the field

**Alternative Motor Action (Interactive Fields) **
Another form of motive power, which does not depend on the Lorentz force and the flow of an electrical current, can in principle be derived from the purely attractive (or repulsive) magnetic force which is exerted on a magnet or on magnetically susceptible materials such as iron when they are placed in the field of another magnet. The movement of a compass needle in the presence of a magnet is an example. In practice however at least one magnet creating the field must be an electromagnet in order to obtain the necessary control of the magnetic field to achieve sustained motion as well as practical levels of torque.

Brushless DC motors and reluctance motors depend on this phenomenon known as "reluctance torque" since no electric currents flow in the rotor. Rotary motion is obtained by sequential pulsing of the stator poles to create a rotating magnetic field which drags along the moving magnet with it.

In AC induction motors the rotating field is obtained by a different method and the basic motor action depends on the Lorentz force, however synchronous AC motors have magnetic rotor elements which are pulled around in synchronism with the rotating field just as in a brushless DC motor.

**Reluctance Torque**
Torque is created due to the reaction between magnetic fields. Consider a small bar magnet in the field of another larger magnet such as the gap between the poles of a horse shoe magnet or one of the pole pairs of an electric motor. (See reluctance motor diagram). When the bar magnet is aligned with the poles of the large magnet its field will be in line with the external field. This is an equilibrium position and the bar will not experience any force to move it. However if the bar is misaligned with the poles, either rotated or displaced, it will experience a force pulling it back into line with the external field. In the case of a lateral displacement, the force diminishes as the distance increases, but in the case of a rotation, the force will increase reaching a maximum when the bar is at right angles to the external field. In other words the torque on the magnet is at a maximum when the fields are orthogonal and zero when the field are aligned.

**Salient Poles **
Motors which depend on reluctance torque normally have "salient poles" - poles which stick out. This is to concentrate the flux into discrete angular sectors to maximise and focus the alignment force between the fields.

**Torque from Rotating Fields **
In motors which depend on rotating fields, such as induction motors, brushless DC and reluctance motors, the instantaneous torque on the rotor depends on its angular position with respect to the angular position of the flux wave. Though the flux wave tries to pull the rotor poles in line with the flux, there will always be inertia and losses holding the rotor back.

**Slip**
The friction, windage and other losses cause the rotor of an induction motor to turn at a slower speed than the rotating field resulting in an angular displacement between the rotating flux wave and the rotating field associated with the rotor poles. The difference between the speed of the flux wave and the speed of the rotor is called the "slip" and the motor torque is proportional to the slip.

**Torque Angle **
Even in synchronous motors in which the rotor turns at the same speed as the flux wave, because of the losses noted above the rotor poles will never reach complete alignment with the peaks in the flux wave, and there will still be a displacement between the rotating flux wave and the rotating field. Otherwise there would be no torque. This displacement is called the "torque angle". The motor torque is zero when the torque angle is zero and is at its maximum when the torque angle is 90 degrees. If the torque angle exceeds 90 degrees the rotor will pull out of synchronism and stop.

**Electrical Machines**

The majority of electrical machines (motors and generators) sold today are still based on the Lorentz force and their principle of operation can be demonstrated by the example below in which a single turn coil carrying electrical current rotates in a magnetic field between the two poles of a magnet.

For multiple turn coils, the effective current is **NI** (Ampere Turns) where **N** is the number of turns in the coil.

If the coil is supplied with a current the machine acts as a motor. If the coil is rotated mechanically, current is induced in the coil and the machine thus acts as a generator.

In rotating machines the rotating element is called the rotor or armature and the fixed element is called the stator.

**Action and Reaction**
In practice, both the motor and the generator effects take place at the same time.

Passing the current through a conductor in the magnetic field causes the conductor to move through the field but once the conductor starts moving it becomes a generator creating a current through the conductor in the opposite direction to the applied current. Thus the motion of the conductor creates a "back EMF " which opposes the applied EMF.

Conversely moving the conductor through the field causes a current to flow through the conductor which in turn creates a force on the conductor opposing the applied force.

The actual current which flows in the conductor is given by:

**I = **__(V - E)__

** R**

Where **V** is the applied voltage, **E** is the back EMF and **R** is the resistance of the conductor (the armature of the motor)..

**The EMF Equation**
From the above, the back EMF in an electric motor is equal to the applied voltage less the volt drop across the armature.

**E = V - RI**

This is known as the "Motor EMF Equation".

The volt drop across the amature **RI** is sometimes called the Net Voltage

**The Power Equation**
Multiplying the voltage by the armature current to get the power gives the following relationship:

**P = EI = VI - I**^{2}R

It shows that
the mechanical power delivered by the motor is equal to the back EMF times the armature current OR the electrical power applied to the motor less the I^{2}R losses in the windings. (Disregarding frictional losses).

This is known as the "Motor Power Equation".

**Operating Equilibrium Under Load**
The "Action and Reaction" effects outlined above provide an important automatic self regulating feedback mechanism in both DC and AC motors for adapting to changes to the applied load. As the load on the motor is increased it tends to slow down, reducing the back EMF. This in turn allows more current to flow generating more torque to accommodate the increased load until a point of balance or equilibrium is reached. Thus the motor will set itself to an appropriate speed for the torque demanded. See also Power Handling below.

**Magnetic Fields**

The motor's magnetic field is provided by the stator and in the above example the stator is a permanent magnet however in the majority of electrical machines the magnetic field is provided electromagnetically by coils wound around the stator poles. The stator windings are also called the field windings and the motor is said to be "field energised".

The rotor is normally wound on an iron core to improve the efficiency of the machine's magnetic circuit.
**Magnetic Circuits**

In the case of electrical machines, the magnetic circuit is the path of the magnetic flux through the stator body, across the air gap, through the rotor and back through the air gap into the stator. The length **l** of this path is known as the mean magnetic path length **MMPL**

Magnetic circuits are designed to produce the maximum flux possible and to concentrate it in the air gap between the rotor and the stator through which the coils move. The flux **Φ** is measured in Webers

The flux density **B** is measured in Teslas and is defined as the magnetic flux **Φ** per unit area **A**. Thus **B = Φ/A** where **A** is the area through which the flux passes.

From the equations above it can be seen that the torque generated by the electric motor or the EMF created by the generator are directly proportional to the magnetic flux density **B** in the region surrounding the moving electrical conductors and for efficient machines, **B** should be as high as possible.

**MagnetoMotive Force (MMF)**

The magnetic flux arising in a magnetic circuit is proportional to the magnetomotive force (MMF) creating it. For an electromagnet, the MMF is the effective current in the magnetising coil measured in Ampere turns **NI** and, as above, this is the actual current **I** times the number of turns **N** in the coil.

Thus **MMF** = **NI** = **Φ** X *R* where **R** is the *reluctance* of the magnetic circuit. The reluctance is the inherent resistance of the material in the magnetic circuit to the setting up of the magnetic flux through it. (For iron the reluctance is very low. For air it is very high)

This equation for the flux in magnetic circuits is analogous to Ohm's law for the current in electric circuits in which:

**EMF = I **X** R** where **R** is the *resistance* of the electric circuit.

Because the reluctance of the air gap between the stator and the rotor is very high, the air gap should be as small as possible to minimise the Ampere turns needed to create the desired flux density.
**Magnetic Force (H)** also called the **Magnetic Field Strength**
The magnetic field strength **H** is the **MMF** per unit length in a magnetic circuit. Thus:

**H=**__NI__

**l**

The magnetomotive force is the cause of the magnetic field, the magnetic force is the effect.

**Flux Density (B)** and **Magnetic Permeability ***(µ*)
For uniform fields, the flux density associated with the magnetic force is proportional to the field strength and is given by:

B=**µ**_{0}**µ**_{r}H

where

**µ**_{0} is the known as the magnetic constant or the permeability of free space.

**µ**_{r} is the relative permeability of the magnetic material.

Unfortunately, the relationship becomes non-linear as the flux density increases and the magnetic material becomes saturated. Then the flux produced by increases in the the magnetic field decreases and levels off and the relaitive permeability **µ**_{r} tends towards 0.

**Saturation**

From the above it can be seen that increasing the MMF (Ampere turns) in a magnetic circuit increases the flux through the circuit but there is a limit to the flux density which can be created in magnetic materials such as iron when the material is said to be saturated. Above this point more and more MMF is needed to create less and less flux. In other words the reluctance increases sharply when the material saturates.

For maximum efficiency, electric machines are usually designed to work just below the onset of saturation.

**Magnetic Poles**

Electric machines can have multiple pole pairs. Multiple pole machines usually provide more efficient magnetic circuits and smoother torque characteristics.

**Commutation**
The connection to the moving coil in the basic machine shown above is made via carbon brushes bearing on a pair of slip rings, one connected to each end of the coil.

If the machine is used as a generator, the direction of the current generated will reverse every half cycle as the arm of the coil passes the opposite poles in succession. If a unidirectional current is required, the slip rings are split and interconnected such that, each half cycle, the current is taken from alternate arms of the coil. This simple switching mechanism is called a commutator.

Similarly when the machine is used as a DC motor, the commutator switches the DC supply voltage to alternate arms of the coil each half cycle in order to achieve unidirectional rotation.

Thus in all wound rotor DC machines, both motors and generators, the current in the rotor windings is AC and it is the commutator which enables the corresponding DC input or output. There are however some notable exceptions. The world's first motors and generators invented by Faraday were unipolar or homopolar machines in which unidirectional current flowed in the conductors. Faraday's motor was a laboratory curiosity with no practical applications but his so called "Faraday Disk" dynamo was able to generate useful current.

For over 100 years, mechanical commutation was the only practical way of switching the direction of the current flow however since the 1970s the availability of high power semiconductors has made electronic commutation possible.

In AC machines the complexities of commutation can be avoided since current can be induced in the rotor windings by transformer action with the stator windings, obviating the need for direct connections between the supply line and the rotating windings. See Induction Motors.

Because the commutator is essentially a mechanical switch, rapidly making and breaking a high current circuit, the switch is prone to sparking and the generation of Radio Frequency Interference (RFI) which can disrupt the working of other electronic circuits in the vicinity.

In very large motors the propensity for sparking can be reduced by the addition of "interpoles" or "commutating poles", narrow auxiliary windings midway between the main stator poles. These are connected in series with the rotor windings and produce an MMF equal and opposite to the rotor MMF so that the effective flux between the main poles is zero. Commutation is designed to occur the instant when the current passes through zero between the negative and positive half cycles and this takes place when the rotor is midway between the main poles. By neutralising the flux in this region the possibility of sparking is reduced.

**Evolution**
The earliest electrical machines depended on permanent magnets to provide the magnetic field, however the best magnetic materials available at the time were only capable of providing very weak fields limiting potential machine applications to laboratory demonstrations. It was eventually realised that much stronger magnetic fields could be generated by using electromagnets powered by the applied or generated line voltage. This allowed the construction of much more powerful machines enabling the development of practical applications. Advances in magnetic materials have now created much more powerful permanent magnets enabling their use in practical machines, simplifying machine construction by eliminating one set of windings. At the same time many features such as encoders, tachogenerators, thermal cut outs, brakes and fans are being built into the machines See also Controllers

**Torque**
Generally speaking the torque produced by a motor is proportional to the current it consumes and also proportional to the flux in the air gap.

**T = K**_{1}I B

**Speed**
**DC Motors**
In DC motors the rotational speed is proportional to the applied voltage and the normal method of speed control is by varying the input voltage.

**N = K**_{2}__ V __

** B**

The speed is however also inversely proportional to the flux in the air gap. This means that the speed increases as the flux provided by the field coils decreases. Theoretically the speed could go to infinity if the current in the field coil is removed, though the motor would most likely be destroyed before this happens. In practice a limited increase in speed can be obtained by reducing the field current in a controlled way. But note from the Torque equation above that reducing the field current also reduces the torque. This method of speed control is called "**Field Weakening**"

**AC Motors**
In AC motors the speed is proportional to the frequency of the applied voltage and inversely proportional to the number of magnetic poles.

**N = K**_{3} * f *

** P **

**Torque - Speed Characteristic **
DC motors produce their maximum torque at zero speed or when they are stalled (when they consume maximum current) and the torque falls off linearly as the speed increases, reaching zero when the reverse voltage generated by the rotating coils in the magnetic field (the back EMF) is equal to the applied voltage.

With AC motors the starting torque at zero speed may be about 70% to 90% of its maximum, rising to a peak as the speed increases then falling sharply to zero as the motor approaches synchronous speed. See note about synchronous motors .

(The torque - speed characteristics of electric motors are in contrast to an internal combustion engines whose torque is very low at low speeds, typically stalling below 800 rpm, but increasing with speed up to a peak at about 80% of its maximum speed falling off only slightly as it reaches maximum speed.)

**Starting**
Some motor designs are not self starting in their basic configuration but they normally incorporate design adaptations to enable self starting so that the user may be unaware of the problem.

**Power Handling**
The motor output power is directly proportional to its speed.

The
output power **P** in Watts is given by:

**P = ωT**

Where **ω** is the speed in radians per second and **T** is the torque in Newton metres

OR

**P = **__ 2π NT__ = __NT__

**60 9.55**

Where **N** is the speed in revolutions per minute (RPM)

**NOTE**: This relationship shows that for a given power, the speed reduces as the load or torque increases and vice versa. This is in some ways equivalent to what occurs in a mechanical gear box and is in line with the Operating Equilibrium mentioned above.

**Maximum Power**
The maximum power which a motor can handle is determined by its maximum permissible temperature. Power handling capacity can be increased by utilising materials capable of withstanding higher temperatures, particularly for the insulation on the windings, or by providing forced cooling which lowers the motor temperature for a given current consumption.

**Corner Power**
Corner power is an alternative way of specifying motor performance which some people find useful for comparing machines.

It is simply the product of the maximum torque the motor can deliver and the maximum speed it can attain. Since the maximum torque rarely, if ever, occurs at the same time as the maximum speed, the actual delivered machine power will always be less than the corner power.

In DC motors the commutation limit is set by the ability of the commutator segments and brushes to handle high voltages (speed limit) and high currents (torque limit).

Note also that at high voltages and currents forced cooling may be required.

**Cooling**
The power handling capacity of an electrical machine is limited by the maximum allowable temperature of its windings.

Higher power motors require higher magnetic fields and the current necessary to provide the higher flux density increases linearly with the motor size. The cross sectional area of the copper cable necessary to carry the current however increases as the square of the cuurent.

Power handling can be increased by using insulation which can withstand higher temperatures or by providing forced cooling to remove the heat from the windings. Forced cooling is not normally required for fractional horsepower machines but larger integral horsepower motors usually incorporate a built in cooling fan to force air through the machine. Forced air cooling can be effective in machines up to 50 megawatts but larger machines with multi megawatt power ratings, as used in the electricity generating industry, must resort to liquid cooling with the coolant being circulated through hollow conductors. The working fluid may be water but for the largest machines hydrogen is used because of its low weight and high thermal capacity.

**Gearing**
For a given torque, the motor power is proportional to the speed. Low speed motors will thus deliver very low power. Applications requiring high torque at low speeds will require very high currents and impractically large motors. Such applications are better served by higher speed motors with gearing mechanisms to reduce the speed and increase the torque.

**Size**
The size of a motor is determined by the torque it has to deliver. For similar motors with similar cooling systems the motor torque is proportional to the volume of the rotor and hence the overall motor volume.

**Efficiency **
As noted above, for a given torque, the motor power is proportional to the speed whereas the electrical and windage losses tend to be roughly constant, rising relatively slowly. Thus the motor efficiency increases with speed.

Efficiency is also dependent on the size of the motor since resistive losses tend to be proportionately much higher in smaller devices than in larger machines which can be designed with more efficient magnetic circuits.

**Cogging**
Cogging is the jerky, non uniform angular velocity of a machine rotor particularly apparent at low speeds in motors with a small number of poles. It occurs because the rotor tends to speed up as it approaches the stator poles and to slow down as it leaves the poles. It is also noticeable when pulsed DC is used if the frequency of the supply waveform is too low. The problem can be reduced by using skewed rotor windings as well as increasing the number of poles in the motor.

**Losses**

Losses reduce the efficiency of the machine and usually result in unwanted heat.
**Copper losses**

These are the I^{2}R heat losses resulting from the current flowing in the windings. The copper losses are variable, depending on the current and hence the load on the machine. The iron and other losses tend to be relatively constant.
- Stator winding resistance
- Rotor winding resistance

**Iron Losses**

These are losses which occur in the magnetic circuit.
- Saturation
This is the wasteful use of energy associated with using materials at flux densities above the saturation point.

- Hysteresis loss

This is the energy needed to magnetise and demagnetise the iron in the magnetic circuit each machine cycle. Since the losses per cycle are fixed, they will increase in line with the frequency. See more information about hysteresis. Special low hysteresis steels have been developed to reduce these losses.
- Eddy current loss

These losses are due to the unwanted, circulating currents which are induced in the iron of the machine's magnetic circuit
by the machine windings. They are minimised by using laminated iron in the magnetic circuits instead of solid iron. The insulating oxide layer on the laminations inhibits eddy current flow between laminations.

**Flux Leakage**
In practical magnetic circuits it is not always possible to concentrate all of the magnetic flux where it is needed for optimum magnetic coupling and the maximum energy interchange between the rotor and the stator. Consequently some of the applied energy is lost.

**Windage / Friction**
These are the mechanical losses resulting from the drag on the movement of the rotor.

**Power Factor**
An induction motor appears to the power line as a large inductor and consequently the line current lags behind the applied voltage. The effective power of the motor will then be **VAcosΦ** where **V** is the applied voltage, **A** is the current which flows and **Φ** is the phase angle by which the current lags the voltage.

**CosΦ** is known as the power factor. When **Φ** = 0 the current is in phase with the voltage, **cosΦ =** 1 and there is no power loss. When **Φ** = 1 the current lags the voltage by 90°,** cosΦ =** 0 and there will be no effective power delivered to the load. The factor (1 - **cosΦ**) represents the extra power which the machine must consume from the source in order to deliver its nominal power.

As with motors there are many different applications of the above principles. See some practical examples in the section on Generators.