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Electromechanical
systems and actuators
Dr. Ibrahim Al-Naimi
Chapter One
Machinery Principles
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Contents
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Actuator classifications
Electric machines
Translational and rotational motions
Magnetic field
Core losses
Faraday’s law
Production of induced force on a wire
Induced voltage in moving conductor
Example of simple machine
Actuator Classification
1. Electrical Actuators
– DC (Separately exited, shunt, series, compound,
permanent magnet)
– AC (Synchronous, Wound rotor, squirrel cage)
– Special (stepper, single phase, universal, brushless…)
2. Pneumatic Actuators (Cylinders, motors,
compressors)
3. Hydraulic Actuators (Cylinders, motors,
compressors)
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Electric Machine
• An electrical machine is a device that converts either
mechanical energy to electrical energy or electrical
energy to mechanical energy.
• When such a device is used to convert mechanical
energy to electrical energy, it is called a generator.
When it converts electrical energy to mechanical
energy, it is called a motor. During this course, we will
concentrate on motors.
• The electrical motors are ubiquitous in modern daily
life. For example, electric motors at home run
refrigerators, freezers, vacuum cleaners, blenders, air
conditioners, fans, and many similar appliances.
Translational Vs Rotational
• When using motors to drive loads, in the majority
of cases there are two types of motion,
translational and rotational.
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Translational Vs Rotational
Translational
Rotational
Quantity
Unit
Quantity
Unit
Displacement (x)
m
Angular displacement (ϴ)
rad
Velocity (v)
m/s
Angular velocity (ω)
rad/s
Acceleration (a)
m/s2
Angular acceleration (α)
rad/s2
Force (F)
N
Torque (τ)
N.m
Mass (m)
kg
Inertia (J)
kg.m2
Power (P)
watt
Power (P)
watt
Work (W)
Joule
Work (W)
Joule
Translational Vs Rotational
Translational
Rotational
𝑑𝜃
𝑑𝑡
𝑑𝜔
𝛼=
𝑑𝑡
𝑑𝑥
𝑑𝑡
𝑑𝑣
𝑎=
𝑑𝑡
𝜔=
𝑣=
𝜔𝑚 =
2𝜋𝑛𝑚
60
𝑛𝑚 = 60 𝑓𝑚
𝐹 = 𝑚𝑎
𝜏 = 𝐽𝛼
𝑊 = 𝐹𝑥
𝑊 = 𝜏𝜃
𝑃=
𝑑𝑊
= 𝐹𝑣
𝑑𝑡
𝑃=
𝑓𝑚 =
𝜔𝑚
2𝜋
𝑑𝑊
= 𝜏𝜔
𝑑𝑡
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The Magnetic Field
Four basic principles describe how magnetic fields
are used in electric machines:
1. A current-carrying wire produces a magnetic field
in the area around it.
2. A time-changing magnetic field induces a voltage
in a coil of wire if it passes through that coil.
3. A current-carrying wire in the presence of a
magnetic field has a force induced on it.
4. A moving wire in the presence of a magnetic field
has a voltage induced in it.
Production of a Magnetic Field
• The following figure shows a rectangular core made
from ferromagnetic material with a winding of N
turns of wire wrapped about one leg of the core.
• By applying a current to the coil, a magnetic field
will be generated in the core.
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Production of a Magnetic Field
Production of a Magnetic Field
Quantity
Equation
Unit
𝑁𝑖
𝑙𝑐
A.turn/m
Magnetic flux density (B)
𝐵 = 𝜇𝐻
T (tesla)
Flux (∅)
∅ = 𝐵𝐴
wb
Permeability
𝜇 = 𝜇𝑟 𝜇0
𝑤ℎ𝑒𝑟𝑒 𝜇0 = 4𝜋 × 10−7 𝐻/𝑚
H/m
Magnetomotive force
ℱ = 𝑁𝑖 = ∅ℛ
A.turn
Magnetic field intensity (H)
Reluctance
𝐻=
ℛ=
𝑙𝑐
𝜇𝐴
A.turn/web
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Production of a Magnetic Field
Production of a Magnetic Field
The Calculations of flux in a core performed by using
the magnetic circuit concepts are always
approximation for the following reasons:
1. Leakage/Linkage flux
2. Fringing effect
3. The reluctance is not constant (the permeability
varies with the amount of flux)
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Production of a Magnetic Field
Production of a Magnetic Field
Example 1
A ferromagnetic core is
shown in the figure below.
Three sides of this core are of
uniform width, while the
fourth side is somewhat
thinner. The depth of the core
(into the page) is 10 cm, and
the other dimensions are
shown in the figure. There is
a 200 turn coil wrapped
around the left side of the
core. Assuming relative
permeability μr of 2500. how
much flux will be produced by
a 1 A input current?
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Energy Losses in Core (Core losses)
• Hysteresis Losses
Energy Losses in Core (Core losses)
• Assume that the flux in the core is initially zero. As
the AC current increases for the first time, the flux
in the core traces out path ab in the previous
figure. However, when the current falls again, the
flux traces out a different path from the one it
followed when the current increased. As the
current decreases, the flux in the core traces out
path bcd, and later when the current increases
again, the flux traces out path deb.
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Energy Losses in Core (Core losses)
• The amount of flux present in the core depends
not only on the amount of current applied to the
windings of the core, but also on the previous
history of the flux in the core. This dependence on
the preceding flux history and the resulting failure
to retrace flux paths is called hysteresis. Path
bcdeb traced out in the figure as the applied
current changes is called a hysteresis loop.
Energy Losses in Core (Core losses)
• When the magnetomotive force is removed, the
flux in the core does not go to zero. Instead, a
magnetic field is left in the core. This magnetic
field is called the residual flux in the core. It is in
precisely this manner that permanent magnets
are produced.
• To force the flux to zero, an amount of
magnetomotive force known as the coercive
magnetomotive force must be applied to the core
in the opposite direction.
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Energy Losses in Core (Core losses)
• Why does hysteresis occur? The atoms of iron
tend to have their magnetic fields closely aligned
with each other. Within the metal, there are many
small regions called domains, In each domain, all
the atoms are aligned with their magnetic fields
pointing in the same direction, so each domain
within the material acts as a small permanent
magnet. The reason that a whole block of iron can
appear to have no flux is that these numerous tiny
domains are oriented randomly within the
material as shown in the previous figure.
Energy Losses in Core (Core losses)
• When an external magnetic field is applied to this
block of iron, it causes domains that happen to point
in the direction of the field to grow at the expense of
domains pointed in other directions. Domains
pointing in the direction of the magnetic field grow
because the atoms at their boundaries physically
switch orientation to align themselves with the
applied magnetic field. The extra atoms aligned with
the field increase the magnetic flux in the iron, which
in turn causes more atoms to switch orientation,
further increasing the strength of the magnetic field.
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Energy Losses in Core (Core losses)
• As the strength of the external magnetic field
continues to increase, whole domains that are aligned
in the wrong direction eventually reorient themselves
as a unit to line up with the field.
• Finally, when nearly all the atoms and domains in the
iron are lined up with the external field, any further
increase in the magnetomotive force can cause only
the same flux increase that it would in free space.
(Once everything is aligned, there can be no more
feedback effect to strengthen the field.) At this
point, the iron is saturated with flux.
Energy Losses in Core (Core losses)
• The key to hysteresis is that when the external
magnetic field is removed, the domains do not
completely randomize again. Because turning the
atoms in them requires energy. The piece of iron
is now a permanent magnet.
• Once the domains are aligned, some of them will
remain aligned until a source of external energy is
supplied to change them.
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Energy Losses in Core (Core losses)
• The fact that turning domains in the iron requires
energy leads to a common type of energy loss in all
machines. The hysteresis loss in an iron core is the
energy required to accomplish the reorientation of
domains during each cycle of the alternating
current applied to the core.
Energy Losses in Core (Core losses)
• Eddy current
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Faraday’s Law
• Faraday's law states that if a flux passes through a
coil of N turns, a voltage will be induced in the coil
that is directly proportional to the rate of change
in the flux with respect to time.
𝑒𝑖𝑛𝑑 = −𝑁
𝑑∅
𝑑𝑡
Where
eind: voltage induced in the coil
N: Number of turns of wire in the coil
Ф: Flux passing through the coil
Minus sign (-): Lenz’s Law
Faraday’s Law
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Production of Induced Force in a Wire
𝑭 = 𝑖 𝒍 × 𝑩 = 𝑖𝑙𝐵𝑠𝑖𝑛𝜃
Where
i: the current in the wire
L: the length of the wire, with direction of I defined to be in the
direction of current flow
B: Magnetic flux density vector
Induced Voltage on a Conductor Moving in
A magnetic Field
𝒆𝒊𝒏𝒅 = 𝒗 × 𝑩 . 𝒍
Where
v: velocity of the wire
l: length of conductor in the magnetic field.
B: Magnetic flux density vector
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Induced Voltage on a Conductor Moving
in a magnetic Field
Example 2
The figure shows a conductor
moving with a velocity of 10
m/s to the right in a magnetic
field. The flux density is 0.5 T,
out of the page, and the wire is
1 m in length, oriented as
shown. What are the
magnitude and polarity of the
resulting induced voltage?
Simple example of Linear DC Machine
• A linear dc machine is about the simplest and easiest-tounderstand version of a dc machine, yet it operates
according to the same principles and exhibits the same
behavior as real generators and motors. It thus serves as a
good starting point in the study of machines.
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Simple example of Linear DC Machine
• A linear dc machine is shown in the previous
figure. It consists of a battery and a resistance
connected through a switch to a pair of smooth,
frictionless rails. Along the bed of this "railroad
track" is a constant, uniform-density magnetic
field directed into the page. A bar of conducting
metal is lying across the tracks.
• How does such a strange device behave? Its
behavior can be determined from an application
of four basic equations to the machine. These
equations are:
Simple example of Linear DC Machine
1. The equation for the force on a wire in the
presence of a magnetic field:
𝑭=𝑖 𝒍×𝑩
2. The equation for the voltage induced on a wire
moving in a magnetic field:
𝒆𝒊𝒏𝒅 = 𝒗 × 𝑩 . 𝒍
3. Kirchhoff's voltage law for this machine.
𝑉𝐵 − 𝑖𝑅 − 𝑒𝑖𝑛𝑑 = 0
⟹ 𝑉𝐵 = 𝑒𝑖𝑛𝑑 + 𝑖𝑅
4. Newton's law for the bar across the tracks:
𝐹𝑛𝑒𝑡 = 𝑚𝑎
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Simple example of Linear DC Machine
Motor Starting
1. Closing the switch produces a current flow i = VB /R
since the bar is initially at rest and eind =0.
2. The current flow produces a force on the bar given by
F = ilB.
3. The bar accelerates to the right, producing an induced
voltage eind as it speeds up.
4. This induced voltage reduces the current flow
i = (VB - eind↑)/ R.
5. The induced force is thus decreased (F = i↓lB) until
eventually F = 0. At that point, eind = VB, i = 0, and the
bar moves at a constant no- load speed vss = VB/BI.
Simple example of Linear DC Machine
Motor Starting
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Simple example of Linear DC Machine
Motor Operation
1. A force Fload is applied opposite to the direction of motion,
which causes a net force Fnet , opposite to the direction of
motion.
2. The resulting acceleration a = Fnet /m is negative, so the
bar slows down (v↓) .
3. The voltage eind = v↓Bl falls, and so the current i = (VB –
eind↓)/R increases.
4. The induced force Find = i↑lB increases until IFindI = IFloadI
at a lower speed v.
5. An amount of electric power equal to eindi is now being
converted to mechanical power equal to Findv, and the
machine is acting as a motor.
Simple example of Linear DC Machine
Motor Operation
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Simple example of Linear DC Machine
Starting Problem
The linear machine shown in the figure is supplied by a 250-V
dc source, and its internal resistance R is given as about 0.1
Ω. (the resistor R models the internal resistance of a real dc
machine, and this is a fairly reasonable internal resistance for
a medium-size dc motor.)
Simple example of Linear DC Machine
Starting Problem
Providing actual numbers in this figure highlights a major
problem with machines (and their simple linear model). At
starting conditions, the speed of the bar is zero, so eind = 0.
The current flow at starting is
𝑖𝑆𝑡𝑎𝑟𝑡 =
𝑉𝐵 250 𝑉
=
= 2500 𝐴
𝑅
0.1 Ω
This current is very high, often in excess of 10 times the
rated current of the machine. Such currents can cause
severe damage to a motor. Both real ac and real dc
machines suffer from similar high-current problems on
starting.
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Simple example of Linear DC Machine
Starting Problem
How can this problem be solved? How can such damage
be prevented?
Question 1
A ferromagnetic core with a relative permeability of
1500 is shown in the next figure. The dimensions are as
shown in the diagram, and the depth of the core is 5 cm.
The air gaps on the left and right sides of the core are
0.070 and 0.050 cm, respectively. Because of fringing
effects, the effective area of the air gaps is 5 percent
larger than their physical size. If there are 300 turns in
the coil wrapped around the center leg of the core and if
the current in the coil is 1.0 A. what is the flux in each of
the left, center, and right legs of the core? What is the
flux density in each air gap?
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Question 1
Question 2
The linear dc machine shown in the next figure has a
battery voltage of 120 V, an internal resistance of 0.3 Ω,
and a magnetic flux density of 0.1 T.
1. What is this machine's maximum starting current?
What is its steady-state velocity at no load?
2. Suppose a 30-N force pointing to the left were
applied to the bar. What would the new steady-state
speed be? Is this machine a motor or a generator?
3. Assume that the bar is unloaded and that it suddenly
runs into a region where the magnetic field is
weakened to 0.08 T. How fast will the bar go now?
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Question 2
References
• Steven Chapman “Electric machinery fundamentals”,
5th edition, McGrow Hill, 2011 (Chapter one)
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