Motors and Generators

INTRODUCTION:

Modern society is geared to using electricity.  Electricity has characteristics that have made it uniquely suited for powering a highly technological society.  There are many energy sources that can be readily converted into electricity.  In Australia, most power plants burn a fuel such as coal or use the energy of falling water to generate electricity on a large scale.  Electricity is also relatively easy to distribute.  Electricity authorities use high voltage transmission lines and transformers to distribute electricity to homes and industries around each state.  Voltages from power stations can be as high as 500 000 volts but by the time this reaches homes, the electricity has been transformed to 240 volts.  While it is relatively economical to generate electric power at a steady rate, there are both financial and environmental issues that should be considered when assessing the long-term impact of supplying commercial and household power. 

The design of a motor for an electrical appliance requires consideration of whether it will run at a set speed, how much power it must supply, whether it will be powered by AC or DC and what reliability is required.  The essentials of an electric motor are the supply of electrical energy to a coil in a magnetic field causing it to rotate. 

The generation of electrical power requires relative motion between a magnetic field and a conductor.  In a generator, mechanical energy is converted into electrical energy while the opposite occurs in the electric motor. 

The electricity produced by most generators is in the form of alternating current.  In general, AC generators, motors and other electrical equipment are simpler, cheaper and more reliable than their DC counterparts.  AC electricity can be easily transformed into higher or lower voltages making it more versatile than DC electricity. 

This module increases students’ understanding of the applications and uses of Physics and the implications for society and the environment.

 Magnetic Flux Density Vector

One measure of the strength of a magnetic field is the Magnetic Flux Density Vector, B.  This is also called the Magnetic Induction Vector.  The higher the value of B, the stronger the magnetic field.  The direction of the B vector at a point in space is the direction of the magnetic field at that point.  The SI Unit for B is called the tesla (T).  Most magnetic fields are much smaller than 1T.  A mathematical definition of B will be given later.

 Moving Charges In A Magnetic Field

A moving electric charge carries with it an associated magnetic field.  Thus, an electric charge moving through a magnetic field experiences a force, due to the interaction of the two magnetic fields present.  The size of this force is given by: 

                                       F = q v B

Where q = size of charge, v = velocity of charge perpendicular to the field and B = magnetic flux density vector.

If the charge enters the field at an angle q to the field direction, instead of perpendicular to it, we must use the component of v that is at right angles to the field direction.  Thus the formula becomes:

                                       F = q v B sin q

The direction of the force on a charge in a magnetic field may be determined by using Fleming’s Left Hand Rule.  Hold the thumb, first finger and second finger of the LEFT hand mutually at right angles.  Point the first finger in the direction of the magnetic field.  Point the second finger in the direction of conventional current flow (ie in the direction of flow of positive charge).  The thumb then points in the direction of the force on the charged particle.

Magnetic Force On Current-Carrying Conductors

Consider a conductor of length L, sitting in a magnetic field of flux density B and carrying a current I, as shown below:

                         

Clearly, a current is simply a flow of charge and since all moving charges experience a force when travelling through a magnetic field, a conductor carrying a current through a magnetic field will also experience a force.  The size of this force can be shown mathematically to be:

                                       F = B I L sin q

Where q is the angle made by the conductor with the magnetic field.  See below.

                        

Note that the magnitude of the force on a current-carrying conductor depends on:

u    The strength of the magnetic field in which it is located (indicated by the size of the magnetic flux density vector);

u    The magnitude of the current in the conductor;

u    The length of the conductor sitting in the external magnetic field; and

u    The angle between the direction of the external magnetic field and the direction of the length of the conductor.

The direction of the force on a current-carrying conductor sitting in a magnetic field is found by Fleming’s Left Hand Rule, as previously described.  It should also be clear that neither a charge travelling parallel to a magnetic field nor a current-carrying conductor lying parallel to a magnetic field will experience any force due to the field, since for both, sinq  = 0.

 Parallel Current-Carrying Conductors

Consider two very long, straight, parallel, current-carrying conductors as shown below:

               

The magnetic field produced by the current flowing through conductor 1 will pass through conductor 2.  Thus, all of the charges flowing through conductor 2 will be flowing through a magnetic field and will thus experience a force.  The same argument can be applied to deduce that conductor 1 will also experience a force.

The size of the force F acting on each of the conductors is given by:

                                                

where k = m₀/2p = 2 x 10^-7 SI Units, I₁ & I₂ are the currents in conductors 1 & 2 respectively, d is the distance between the conductors and l is the common length of the conductors.  (m₀ is the permeability of free space and is a measure of the ability of free space to support a magnetic field.)

Fleming’s LHR can be used to show that: 

u    When the currents in the conductors are in the SAME direction, the force between the conductors is ATTRACTIVE.

u    When the currents in the conductors are in OPPOSITE directions, the force between the conductors is REPULSIVE.

Torque in Current Loops in a Magnetic Field

A torque is defined as the turning moment of a force.  The torque about an axis of rotation is the product of the perpendicular distance of the axis from the line of action of the force and the component of the force in the plane perpendicular to the axis. See the diagram below.

               

For the situation above, the torque t on the bar about the pivot is:

                                      t =  F d

Consider a rectangular coil of wire carrying a current I and sitting in a magnetic field of flux density B, with its plane parallel to the field direction, as shown below:

                    

For this coil: 

(a)    force on AB is down into the page by Fleming’s LHR

(b)   force on CD is up out of the page by Fleming’s LHR

Therefore, the coil turns under the action of an applied net torque, with CD coming up out of the page and AB going down into the page.  Once the coil has passed through the position where its plane is perpendicular to the field direction, the direction of the net torque is reversed.  (Use Fleming’s LHR to verify this for yourself – remember the current direction in the coil stays the same throughout.)  Thus, the coil will eventually stop and then turn in the opposite direction.  And so the motion will continue.

This tendency of a current-carrying loop to turn whenever it sits in a magnetic field is called the “motor effect”.

The size of the torque on a coil of n turns of wire may be shown to be:

                        t  =  B I A n cosq 

where B = magnetic flux density of the field, I = current flowing in coil, A = area of coil, n = number of turns of wire in coil and q= initial angle made by plane of coil and the B field direction.

Note that when q = 90^o (coil perpendicular to field direction), no torque exits since then F and d are both in the same plane.

   

 The DC Electric Motor

One simple application of the motor effect is the DC electric motor.  A simple electric motor consists of a current-carrying loop situated in a magnetic field, with its plane initially parallel to the field direction.  Clearly, for the loop to continue to rotate in one direction, the current running through the loop must reverse direction just as the loop reaches the position where it is perpendicular to the field direction.  A split ring commutator is used to achieve this reversal of the current direction.

The split ring commutator is attached to the loop and conducts current into the loop by rubbing against the brushes.  The brushes are usually carbon rods that carry current from the external power source to the commutator.  See the diagram below (note that it has not been drawn to scale – commutator has been drawn larger than is actually the case):

                        

The split ring is arranged so that each half of the commutator changes brushes just as the loop reaches the position where its plane is perpendicular to the field direction. Changing brushes reverses the current in the loop.  As a result, the direction of the force on each side of the loop is reversed and the loop continues to rotate in the same direction.  This process is repeated each half-turn.  Thus, the loop spins in the magnetic field.

In practice, electric motors have several rotating loops.  Together they make up the armature (or rotor) of the motor.  The magnetic field in which the armature sits is called the field structure (or stator) of the motor.  This can be produced either by permanent magnets as in the simple case shown above or more usually by current-carrying coils called field coils wound around iron cores called pole pieces.  These sit opposite one another inside the motor frame.

 Magnetic Flux

The entire group of field lines that flow out of the N pole of a magnet constitute the flux of the magnet, represented by f (phi).  The SI Unit of magnetic flux is theweber (Wb).  Most magnets have flux values in the microweber range (mWb).

Two magnets are of equal strength if they have the same flux (the same total number of lines emerging from their N poles).  But if the area of the pole face of one magnet is half that of the other, then the concentration of lines of force must be twice as great in the magnet with the smaller pole face.  This degree of concentration of flux is what we called earlier the flux density, B.

So clearly B =  f /A.

Thus, if a uniform magnetic flux density B, extends over an area A, the magnetic flux is given by:

                                      f  =  B A

The Discovery of Electromagnetic Induction

The term “electromagnetic induction” refers to the creation of an electromotive force (voltage) in a conductor moving relative to a magnetic field.  The effect was discovered by the British scientist Michael Faraday (1791-1867).

In 1831, Faraday discovered that moving a magnet near a wire induces an electric current in that wire.  In one experiment he showed that when a permanent magnet moved towards a coil of wire connected to a sensitive galvanometer, a current was induced in one direction in the coil.  When the magnet was stationary or inside the coil, no current flowed through the coil.  When the magnet was removed from the coil, another current was induced in the coil, this time in the opposite direction to the original induced current.  Faraday reasoned that the presence of an induced current implied the presence of an induced electromotive force (emf) that caused the current.

In further experiments Faraday showed that an induced emf and a corresponding induced current was produced whenever there was relative motion between the magnet and the coil.  He also showed that this induced emf & current were proportional to: 

(a)    The relative velocity of the magnet and coil;

(b)   The strength of the magnet;

(c)    The number of turns of wire per unit length.

In the same year Faraday demonstrated the induction of one electric current by another.

Faraday’s Law of Electromagnetic Induction

Faraday eventually deduced from his experiments that an emf was induced in the coil, only when magnetic field lines were being cut by the coil.  Faraday’s Law of Electromagnetic Induction states that:  An emf is induced whenever a coil or circuit experiences a change of magnetic flux with time and the magnitude of the emf depends on the rate of change of the magnetic flux through the coil or circuit.

Mathematically, for a conductor of N turns of wire, cutting through a magnetic flux of Df in a time of Dt, the emf e, induced across the ends of the conductor is:

                                    

 Origin of Induced emf

Let us now consider how an induced emf originates.  The diagram below shows a magnetic field directed down into the plane of the page.  A copper wire is being moved to the right through this magnetic field at a constant velocity v.

        

Since the copper wire contains many free electrons, these electrons are literally moving to the right through the magnetic field.  Therefore we have a situation where charged particles, electrons, are moving through a magnetic field.  We know from our earlier work that whenever this happens the charged particles experience a force.  The size of this force is F = qvB.

Fleming’s Left Hand Rule gives the direction of this force.  Applying this rule to the motion of the electrons we have: field direction (index finger) down into the page, conventional current direction (2^nd finger) to the left of the page (since the electrons are moving to the right) and therefore the direction of the force on the electrons (indicated by the thumb) is down towards the bottom of the page, as indicated by the arrow inside the copper wire in the above diagram.

Thus, in the above situation, electrons will move down to the bottom end of the wire making that end negatively charged and leaving the top end of the wire positively charged.  It is this charge separation between the ends of the wire that creates the emf or potential difference between the ends of the wire.  If the wire were moved through the field whilst being attached to an external circuit, it would act as a battery for the circuit, supplying current that would flow around the circuit.

Direction of Induced emf – Lenz’s Law

Lenz’s Law states that the direction of an induced current is always such that the changes causing the induction are opposed.  In other words, an induced emf always opposes the changes that caused it.

To remind us of this fact, a minus sign is included in the equation for induced emf:

                                                

Lenz’s Law is really a consequence of the conservation of energy law, since if the induced emf did not oppose the changes that caused it, then it would be possible to create a self-perpetuating energy supply.  The Second Law of Thermodynamics proves that such an energy supply is impossible.

 Back emf in Motors

Lenz’s Law can be used to explain an interesting effect in electric motors.  In an electric motor, a current supplied to a coil sitting in a magnetic field causes it to turn.  However, while the coil of the motor is rotating, it experiences a change in magnetic flux with time and by Faraday’s Law an emf is induced in the coil.  By Lenz’s Law this induced emf must oppose the supplied emf driving the coil.  Thus, the induced emf is called a back emf.  As the coil rotates faster, the back emf increases and the difference between the constant supplied emf and the back emf gets smaller.  Clearly, this difference between the two emf’s is equal to the potential difference across the motor coil and hence determines the actual current in the coil.

It is interesting to note that when the motor is first turned on and the coil begins to rotate, the back-emf is very small, since the rate of cutting flux is small.  This means that the current passing through the coil in the forward direction is very large and could possibly burn out the motor.  To ensure that this does not happen, adjustable starting resistors in series with the motor are often used, especially with large motors.  Once the motor has reached its normal operating speed, these starting resistors can be switched out, since by then the back emf has reached a maximum and has thereby minimised the current in the coil.

Note also that if the load on the motor is increased at some time, the motor will slow down, reducing the back-emf and allowing a larger current to flow in the coil.  Since torque is proportional to current, an automatic increase in torque will follow an increase in load on the motor.

Eddy Currents

When a solid conductor is placed in a region of changing magnetic flux, circular eddy currents are induced in the conductor.  Lenz’s Law can be used to explain the direction of flow of eddy currents in particular cases.  Consider the case below.  A uniform magnetic field is set up by placing a magnetic north pole above the plane of this page and a south pole below the plane of the page.  The magnetic field direction is therefore down into the page as shown.  Next a copper sheet originally sitting stationary in the magnetic field is pulled out of the field in the plane of the page as shown below.  By Faraday’s Law, eddy currents will form where there is a change of flux with time, that is along the right hand edge of the field where the metal sheet is leaving the field.

                

By Lenz’s Law, the induced eddy currents must oppose the change that caused them.  That is they must oppose the relative motion between the conductor and the magnetic field.

The easiest way to determine the direction of the currents is to ask which direction of the current around the loop would produce a magnetic field that will oppose the motion of the conductor.  Clearly, the clockwise direction of the eddy currents as shown in the diagram would produce a south pole inside the loop on this side of the metal sheet and a north pole inside the loop on the other side.  The south pole on this side of the metal sheet would be attracted to the north pole of the magnet (on this side of the sheet) producing the original field.  Likewise the north pole created by the eddy currents on the other side of the sheet will be attracted towards the south pole of the magnet on the other side of the sheet.  The net effect is that there is an attractive force that acts on the copper sheet and opposes the motion of the sheet to the right.

As usual in Physics there are many different ways to reach the same conclusion.  A variation on the above is to realize that as the conductor is pulled out of the field, the magnetic flux passing through the conductor at the right hand edge of the field changes from a particular value to zero.  Ultimately then, the change at work here is the disappearance of field lines along the right hand edge of the field as the conductor is pulled out of the field.  So, the eddy currents will be in such a direction as to create a magnetic field that strengthens the original field by putting new field lines in to replace those that are disappearing.  Thus, the direction of the eddy currents must be clockwise as shown above.

We can easily verify the direction of the eddy currents in the above example by using Fleming’s LHR.  Clearly, if the eddy current in the magnetic field is moving up towards the top of the page and the field direction is down into the page, by Fleming’s LHR, the force on the metal sheet is towards the left, opposing its motion to the right.  Thus, the eddy currents are in a direction such that the changes causing them are opposed.

The current Syllabus asks you to “explain the production of eddy currents in terms of Lenz’s Law”.  

Generators

An important application of electromagnetic induction is in the generation of electric current.  AC generators produce an electric current via the motion of coils in a magnetic field or by rotating a magnet within a stationary coil.  The term alternator is also often used interchangeably with the term electric generator.  Strictly speaking, an alternator refers to an electromagnet rotating inside a fixed coil, such as is the case in most power stations. Consider the diagram of a simple AC generator shown below.

 

Clearly, the main components of a generator are: 

u    The armature – a coil wound around a metal core and mounted between the poles of an electromagnet.

u    The electromagnet consisting of an iron core surrounded by a set of coils called the field windings.  A steady current flows through these coils to produce the required magnetic field.

u    The slip rings – each end of the armature coil is connected to a metal ring.  These rings are mounted on the armature shaft but are insulated from it and from each other.

u    The graphite brushes – these connect the slip rings to an external circuit and conduct the current induced in the armature coil to the external circuit.

The armature is mechanically driven by a steam turbine or a belt & pulley system or by hydroelectric means.  As the armature turns, one side moves up through the magnetic field and the other side moves downwards.  The coil thus experiences a change of magnetic flux with time.  The result is that an emf is induced in one direction in one side of the coil and in the other direction in the other side of the coil.  Thus, these emf’s act in the same sense around the coil.  The ends of the coil are connected to slip rings against which rest graphite brushes.  When these brushes are connected across an external circuit, the induced emf produces an electric current.

Each time the coil passes through the position where its plane is perpendicular to the magnetic field lines, the direction of the emf in the coil is reversed.  Hence analternating current is produced at a frequency equal to the number of revolutions per second of the armature.

An alternating current generator may be converted to a direct current generator in a couple of ways: 

u    By using a split ring commutator instead of slip rings.  The split ring commutator is mounted on the armature shaft but is insulated from it.  The commutator reverses the connections of the coil to the external circuit each time the current in the coil reverses.  Thus, a DC output is achieved from the AC generator.

u    By using a bridge rectifier circuit.  This is an arrangement of electronic components (diodes) that converts the AC output from the generator to a DC output. 

Note that in an electric current generator, mechanical energy is transformed into electrical energy.  In an electric current motor, electrical energy is transformed into mechanical energy.

Effects of AC Generators

The development of AC generators has had both positive and negative effects on society and the environment.  Firstly, from a social point of view, electricity generation has allowed the development of the highly mechanized and electronic lifestyles to which people in the developed world have become accustomed.  Our lives are made easier every day by the use of vast numbers of electrical gadgets.  Electricity runs our lighting, our heaters & air conditioners, our computers and communications equipment, our refrigerators, toasters, electric fry pans & stoves, washing machines, vacuum cleaners, stereos, TV’s, garden equipment, industrial equipment and so on – the list is almost endless.  Unfortunately, because electricity has greatly reduced the amount of physical labour necessary to live our everyday lives, it has also resulted in negative social effects such as a reduction in unskilled jobs and a reduction in the size of work-forces needed to perform certain jobs, which have led to increased unemployment.

Secondly, in terms of the environment, the development of AC generators has had mainly negative effects.  Most power generation stations around the world still use fossil fuels as their energy source.  Fossil fuel power stations produce thermal pollution, acid rain and air pollution due to the release of particulate matter and oxides of nitrogen and sulfur.  Fossil fuel power stations release huge amounts of carbon dioxide into the atmosphere, which adds to the Greenhouse Effect, which is believed to be raising Earth’s temperature.  Fossil fuel power stations also indirectly cause the land desecration and pollution associated with the coal mining, necessary to maintain supply of fossil fuel.

 The AC Electric Motor

An AC electric motor consists of two main parts: 

u    The armature or rotor – usually cylindrical that rotates about the axis of the motor’s shaft.  The rotor usually completes one revolution for each cycle of the AC electricity supply.

u    The field structure or stator – this is the stationary part of the motor usually connected to the frame of the machine.  It supplies the external magnetic field in which the rotor sits and which produces the torque on the rotor.

Both the rotor and stator have a core of ferromagnetic material to enhance the magnetic field.  This core usually consists of thin laminations of steel separated by thin insulating layers to reduce the size of induced eddy currents that would reduce the efficiency of the motor. 

In some AC motors slip rings are used to conduct electricity to and from the motor.  Note that AC motors (with a few exceptions) do not use split ring commutators. 

AC motors can be classified as either single-phase or polyphase motors.  Single-phase motors run on only one of the three phases of current produced by power stations and can therefore operate on the domestic electricity supply.  Polyphase motors run on two or three of the phases of current produced by power stations and are mainly used for high power applications including heavy industry. 

We will now consider single-phase AC induction motors as an example of AC motors.

The Single-Phase AC Induction Motor

The single-phase AC induction motor is the most common AC motor in use today.  A changing magnetic field in the stator induces an AC current in the rotor.  The current in the rotor produces its own magnetic field, which then interacts with the magnetic field of the stator, causing the rotor to turn.  Clearly, the name induction motor comes from the fact that no current is fed directly to the rotor from the mains supply.  Current is induced in the rotor by the changing magnetic field of the stator. 

The rotor of an induction motor consists of a cylindrical arrangement of copper or aluminium conducting bars attached to two end rings at either end of the bars.  These end rings short circuit the bars and allow current to flow from one side of the cylinder to the other.  This type of rotor is usually referred to as a squirrel cage, owing to its resemblance to the cage or wheel that people use to exercise pet squirrels or mice.  See diagram below.

    

The squirrel cage fits into a laminated iron core or armature, which is mounted on the shaft of the motor.

The stator consists of a number of coils of wire wrapped on laminated iron cores.  The stator surrounds the rotor.  Single-phase alternating current flowing through the stator coils produces a changing magnetic field that threads through the rotor.  This changing magnetic field induces an alternating current in the rotor, which in turn sets up its own changing magnetic field.  Various special techniques beyond the scope of this course are used to ensure that the changing magnetic field produced by the stator actually rotates and drags the magnetic field of the rotor around with it.  Thus, the rotor rotates in the same direction as the rotating field of the stator.