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ELECTROTECHNICS
Motors and Actuators
When considering logical switching circuits, we dealt with devices which were
in either the on or off state – high or low levels. When we tackled analogue
circuitry, our interest focussed on high precision manipulation of electrical
signals. With either of these subject areas, the signals are only a few volts in
potential and the currents are measured in milliamps - usually fractions of a
milliamp. The power levels are consequently very tiny; the energy levels of
the signals in logic circuits and in operational amplifier circuits are of the order
of a few milliwatts.
In the last part of this introduction to electrotechnics, we shall be looking at
high power circuitry. We shall see what happens when electricity turns
corners, and the significance of turning large currents on and off. This is an
essential part of motors and actuators. If you need to get significant
mechanical effort out of a device, it is necessary first of all, to put considerable
electrical power in. You can't get something for nothing; the power has to
come from somewhere. So with large motors it is often necessary to put in
hundreds of volts and many amperes of current if it is wished to produce
power outputs of the order of Kilowatts.
To bring everybody up to a working level of fundamental physics, we shall
quickly look at some of the basics – starting with magnetism.
The Bohr model declares that at the nuclear level, an atom may be
considered to comprise a heavy nucleus which is positively charged, about
which negatively charged electrons move in orbits. We have since discovered
that the electrons follow rather “fuzzy” orbits and that the nucleus and the
electron also spin on their own axes.
Magnetism in Crystalline Solids
A moving electric charge creates a magnetic field; this was discovered in
1825 by William Sturgeon an English "electrician". In the atom we have
several moving electric charges. The magnetic effect (moment) of the atom is
the vector sum of all the component effects (magnetic moments).
In a crystalline structures, such as iron, cobalt and nickel even when they are
unmagnetised, they contain tiny neighbouring regions called domains, in
which the magnetic moments of the atoms align creating completely
magnetised areas, each very small in size. However, the individual domains
do not align with each other, which is why there is no overall magnetic effect
in the crystalline material. The magnetic fields of the randomly oriented
domains cancel each other out. We do not understand what determines the
domain boundaries.
When a small external magnetic field is applied to an unmagnetised piece of
the crystalline iron, cobalt or nickel, initially nothing happens. However, as the
field strength is increased, the domains start to swing round to align with the
external field. Eventually, when the applied field is sufficiently strong, all the
domains align, and the maximum flux density is achieved - this is known as
saturation.
If the magnetising force is decreased, the flux density decreases. But as the
external force is reduced to zero, the flux density does not fall to zero, and
some magnetism is retained in the crystalline material. This is known as
residual magnetism, or residual flux, or remanence.
Relationships in Magnetism
To establish mathematical relationships, the following physical phenomena
have been named:
Magnetic flux Ø, Webers
Magnetic flux density B, Teslas
B= Ø
Webers/square metre
A
Where:
A is the cross-sectional area perpendicular to the flux path.
Magnetic Flux vs Magnetic Field Intensity
As the external field, H, increases in value, the magnetic flux (B) increases.
As the external field (H) falls to zero, there is some remanence, and B does
not fall to zero.
After the initial magnetisation, the crystalline material follows this hysteresis
curve as the external field is increased, decreased, made negative & positive.
There are different formulations of iron alloys for which the hysteresis curve
follows different paths.
If it is wished to create a permanent magnet, then a curve with a high residual
magnetism is required.
However, for applications where it is wished to regularly change the polarity of
the magnetic flux, low residual magnetism is required. The reason for this is
that energy is required to get rid of the residual magnetism as polarity is
changed.
This has two effects:
i.
a material with high hysteresis gets hot under conditions of
alternating field, as it absorbs the energy
ii.
This is a waste of power (called iron losses) which makes the
operation inefficient.
Magnetic Flux vs Magnetic Field
Magnetic Flux
B = µH
Magnetic Field Intensity
µ is the permeability
B = µo µr H
µ o = permeability of free space = 4π x 10-7
µ r = relative permeability
Air ≈ 1
Water ≈ 1
Mild steel ≈ 2,500
Special alloys of steel ≈ 6,000
Electromagnetism
In 1819, Hans Christian Oersted noticed that the passage of current through a
wire affected a magnet placed nearby; a delicately-balanced compass needle.
In fact there is always a magnetic flux created around a wire carrying a
current.
The Corkscrew rule
If you imagine a corkscrew applied along the line of the current, then the
magnetic field follows the direction of rotation as shown above
i.e. clockwise.
The advent of the digital clock has started to destroy the concept of clockwise.
I just hope they never replace corks with plastic tops or electrical engineering
will be finished!
Alternative rule:
Hold the wire in the palm of the right hand with the thumb extended. If the
thumb points in the direction of the current then the fingers will curl round the
wire (not literally) in the direction of the magnetic flux.
The Solenoid
It is now possible to apply the principles we have just covered, and see what
happens to electricity when it goes round corners. We can do this by passing
the electricity through a coil of wire wound on a non-magnetic former – a
cardboard tube, or a plastic pipe, for instance
If we use the coil on a hollow non-magnetic tube, and place an unmagnetised
soft iron bar half into the tube:
the magnetic domains in the soft iron bar become aligned with
the magnetic field created by the electric current flowing in the
coil of wire. The South poles in the domains swing towards the
North pole created in the coil, and consequently the iron bar is
attracted into the solenoid.
This is an elementary actuator and this solenoid mechanism - (the name
solenoid implies a coil and a moving core) - is used in many on-off
applications in textile manufacture and paper production; notably for the
driving of valves controlling fluid and gas flow in dyeing and all the water
processes for paper.
Incidentally, soft iron is soft in the magnetic sense – it loses its magnetism
easily when the external magnetic field is removed. It would leave a great big
dent in your skull if you were bashed over the head with it – just like any other
iron bar!
Electromagnetic Formulae
Magnetic Field Intensity
H=N.I
ℓ
N . I = number of turns of wire on coil x current (in amps).
ℓ = mean length of flux path.
Magnitising Force,
F = N . I ( m.m.f.)
ampere-turns
magneto-motive force
Faraday's Law
In 1831 Michael Faraday discovered the principle of electromagnetic
induction. He found that moving a magnet through a coil of wire caused an
electric current to flow. This is the result of the coil cutting the lines of
magnetic flux. The speed of the cutting affects the induced effect.
He stated that the induced EMF in a circuit is directly proportional to the rate
of change of flux-linkage, or to the change of magnetic flux.
E ∝ dNØ
dt
where:
d Ø = rate of cutting flux
dt
N = number of conductors cutting the flux
Lenz's Law
This allowed a scientist called Lenz to produce the smallest contribution to
posterity ever: he added a minus sign.
E = -dNØ
dt
This is the Faraday-Lenz law.
The Permanent Magnet Stepping Motor
In exploring the working of the electric motor, I propose to use what is
probably the most modern type of motor in common use today - the stepping
motor. This was developed before and during the Second World War. In past
times this would have been regarded as a very crude type of motor, but it has
come to the fore in the computer age because its stepping action is
compatible with the digital nature of computer output signals.
Stepping motors use a permanent magnet rotor. This is the part built on the
axle through the motor and this turns when the motor is in operation.
The rotor is not actually rectangular – it is a cylindrical magnet.
Around the perimeter of the motor is the stator. This as its name implies stays
stationary while the rotor is spinning. The stator consists of a series of coils
wound on to the projecting pole pieces.
The motor operates as follows in a simplified form:
1
2
3
4
1
A
B
C
D
A
on
on and A off
on and B off
on and C off
on and D off
A
1
0
0
0
1
B
0
1
0
0
0
C
0
0
1
0
0
D
0
0
0
1
0
This describes the action of a single rotation of the motor.
Note that each stage requires the switching on and off of a set of coils.
Consequently, an independent piece of electronics is required to drive the
motor by turning on and off a direct current power supply to each stator coil in
turn. This is highly inefficient, but makes the motor very controllable.
The stator can be moved to any position at will. Also, by changing the order
of coil switching, it can be made to rotate in either direction.
i.e. instead of A, B, C, D, A . . . . . . . (CW)
clockwise
use
A, D, C, B, A . . . . . . . (CCW)
counter-clockwise
We can easily improve the power transmission efficiency of the motor can't
we?
1) Make the opposite poles the opposite polarity so there are twice as
many coils on at any one time.
2) A much more subtle improvement:
Turn on A and B - both South.
As well as C and D - both North.
Now the rotor stops between the poles instead of being aligned with the poles.
But all the coils are on together, so our motor is starting to pack more of a
punch. It is still not an efficient power user though.
The Bipolar Stepping Motor
We have now looked at the permanent magnet stepping motor. The main
reason for choosing this as a starting point was that it is the easiest for me to
draw, and this gives you a fighting chance of understanding it.
Now, as we saw, the fundamental idea is that the poles around the stator are
energised in sequence, to attract the permanent magnetic poles on the rotor
around the circumference one position; or one step at a time.
It can be seen that if a single coil is wound round each of the pole pairs on
the stator, then the sequence starts by attracting a permanent pole (say a
North) on the rotor with an energised South pole on the stator.
The pole on the rotor which is physically and magnetically opposite to our
chosen pole is attracted by the opposite pole on the stator.
Then the next pole on the stator is energised and the original one turned off,
and the rotor moves to the next step round.
This is fine until we get half way round the revolution of the rotor. At this point
it is necessary to continue the motion by producing a south pole on the stator
where there was originally a north when we energised the first step.
In other words, the direction of the current in the coil needs to be reversed.
This means that we cannot drive the motor simply by turning the current in the
coils on and off - it is necessary to swap the polarity of each end. This is turn
means that the drive electronics is more complicated that might be expected.
Hence the motor requires Bi-polar drive.
So in the diagram - the table should read not A, B, C, D; but A, B, A, B.
Alternatively, the digital drive shown in the table might be regarded as being
applied to the four ends for the two drive coils where A & C are the ends of
one coil, and B & D are the ends of the other coil.
1
2
3
4
1
Coil 1
A A1
+ +
+
+ + -
Coil 2
B B1
+
+
+
+
+
-
As drawn in the diagram, this bi-polar motor has a two-phase stator (that is
two pole pairs) and a two pole rotor: one North and one South: two “teeth”, for
reasons that will become clear.
A single rotor revolution, energising one phase at a time takes 4 steps of 90o
before returning to the starting point.
We have discovered that we can increase the power fed into the motor by
driving two phases simultaneously. The rotor now steps midway between the
stator poles. But it still does 4 steps to the revolution.
Even with two phases energised together, the stepping motor is not efficient in
electrical terms. What the stepping motor is good at is positional accuracy
with excellent repeatability.
•
•
•
•
•
One revolution is precisely one revolution.
Any number of motors can be synchronised.
It can reliably operate at very low speeds
one step per week.
The motor can be reliably used in open loop control.
This means that you don't have to monitor what it has done- it does
what you tell it.
Of course, only a limited amount of torque is available in a given volume of
motor for only two phases can be on at any one time.
The Unipolar Stepping Motor
To maximise its advantages, the stepping motor is often manufactured in such
a way as to reduce the step size, so that its incremental movement is small
and its positional accuracy is improved.
This is done by increasing the number of phases on the stator, usually as high
as 4. and occasionally 5. (4 phases means 8 poles in 4 pairs).
The number of teeth on the rotor can be increased, commonly to 50.
This means that we get 4 x 50 = 200 steps per revolution with a 4 phase 50
tooth motor.
As the power-to-weight ratio has been sacrificed and there is no pretence to
high efficiency, two further things can be done with stepping motors - the
number of steps per revolution can be effectively doubled (from 200 or 400)
(or from 48 to 96) by what is known as half stepping. That means
alternatively turning on one pole and then two poles of the stator. So instead
of jumping from one phase to the next or from midway between two phases to
midway between the next two, it does both, and in sequence.
Counter Clockwise (C.C.W.) Half Step Sequence
A
B A1 B 1
1
1
0
0
1
0
1
0
0
2
0
1
1
0
3
0
0
1
0
4
0
0
1
1
5
0
0
0
1
6
1
0
0
1
7
1
0
0
0
8
1
1
0
0
1
As far as speed of coil switching goes, coils are only switched on and off 4
times as the motor passes one rotor tooth between 4 phases . So, speed
should not be sacrificed. But torque and power are reduced as there is only 1
coil on for half the time. In full-step mode, two coils can be on all the time - at
each step.
Having sacrificed all pretence to power and efficiency, there is another
modification which can be done to simplify the drive of stepper motors. Each
drive coil can be centre-tapped. Now, by supplying power to the centre
tapping and by switching the two halves of the coils separately, the polarity of
the phase can be swapped using only uni-polar switching. Now we can
simplify the drive electronics but only two half coils out of 8 can be on at any
time, so efficiency is poorer still.
The inefficiency of the motor derives also from the fact that in a single
revolution there are either 200 full steps or 400 half steps and each motor
phase has its current and polarity reversed 50 times in a single rotation.
There is a consequential loss of energy as the magnetic fields are repeatedly
destroyed.
As the speed of the motor increases there is progressively less time to get the
power into each coil. Consequently, the torque tends to fall from a maximum
at 0 steps per minute to 25% of this torque at 1,000rpm with a simple drive, or
up to 3,000rpm with a very sophisticated and expensive drive.
Bearing in mind the cost of the motor and drive, the motor does not go very
fast.
Multi-tooth Commercial stepping Motor
Rotor Step Response
There is another source of losses in efficiency. This derives from the
mechanical oscillation which sets in at each step.
There are several terms which are relevant to stepping motors.
Pull in rate - the maximum rate at which a stepping motor can start and stop a given
load inertia and torque without losing step.
Pull out rate - the stepping rate at which a stepping motor loses synchronisation when
driving a given load or inertia.
Slew rate - rate at which stepping can be increased with out losing synchronism.
Stepping Motor Advantages
•
•
•
•
•
Considerable power at zero speed.
Strong detent power when at rest.
Positional accuracy
One revolution is precisely that;
Any number of motors can be synchronised
Ideal for open loop control.
Operates reliably at low speeds
One step per week or per month if required.
Digital operation makes it computer compatible
The on/off drive control can simply be generated by digital logic
Ideal for closed loop control, as the computer is the obvious
choice for calculating feed back requirements.
Can rotate either way.
Stepping Motor Disadvantages
•
•
•
•
•
High rotor inertia
has heavy solid permanent magnet rotor.
Limited speed
1,000 rpm simple drive electronics
3,000 rpm sophisticated drive.
'Notchy' in operation
only starts to become smooth over 100 rpm.
Poor efficiency
only one/two of its phases on at any time
considerable losses due to fast switching of phase polarity.
Expensive; needs a rectified d.c. power supply and controlled drive
electronics.
The d.c. Motor
A simple form of a d.c. motor is shown in the diagram.
It consists of a coil of wire shown nearly horizontal in a magnetic field.
Fleming's left hand rule for motors.
First finger - Field
Second finger - Current
Thumb - Motion.
This indicates that the single-turn coil will have a tendency to move down on
the left and up on the right. So it will rotate counter clockwise, as seen from
this end.
The current is passed to the coil by contacts at the front part of the
arrangement. So straight away we can see one of the drawbacks of d.c.
motors - electrical power has to be supplied to a moving part.
Things get worse yet. As the coil comes up to the vertical, the mechanical
force on each conductor of the coil is in the vertical plane and there is no
useful power to be supplied.
That is not all, whilst the inertia of the coil assembly will take the rotor through
the vertical, the force on the left hand wire (current going away from the
contact) is down. So if constant d.c. current is applied to the coil, it will align
vertically in the magnetic field. It will oscillate until its energy dissipates, then
it will stop.
To make it keep going, we need to swap the direction of the current as the coil
reaches the point where it is perpendicular to the magnetic field.
A cunningly designed component does this very neatly …
The Commutator
The task of switching the coils is performed by arranging the contacts as
below. The contacting device is known as a commutator.
The contacts turn with the coil and as the coil passes through the vertical
(perpendicular to the field) the contacts are swapped from one battery polarity
to the other and the current flows through the coil in the opposite direction.
Or to put it another way, whichever side of the coil is adjacent to the North
pole always has current passing in the same direction. So it always
experiences the same angular forces and rotation continues the same way.
Multi-segment Armature
In practice, the motor consists of several equally spaced coils wound on a soft
iron core. These are connected to a multi-segment commutator. The
advantage is that the torque is made more nearly constant, and there is no
dead spot in the cycle.
A Schematic Diagram of the Multi-pole Commutated d.c. Motor
If the soft iron core was solid, there would be considerable wasted power as
the result of eddy currents generated in the iron by induction. These are
reduced by increasing the resistance of the core by laminating with insulated
varnished sections perpendicular to the rotational axis armature.
Back Reaction in Motors
As the motor rotates as a result of the reaction produced by the current and
the magnetic field. The Faraday Lenz law is still in force in the rotating coils .
Hence the armature rotating in the magnetic field has an EMF induced in its
windings as a result of these conductors cutting the field. The induced EMF
opposes the applied voltage because of Lenz's minus sign, and is known as
back EMF.
V – E
= I .R
(coil resistance)
(applied) (induced) (current in coils)
E ∝ armature speed.
So, as the motor speeds up, the current falls.
V.I
Input power
= I2 R + E . I
Coil heating
Mechanical work rate
(= difference between power in and power wasted)
Efficiency = Mechanical power obtained
Electrical power supplied
= E I x 100%
VI
= E x 100%
V
Multi-Segment Armature
The motor coils are wound on to a soft iron core (or former). This is to enhance the
magnetic flux intensity (B) (for the given magnetic field intensity,
H = N.I
ℓ
I keep referring to soft iron. This doesn't mean it is soft like putty - this means
magnetically soft. Let us return temporarily to our old friend, the B-H curve.
Ferromagnetic Materials
Ferromagnetic materials can be magnetically hard or soft.
Soft
i.
ii.
iii.
iv.
Low remanence (not all)
Low coercivity
The area of the B-H hysteresis curve is proportional to the
coercive energy or hysteresis loss.
High saturation flux density
Narrow hysteresis loop
Hard
i. High remanence (so magnet is "strong")
Self demagnetisation is much slower - this is why keepers,
which confine the magnetism to a closed loop are necessary.
ii. High coercivity (unlikely to be demagnetised by stray fields)
iii. High saturation flux density
The Force on a Conductor
F = Force on the conductor (N)
B = Magnetic Flux Density (T)
I = Current in the conductor (A)
L = Length of the conductor (m)
F ∝ I L Sin 0 (experimental result)
F = B I L Sin 0 (from definition of magnetic flux)
Magnetic Flux
One Tesla is the magnetic flux density of a field in which a force of 1 Newton acts on
a metre length of conductor carrying a current of 1 ampere perpendicular to the field.
Torque on a Coil in a Magnetic Field
1)
2)
3)
4)
The coil W X Y Z is suspended in a magnetic field of flux density B.
The plane of the coil is parallel to the field.
A current I flows round the coil.
The coil can turn about its axis U-V.
By Fleming’s left hand rule; the side of the coil W Z experiences a force into
the screen and on equal but opposite force acts on X Y. As the plane of the
coil is parallel to the field, there is no force on W X or Z Y.
Torque on a Coil in a Magnetic Field
The forces on W Z and X Y constitute a couple whose torque T is given by
T = F.d
where:
d is the coil width
As the currents in W Z and X Y are at 90o to the field:
F = B I L sin 90o = B I L
where:
L is the length of the vertical sides
Substituting for F (using T = Fd)
T = B .I .L .d .
i.e. T = B I A
T=BIAN
where:
A is the area of the coil,
for a coil of N turns.
Torque of a Coil in a Magnetic Field
In a radial field, where the plane of the coil is always parallel to the field,
T = B I A N applies to all orientations.
However, in a uniform field, as soon as the coil turns it is no longer parallel to
the field.
So the magnitude and direction of the forces does not change. However, the
separation of the forces alters, so the Torque is reduced.
T = F . b cos 0
T = B I A N cos 0
As a result of the reaction produced by the current and the magnetic field, the
motor armature rotates. However, the Faraday-Lenz law has not been
repealed. Consequently, as the armature rotates in the magnetic field, an
EMF is induced in its winding, because the rotating conductors are cutting
through the field. If you can remember Lenz's minus sign, you will realise that
the induced voltage opposes the applied voltage, and is known as back EMF.
V – E
= I .R
(coil resistance)
(applied) (induced) (current in coils)
E ∝ armature speed.
So, as the motor speeds up, the current falls.
V.I
Input power
= I2 R + E . I
Coil heating
Mechanical work rate
(= difference between power in and power wasted)
Efficiency = Mechanical power obtained
Electrical power supplied
= E I x 100%
VI
= E x 100%
V
It will be noted that efficiency is improved as the coil resistance is reduced.
Hence most motors have a coil resistance of less than 1 R.
It will be noted to that, at switch-on,
E=0
So the full supply voltage is applied across the low resistance coils. These
coils would burn out if a series resistance, or an electronic current controller
was not placed in series with the motor. The series rheostat is usually
controlled by an electromagnet powered by the motor drive voltage.
During normal running the back EMF is only slightly less than the supply P.D.
Small motors have higher coil resistances and don't normally have a starting
resistor. They do have high switch-on surges of current though.
In large motors, the magnetic field is usually provided by electro-magnets.
In the series-wound motor, the field coil is wired is series with the armature.
This provided large torque at low speeds and is useful for powering
locomotives and electric vehicles.
In the shunt wound motor, the field coils and the armature are in parallel.
Such motors are relatively insensitive to variations of load.
These are used for record player drive motors.
Shunt and Series Wound Motors
The speed and power of the d.c. motor is easily controlled by electronic
means. Hence it is becoming incorporated into a higher percentage of
modern equipment. Particularly into servo controlled feedback systems which
you will learn about next year.
The commutator is used to mechanically drive a segmented motor.
The coils are divided into segments to reduce the effect of armature
inductance and to reduce the torque ripple.
Brushes wear, and we get sparking, heating, radiation and erosion.
Permanent magnet d.c. motor
Brushless Motor
N
S
The commutation is electronic with semiconductor control. The
semiconductors are switched using opto-sensors on the shaft.
This is not a stepper with positional control, it uses (mechanical) rotational
sensing for the solid state commutation and speed may be controlled by
voltage variation.
Steppers have their speed limited by coil inductance switching, these
3-phased or 6-phased motors don't suffer from such limitations – so they can
rotate much faster.
You should by now have gained an understanding of how simple electric
motors work. And you should also have an appreciation of why different types
of motor demonstrate different inherent behavioural characteristics. This
should enable you to start choosing your motor – ready for Mechatronics in
the final year.