Slides electromechanical

AV-222
Electromechanical Systems
Dr Salman Aslam
Wing Commander, PAF
Associate Professor
Avionics Department
College of Aeronautical Engineering
PAF Academy Risalpur
,

AV-222
readme
1. Introduction
2. Theory
(a) Electromagnetics
(b) Power
(c) Drive electronics
(d) Mechanics
(e) Transformers
(f) Motors & Generators
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Textbook
These slides are under construction. Should be done by
the end of the semester around Aug 2015.
2 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Textbook
3 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Famous scientists
Andre Marie Ampere
http://en.wikipedia.org/wiki/Andre-Marie_Ampere
4 / 412
• 1775-1836, France
• Started teaching himself advanced math at the age of 12
• Ampere showed that two parallel wires carrying electric currents
attract or repel each other, depending on whether the currents
ﬂow in the same or opposite directions, respectively - this laid the
foundation of electrodynamics

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Famous scientists
Michael Faraday
http://en.wikipedia.org/wiki/Michael_Faraday
5 / 412
• 1791-1867, England
• Discovered benzene and electromagnetic induction
• When asked by the British government to advise on the
production of chemical weapons for use in the Crimean War
(1853-1856), Faraday refused to participate citing ethical reasons

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Course Overview
Magnetic field creation and 3 applications
• This course is about transformers, motors and generators
• Magnetic fields are the fundamental mechanism by which energy
is converted from one form to another in all these devices
• Create a magnetic field: This is the first step.
(Creation, Ampere’s Law): A current carrying wire produces a
magnetic field in the area around it. Now that a magnetic field
has been generated, one of the following 3 are possible if you have
a conductor placed in a magnetic field:
1 Change a magnetic field to create a voltage
(transformer action, Faraday’s Law): A time-changing
magnetic field induces a voltage in a coil of wire if it passes
through that coil
2 Put a current-carrying wire in the magnetic field
(motor action, Lorentz Law): A current-carrying wire in
the presence of a magnetic field has a force induced on it
3 Put a moving wire in the magnetic field
(generator action, Faraday’s Law): A moving wire in the
presence of a magnetic field has a voltage induced on it
Chapman 5th ed, pg 8
6 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Voltage, Current and Resistance
An overview
http://www.build-electronic-circuits.com/wp-content/uploads/2014/09/
Ohms-law-cartoon-by_unknown.jpg
7 / 412

Maxwell’s equations
Summary
• E and H are the electric and magnetic field intensities measured in V/m and A/m respectively.
• D and B are the electric and magnetic field densities respectively, measured in coulombs and
teslas respectively.
• D = E, where is permittivity. The permittivity of free space is 0 = 8.854x10−12 F/m.
• B = µH, where µ is permeability. The permeability of free space is µ0 = 4πx10−7 H/m.
• J is current density measured in A/m2.
• φ is flux measured in Webers.
Ampere’s Law I = L
H.d = A
(J + ∂D
∂t ).dA × H =J + ∂D
∂t
Faraday’s Law V = L
E.d = − A
∂B
∂t .dA = −dφ
dt × E =−∂B
∂t
Gauss’s Law A
B.dA =0 .B =0
Gauss’s Law A
D.dA =ρ .D =ρ
• Maxwell introduced 2 new things:
• The induced voltage A
∂B
∂t
.dA
• The displacement current A
∂D
∂t
.dA
• The conduction current density is J = σE (Ohm’s Law) while the displacement current density is
JD = ∂D
∂t
. Therefore, conduction current I = A J.dA and displacement current ID = A JD.dA.
The displacement current is a result of the time-varying electric field, eg, current through a
capacitor when a time-varying voltage is applied to its plates.
• For the time invariant form, ∂B
∂t
= ∂D
∂t
= 0. This means that the divergence equations remain the
same and only the curl equations change.
,

Summary
H.d = A
(J + ∂D
∂t ).dA × H =J + ∂D
∂t
E.d = − A
∂B
∂t .dA = −dφ
dt × E =−∂B
∂t
Gauss’s Law A
B.dA =0 .B =0
Gauss’s Law A
D.dA =ρ .D =ρ
• We see that
• A B.dA = φ (from Faraday’s Law)
• A B.dA = 0 (from Gauss’ Law for a closed surface, meaning that no monopole exists)
• Also, notice
• A(J + ∂D
∂t
).dA = σ A E.dA + A
∂E
∂t
.dA = I (from Ampere’s Law)
• A B.dA = µ A H.dA = φ (from Faraday’s Law)
• Now, notice parallels between
• E and H (intensities)
• B and J, D (densities)
• I and φ (what ﬂows in circuits)
• µ and σ, (material constants)
,

Summary
H.d = A
(J + ∂D
∂t ).dA × H =J + ∂D
∂t
E.d = − A
∂B
∂t .dA = −dφ
dt × E =−∂B
∂t
Gauss’s Law A
B.dA =0 .B =0
Gauss’s Law A
D.dA =ρ .D =ρ
• For a conductor of length meters in a uniform magnetic ﬂux density B,
• Motor action: If the conductor carries current i, then the force on it is F = i( × B)
• Generator action: If the conductor moves with velocity v, the voltage induced in it is
e = (v × B).
,

Summary
H.d = A
(J + ∂D
∂t ).dA × H =J + ∂D
∂t
E.d = − A
∂B
∂t .dA = −dφ
dt × E =−∂B
∂t
Gauss’s Law A
B.dA =0 .B =0
Gauss’s Law A
D.dA =ρ .D =ρ
• For an inductor, the voltage that is induced by the time variations in the current of a circuit is
called the electromotive force (emf) of self-induction, and is expressed in terms of the
self-inductance L by
e = N dφ
dt
= L dI
dt
⇒ Nφ = LI
⇒ L = Nφ
I
Inductance is therefore the ﬂux linkage per ampere
,

From Current to Induced Voltage
An overview
electric charges
separation motion
Electric field Magnetic field
current
(amperes)
Ampere's Law
magnetic field
intensity
magnetic flux
density
magnetic
flux
if changing
"magnetic current" Faraday's Law
(induced voltage)
In a magnetic circuit, such as a transformer core,
where,
,
12 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Ampere’s Law (1/4)
Ampere’s circuit law states that the line integral of the
tangential component of H around a closed path is the
same as the net current Ienc enclosed by the path
H.d = Ienc
H is the magnetic ﬁeld intensity measured in
ampere-turns/m
Chapman, pg 8
Elements of Electromagnetics, Sadiku pg 273
13 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1: wire
H.d = Ienc
⇒ B
µ .d = Ienc
⇒
2π
0
Brdθ = µIenc
⇒ B = µ
2π
Ienc
r
- http://www.physics.upenn.edu/courses/gladney
- also see Biot-Savart Law
14 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2: wire wound on core
• We have a core with a winding of N turns of wire wrapped about
one leg of the core
• If the core is made of ferromagnetic material, then all the
magnetic ﬁeld produced by the current will remain inside the core
• Therefore, the path of integration in Ampere’s Law is the mean
path length of the core, c
Chapman, pg 8
15 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2: wire wound on core cont.
H.d = Ienc
⇒ H c = Ni
⇒ B
µ c = Ni
⇒ B = Ni
c
µ
(B = µH)
⇒ φ = Ni
c
µA
(φ = BA)
⇒ = Ni
R (R = c
µA )
• Ni is the mmf (magnetomotive force, F), equivalent to voltage
• B is the magnetic ﬂux density measured in webers/m2, or teslas
• φ is the total ﬂux measured in webers and is equivalent to current
• The reluctance R is equivalent to resistance
Note
- H is linearly related to F (think voltage)
- B is linearly related to φ (think current)
16 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Faraday’s Law (1/5)
If a flux passes through a turn of a coil of a wire, a
voltage will be induced in the turn of wire that is
directly proportional to the rate of change in the flux
with respect to time
eind = −
dφ
dt
where eind is the voltage induced in the turn of the coil
and φ is the flux passing through the turn.
The minus sign in the equation is an expression of
Lenz’s Law
17 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
If a coil has N turns and if the same ﬂux passes through
all of them, then the voltage induced across the whole
coil is given by
eind = −N
dφ
dt
18 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Determine polarity of eind using Lenz’s Law
Lenz’s Law states that the direction of voltage buildup
in the coil in Faraday’s Law is such that if the coil ends
were short-circuited, it would produce current that
would cause a ﬂux opposing the original ﬂux change
To see this clearly, consider the example on the next
slide
Chapman, pg 30
19 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Determine polarity of eind using Lenz’s Law
• In the left figure below, φ is increasing and will
therefore induce a voltage eind in the coil
• In the right figure below, a current i flowing as
shown would produce a flux in the opposite
direction of φ
• The polarity of the voltage will be such that it
could drive the current i in an external circuit
Chapman, pg 30
20 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Determine polarity of eind using Lenz’s Law cont.
21 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Analogy between electric and magnetic
circuits (1/3)
Conductivity σ Permeability µ
Field intensity E Field intensity H
Current I = J.dA Magnetic flux φ = B.dA
Current density J = I
A
= σE Flux density B = φ
A
= µH
Electromotive force (emf) V Electromotive force (mmf) F
Resistance R Reluctance R
Conductance G = 1/R Permeance P = 1/R
• Permeability is the measure of the ability of a material to support
the formation of a magnetic field within itself. Hence, it is the
degree of magnetization that a material obtains in response to an
applied magnetic field.
• In SI units, permeability is measured in henries per meter.
• A good magnetic core material must have high permeability.
Elements of Electromagnetics, Sadiku, pg 348
22 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
circuits (2/3)
Chapman, pg 11
23 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
circuits (3/3)
Determine polarity of mmf in magnetic circuit
Chapman, pg 12
24 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Hysteresis
https://www.kjmagnetics.com/blog.asp?p=magnet-grade
25 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetization curve (1/2)
Chapman, pg 22
26 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetization curve (2/2)
Chapman, pg 26
27 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
AC circuits
Powers
Voltage V = V ∠α
Current I = I∠β
Phase lag θ = α − β (θ is negative for inductive circuit)
Power factor PF = cos θ
Power
Real P = V I cos θ (equal to average power)
Reactive Q = V I sin θ
Complex S = P + jQ
= V I cos θ + jV I sin θ
= V I∠θ
= V I∠(α − β)
= V ∠αI∠−β
= VI∗
Apparent S = V I
= |S|
Instantaneous p(t) =
√
2V cos(ωt)
√
2I cos(ωt − θ) (assume α = 0)
= 2V I cos ωt cos(ωt − θ)
= V I cos θ(1 + cos 2ωt) + V I sin θ sin 2ωt
= P + P cos(2ωt) + Q sin(2ωt)
Chapman 5th ed, pg 47-51
28 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
DC Motor Drivers (1/5)
Stepper → Driver stage → L298
29 / 412
Step 1: Pick an L-298.
Connect 2 voltages (5V, 36V), 2 capacitors (100 nF), 2 resistors (RSA,
RSB ), and ground it.

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
30 / 412
Step 2: Study the circuit.
Notice that we have 2 similar circuits which are totally independent of
each other. The left circuit is controlled by EnA while the right circuit
is controlled by EnB.

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
31 / 412
Step 3: Let’s focus on only one side of the circuit. The
other side works exactly the same way.
Let’s use the left side. Connect a coil (motor winding) as shown.

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
32 / 412
Step 4a: Current ﬂow.
Let EnA=1n1=5V. This causes current to ﬂow through the coil.

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
33 / 412
Step 4b: Current ﬂow.
Let EnA=1n2=5V. This causes current to ﬂow through the coil in the
opposite direction.

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motion
Displacement, velocity, acceleration
• Displacement
• Linear: r
• Angular: θ (radians)
• Velocity
• Linear: v = dr/dt
• Angular: ω = dθ/dt
• ωm: radians/sec
• fm: revs/sec
• nm: revs/min
• Acceleration
• Linear: a = dv/dt
• Angular: α = dω/dt
34 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motion
Force, torque, work, power
• Force: F
• Torque: τ = rF sin θ
• Work: W = Fdr
• Work: W = τdθ (rotational motion)
• Power: P = dW /dt = d(Fr)/dt = Fdr/dt = Fv
• Power: P = dW /dt = d(τθ)/dt = τdθ/dt = τω (rotational motion)
35 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling (1/4)
Constant acceleration model
¨s(t) = a
t
t0
¨s(τ)dτ =
t
t0
a dτ
˙s(τ)|t
t0
= a τ|t
t0
˙s(t) − ˙s(t0) = at − at0 Notice this is vf = vi + at
t
t0
˙s(τ)dτ −
t
t0
˙s(t0)dτ =
t
t0
aτdτ −
t
t0
at0dτ
s(τ)|t
t0
− ˙s(t0)τ|t
t0
= 1
2
a τ2 t
t0
− at0τ|t
t0
s(t) − s(t0) − ˙s(t0)t + ˙s(t0)t0 = 1
2
at2 − 1
2
at0
2 − at0t + at0
2
let initial time t0 = 0, initial distance s(t0) = si = 0, and some initial
velocity ˙s(t0) = vi , to get the familiar equation,
s(t) = vi t +
1
2
at2
36 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling (2/4)
Constant acceleration model
• The equations s = si + vi t + 1
2
at2 and vf = vi + at
can be written in discrete time with sampling time T as,
s
vf
=
1 T
0 1
si
vi
+
1
2
T2
T
a
and writing in terms of states x, we get,
xkT =
xkT
˙xkT
=
1 T
0 1
xkT−1
˙xkT−1
+
1
2
T2
T
a
• For simplicity, let T = 1,
xk =
xk
˙xk
=
1 1
0 1
xk−1
˙xk−1
+
1
2
1
a
• It may be noted that the following subsitution may be used since
f = ma and using f seems more logical to use as input. Keep in
mind that both formulations are equivalent.
1
2
T2
T
a =



1
2
T2
m
T
m


 f
37 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling (3/4)
Classical mechanics
Description Symbol Formula Units
radius r - m
angular velocity ω dθ
dt
rad/sec
1 linear momentum p mv kg m/sec
2 force F ma kg m/sec2 = N
3 angular momentum L r × p = Iω kg m2/sec
4 torque τ r × F kg m2/sec2 = N m
5 moment of inertia I mr2 kg m2
First, focus only on blue, then focus only on green
http://en.wikipedia.org/wiki/Torque
38 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling (4/4)
Damping
Applied force
displacement
damping coeﬃcient,
in this case,
wall friction b
spring constant k
Oscillatory force
(Hooke's Law)
Damping force
Net force
3
constants
k, b, M
Mass M
Units
k: N/m = kg/s2
b: N s/m=kg/s
M: kg
Dorf pg 45, http://en.wikipedia.org/wiki/Damping
39 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (1/12)
Magnetic circuit
• A Transformer is a device that changes AC electric power at one
voltage level to AC electric power at another voltage level through
the action of a magnetic ﬁeld.
• It consists of two or more coils of wire wrapped around a common
ferromagnetic core. These coils are not directly connected. The
only connection between the coils is the common magnetic ﬂux
present within the core.
Chapman, pg 18

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (2/12)
Turn ratios
Vp
Vs
= Is
Ip
=
Np
Ns
= a
Vp/Ip
Vs /Ip
= a
⇒
Vp/Ip
Vs /(Is /a) = a
⇒
Zp
Zs
= a2
Chapman, pg 89
41 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (3/12)
Equivalent circuit
• The losses that occur in real transformers have to be accounted
for in any accurate model of transformer behavior.
• The major items to be considered in the construction of such a
model are:
• Windings: Copper I2R losses
• Windings: Leakage ﬂux
• Core: Eddy current losses
• Core: Hysteresis losses
• It is possible to construct an equivalent circuit that takes into
account all the major imperfections in real transformers.
Chapman 5th ed, Sec 2.5, pg 86-94
42 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (4/12)
Equivalent circuit # 1
43 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (5/12)
44 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (6/12)
• We will mostly be using the simpliﬁed equivalent circuit given
below
• The magnetizing branch has been moved to make calculations
easier
45 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (7/12)
• A very simpliﬁed equivalent circuit that will not be used much
• The magnetizing branch has been completely eliminated
46 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (8/12)
Equivalent circuit
For the magnetizing branch,
Resistance, (Ω) = Rc
Reactance, (Ω) = Xm
Impedance, (Ω) = ZE
= Rc//jXm
= jRc Xm
Rc +jXm
Conductance, (Siemens) = Gc = 1
Rc
Susceptance, (Siemens) = Bm = 1
Xm
Admittance, (Siemens) = YE = 1
ZE
= Rc +jXm
jRc Xm
= 1
Rc
− j 1
Xm
47 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (9/12)
Equivalent circuit
Open Circuit Test
• One transformer winding is open-circuited and the
other winding is connected to full rated line voltage
•
48 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Transformers (10/12)
Autotransformer
VC
VSE
= ISE
IC
= NC
NSE
VL
VH
= IH
IL
= NC
NSE +NC
SW
SIO
= NSE
NSE +NC
Chapman, pg 110-113
49 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Autotransformer
50 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Regulation
• Because a real transformer has series impedance within it, the
output voltage of a transformer varies with the load if the input
voltage remains constant
• To conveniently compare transformers in this respect, it is
customary to define a quantity called voltage regulation (VR)
• Full-load voltage regulation is a quantity that compares the
output voltage of the transformer at no load with the output
voltage at full load
• It is defined as
VR =
VS,nl −VS,fl
VS,fl
× 100%
=
Vp
a
−VS,fl
VS,fl
× 100% since Vs =
Vp
a
at no load
• Usually, it is good practice to have as small a voltage regulation
as possible
• For an ideal transformer, VR=0 %

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Deﬁnition
A motor is an electrical machine that coverts electrical
energy to mechanical energy
52 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Theory
The ﬁgure below shows a conductor present in a uniform
magnetic ﬂux density B, pointing into the page. The conductor is
meters long and contains a current of i amperes.
The force induced on the conductor is given by,
F = i( × B)
53 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Theory cont.
The direction of deﬁned to be in the direction of current ﬂow
The direction of the force is given by the right hand rule
(see Example 1.7 )
54 / 412

Motors
Types
Wound
Rotor
Squirrel
Cage
Shaded
Pole
Capacitor
Split
Phase
Capacitor
Start
Permanent
Split
Capacitor
Two Valve
Capacitor
Reluctance
Start
Wound
Field
Perm.
Magnet
Reluctance Hysteresis
Multiple
Speed
Pole
Switching
suonorhcnySnoitcudnI
Single/PolyphaseSingle-PhasePolyphase
Multiple
Speed
Single
Speed
Synchronous
Phase-Locked Loop
Steppers
Synchronous Induction
Switched Synchronous
ReluctanceReluctance
Reluctance
Perm.
Magnet
Inverter PM Assisted
Synchronous
Reluctance
Driven
Rotor
Control
Stator
Control
Perm.
Magnet
Wound
Rotor
Electronic
Commu-
tation
Hybrid
Variable
Frequency
Brushless
DC Motor
Square
Drive
Sine
Drive
Series
AC-DC
Split
Field
Conventional
Construction
Moving
Coil
DC
Torquer
dnuopmoCtengaM.mrePtnuhS
(universal)
(brushed)
SMMA, The Motor & Motion Association, http://www.smma.org/technical-info.htm
- The words ”universal” and ”brushed” have been added later
- All these motors are rotating motors, linear DC and AC motors also exist
55 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Types cont.
• In this course, we aim to study the following six types of motors:
1 DC linear
2 DC brushed
3 AC synchronous
4 AC induction
5 Electronically controlled: brushless (BLDC)
6 Electronically controlled: stepper
• In the next slide, we present the voltages on the rotor and stator
for these kinds of motors, followed by a uniform graphical
representation of magnetic, electrical and mechanical signals
56 / 412

Motors
Comparison of voltages on rotor and stator
Rotor
(DC voltage)
Rotor
(no voltage)
Rotor
(permanent magnet)
Stator (DC voltage)
1. Linear DC motor
(Strictly speaking,
should not use the
word ”rotor” here
since there is linear
motion)
- -
Stator
(DC voltage applied
through commuta-
tor)
Mechanical
commutation
2. Brushed DC
motor
- Electronic
commutation
5. Brushless DC
(BLDC)
motor
6. Stepper motor
Stator
(AC 3-phase) 3. Synchronous AC
motor
4. Induction AC
motor
-
http://electronics.stackexchange.com/questions/93710/
how-do-dc-motors-work-with-respect-to-current-and-what-consequence-is-the-curre,
57 / 412

1. Linear DC Motor
Electrical, magnetic and mechanical signal flow
Electromagnet (linearly moving conductor)
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
+
-
Induced
voltage Lorentz
force
Newton's
2nd Law
Faraday's
Law
1
23
4
Electromagnet (stator)
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
58 / 412

2. Brushed DC Motor
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
Electromagnet (rotor)
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
+
-
Induced
voltage
Mechanical
commutation
Lorentz
force
Torque
Newton's
2nd Law
Faraday's
Law
1
23
4
59 / 412

3. AC Synchronous Motor
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
3-phase AC
voltage
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
+
-
Induced
voltage
Slip rings
(rotary joints)
Lorentz
force
Torque
Newton's
2nd Law
Faraday's
Law
1
23
4
rotating
,
60 / 412

4. AC Induction Motor
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
3-phase AC
voltage
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
Current
Induced
voltage Lorentz
force
Torque
Newton's
2nd Law
Faraday's
Law
2
34
1
rotating
,
61 / 412

5. Brushless DC (BLDC) Motor
Magnetic
flux density
Magnetic
field intensity
KVL
Ampere's
Law
Material
properties
Magnetic
"current"
Magnetic
flux
Magnetomotive
force (mmf)
Cater
for turns
CurrentApplied
DC
voltage
+
Electrical
commutation
- 1
Permanent magnet (rotor)
Magnetic
flux density
Magnetic
"current"
Magnetic
flux
Torque
Newton's
2nd Law
Faraday's
Law
23
4
62 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Feature Comparison
http://www.nidec.com/en-NA/technology/capability/brushless/
63 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Motors
Windings
There are 2 kinds of windings in electromechanical machines:
1 Field winding: In general, this term applies to the windings that
produce the main magnetic field
• For synchronous machines, the field windings are on the
rotor (Chapman, pg 267)
• For DC machines, the field windings are on the stator
(Chapman, pg 520)
2 Armature winding: This term applies to the windings where the
main voltage is induced (Chapman, pg 267, 520)
64 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Linear DC Motor (1/12)
Overview
• A linear DC motor is the simplest and easiest-to-understand DC
motor
• Yet, it operates according to the same principles and exhibits the
same behavior as real motors
65 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Overview cont.
• A linear DC motor is shown below
• 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
66 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Overview cont.
• The behavior of the linear DC motor, like any DC motor, is
governed by four equations that come into play in the following
sequence:
1 Kirchoﬀ’s Law i = VB −eind
R
2 Lorentz Force F = i( × B)
3 Newton’s 2nd Law Fnet = ma
4 Faraday’s Law eind = (v × B).
67 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Starting at no load
To start the motor, simply close the switch. After this, the
following sequence of events happens:
1 Kirchoff’s Law: compute current
• A current flows in the bar which is given by i = VB −eind
R
• Since the bar is initially at rest, eind = 0 and so i = VB
R
• The current flows down through the bar across the tracks
2 Lorentz Force: compute force
• A current flowing through a wire in the presence of a
magnetic field induces a force on the wire
• This force is F = i B to the right
3 Newton’s 2nd Law: compute acceleration
• The bar will accelerate to the right (due to Newton’s Law)
• The velocity of the bar begins to increase
4 Faraday’s Law: compute induced voltage
• A voltage appears across the bar which is given by
eind = vB
• This voltage reduces the current in the bar due to
Kirchoff’s Law (back to step 1!)
68 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Starting at no load cont.
Given below is the linear DC motor under starting conditions and no
load.
69 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The result of this action is that the bar will eventually reach a
constant steady-state speed where the net force on the bar is zero
• This will occur when eind has risen all the way up to equal the
voltage VB
• At this time, the bar will be moving at a speed given by
VB = eind = vss B , and so vss = VB
B
• The bar will continue to coast along at this no-load speed forever
unless some external force disturbs it (Newton’s ﬁrst law of
motion)
• This is precisely the behavior observed in real motors on starting
• On the next slide, we show the velocity v, induced voltage eind
and induced force Find , from when the motor is started till it
starts running at no-load steady-state
70 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
71 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Applying an external load
• Assume that the linear DC motor is initially running at the
no-load steady-state conditions described previously
• What will happen to this motor if an external load is applied to it?
• Examine the ﬁgure below where the load is applied to the bar
opposite to the direction of motion
• Since the bar was initially moving with steady state velocity,
application of the force Fload will result in a net force on the bar in
the direction opposite the direction of motion (Fnet = Fload − Find )
• The eﬀect of this force will be to slow the bar
72 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Applying an external load cont.
• But just as soon as the bar begins to slow down, the induced
voltage on the bar drops
• As the induced voltage decreases, the current ﬂow in the bar rises
• Therefore the induced force rises too
• The overall result of this chain of events is that the induced force
rises until it is equal and opposite to the load force, and the bar
again travels in steady state, but at a slower speed
• On the next slide, we show the velocity v, induced voltage eind
and induced force Find , from when a load is attached to a motor
running at steady state, and compare with starting at no load
73 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
74 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• A question that can come to mind is, why is the steady state
velocity slower than before?
• Remember that the force that the motor must supply has
increased, and since power P is a product of induced force Find
and velocity v, the velocity must decrease
• The power consumed by the bar is eind i
• This power is converted to Find v
• Therefore, Pconv = eind i = Find v
75 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction
https://www.youtube.com/watch?v=o_VjkUTZQXg
76 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Linear DC generator (1/2)
Operation
• Once again, consider the Linear DC machine initially running at
no-load steady-state conditions
• Now, what will happen if we apply a force in the direction of
motion to it?
• See the ﬁgure below
• Fapp is applied to the bar in the direction of motion
Chapman, pg 41
77 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Linear DC generator (2/2)
Operation cont.
1 Increasing velocity and voltage Since the bar was initially at
steady state, application of the force Fapp will result in a net force
on the bar in the direction of motion Fnet = Fapp − Find . The
eﬀect of this force will be to speed up the bar causing the induced
voltage eind to increase and become more than VB .
2 Increasing reverse current and force As the induced voltage
increases, the current i starts to increase in the reverse direction.
This creates an increasing induced force to the left.
New steady state (faster constant velocity) The overall result of this
chain of events is that the induced force increases till it is equal and
opposite to the applied force and the bar again travels in steady state,
but at a faster speed
78 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Brushed DC Motor (1/86)
Introduction
• A very simple motor can be made from two permanent magnets,
one static, one able to rotate, and the interaction of these
magnets creates rotation
• But there is a problem here, the rotating magnet will not rotate if
its north pole is aligned with the stationary magnet’s south pole
• So, we need to keep changing polarities of the rotating magnet, a
process called commutation
commutation
commutation
79 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Introduction cont.
• How to change polarities, i.e, how to do commutation?
• Well, ﬁrst of all, make the rotating magnet an electromagnet so
we have control over its polarities
• Now, there are 2 ways of changing polarities of the electromagnet
1 Mechanical commutation: This gives us a brushed DC
motor
2 Electrical commutation: This gives us a brushless DC motor
(BLDC)
• This gives us the simplest DC motor
• Simplest DC motor: consists of one permanent magnet and one
electromagnet
• The permanent magnet produces a uniform magnetic ﬁeld
• The electromagnet is made from a simple DC current
carrying loop
• Let us see a couple of animations of this before getting into
the mathematics and explanation
80 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Definitions
• Mechanical
• Rotor: The rotating part of the motor.
• Stator: The stationary part of the motor.
• Electrical
• Armature: The power-producing component of the motor.
The armature can be on either the rotor or the stator.
• Field: The magnetic field component of the motor. The
field can be on either the rotor or the stator and can be
either an electromagnet or a permanent magnet.
• For a brushed DC motor, the armature is on the rotor and the
field is on the stator
• The armature circuit is represented by an ideal voltage source EA
(also written as eind ) and a resistor RA.
• This representation is really the Thevenin equivalent of the entire
rotor structure, including rotor coils, interpoles, and compensating
windings, if present.
http://en.wikipedia.org/wiki/Armature_(electrical_engineering)
81 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Deﬁnitions cont.
• The distortion of the ﬂux in a machine as the load is increased is
called armature reaction.
• To take care of this, compensating windings are connected in
series with the rotor windings, so that whenever the load changes
in the rotor, the current in the compensating windings changes,
too
Chapman 5th ed, pg 433 (armature reaction), 443 (compensating windings)
82 / 412

Single rotating loop in uniform magnetic ﬁeld (1/15)
http://web.ncf.ca/ch865/englishdescr/DCElectricMotor.html ,
83 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• On the previous animation, the method of connecting the wire to
the commutator is not shown
• This is done through brushes
• On the next slide, we look at another animation to get a better
feel for how a DC current carrying loop placed in a magnetic ﬁeld
works
• This animation clearly shows brushes
84 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
https:
//nationalmaglab.org/education/magnet-academy/watch-play/interactive/dc-motor
85 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The Lorentz force is given by F = i( × B)
• The direction of defined to be in the direction of current flow
• The direction of the force is given by the right hand rule
• Note that there is zero force on the wire sides that are parallel to
the magnetic flux B
• When the loop is in the horizontal position, current flow is
stopped and it tips over using its momentum
86 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The figure below shows a simple DC motor consisting of a large
stationary magnet producing an essentially constant and uniform
magnetic field B and a DC current carrying loop of wire abcd
placed within that field.
• The rotating part of the motor, the loop, is called the rotor.
• The stationary part of the machine, the stationary magnet, is
called the stator.
87 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The magnetic ﬁeld B always points to the right and is in the
plane of the paper
• Segments ab and cd are always out of the plane of the page and
are perpendicular to B
• Segments bc and da are always in the plane of the page and are
continuously changing angles with B
88 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Segment ab
• Lorentz force F = i( × B)
• The angle between and B is always 90 deg
• The induced force is Fab = i B down
• Torque τ = r × F
• The angle between r and F changes between 0 and 90 deg
• The induced torque τab = ri B sin(θab) clockwise
89 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Segment bc
• In this segment, the angle between and B changes
between 0 and 180 deg
• The induced force is Fbc = i B into the page
• The angle between r and F is always 0 deg
• The induced torque τbc = 0
90 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Segment cd
• The induced force is Fcd = i B up.
• The angle between and B is always 90 deg
• The angle between r and F changes between 0 and 90 deg
• The induced torque τcd = ri B sin(θcd ) clockwise
91 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Segment da
• In this segment, the angle between and B changes
between 0 and 180 deg
• The induced force is Fda = i B out of the page.
• The angle between r and F is always 0 deg
• The induced torque τda = 0
92 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Torque is only produced by segments ab and cd
• θab = θcd = θ
• The total induced torque is τind = 2ri B sin θ
• Notice that the torque is maximum when the plane of the loop is
parallel to the magnetic ﬁeld, and the torque is 0 when the plane
of the loop is perpendicular to the magnetic ﬁeld
• Given below is the variation of torque as the loop rotates
93 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Deﬁne Bloop = µi
G
, G depends on the geometry of the loop
⇒ i =
BloopG
µ
τind = 2ri Bs sin θ B=Bs (s for stator) to distinguish from Bloop
= 2r
BloopG
µ
Bs sin θ Substitute i =
BloopG
µ
= AG
µ
BloopBs sin θ Substitute A = 2r is the area of the loop
= kBloopBs sin θ k depends on the construction of the machine
= kBloop × Bs
• θab=θcd =θ is also the angle between Bloop and Bs
94 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
τind = kBloop × Bs
• This produces a torque vector into the page, indicating that the
torque is clockwise, with the magnitude given by kBloopBs sin θ
• Thus, the torque produced in the loop is proportional to
• The strength of the loop’s magnetic ﬁeld
• The strength of the external magnetic ﬁeld
• The sine of the angle between them
• A constant representing the construction of the machine
(geometry, etc.)
95 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Now, mapping our newly created Bloop onto segments ab and cd,
shown in the left and right ﬁgures below
96 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• τind = kBloop × Bs
• τind is directed into the plane of the paper, i.e., the torque
is clockwise
• The torque induced in the loop is proportional to the
strength of the loop’s magnetic field, the strength of the
external magnetic field, and the sine of the angle between
them
• This equation also shows that if there are 2 magnetic fields
present in a machine, a torque will be created that will tend
to line up the magnetic fields
• The torque therefore depends on
1 Rotor magnetic field
2 Stator magnetic field
3 Sine of the angle between them
4 A constant representing the construction of the machine
(geometry etc.)
97 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Single rotating loop in magnetic ﬁeld generated by
curved pole faces(1/3)
• The loop of rotor wire lies in a slot carved in a ferromagnetic core
• The iron rotor, together with the curved shape of the pole faces,
provides a constant-width air gap between the rotor and stator
• The reluctance of air is much higher than the reluctance of the
iron in the machine
98 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• To minimize the reluctance of the flux path through the machine,
the magnetic flux must take the shortes t possible path through
the alr between the pole face and the rotor surface
• Since the magnetic flux must take the shortest path through the
air, it is perpendicular to the rotor surface everywhere under the
pole faces
• Also, since the air gap is of uniform width, the reluctance is the
same everywhere under the pole faces
• The uniform reluctance means that the magnetic flux density is
constant everywhere under the pole faces
99 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• As before, the torque is τind = 2ri B sin θ = 2ri B, since θ = 90o
• Since there are two poles, the area of the rotor under each pole
(ignoring the small gaps between poles) is Ap = πrl
• Therefore, φ = BAp
• We can therefore rewrite τind = 2
π
ApiB = 2
π
φi
• Thus, the torque produced in the machine is the product of the
ﬂux in the machine and the current in the machine, times some
quantity representing the mechanical construction of the
machine (the percentage of the rotor covered by pole faces)
• In general, the torque in any real machine will depend on th e
same three factors:
1 The ﬂux in the machine
2 The current in the machine
3 A constant representing the construction of the machine
100 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Working
http://www.learnengineering.org/2014/09/DC-motor-Working.html
101 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Types
1 Separately excited (pg 468)
• Field circuit is supplied from a separate constant-voltage
power supply
2 Shunt (parallel) (pg 469)
• Field circuit gets its power directly across the armature
terminals
3 Series (pg 493)
• Field windings consist of a relatively few turns connected in
series with the armature circuit
4 Compound (pg 500)
• A motor with both a shunt and series ﬁeld
5 Permanent magnet (pg 491)
• Field comes from a permanent magnet rather than a circuit
102 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 1: Separately excited
• The equivalent circuit of a DC motor is given below
• In this figure, the armature circuit is represented by an ideal
voltage source EA and a resistor RA
• The brush voltage drop is represented by a small battery Vbrush
opposing the direction of current flow in the circuit
• The field coils, which produce the magnetic flux, are represented
by inductor LF and resistor RF
• The separate resistor Radj represents an external variable resistor
used to control the amount of current in the field circuit
103 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 1: Separately excited cont.
• There are a few variations and simpliﬁcations of the basic
equivalent circuit
• The brush drop voltage is often small, and therefore in cases
where it is not too critical, the brush drop voltage may be left out
or approximately included in the value of RA
• Also, the internal resistance of the ﬁeld coils is sometimes lumped
together with the variable resistor, and the total is called RF
104 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
So, there are 4 equations required to analyze a DC motor:
1 KVL, IA = VT −EA
RA
2 The induced torque τind = KφIA
3 The internally generated voltage EA = Kφω
4 The magnetization curve relates EA with the ﬁeld current IF
1.
2.
Armature
4. Magnetization
curve
Relation between
ﬁeld circuit and
armature circuit
3.
105 / 412

ampere-turns
webers
Magnetization curve of a ferromagnetic material Magnetization curve of a DC motor
Chapman 5th ed, pg 467-469 ,
106 / 412

ampere-turns
webers
Magnetization curve of a ferromagnetic material Magnetization curve of a DC motor (3D)
107 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
So, how can we use the magnetization curve?
• IF → φ
• If I change my field current IF by a certain ratio, the ratio
with which the resulting flux φ changes is linear up to a
certain point before saturation sets in
• Using the magnetization curve, if I know the ratio with
which IF changes, I can find the ratio with which the flux φ
changes despite the non-linearity due to saturation
• So, for IF 1 and IF 2, read the corresponding EA1 and EA2
from the magnetization curve
• Remember that the magnetization curve is given for a fixed
value of ω
• Then,
EA1
EA2
= Kφ1ω
Kφ2ω
⇒ φ1
φ2
=
EA1
EA2
• This idea is used in Example 8.3
108 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 2: Shunt
• In a separately excited motor, two power supplies are used,
1 VF to supply the ﬁeld circuit
2 VT to supply the armature circuit
• If only one power supply is used for both ﬁeld and armature
circuits, we get a shunt DC motor
Therefore,
a shunt DC motor is equivalent to a
separately excited DC motor,
as long as VF = VT
109 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 2: Shunt cont.
110 / 412

Motor winding on left and terminal characteristics on right
+
-
+ -
http://www.learnengineering.org/2014/09/DC-motor-Working.html ,
111 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The voltage supplied by the user, VT , which is constant in most
cases and is parallel to VF , is used for the generation of 2 kinds of
currents:
1 Stator: Field current IF which generates a magnetic ﬁeld
φF .
2 Rotor: Armature current IA which generates a magnetic
ﬁeld whose interaction with φF causes the rotor to rotate,
in turn inducing a voltage EA
• Therefore, the current supplied by the user, the load current, can
be given by IL = IF + IA
112 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• How does a shunt dc motor respond to a load?
• Suppose that the load on the shaft of a shunt motor is increased
• Step 2: Then, the load torque τload will exceed induced torque
τind = KφIA
• Step 3: The motor will start to slow down
• Step 4: When the motor slows down, its internal generated
voltage EA = Kφω drops
• Step 1: This causes the armature current to increase, since
VT = EA + IARA
• Step 2: As the armature current increases, so does the induced
torque until it equals the load torque at a lower mechanical speed
of rotation
113 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• For a motor, the output quantities are shaft torque
and speed
• Therefore, the terminal characteristic of a motor is a plot of its
output torque versus speed
VT = EA + IARA
= Kφωm + τind
Kφ
RA
⇒ ωm = VT
Kφ
− RA
(Kφ)2 τind
• This equation is just a straight line with a negative slope
114 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Speed control can be achieved by
1 Adjusting the field resistance RF and thus the field flux
2 Adjusting the terminal voltage applied to the armature
3 Inserting a resistor in series with the armature circuit (less
common)
115 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 3: Series
• A series DC motor is a DC motor whose ﬁeld windings consist of
a relatively few turns connected in series with the armature circuit
• The equivalent circuit is shown below
• Armature current, ﬁeld current and line current are the same
• KVL is
VT = EA + IA(RA + RS )
116 / 412

Type # 3: Series cont.
Motor winding on left and terminal characteristics on right
http://www.learnengineering.org/2014/09/DC-motor-Working.html ,
117 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The terminal characteristics of a series DC motor is very different
from that of the shunt motor
• The basic behavior of a series DC motor is due to the fact that
the field flux is directly proportional to the armature current
(φ ∝ IA), at least until saturation is reached
• As the load on the motor increases, its armature current increases,
and so does the field flux
• An increase in flux decreases the speed of the motor
• So we have a ”double drop” in velocity
• Therefore, a series DC motor has a sharply drooping torque-speed
characteristic
118 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The equations are
τind = KφIA
φ = cIA
⇒ τind = KcIA
2
• Since torque is directly proportional to the armature current
squared, the series DC motor gives more torque per ampere than
any other DC motor
• It is therefore used in applications requiring very high torque
• Examples of such applications are the starter motors in cars,
elevator motors, and tractor motors in locomotives
119 / 412

• To determine the terminal characteristics of a series DC motor, an analysis will be
carried out based on the assumption of a linear magnetization curve
• In a magnetization curve, we plot φ vs IF , but since IA = IF , it is a plot of φ vs IA, implying
that φ = cIA
• As shown earlier,
τind = KcIA
2 (but IA = φ
c
)
= K
c
φ2
⇒ φ = c
K
√
τind
• The KVL equation is,
VT = EA + IA(RA + RS )
= Kφω + τind
Kc
(RA + RS )
= K c
K
√
τind ω + τind
Kc
(RA + RS )
VT − τind
Kc
(RA + RS ) =
√
Kc
√
τind ω
⇒ ω = VT√
Kc
√
τind
− RA+RS
Kc
• A problem here is that if τind = 0, then its speed goes to ∞
120 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• In practice, the torque can never go to zero because of the
mechanical, core and stray losses that must be overcome
• However, if no other load is connected to the motor, it can turn
fast enough to seriously damage itself
• Never completely unload a series motor, and never connect one to
a load by a belt or other mechanism that could break
• If that were to happen, and the motor were to become unloaded
while running, the results could be serious
121 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Unlike with the shunt DC motor, there is only one eﬃcient way to
change the speed of a series DC motor
• This method is to change the terminal voltage of the motor
• If the terminal voltage is increased, the ﬁrst term in
ω = VT√
Kc
√
τind
− RA+RS
Kc
increases, resulting in a higher speed for
any given torque
• Until the last 40 years or so, there was no convenient way to
change VT , so the only method of speed control available was the
wasteful series resistance method
• That has all changed today with the introduction of solid-state
control circuits
122 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 4: Compound
• A compounded DC motor has both a shunt (parallel) and a series
field
• There are 2 ways to connect this motor, long shunt and short
shunt
• So, there are 2 field coils and one armature coil
• If the mmf of the shunt field coil enhances the mmf of the series
field coil, the situation is called cumulative compounding
• If the mmf of the shunt field coil diminshes the mmf of the series
field coil, the situation is called differential compounding
• The advantage of this motor is that it combines the speed
regulation of a shunt motor with the high starting torque of a
series motor
123 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 4: Compound: long shunt
http://www.electrical4u.com/compound-wound-dc-motor-or-dc-compound-motor/
124 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 4: Compound: short shunt
http://www.electrical4u.com/compound-wound-dc-motor-or-dc-compound-motor/
125 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Type # 5: Permanent magnet
http://autosystempro.com/tag/motor/
126 / 412

Comparison of equivalent circuits
3. SERIES
2. SHUNT1. SEPARATELY EXCITED
5a. COMPOUNDED
(cumulatively)
5b. COMPOUNDED
(diﬀerentially)
t
4. PERMANENT MAGNET
127 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Power ﬂow and losses
128 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Eﬃciency
129 / 412

Modeling
Dorf pg 63-65 ,
130 / 412

Modeling cont.
Laplace Domain
1
2
plug I(s) from eqn 1 into eqn 2
+
-
+
-
angular velocity (rad/sec) multiply by 60/2pi to go to rpm
angular distance (rad)
Typical values are:
R: electric resistance 1 Ohm
L: electric inductance 0.5 H
J: moment of inertia of the rotor 0.01 kg.m^2
b: motor viscous friction constant 0.1 N.m.s
Kb: electromotive force constant 0.01 V/rad/sec
Km: motor torque constant 0.01 N.m/Amp
Giving:
1
2
motor torqueload torque
back emfarmature voltage
Time Domain
1
2
diﬀerential equations
state space
Dorf uses va, ia, Ra, La, while we use v, i, R, L for armature values
Dorf pg 63-65, http://ctms.engin.umich.edu/CTMS/index.php ,
131 / 412

Modeling cont.
Laplace Domain
1
2
plug I(s) from eqn 1 into eqn 2
+
-
+
-
angular velocity (rad/sec) multiply by 60/2pi to go to rpm
angular distance (rad)
Typical values are:
R: electric resistance 1 Ohm
L: electric inductance 0.5 H
J: moment of inertia of the rotor 0.01 kg.m^2
b: motor viscous friction constant 0.1 N.m.s
Kb: electromotive force constant 0.01 V/rad/sec
Km: motor torque constant 0.01 N.m/Amp
Giving:
1
2
motor torqueload torque
back emfarmature voltage
Time Domain
1
2
diﬀerential equations
state space
Dorf uses va, ia, Ra, La, while we use v, i, R, L for armature values
Dorf pg 63-65, http://ctms.engin.umich.edu/CTMS/index.php ,
132 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling cont.
In z domain, the open loop transfer function of a DC motor
is given by,
G(z) = Z G0(s)Gp(s)
= Z 1−e−sT
s
2
s2+12s+20.02
= (1 − z−1)Z 2
s3+12s2+20.02s
= (1 − z−1)Z 0.0999
s
− 0.1249
s+2.0025
+ 0.025
s+9.9975
= (1 − z−1) 0.0999
1−z−1 − 0.1249
1−e−2.0025T z−1 + 0.025
1−e−9.9975T z−1
= 0.0999 −
0.1249(1−z−1
)
1−e−2.0025T z−1 +
0.025(1−z−1
)
1−e−9.9975T z−1
133 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling cont.
˙x1
˙x2
=
−R/L −Kb/L
Km/J −b/J
x1
x2
+
1/L
0
v
⇒
˙x1
˙x2
=
−2 −0.02
1 −10
x1
x2
+
2
0
v
y = 0 1
x1
x2
134 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling cont.
C(sI − A)−1B = 0 1
s + 2 0.02
−1 s + 10
−1
2
0
= 0 1


s + 10 1
−0.02 s + 2


T
(s+2)(s+10)−(0.02)(−1)
2
0
= 0 1


s + 10 −0.02
1 s + 2


s2+12s+20.02
2
0
=
1 s − 2


2
0


s2+12s+20.02
= 2
s2+12s+20.02
135 / 412

Modeling cont.
G1(s) =
θ(s)
V(s)
=
1
s
Km
[(Ls + R)(Js + b) + KbKm]
Gp(s) =
˙θ(s)
V (s)
=
Km
[(Ls + R)(Js + b) + KbKm]
Note that we have set Td (s) = 0 to compute G1(s) and Gp(s).
Dorf pg 64 ,
136 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Modeling cont.
A motor can be represented simply as an integrator. A
voltage applied to the motor will cause rotation. When
the applied voltage is removed, the motor will stop and
remain at its present output position. Since it does not
return to its initial position, we have an angular
displacement output without an input to the motor.
See Nise pg 381 for a discussion on ﬁnding the transfer
function of a motor.
See Nise pg 451 for a nice motor transfer function
diagram.
Nise pg 343
137 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Computing parameters
• A brushed DC motor has 6 parameters, but we have to measure 5:
1 Armature resistance Ra
2 Armature inductance La
3 Moment of inertia of the rotor J
4 Viscous friction coefficient B
5 Back emf constant Kb = Torque constant KT
• The first 4 parameters can be seen in the figure of the armature
below:
• The equation is given by ea = iaRa + La
dia
dt
+ eb
• The input voltage is ea, the resultant current is ia and eb is the
back EMF
https://www.coursehero.com/file/1801696/ge320Lab2/
138 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Computing parameters cont.
Step 1. Find Ra
1 Original equation: ea = iaRa + La
dia
dt
+ eb
2 Rotation: no, therefore eb = 0 since eb ∝ ω
3 Response: steady state, therefore dia
dt
= 0
4 Extra steps: none
5 New equation: ea = iaRa
6 Measure: ea, ia
Step 2. Find La
dia
dt
+ eb
2 Rotation: no, therefore eb = 0 since eb ∝ ω
3 Response: transient
4 Extra steps: put a resistor Rs in series with the motor so that we
can then measure the voltage drop Vs across Rs to graphically
obtain τ
5 New equation: ea = ia(Ra + Rs ) + La
dia
dt
⇒ τ = La
Ra+Rs
6 Measure: Vs (to get ia = Vs /Rs ) with time to get τ
139 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Step 3. Find Kb (KT = Kb)
dia
dt
+ eb
2 Rotation: yes
3 Response: steady state, therefore dia
dt
= 0
4 Extra steps: none
5 New equation: ea = iaRa + Kbω
6 Measure: ea, ia, ω
Step 4. Find B
1 Original equation: Tm = KT ia = J dω
dt
+ Bω
2 Rotation: yes
3 Response: steady state, so dω
dt
= 0
4 Extra steps: none
5 New equation: KT ia = Bω
6 Measure: ia, ω
140 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Step 5. Find J
1 Original equation: Tm = KT ia = J dω
dt
+ Bω
2 Rotation: yes
3 Response: transient
4 Extra steps: cut current so that ia = 0
5 New equation: 0 = J dω
dt
+ Bω ⇒ τ = J
B
6 Measure: ω with time to get τ
141 / 412

Construction: brushes but no commutator
https://www.youtube.com/watch?v=WKklyuzghQg ,
142 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction in IE workshop at CAE
• Basic structure
143 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction in IE workshop at CAE
• Basic structure
144 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction (Porter Cable 690 Router motor)
• This is the serviceable portion of the brush assembly.
• The unit consists of a graphite brush and integral spring assembly.
• Observe the curvature of the brush where it mates with the
motor’s commutator.
• Also notice there is plenty of length remaining in this brush, so
many more years of service may be expected from this brush.
http://www.ncwoodworker.net/forums/content.php?r=
33-Brush-Inspection-and-Maintenance-for-Universal-Motors
145 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Notice the smooth face where the brush mates with the motor’s
commutator.
• A little bit of wear along the trailing edge can be seen, but this is
typical of normal wear.
• A brush in good condition will look much like this brush – smooth
faces, plenty of length, and no signs of abnormal wear, arcing or
pitting
146 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The photo below shows the brush housing (brass housing at left),
the graphite brush (center, just visible between brush housing and
motor commutator), and the motor commutator (the circular
array of copper conduction strips).
147 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Notice how intimately the brush and commutator mate with one
another, indicative of a well seated brush.
• Also notice no obvious damage, pitting, or overheating in the
commutator (the copper strips).
148 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The blackening is normal and is residue from the graphite brush –
it also provides lubrication between the brush and commutator.
149 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• A view from another angle of brush housing, brush, and
commutator.
• Also visible in the background are the motor windings.
150 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: rotor windings
• Three ways to classify
1 connection (need a better word!)
• progressive
• retrogressive
2 plex
• simplex
• duplex
• triplex
• multiplex
3 sequence
• lap
• wave
• frog-leg
Chapman, pg 492
151 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Wave winding
http://www.sciencedirect.com/science/article/pii/S0736584512000828
152 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Wave winding
http://www.gotwind.org/forum/viewtopic.php?t=3545
153 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Lap vs Wave winding
http://www.tpub.com/neets/book5/15g.htm
154 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Lap vs Wave winding
• Lap winding
• Advantage: If high current is required, it can be
split among several paths, so the size of individual
rotor conductors remains reasonable
• Disadvantage: A very tiny imbalance among the
voltages in the parallel paths will cause large
circulating currents through the brushes and
potentially serious heating problems
• Wave (series) winding
• Advantage: Can be used to build high-voltage DC
machines
• Disadvantage:
Chapman, pg 493
155 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Winding table
156 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Commutator
http://encyclopedia2.thefreedictionary.com/Commutation
157 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
http://www.daviddarling.info/encyclopedia/C/commutator.html
158 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Commutator (clean)
http://homerecording.com/bbs/general-discussions/
analog-only/reel-motors-tascam-34b-grind-halt-296058/
159 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction: Commutator (dirty)
http://homerecording.com/bbs/general-discussions/
analog-only/reel-motors-tascam-34b-grind-halt-296058/
160 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
http://mrmackenzie.co.uk/category/standard-grade/using-electricity/
161 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
http://www.rctech.net/forum/rookie-zone/522906-boosted.html
162 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
http://www.answers.com/topic/commutator
163 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Brushed DC Generator (1/10)
• This is the simplest possible machine that produces a sinusoidal
ac voltage (and dc voltage with a commutator installed)
• This case is not representative of real ac machines, since
the ﬂux in real ac machines is not constant in either
magnitude or direction
• However, the factors that control the voltage and torque on
the loop will be the same as the factors that control the
voltage and torque in real ac machines
Chapman, pg 230-238
164 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The figure below shows a simple generator consisting of a large
stationary magnet producing an essentially constant and uniform
magnetic field and a rotating loop of wire within that field.
• The rotating part of the machine is called the rotor.
• The stationary part of the machine is called the stator.
165 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• e = (v × B).
166 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• (v × B)
• The magnetic ﬁeld B always points to the right and is in
the plane of the paper
• The velocity v takes on every possible direction in
counter-clockwise direction for all segments and is always in
the plane of the page
• v × B is therefore always out of the plane of the page
• (v × B).
• Segments ab and cd are always out of the plane of the page
and so voltage is induced in them
• Segments bc and da are always in the plane of the page and
so voltage is not induced in them
167 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
1 Induced voltage for segments in the plane of the page
1 Segment ab: eba = vB sin(θab) into the page
2 Segment cd: edc = vB sin(180o − θcd ) =vB sin(θcd ) out of the
page
2 Induced voltage for segments out of the plane of the page
1 Segment bc: ebc = 0
2 Segment da: eda = 0
168 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Since both induced emfs reinforce each other, the total induced
voltage eind = 2vB sin θ
169 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• eind = 2vB sin θ
• θ = ωt
• v = rω (r is the radius of rotation)
• eind = 2rωB sin(ωt)
• A = 2r (area of the loop)
• eind = ABω sin(ωt)
• φmax = AB (maximum ﬂux)
• eind = φmax ω sin(ωt)
• Therefore, the induced voltage is sinusoidal, and depends
on the ﬂux and the speed of rotation
170 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
curved pole faces (1/3)
• Single loop of wire rotating about a ﬁxed axis
• If the rotor is rotated, a voltage will be induced in the wire loop
given by Faraday’s Law
171 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motorac.html
172 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
This is the same as a single rotating loop in a uniform
magnetic ﬁeld for the DC motor case except that the commutator is
replaced with slip rings
173 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
3φ Synchronous & Induction AC motors
Rotating magnetic field (1/7)
• In a current carrying loop placed in a magnetic field,
τind = kBloop × Bs
• This equation shows that if there are 2 magnetic fields present in
a machine, a torque will be created that will tend to line up the
magnetic fields
• If one magnetic field is produced by the stator of an ac machine,
and the other one is produced by the rotor of the machine, then a
torque will be induced in the rotor which will cause the rotor to
turn and align itself with the stator magnetic field
174 / 412174 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• If there were some way to make the stator magnetic field rotate,
then the induced torque in the rotor would cause it to constantly
”chase” the stator magnetic field around in a circle
• This in a nutshell, is the basic principle of all ac motor operation
• How can the stator magnetic field be made to rotate?
• The fundamental principle of ac machine operation is that if a
three-phase set of currents, each of equal magnitude and differing
in phase by 120o, flows in a three phase winding, then it will
produce a rotating magnetic field of constant magnitude
• The three-phase winding consists of three separate windings
spaced 120 electrical degrees apart around the surface of the
machine
175 / 412175 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The rotating magnetic field concept is illustrated in
the simplest case by an empty stator containing just
three coils, each 120o apart
• Since such a winding effectively produces only one north and one
south pole, it is a two pole winding
• In the figure below, current
• iaa(t) in coil aa flows into the a end and out of the a end
• ibb(t) in coil bb flows into the b end and out of the b end
• icc (t) in coil cc flows into the c end and out of the c end
176 / 412176 / 412

• The orientation of the three coils in the previous figure can be visualized better in this figure
• The three coils are placed 120o apart
• Notice the resultant rotating magnetic field, shown by the green letters N and S
http://www.learnengineering.org/2013/08/
three-phase-induction-motor-working-squirrel-cage.html ,
177 / 412177 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The currents in the three coils are given by
iaa (t) = IM sin(ωt) A
ibb (t) = IM sin(ωt − 120o) A
icc (t) = IM sin(ωt − 240o) A
• The magnetic ﬁeld intensites are given as follows. The angles are
spatial angles.
Haa (t) = HM sin(ωt)∠0o A.turns/m
Hbb (t) = HM sin(ωt − 120o)∠120o A.turns/m
Hcc (t) = HM sin(ωt − 240o)∠240o A.turns/m
Baa (t) = BM sin(ωt)∠0o T
Bbb (t) = BM sin(ωt − 120o)∠120o T
Bcc (t) = BM sin(ωt − 240o)∠240o T
• The magnetic ﬂux densities are given by
Baa (t) = BM sin(ωt)∠0o T
Bbb (t) = BM sin(ωt − 120o)∠120o T
Bcc (t) = BM sin(ωt − 240o)∠240o T
178 / 412178 / 412

• We now compute the net magnetic ﬂux density
Bnet (t) = Baa + Bbb + Bcc
= BM sin(ωt)∠0o + BM sin(ωt − 120o)∠120o + BM sin(ωt − 240o)∠240o
= BM sin(ωt)ˆx−
0.5BM sin(ωt − 120o)ˆx +
√
3
2
BM sin(ωt − 120o)ˆy−
0.5BM sin(ωt − 240o)ˆx −
√
3
2
BM sin(ωt − 240o)ˆy
= BM sin(ωt) − 0.5BM sin(ωt − 120o) − 0.5BM sin(ωt − 240o) ˆx+
√
3
2
BM sin(ωt − 120o) −
√
3
2
BM sin(ωt − 240o) ˆy
= 1.5BM sin(ωt)ˆx − 1.5BM cos(ωt)ˆy
• The magnetic ﬂux density is a constant 1.5BM and the angle changes continually in a
counterclockwise direction at angular velocity ω.
179 / 412179 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The rotating magnetic ﬁeld of the stator can be represented as a
north pole and a south pole
180 / 412180 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Simplest AC Motor (1/1)
Single rotating loop in uniform magnetic ﬁeld
This is the same as a single rotating loop in a uniform
magnetic ﬁeld for the DC motor case except that the commutator is
replaced with slip rings
181 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Introduction
• Stator: Rotating magnetic field (created by 3-phase AC currents)
• Rotor: Fixed magnetic field (created by DC current)
Synchronous vs Induction motor
Stator same
Rotor DC field vs no DC field on the rotor
• The basic principle of synchronous motor operation is that the
rotor ”chases” the rotating stator magnetic field around in a
circle, never quite catching up with it
Chapman, pg 346
182 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Operation
• Given below is a 2-pole synchronous motor
• The current in the stator produces a rotating
magnetic field BS
• The current in the rotor produces magnetic field BR
• Therefore, there are two magnetic fields present in the motor and
the rotor field will tend to line up with the stator field, just as two
bar magnets will tend to line up if placed near each other
• Since the stator magnetic field is rotating, the rotor magnetic field
(and the rotor itself) will constantly try to catch up
183 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Starting
• The net starting torque is 0!
184 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Starting
Three starting methods:
• Reduce the speed of the stator magnetic ﬁeld.
• Use an external prime mover.
• Use amortisseur windings. This is by far the most popular way to
start a synchronous motor. Amortisseur windings are special bars
laid into notches carved in the face of a synchronous motor’s rotor
and then shorted out on each end by a large shorting ring.
http://en.wikipedia.org/wiki/Squirrel-cage_rotor
185 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Starting: amortisseur windings (squirrel cage)
• Squirrel cage for an actual motor
http://en.wikipedia.org/wiki/Squirrel-cage_rotor
186 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
187 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
• The induced torque is sometimes counterclockwise and sometimes
0 but it is always in the same direction
• Since there is a net torque in a single direction, the motor’s rotor
speeds up
• Although the motor’s rotor will speed up, it can never quite reach
synchronous speed
• Once the motor starts up, the rotor DC current is restored and
the motor locks into synchronous speed
188 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous Motors
Equivalent circuit (for each phase)
189 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Induction Motors
Introduction
• Same as a synchronous motor with amortisseur windings
• In other words, there is no DC current in the rotor
• The stator is the same as the synchronous motor
Chapman, pg 346
190 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Synchronous generator
Y-connection
191 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
∆-connection
Chapman, pg 278
192 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Chapman, pg 279
193 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Power losses
Chapman, pg 281
194 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
OCC (open circuit characteristic)
1 Field current IF is set to 0
2 Terminals are disconnected from all loads, and therefore IA = 0
and EA = Vφ
3 Then IF is increased gradually in steps, and VT is measured
4 Therefore, a plot of IF vs VT , the OCC, can be constructed
5 However, note that,
• In a Y-connection, VT =
√
3Vφ
• In a ∆-connection, VT = Vφ
• Therefore, a plot of IF vs Vφ can also be constructed, and
it is also called the OCC
6 Also note that since we have an open circuit, EA = Vφ and
therefore a plot of IF vs EA, again also called the OCC, can be
constructed
7 Also worth noting is that Vφ or EA cannot be measured directly
while VT can
• Although called OCC, the name is only because open circuit is
used to make the plots
• Otherwise, you can see what ﬁeld current IF is needed to create
what induced EA even when a load is connected
Chapman, pg 283
195 / 412

Operating alone: changing load conditions
• Terminal voltage
• In DC machines, denoted by VT
• In AC machines, denoted by Vφ since it’s on a phase by phase basis
• Phasor directions
1 Vφ: Reference phasor direction is ﬁxed at 0o
2 IA:
• Inductive load: lags Vφ (not necessarily by 90o)
• Resistive load: has the same direction as Vφ
• Capactive load: leads Vφ (not necessarily by 90o)
3 jXs IA: leads IA by 90o
4 EA: has constant magnitude, i.e., vector tip moves along a circle
Chapman, pg 290 ,

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Induction Motors
3 phase induction motor energy efficiencies over the years
US Department of Energy, Advanced Manufacturing Office, Premium Efficiency Motor Selection
and Application Guide,
http://energy.gov/sites/prod/files/2014/04/f15/amo_motors_handbook_web.pdf
197 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Induction Motors
Chapman, pg 394
198 / 412

Stepper motor (1/11)
Sequence
http://wineyardstudents.blogspot.com/2011/05/stepper-motor.html
,
199 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
http://cr4.globalspec.com/blogentry/1749/Making-a-Telescope-Part-3-The-Mount
200 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• Like other types of electric motors that produce a rotating force a
stepper motor consists of two primary components a stator which
is the stationary part of the motor and a rotor which is the part
that rotates and is used to drive whatever it is connected to.
• In our case we have a four phase 9 stepper motor but there are a
few other things that you may need to use:
• Deﬁnitions
• Phases: This is the number of separate coils that make up
the system.
• Step Angle: This is the angle that the motor steps through
every time the next coil in sequence is energized.
• Holding Torque: This is the amount of force that is needed
to cause the rotor to turn while being locked in position by
an energized coil.
• Driving or Dynamic Torque: This is the amount of torque
the motor can supply as it steps from one step to the next.
• Voltage: This is fairly obvious and is the voltage that is
needed to operate the motor.
• Holding Current: This is the current that the coils draw
when in the locked position.
• Dynamic or Peak Current: This is the current the motor
draws as it steps from one step to the next.
201 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• The Rotor
• It is the part of the motor that rotates.
• Consists of a cylindrically shaped permanent magnet that
has multiple magnetic pole pairs arranged in a radial
manner around its axis.
• As the rotor turns a ﬁxed point adjacent to its
circumference will see a sequence of alternating magnetic
poles.
• The rotor can be though of as a series of horse shoe
magnets arranged so their poles form a circle with equally
spaced around its circumference
• In this case we have 10 pole pairs labeled a-j and
represented by the Grey U shapes arranged at 36
increments with their polarity shown by the RED N for the
north poles and BLUE S for the south poles.
• Something that is worth mentioning is that while each of
the poles is separated by 18 it is the 36 angle between the
pair of poles or next pole of the same polarity that is
important.
202 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• The Stator
• This consists of a series of coils that are equally spaced
• In our system we have 8 coils, but they are interconnected
so that electrically there are only 4 coils A-Red, B-Green,
C-Blue, and E-Purple that are spaced at 45 intervals.
• When there is no power to the stepper motor the rotor will
rotate fairly freely but it will try and stop so that one of the
poles aligns with one of the coils.
• In this instance the rotor will try and settle in increments of
9 or 40 separate points.
203 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• Step 0
• In the image on the left shows what would happen when
power was applied to the stator coils labeled A and drawn
in red.
• The magnetic ﬁelds these coils produce will then cause the
rotor to turn till the North pole of magnet a aligns with the
South pole of the red coil A.
• On the opposite side of the rotor the North pole of magnet
f would align with the South pole of the other red A coil.
• Something worth noting is that provided the holding torque
is not exceeded the rotor will stay locked in this position
until the power is removed from the red A coils.
• Unlike other forms of electric motor a locked rotor will not
result in damage to the motor or burnt out coils.
204 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• Step 1
• If we now remove the power to the red A coils and apply it
to the green B coils the rotor will rotate till the North of
rotor magnet b aligns with the South of stator green B coil.
• On the other side of the rotor the North of magnet g will
align with South of the other stator green B coil.
• The important thing to note here is that even though the
magnetic ﬁeld of the stator has rotated through 45 the
rotor has only rotated through 9.
• If we now continue to energize each of the coils red-A,
green-B, blue-C and purple E in sequence the motor will
step through 9 each time a coil is energized.
205 / 412

4 phase
• Advantages
1 Simplified Feedback: There are several advantages related to feedback:
(a) Position: Since the motor can only be in one of the positions defined by the coils and
permanent magnets in the coil finding the position of the system. All you need to do is
start from a known position and then count the steps in either direction to calculate
the position.
(b) Speed: Since the speed the rotor turns at is governed by how rapidly you step from
phase to phase you don’t need a feedback mechanism to calculate the speed the motor
is rotating at.
2 Locked Rotor: Unlike with other motors a locked rotor will not result in the current
through the coils causing them to overheat and burn out. It can also be very helpful in
situations where there needs to be some sort of breaking mechanism that can hold it in
a desired position.
3 Simplified Drive Electronics: Unlike other types of motor where the current and voltage
being applied to the motor need to be controlled through a range stepper motor coils
only need to be either on or off. This makes the driving circuit much simpler and
consequently more reliable and less expensive.
4 Reduced Maintenance: Since there is no commutator, brushes, etcetera that are prone
to wear and contamination stepper motors require less maintenance and have longer
life expectancies than other DC or servo motors.
,
206 / 412

4 phase
• Disadvantages
1 Step Induced Oscillations: Because stepper motor move in a sudden jerky manner
between each step the steps can set up vibrations in the drive train that can be
detrimental to the process and equipment.
2 Fine Control: The staccato or jumping motion of stepper motors can be a serious
problem. As the motors can only be in speciﬁc positions as designated by the geometry
of the rotor and stator you can have problems in applications where a smooth or
continuous drive is required. To a certain extent this can be overcome by having steps
that are around an order of magnitude smaller than required in the application,
however, it is something that engineers need to be aware of.
,
207 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
http://www.instructables.com/id/How-to-make-an-H-bridge/step2/The-truth-about-H-bridges/
208 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
4 phase
• When the coils on ”Relay 1” and ”Relay 4” are pulled high
(electricity is flowing through them), then the motor will spin
forwards (see ”Image 1”).
(electricity is flowing through them), then the motor will spin
backwards (see ”Image 2”).
(electricity is flowing through them), then the motor will stop
spinning (see ”Image 3”).
(electricity is flowing through them), then the motor will stop
spinning (see ”Image 4”).
• ********WARNING***********
• You want AVOID:
• ”Relay 1” and ”Relay 3” being pulled high. This is a short circuit
since there is no load for the electricity to pass through. Bad
things will happen! (see ”Image 5”)
• ”Relay 2” and ”Relay 4” being pulled high. This is a short circuit
since there is no load for the electricity to pass through. Bad
things will happen! (imagine ”Image 6”)
• More than 2 relays being pulled high at one time. Bad things will
happen.
209 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Brushless DC Motor (1/28)
Analogy
•
210 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Analogy
•
211 / 412

Construction of a simple motor
https://www.youtube.com/watch?v=ms3KOZexkmI ,
212 / 412

Construction of a simple motor
https://www.youtube.com/watch?v=Kudzft19coo ,
213 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Analogy
• A humorous analogy help to remember it is to think of BLDC
operation like the story of the donkey and the carrot
• The donkey tries hard to reach the carrot, but the carrot keeps
moving out of reach
http://www.learnengineering.org/2014/10/Brushless-DC-motor.html
214 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Brushless DC Motor (BLDC) (6/28)
Introduction
http://www.freescale.com/ﬁles/sensors/doc/app note/AN3461.pdf
215 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Introduction
The permanent magnet synchronous motor (PMSM)
can be thought of as a cross between an AC induction
motor and a brushless DC motor (BLDC). They have
rotor structures similar to BLDC motors which contain
permanent magnets. However, their stator structure
resembles that of its ACIM cousin, where the windings
are constructed in such a way as to produce a sinusoidal
ﬂux density in the airgap of the machine. As a result,
they perform best when driven by sinusoidal waveforms.
http://www.ti.com/lsds/ti/apps/motor/permanent magnet/overview.page
216 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Construction
217 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Phases
• A single phase BLDC motor has current passing
through one coil only
• A twp phase BLDC motor has current passing
through two coils simultaneously
218 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Commutation Steps for Single Phase Machine
http://www.ti.com/motor, https://www.youtube.com/watch?v=0mQunSe2 FM
219 / 412
Let’s look at the stator
• The stator above has 6 poles, or 3 pole pairs)
• Single wire is used for a pole pair, A and ¯A create an opposite
polarity

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
220 / 412
Step 1.
• To get that rotor to rotate, you need to commutate the stator
field such that the rotor is always chasing that magnetic field
• To do this, you turn on, in sequence, different pole pairs

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
221 / 412
Step 2.
• Turn the current oﬀ in A and ¯A and turn the current on in ¯C and
C creating a North and South electromagnetic pole
• The rotor is then attracted to it

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
222 / 412
Step 3.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
223 / 412
Step 4.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
224 / 412
Step 5.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
225 / 412
Step 6.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
226 / 412
Back to where we started from.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The problem with the single phase setup is that only one winding
is being used to create torque
https://www.youtube.com/watch?v=ZAY5JInyHXY
227 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Commutation Steps for Two Phase Machine
S
N
S
N
S
N
S
N
A
B
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
228 / 412
Step 1.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
S
N
S
N
S
N
S
N
A
C
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
229 / 412
Step 2.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
N
S
N
S
S
N
S
N
BC
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
230 / 412
Step 3.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
N
S
N
S
N
S
N
S
A
B
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
231 / 412
Step 4.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
N
S
N
S
N
S
N
S
A
C
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
232 / 412
Step 5.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
S
N
S
N
N
S
N
S
BC
S
N
A
A
B
B
C
C
CurrentTorque
Vcc
233 / 412
Step 6.
•

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• The trick is when do you turn on that adjacent pole
• There’s no positional information in the diagram shown, you don’t
know where the rotor is so you don’t know when you’re supposed
to turn on that next magnetic pole
• The turning on, the timing is extremely critical, you always want
to maximize the torque
• If you turn on that ﬁeld too early or too late, you will have
performance issues
• Therefore, typically sensors are added to the system
234 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Mathematical Model
Stator windings:
• Total ﬂux (as a result of stator currents and rotor permanent
magnet):


ψa
ψb
ψc

 =


Laa Lab Lac
Lba Lbb Lbc
Lca Lcb Lcc




ia
ib
ic

 +


ψam
ψbm
ψcm


=


Ls −Ms −Ms
−Ms Ls −Ms
−Ms −Ms Ls




ia
ib
ic

 +


ψam
ψbm
ψcm


• Terminal voltage:


va
vb
vc

 =


Rs 0 0
0 Rs 0
0 0 Rs




ia
ib
ic

 +



dψa
dt
dψb
dt
dψc
dt



http://www.ti.com/motor
235 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Comparison
http://ww1.microchip.com/downloads/en/AppNotes/00885a.pdf
236 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Comparison
Also read http://www.teslamotors.com/blog/
induction-versus-dc-brushless-motors
http://ww1.microchip.com/downloads/en/AppNotes/00885a.pdf
237 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Servomotors
Overview
• A servomechanism, sometimes shortened to servo, is an automatic
device that uses error-sensing negative feedback to correct the
performance of a mechanism and is defined by its function
• A servomotor is a rotary actuator that allows for precise control of
angular position, velocity and acceleration
• As the name suggests, a servomotor is a servomechanism
• More specifically, it is a closed-loop servomechanism that
uses position feedback to control its motion and final
position
• The input to its control is some signal, either analogue or
digital, representing the position commanded for the output
shaft
• It consists of a suitable motor coupled to a sensor for
position feedback
• It also requires a relatively sophisticated controller, often a
dedicated module designed specifically for use with
servomotors
https://en.wikipedia.org/wiki/Servomechanism
https://en.wikipedia.org/wiki/Servomotor
238 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Servomotors
Can be AC or DC
• The type of motor is not critical to a servomotor and different
types may be used
• At the simplest, brushed permanent magnet DC motors are used,
owing to their simplicity and low cost
• Small industrial servomotors are typically electronically
commutated brushless motors
• For large industrial servomotors, AC induction motors are typically
used, often with variable frequency drives to allow control of their
speed
• For ultimate performance in a compact package, brushless AC
motors with permanent magnet fields are used, effectively large
versions of Brushless DC electric motors
https://en.wikipedia.org/wiki/Servomotor
239 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Solenoid
• A solenoid is simply a specially designed electromagnet
• A solenoid usually consists of a coil and a movable iron
core called the armature.
• When current flows through a wire, a magnetic field is set up
around the wire
• If we make a coil of many turns of wire, this magnetic field
becomes many times stronger, flowing around the coil and
through its center in a doughnut shape
• When the coil of the solenoid is energized with current, the core
moves to increase the flux linkage by closing the air gap between
the cores
http://mechatronics.mech.northwestern.edu/design_ref/actuators/solenoids.html
240 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Solenoid
• The movable core is usally spring-loaded to allow the
core to retract when the current is switched off
• The force generated is approximately proportional
to the square of the current and inversely proportional to the
square of the length of the air gap
• Solenoids are inexpensive, and their use is primarily limited to
on-off applications such as latching, locking, and triggering
• They are frequently used in home appliances (e.g. washing
machine valves), office equipment (e.g. copy machines),
automobiles (e.g. door latches and the starter solenoid), pinball
mahines (e.g., plungers and bumpers), and factory automation
http://mechatronics.mech.northwestern.edu/design_ref/actuators/solenoids.html
241 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Electric Vehicles (86/86)
Chevrolet FNR
http://www.extremetech.com/extreme/
203862-this-chevrolet-fnr-concept-car-is-science-fiction-made-real
242 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism
World’s strongest magnet: 27T
• Built by MagLab, largest and highest powered magnet
lab in the world
• Demonstrated on 5 June 2015
https://nationalmaglab.org/news-events/news/
maglab-claims-record-with-novel-superconducting-magnet
http://nextbigfuture.com/2015/06/new-superconducting-magnet-already-at.html
243 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (1/12)
The Geomagnetic Field
• The magnitude of the Earth’s magnetic field (the geomagnetic
field) varies over the surface of the earth from a minimum of
22µT (0.22 Gauss) over S. America to a maximum of 67µT (0.67
Gauss) south of Australia
• The heading of an eCompass is determined from the relative
strengths of the two horizontal geomagnetic field components and
these vary from zero at the magnetic poles to a maximum of
42µT over E. Asia
• Detailed geomagnetic field maps are available from the World
Data Center for Geomagnetism at
http://wdc.kugi.kyoto-u.ac.jp/igrf/
http://cache.freescale.com/files/sensors/doc/app note/AN4247.pdf
244 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (2/12)
The Geomagnetic Field cont.
• Although the Earth’s magnetic field is relatively stable over time,
electric currents in the ionosphere can cause daily alterations
which can deflect surface magnetic fields by as much as one
degree
• Normally, daily variations in field strength are on the order of
0.025µT (0.25 mGuass), which would equate to about 0.03
degree variation in heading
• This small change of heading is on the same order of magnitude
as the resolution of most MEMS based magnetometers, so in
most cases, the Earth’s magnetic field can be considered constant
wrt time
http://www.vectornav.com/support/library/magnetometer
245 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (3/12)
Magnetometer calibration
• Magnetic measurements will be subjected to distortions:
1 Hard iron: Created by objects that produce a magnetic field
2 Soft iron: Deflections or alterations in the existing magnetic
field
246 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (4/12)
Magnetometer calibration cont.
• A common way of visualizing and correcting hard and soft iron
distortions is to plot the output of the magnetometer on a 2D
graph
• The following plot shows measurements taken by the
magnetometer as the device is slowly rotated around the Z-axis
• In the event that there are no hard or soft iron distortions present,
the measurements should form a circle centered at X=0, Y=0.
• The radius of the circle equals the magnitude of the magnetic ﬁeld
247 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (5/12)
• The eﬀect of hard iron distortions on the plot will be to shift the
center of the circle
• As shown in the plot the center of the circle with hard iron
distortions is now at X=200, Y=100
• From this we can conclude that there is 200 mGauss hard iron
bias in the X-axis and 100 mGauss hard iron bias in the Y-axis
• Hard iron distortions will only shift the center of the circle away
from the origin
• Hard iron distortions will not distort the shape of the circle.
248 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (6/12)
• Soft iron distortions on the other hand distort and warp the
existing magnetic ﬁelds
• When you plot the magnetic output, soft iron distortions are easy
to recognize since they will distort the circular output
• Soft iron eﬀects warp the circle into an elliptical shape
• The center of the ellipse below is still located at X=200 mGauss
and Y=100mGauss since the hard iron distortions are the same as
before but now the major axis is aligned 30 degrees up from the
body frame X direction due to soft iron distortions
249 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (7/12)
• It is possible to eliminate the effects of both hard and soft iron
distortions on the magnetometer outputs
• VectorNav products use the following calibration model to
correct for hard and soft iron distortions
M =


C1 C2 C3
C4 C5 C6
C7 C8 C9




Hx − C10
Hy − C11
Hz − C12


• The above model consists of 12 hard and soft iron compensation
parameters
• The first 9 parameters correct for the soft iron while the last
three, C10, C11, C12 parameters compensate for the hard iron
• For the previous figure, the hard and soft iron calibration
parameters would be
M =


C1 C2 C3
C4 C5 C6
C7 C8 C9




Hx − C10
Hy − C11
Hz − C12


250 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (8/12)
• Measured magnetometer locus - no correction applied:
251 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (9/12)
• Measured magnetometer locus - hard iron correction applied:
252 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (10/12)
• Measured magnetometer locus - hard and soft iron correction
applied:
253 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (11/12)
1 Raw mode. Put magnetometer in IMU mode, i.e., it should give
raw values and not fused values. These raw values will be in
Gauss or Teslas. For the NV-100, they are in Gauss. Note that
these values must vary between 0.22 and 0.67 Gauss, and if the
values are more than these values, we have hard and/or soft iron
distortions
2 Find North and South poles. Rotate magnetometer 360 degrees
and observe the following:
1 Hx must reach a maximum positive value when it is aligned with the North pole
of the Earth’s magnetic ﬁeld.
2 Turning it CW by 90 degrees should give a value of 0 since it is now orthogonal
to the Earth’s magnetic ﬁeld and pointing towards East
3 Turning it CW by another 90 degrees, i.e., a total of 180 degrees should give
you a maximum negative value showing it is pointing towards the South pole
4 Turning it CW by another 90 degrees, i.e., a total of 270 degrees should again
give you a value of 0 showing it is pointing West
5 Finally, turning it CW by another 90 degrees, i.e., a total of 360 degrees should
again give you a maximum positive value showing you are again aligned north
6 The above process can be repeated with Hy
7 Finding the angle as atan(Hy/Hx) or atan(-Hy/Hx) depending on how you set it
up should give you the angle of rotation
254 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Magnetism (12/12)
3 Plot Hx and Hy points. Now, rotate magnetometer through 360
degrees and plot Hx vs Hy. You should get a zero-centered circle
if there are no hard or soft iron distortions. If it is a shifted circle,
you have hard iron distortions. If it is an ellipse instead of a circle,
you have soft iron distortions. If you have a shifted ellipse, you
have hard and soft iron distortions.
4 Finding parameters of hard and soft iron distortions. Use the
following steps for manual removal. Automatic removal will
require knowledge of transforming a shifted ellipse to a centered
circle.
1 Shift the ellipse or circle to the center.
2 See what angle the ellipse makes with the y-axis and ﬁnd a
rotation matrix to rotate it so that one of the axes of the
ellipse is y-axis aligned
3 Compress Hx or Hy so that the ellipse is now a circle
5 Using above parameters to remove hard and soft iron
distortions. Now, for every measurement of Hx and Hy, apply
above parameters and check that indeed as the magnetometer
rotates, the angles are more accurate than before. Also, angles
should be evenly spaced.
255 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Tesla Motors
Induction motor in vehicles
256 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 1: Lab and area familiarization
• Get familiar with the lab environment
• Get familiar with the MES environment
257 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 2: Transformers Lab
Measuring parameters
• This is the setup for an open circuit test in the lab:
258 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 2: Transformers Lab
Measuring parameters cont.
• This is the setup for a short circuit test in the lab:
259 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 3: Matlab Usage
Numericals and plots
• Be able to solve numericals related to
electromechanical systems in Matlab
• Be able to make plots related to electromechanical
systems in Matlab
260 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 4: DC motor modeling, Matlab
• Go to the University of Michigan website
http://ctms.engin.umich.edu
• Click ”MOTOR SPEED” at the top
• Complete SYSTEM MODELING and SYSTEM ANALYSIS parts
261 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 5: DC motor modeling, Matlab
(part 2)
• Solve Example 7.1, part (a) and (b)
• In this example, there is no notion of time, i.e., how long
does it take the motor to reach no-load steady-state ω
• Now, instead of just using the formula to find no-load
steady-state ω, write a software loop to model the motor feedback
loop and find ω and τ in increments of 0.001 sec upto 0.5 sec
• Use moment of inertia of the rotor, J = 0.01 kg m2
• Make the following 3 plots:
1 ω against time
2 τ against time
3 ω against τ
• Verify that the results of this lab tally with the results of
the solved example, as well as the results of the previous lab
provided that L = 0 H and motor viscous friction constant
b = 0 Nms
• Investigate the effect of varying J, R, φ
262 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Lab # 6: BKB Universal Lab Machine
DC shunt motor
• Front panel, starter motor, motor, generator
263 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
DC shunt motor cont.
• Load bank (bulbs), Power supply
264 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Front panel
265 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Stator coils
266 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Rotor coils
267 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Search coils
268 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
• Dynamometer
269 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
All examples
• Ch 1, Intro to Machinery Principles: 11 examples
• Ch 2, Transformers: 10 examples
• Ch 3, AC Machinery Fundamentals: 3 examples
• Ch 4, Synchronous Generators: 2 examples
• Ch 5, Synchronous Motors: 8 examples
• Ch 6, Induction Motors: 3 examples
• Ch 7, DC Machinery Fundamentals: 8 examples
• Ch 8, DC Motors and Generators: 4 examples
• Ch 9, Single-phase and special purpose motors: 9 examples
• Total: 58
Chapman 5th ed
270 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-1
Magnetic circuits: computing ﬂux
271 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-1 cont.
272 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-1 cont.
273 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-1 cont.
274 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-2
275 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-2 cont.
276 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-2 cont.
277 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-2 cont.
278 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-3
279 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-3 cont.
280 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-3 cont.
281 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-3 cont.
282 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-4
Magnetic circuits: computing relative permeability
283 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-4 cont.
284 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-4 cont.
285 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-4 cont.
286 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-5
Magnetic circuits: current, relative permeability, reluctance
287 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-5 cont.
288 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-5 cont.
289 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-5 cont.
290 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 1-5
291 / 412

Problem 1-5 cont.
1 c l e a r ; c l c ; c l f ;
2 %t u r n s
3 N = 500;
4 %p e r m e a b i l i t y
5 mu0 = 4∗ p i ∗10E−7; % p e r m e a b i l i t y of a i r (H/m)
6 mur = 800; % r e l a t i v e p e r m e a b i l i t y
7 %l e n g t h s
8 l e n l e f t = (7.5+15+7.5) /100; % l e n g t h ( meters )
9 l e n t o p = (5+20+2.5) /100; % l e n g t h ( meters )
0 l e n r i g h t = l e n l e f t ; % l e n g t h ( meters )
1 len bottom = l e n t o p ; % l e n g t h ( meters )
2 %a r e a s
3 a r e a l e f t = (10∗5) /1E4 ; % area ( sq meters )
4 a r e a t o p = (15∗5) /1E4 ; % area ( sq meters )
5 a r e a r i g h t = (5∗5) /1E4 ; % area ( sq meters )
6 area bottom = (15∗5) /1E4 ; % area ( sq meters )
7 %r e l u c t a n c e s
8 R l e f t = l e n l e f t / (mu0 ∗ mur ∗ a r e a l e f t ) ; % r e l u c t a n c e (A t u r n s /Wb)
9 R top = l e n t o p / (mu0 ∗ mur ∗ a r e a t o p ) ; % r e l u c t a n c e (A t u r n s /Wb)
0 R r i g h t = l e n r i g h t / (mu0 ∗ mur ∗ a r e a r i g h t ) ; % r e l u c t a n c e (A t u r n s /Wb)
1 R bottom = len bottom / (mu0 ∗ mur ∗ area bottom ) ;% r e l u c t a n c e (A t u r n s /Wb)
2 R = R l e f t+R top+R r i g h t+R bottom ; % t o t a l r e l u c t a n c e (A t u r n s /Wb)
3 %f l u x
4 phi = 0 . 0 0 5 ; % f l u x ( webers )
5 %part ( a )
6 I = phi∗R/N; % c u r r e n t ( amperes )
7 %part ( b )
8 B top = phi / a r e a t o p ; % f l u x d e n s i t y ( t e s l a s )
9 B r i g h t = phi / a r e a r i g h t ; % f l u x d e n s i t y ( t e s l a s )
Chapman 5th ed, pg 56 ,
292 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 1-7
Motors: Lorentz force
In this , B = 0.25T, l = 1.0m, I = 0.5A, ﬁnd F.
F = ilB sin θ = (0.5A)(1.0m)(0.25T) sin(90o) = 0.125N
to the right
293 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-1
Transformers: advantage
294 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-1 cont.
295 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-1 cont.
1 c l e a r ; c l c ;
2 %Given
3 V = 480; %v o l t a g e
4 Z l i n e = 0.18 + 0.24 j ; %impedance ( l i n e )
5 Z load = 4 + 3 j ; %impedance ( load )
6 Z t o t a l = Z l i n e+Z load ; %impedance ( t o t a l )
7 a T1 = 0 . 1 ; %t u r n s r a t i o (T1)
8 a T2 = 10; %t u r n s r a t i o (T2)
9 % part ( a )
10 % −−−−−−−−
11 I l i n e = V/ Z t o t a l ; %c u r r e n t
12 V load = I l i n e ∗Z load ; %v o l t a g e
13 P l o s s e s = abs ( I l i n e ) ˆ2∗ r e a l ( Z l i n e ) ; %power
14 % part ( b )
15 % −−−−−−−
16 Z l o a d l e f t T 2 = a T2 ˆ2 ∗ Z load ;
17 Z l o a d l e f t T 2 l e f t T 1 = a T1 ˆ2 ∗ Z l o a d l e f t T 2 ;
18 Z l i n e l e f t T 1 = a T1 ˆ2 ∗ Z l i n e ;
19 Z t o t a l = Z l i n e l e f t T 1 + Z l o a d l e f t T 2 l e f t T 1 ;
21 I G = V/ Z t o t a l ;
22 I l i n e = I G∗a T1 ;
23 I l o a d = I l i n e ∗a T2 ;
25 V load = I G∗Z load ;
27 P l o s s e s = abs ( I l i n e ) ˆ2∗ r e a l ( Z l i n e )
28 %Notes
29 %To f i n d P l o s s e s , we used the magnitude of c u r r e n t
30 %and the r e a l part of Z l i n e
296 / 412

Example 2-2
Transformers: ﬁnding parameters
297 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-2 cont.
• For both the open circuit and short circuit tests, we have 8
variables:
1 P: can be measured (given in this example)
2 V : can be measured (given in this example)
3 I: can be measured (given in this example)
4 cos θ
5 Rc : transformer parameter to be computed
6 Xm: transformer parameter to be computed
7 Reqs : transformer parameter to be computed
8 Xeqs : transformer parameter to be computed
• For the open circuit test, first find cos θ, then find Rc , Xm.
• For the short circuit test, first find cos θ, then find Reqs , Xeqs .
298 / 412

Example 2-2 cont.
299 / 412

Example 2-2 cont.
300 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-2 cont.
301 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-2 cont.
1 c l e a r ; c l c ;
2 %GIVEN
3 %−−−−−
4 a = 8000/240; % t u r n s r a t i o
5 %open c i r c u i t ( secondary side , because low v o l t a g e )
6 Voc = 240; % v o l t a g e
7 I o c = 7 . 1 3 3 ; % c u r r e n t
8 Poc = 400; % power
9 %s h o r t c i r c u i t ( primary side , because low c u r r e n t )
10 Vsc = 489; % v o l t a g e
11 I s c = 2 . 5 ; % c u r r e n t
12 Psc = 240; % power
13 %COMPUTATIONS
14 %−−−−−−−−−−−−
15 %open c i r c u i t t e s t
16 PFoc = Poc /( Voc∗ I o c ) ; % power f a c t o r = cos (
→theta )
17 thetaoc = −acos ( PFoc ) ; % n e g a t i v e s i g n f o r
→ l a g g i n g
18 [ I x , I y ] = p o l 2 c a r t ( thetaoc , I o c ) ;
19 I = I x + j ∗ I y ;
20 Y E = I /Voc ;
21 Rc = 1/ r e a l ( Y E ) ;
22 Xm = −1/imag ( Y E ) ; % Y E=(1/Rc)−j (1/Xm)
23 %s h o r t c i r c u i t t e s t
24 PFsc = Psc /( Vsc∗ I s c ) ; % power f a c t o r = cos (
→theta )
25 t h e t a s c = −acos ( PFoc ) ; % n e g a t i v e s i g n f o r
→ l a g g i n g
26 [ I x , I y ] = p o l 2 c a r t ( thetasc , I s c ) ;
27 I = I x + j ∗ I y ;
28 Z E = Vsc/ I ;
302 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5
Transformers: voltage regulation and eﬃciency
303 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
304 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
305 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
306 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
307 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
308 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
309 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
310 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-5 cont.
311 / 412

Example 2-5 cont.
1 c l e a r ; c l c ; format compact ; % a l l a n g l e s are i n r a d i a n s
3 % ===============================================
4 % GIVEN
5 % ===============================================
6 S rated mag = 15000; % r a t e d value , VA
7 pri V rated mag = 2300; % r a t e d value , V
8 sec V rated mag = 230; % r a t e d value , A
9 a = pri V rated mag / sec V rated mag ; % t u r n s r a t i o
0 sec Voc mag = 230; % open c i r c u i t t e s t ( low v o l t a g e s i d e )
1 sec Ioc mag = 2 . 1 ; % open c i r c u i t t e s t ( low v o l t a g e s i d e )
2 sec Poc mag = 50; % open c i r c u i t t e s t ( low v o l t a g e s i d e )
3 pri Vsc mag = 47; % s h o r t c i r c u i t t e s t ( high v o l t a g e s i d e )
4 p r i I s c m a g = 6; % s h o r t c i r c u i t t e s t ( high v o l t a g e s i d e )
5 pri Psc mag = 160; % s h o r t c i r c u i t t e s t ( high v o l t a g e s i d e )
312 / 412

Example 2-5 cont.
1 % ===============================================
2 % COMPUTATIONS
3 % ===============================================
5 % I . OPEN CIRCUIT TEST ( goal i s to f i n d Rc , Xm)
6 % −−−−−−−−−−−−−−−−−−−−
7 % f i n d power f a c t o r
8 PFoc = sec Poc mag / ( sec Voc mag∗sec Ioc mag ) ; % power f a c t o r
0 % f i n d complex open c i r c u i t v o l t a g e and c u r r e n t
1 sec Voc = sec Voc mag∗(1+0 j ) ; %a r b i t r a r i l y given an angle of 0
3 I o c t h e t a = −acos ( PFoc ) ; % n e g a t i v e s i g n f o r l a g g i n g
4 [ I x I y ] = p o l 2 c a r t ( I o c t h e t a , sec Ioc mag ) ;
5 s e c I o c = I x + j ∗ I y ;
7 % f i n d admittance
8 sec YE = s e c I o c / sec Voc ; % YE=(1/Rc)−j (1/Xm)
9 sec Rc = 1/ r e a l ( sec YE ) ;
0 sec Xm = −1/imag ( sec YE ) ;
313 / 412

Example 2-5 cont.
1 % I I . SHORT CIRCUIT TEST ( goal i s to f i n d Req , Xeq )
2 % −−−−−−−−−−−−−−−−−−−−−−
3 % f i n d power f a c t o r
4 PFsc = pri Psc mag /( pri Vsc mag∗ p r i I s c m a g ) ; % power f a c t o r
6 % f i n d complex s h o r t c i r c u i t v o l t a g e and c u r r e n t
7 p r i V s c = pri Vsc mag ∗(1+0 j ) ; %j u s t given an angle of 0
9 I s c t h e t a = −acos ( PFsc ) ; % n e g a t i v e s i g n f o r l a g g i n g
0 [ I x I y ] = p o l 2 c a r t ( I s c t h e t a , p r i I s c m a g ) ;
1 p r i I s c = I x + j ∗ I y ;
3 % f i n d impedance
4 pri ZE = p r i V s c / p r i I s c ;
5 p r i R e q = r e a l ( pri ZE ) ;
6 pri Xeq = imag ( pri ZE ) ;
9 % I I I . REFERRING Rc , Xm, Req , Xeq TO OPPOSITE SIDES
0 % −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
1 p r i R c = ( a ˆ2)∗sec Rc ; %r e f e r r e d to primary
2 pri Xm = ( a ˆ2)∗sec Xm ;
4 sec Req = (1/ a ˆ2)∗ p r i R e q ; %r e f e r r e d to secondary
5 sec Xeq = (1/ a ˆ2)∗pri Xeq ;
314 / 412

Example 2-5 cont.
1 % IV . REGULATION
2 % −−−−−−−−−−−−−−
3 r e g u l 1 = func POWER TRANSFORMER RegulationVsKnown ( S rated mag , sec V rated mag , 0.8 ,
→−1, sec Req , sec Xeq )
→0 , sec Req , sec Xeq )
→1 , sec Req , sec Xeq )
7 % ===============================================
8 % PRINT RESULTS
9 % ===============================================
0 disp ( ’On primary s i d e ’ )
1 disp ( ’−−−−−−−−−−−−−−−’ )
2 p r i R c
3 pri Xm
4 p r i R e q
5 pri Xeq
6 disp ( ’ ’ )
7 disp ( ’On secondary s i d e ’ )
8 disp ( ’−−−−−−−−−−−−−−−−−’ )
9 sec Rc
0 sec Xm
1 sec Req
2 sec Xeq
3 disp ( ’ ’ )
4 disp ( ’ Re gu la tio n ’ )
5 disp ( ’−−−−−−−−−−’ )
6 s p r i n t f ( ’ r e g u l a t i o n : %.2 f pe rcen t ’ , r e g u l 1 )
315 / 412

Example 2-5 cont.
1 %Vp , Vs need to be both r e f l e c t e d on primary side , or both on secondary s i d e
3 f u n c t i o n r e g u l = func POWER TRANSFORMER Regulation (Vp , Vs )
5 % use same names as book
6 Vnl = abs (Vp) ;
7 V f l = abs ( Vs ) ;
9 % step 3: f i n d r e g u l a t i o n
0 r e g u l = ( Vnl−V f l ) / V f l ∗100;
316 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2-7
Transformers: regulation
317 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2-7 cont.
318 / 412

Problem 2-7 cont.
1 c l e a r ; c l c ; format compact ; % a l l a n g l e s are i n r a d i a n s
2 % ===============================================
3 % GIVEN
4 % ===============================================
5 Srated mag = 30000; % r a t e d value , VA
6 pri Vrated mag = 8000; % r a t e d value , V
7 sec Vrated mag = 230; % r a t e d value , A
9 p r i R c = 100E3 ; % magnetizing branch
0 pri Xm = 20E3 ; % ”
1 p r i Z e q = 20+100 j ; % t r a n s f o r m e r impedance
4 a = pri Vrated mag / sec Vrated mag ; % t u r n s r a t i o
319 / 412

Problem 2-7 cont.
1 % ===============================================
2 % COMPUTATIONS
3 % ===============================================
4 a = pri Vrated mag / sec Vrated mag ; % t u r n s r a t i o
6 %given
7 pri Vp = 7967∗(1+0 j ) ;
8 sec Z L = 2+0.7 j ; %use −3j f o r part ( b )
0 %computations on primary s i d e
1 p r i Z L = aˆ2∗ sec Z L ;
2 p r i Z t o t = p r i Z e q + p r i Z L ;
3 p r i I s = pri Vp / p r i Z t o t ; %p r i I s = s e c I s /a
4 p r i V s = p r i I s ∗ p r i Z L ;
5 VR = func POWER TRANSFORMER Regulation ( pri Vp , abs ( p r i V s ) )
7 %computations on secondary s i d e
8 sec Vp = pri Vp /a ;
9 s e c Z t o t = p r i Z t o t /a ˆ2;
0 s e c I s = sec Vp / s e c Z t o t ;
1 sec Vs = s e c I s ∗ sec Z L ;
2 VR = func POWER TRANSFORMER Regulation ( sec Vp , sec Vs )
320 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-7
Transformers: autotransformer
321 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-7 cont.
322 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-7 cont.
323 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 2-7 cont.
324 / 412

Problem 2.14
Transformer
I = VG
Zline +Zload
= 13,200
60 ∠53.1o +500 ∠36.87o = 23.66∠−38.6o A
SG = VG I∗ = 13, 200(23.66∠38.6o) = 312, 312 ∠38.6o VA
Chapman, pg 148 ,
325 / 412

Problem 2.14 cont.
Transformer
I = VG
Zline +Zload
= 13,200
0.6 ∠53.1o +500 ∠36.87o = 26.37∠−36.89o A
SG = VG I∗ = 13, 200(26.37∠36.89o) = 278, 393 ∠36.89o VA
,
328 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2.14 cont.
Transformer
• Initially, the ratio of the load voltage magnitude to
the input voltage was |VL|
|VG | = 11,830
13,200 = 0.896
• This increased to |VL|
|VG | = 13,185
13,200 = 0.9989
• Initially, the line losses were Pline = 20.1 kW
• These decreased by 80 times to Pline = 250 W
331 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2.15
Transformer
SW = 5000 VA
480/120
600V source to 120V load ⇒ NSE = 4NC
Chapman, pg 148
332 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2.15 cont.
Transformer
SW
SIO
= NSE
NSE +NC
5000
SIO
= 4NC
4NC +NC
⇒ SIO = 5
4(5000) = 6250 VA
Ipmax = 6250
600 = 10.4 A
Ismax = 6250
120 = 52.1 A
SIO is 1.2 times SW
Chapman, pg 148
333 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2.16
Transformer
SW = 5000 VA
480/120
600V source to 480V load ⇒ NSE = 1/4NC
Chapman, pg 149
334 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Problem 2.16 cont.
Transformer
SW
SIO
= NSE
NSE +NC
5000
SIO
= NSE
NSE +4NSE
⇒ SIO = 5(5000) = 25, 000 VA
Ipmax = 25,000
600 = 41.67 A
Ismax = 25,000
480 = 52.1 A
SIO is 5 times SW
335 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 5.2
Synchronous generator: changing load conditions
Chapman, pg 291
336 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 5.2 cont.
337 / 412

Example 5.2 cont.
Note: VT = Vφ since we have a 3 phase ∆-connected machine.
For part (c), use IL to find IA, use IA to find a new higher EA when the load is connected.
Find IF corresponding to this new EA from the OCC curve. But the OCC curve is for VT , not EA!
How can you use the OCC curve? The way to look at this is as follows: By looking at the OCC curve, you find the IF needed for open
circuit VT , but this then will drop to 480V when the load is connected.
Voltage = 480V
Frequency, fe = 60Hz
Connection = ∆
Number of poles, p = 4
Synchronous reactance, Xs = 0.1Ω
Armature resistance, RA = 0.015Ω
Full load current, IL = 1200A, 0.8 PF lagg.
= 1200A∠−36.87o
Full load friction/windage losses = 40 kW
Full load core losses = 30 kW
(a) Speed of rotation, fm =?
(b) Field current If if no load VT = 480V =?
(c) Field current If if IL = 1200A, 0.8 PF lagging load and VT = 480V =?
(d) Input power Pin, output power Pout , efficiency η =?
(e) If load suddenly disconnected , VT =?
(f) Field current If if IL = 1200A, 0.8 PF leading load and VT = 480V =?
∆-connection ⇒ VT = Vφ, IL =
√
3Iφ =
√
3IA
No load ⇒ VT = EA
,
338 / 412

Example 5.2 cont.
(a) fm = fe
p/2
= 60
4/2
= 30Hz = 1800rpm
(b) If = 4.5A read directly from OCC curve (VT vs If plot)
(c) IA = Iφ = IL√
3
= 1200∠−36.87o
√
3
= 692.8∠−36.87o
EA = Vφ + RAIA + jXs IA
= 480∠0o + (0.015)(692.8∠−36.87o) + j(0.1)(692.8∠−36.87o) = 532∠5.3o
If = 5.7A from OCC curve
,
339 / 412

Example 5.2 cont.
(d) Pout =
√
3VT IL cos θ
=
√
3(480)(1200) cos(−36.87o)
= 798 kW
Pelec. losses = 3IA
2
RA
= 3(692.8)2(0.015)
= 21.6 kW
Pin − P stray losses − Pfric.&wind. losses − Pcore losses − PCu losses = Pout
⇒ Pin − P stray losses − Pmech. losses − Pcore losses − Pelec. losses = Pout
⇒ Pin − 0 kW − 40 kW − 30 kW − 21.6 kW = 798 kW
⇒ Pin = 889.6 kW
eﬃciency η = Pout
Pin
× 100% = 798 kW
889.6 kW
× 100% = 89.75%
,
340 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 7-1
DC motors: simple rotating loop
341 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
For this motor,
• The area of the rotor under each pole is A = Ap = πrl
due to the curved nature of the stator poles
• K = 2
π
Chapman 5th ed, pg 413, 406 (ﬁgure)
342 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
343 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
344 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
345 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
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- Other
- Universal motor
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3. Applications
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,
Example 7-1 cont.
346 / 412

AV-222
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1. Introduction
2. Theory
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(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
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- Universal motor
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3. Applications
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,
Example 7-1 cont.
347 / 412

AV-222
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1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
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3. Applications
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5. Problems
,
Example 7-1 cont.
348 / 412

Example 7-1 cont. I
%Example 7.1 , Chapman 5 th ed , pg 413
c l e a r ; c l c ; format compact
% =================================
% INITIALIZATION
% =================================
% p h y s i c a l
r = 0 . 5 ; % r a d i u s ( meters )
l = 1; % l e n g t h ( meters )
A = p i ∗r∗ l ; % area ( meters ˆ2)
K = 2/ p i ; % machine constant ( no u n i t s )
% e l e c t r i c a l
R = 0 . 3 ; % r e s i s t a n c e ( ohms )
VB = 120; % a p p l i e d v o l t a g e ( v o l t s )
% magnetic
B = 0 . 2 5 ; % magnetic f l u x d e n s i t y ( t e s l a s )
phi = B∗A; % phi ( webers )
% =================================
% COMPUTATIONS
% =================================
%part ( b )
%−−−−−−−−
I s t a r t = VB/R; %s t a r t u p
e i n d = VB; %no load steady state , c u r r e n t=0
w = e i n d /(K∗phi ) ; %”
,
349 / 412

Example 7-1 cont. II
%part ( c )
%−−−−−−−−
tau = 10; % load torque (Nm)
I = tau /(K∗phi ) ; % step 2: f o r c e / torque equation
e i n d = VB−I ∗R; % step 1: KVL ( motor equation )
w = e i n d /(K∗phi ) ; % step 4: Faraday
P mech = tau ∗ w; % output power : mechanical
P e l e c = VB ∗ I ; % i n pu t power : e l e c t r i c a l
%part ( d )
%−−−−−−−−
tau = 7 . 5 ; % load torque (Nm)
I = tau /(K∗phi ) ; % step 2: f o r c e / torque equation
e i n d = VB+I ∗R; % step 1: KVL ( g e n e r a t o r equation )
w = e i n d /(K∗phi ) ; % step 4: Faraday
%part ( e )
%−−−−−−−−
B = 0 . 2 ;
phi = B∗A; % phi ( webers )
e i n d = VB; % no load steady state , c u r r e n t=0
w = e i n d /(K∗phi ) ; % ”

AV-222
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1. Introduction
2. Theory
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(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
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- Universal motor
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
• Dimensions
• r = 0.5 m
• = 1.0 m
• Field
• B = 0.25 T = 0.25 Wb/m2
• φ = BAp = B(πr ) = (0.25 T)(π × 0.5 m × 1.0 m) =
0.125π Wb
• Ap is area of rotor under pole face
• External
• VB = 120 V
• R = 0.3 Ω
Chapman 5th ed, pg 413, 409 (Ap)
351 / 412

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- DC
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
(a) At t = 0, the following sequence occurs
1 Voltage and velocity: eind = 0, ω = 0
2 Current and torque: i = VB −eind
R
= 120
0.3
= 400 A,
τind = 2
π
φi = 2
π
(0.125π)(400) = 100 NM
3 Velocity and voltage ↑: Motor starts to rotate, i.e., ω starts
to increase causing eind = 2
π
φω to increase
4 Current and torque ↓: This decreases i and therefore τind
Steady state is reached with τind = 0 and eind = VB . So, we went
from eind = 0 to eind = VB
352 / 412

AV-222
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1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
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- Universal motor
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
(b) i = 400 A (see previous part)
eind = 2
π
φω
120 = 2
π
(0.125π)ω
⇒ ω = 480 rad/sec
353 / 412

AV-222
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2. Theory
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(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
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- Universal motor
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
(c)
τind = 2
π
φi
10 = 2
π
(0.125π)i
⇒ i = 40 A
eind = VB − iR motor
= 120 V − (40 A)(0.3Ω)
= 108 V
eind = 2
π
φω
108 = 2
π
(0.125π)ω
Power supplied to shaft = τω = (10 NM)(432 rad/sec) = 4, 320W
Power out of battery shaft = VB i = (120 V)(40A) = 4, 800W
354 / 412

AV-222
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- DC
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3. Applications
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5. Problems
,
Example 7-1 cont.
(d)
τind = 2
π
φi
7.5 = 2
π
(0.125π)i
⇒ i = 30 A
eind = VB + iR generator
= 120 V + (30 A)(0.3Ω)
= 129 V
eind = 2
π
φω
129 = 2
π
(0.125π)ω
355 / 412

AV-222
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1. Introduction
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(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
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- Universal motor
- Reluctance motor
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3. Applications
4. Labs
5. Problems
,
Example 7-1 cont.
(e) φ = BAp = B(πr ) = (0.2 T)(π × 0.5 m × 1.0 m) = 0.1π Wb
eind = 2
π
φω
120 = 2
π
(0.1π)ω
When the ﬂux decreases, the speed increases !
356 / 412

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- DC
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- Universal motor
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3. Applications
4. Labs
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,
Example 8-1
DC shunt motor
357 / 412

AV-222
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- DC
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- Brushed
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- Universal motor
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,
Example 8-1 cont.
DC shunt motor
358 / 412

AV-222
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- DC
- Linear
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- Universal motor
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5. Problems
,
Example 8-1 cont.
DC shunt motor
359 / 412

AV-222
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- DC
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,
Example 8-1 cont.
DC shunt motor
360 / 412

AV-222
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1. Introduction
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- DC
- Linear
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- Universal motor
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
361 / 412

AV-222
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- DC
- Linear
- Brushed
- AC
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- Universal motor
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
362 / 412

AV-222
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1. Introduction
2. Theory
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(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
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- Universal motor
- Reluctance motor
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
363 / 412

Example 8-1 cont. I
DC shunt motor
%Example 8.1 , Chapman 5 th ed , pg 472
c l e a r ; c l c ; format compact ;
w vec = [ ] ;
ta u ve c = [ ] ;
V T = 250;
R A = 0 . 0 6 ;
R F = 50;
w nl = 1200;
% part ( a )
I L = 100;
I F = V T/R F ;
I A = I L − I F ;
E A = V T−I A∗R A ;
w = (1200/250)∗E A ;
tau = E A∗I A /(w∗2∗ p i /60) ;
w vec = [ w vec w ] ;
ta u ve c = [ ta u ve c tau ] ;
% part ( b )
I L = 200;
I F = V T/R F ;
I A = I L − I F ;
w = (1200/250)∗E A ;
tau = E A∗I A /(w∗2∗ p i /60) ;
,
364 / 412

Example 8-1 cont. II
DC shunt motor
% part ( c )
I L = 300;
I F = V T/R F ;
I A = I L − I F ;
w = (1200/250)∗E A ;
tau = E A∗I A /(w∗2∗ p i /60) ;
% part ( d )
p l o t ( tau vec , w vec ) ;
hold on ;
p l o t ( tau vec , w vec , ’ o ’ ) ;
g r i d on ;

AV-222
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1. Introduction
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(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
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- Universal motor
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
150 200 250 300 350 400 450 500 550 600
1110
1120
1130
1140
1150
1160
1170
1180
Torque (NM)
Angularvelocity(rpm)
366 / 412

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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
1 Input: constant
Terminal voltage, VT = 250 V is constant.
(remember that terminal voltage supplied by the user is used to
generate both field and armature currents)
2 System: unchanged
1 Stator (field): Since field resistance and VT are constant, IF
is constant and so flux φ is constant
2 Rotor (armature): The input and system are unchanged,
and so
EA0
EA1
= ω0
ω1
3 Output: changing
Load current IL increases from 100A to 200A to 300A
4 No load conditions IL = 0 ⇒ EA = VT
EA0
=250 V
ω0 =
1200 rev/min
60 sec/min
= 20 rev/sec
367 / 412

AV-222
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- DC
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- Brushed
- AC
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
• I need ω1, ω2, ω3 but I do not have EA1
, EA2
, EA3
• All I have is IL1
, IL2
, IL3
• So, let’s see how to get EA for a given IL
• We have 7 variables (3 unknown) and 3 equations:
1 VT
2 IL
3 IF : unknown
4 RF
5 EA: unknown
6 IA: unknown
7 RA
VT = EA + IARA
VT = IF RF
IL = IF + IA
368 / 412

AV-222
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- DC
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- Brushed
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3. Applications
4. Labs
5. Problems
,
Example 8-1 cont.
DC shunt motor
• I want a relation between IL and EA. We have:
(a) IA = IL − IF (b) IF = VT
RF
and therefore, IA = IL − VT
RF
,
VT = EA + IL − VT
RF
RA
⇒ 250 = EA + IL − 250
50
0.06
⇒ EA = 250 − 0.06(IL − 5)
⇒ EA1
= 244.3V (IL1
= 100A)
⇒ EA2
= 238.3V (IL2
= 200A)
⇒ EA3
= 232.3V (IL3
= 300A)
369 / 412

AV-222
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1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
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- Universal motor
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3. Applications
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5. Problems
,
Example 8-1 cont.
DC shunt motor
EA0
EA1
= n0
n1
⇒ 250
244.3 = 1200
n1
⇒ n1 = 1173 rpm
EA0
EA2
= n0
n2
⇒ 250
238.3 = 1200
n2
⇒ n2 = 1144 rpm
EA0
EA3
= n0
n3
⇒ 250
232.3 = 1200
n3
⇒ n3 = 1115 rpm
370 / 412

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5. Problems
,
Problem 8-1
DC shunt motor
371 / 412

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3. Applications
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,
Problem 8-1 cont.
DC shunt motor
372 / 412

AV-222
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- DC
- Linear
- Brushed
- AC
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- Universal motor
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3. Applications
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5. Problems
,
Problem 8-1 cont.
DC shunt motor
In this question, we use
EA1
EA2
= Kφ1ω1
Kφ2ω2
= ω1
ω2
, where φ1 = φ2
since the ﬁeld current does not change.
First, the no load condition gives us the ﬁrst two lines below, while KVL
and the magnetization curve gives us the third and fourth lines:
IF = 0.96A
ω1 = ? rpm
EA1 = 240 V (at no load)
ω1 = 1800 rpm
EA1 = 241 V (acting as generator)
This question can be done in 1 step:
1 We have
EA1
EA2
= ω1
ω2
⇒ 240
241
= ω1
1800
⇒ ω1 = 1793 rpm
NOTE: Just because rated velocity is 1800 rpm DOES NOT MEAN
that this is no-load velocity. It appears like that in Example 8.1(pg 472),
but over there, it is clearly mentioned that no load ω is 1200 rpm which
happens to be the same as the rated ω
373 / 412

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3. Applications
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5. Problems
,
Problem 8-1
DC shunt motor
• Notice that IF is held constant at 0.96A, whether no load or
whether loaded
• First operationg point: For the above IF , one possible
operating point that we get from the magnetization curve is
EA = 241 V and ω = 1800, and it appears that this
operating point is achieved IF the machine is acting as a
generator
• Second operationg point: For the above IF , another
possible operating point is at EA = 240 V, i.e., no load
374 / 412

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3. Applications
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5. Problems
,
Example 8-3
DC shunt motor
• The distortion of the ﬂux in a machine as the load is increased is
called armature reaction.
• To take care of this, compensating windings are connected in
series with the rotor windings, so that whenever the load changes
in the rotor, the current in the compensating windings changes,
too
Chapman 5th ed, pg 486, 433 (armature reaction), 443 (compensating windings)
375 / 412

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,
Example 8-3 cont.
DC shunt motor
376 / 412

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,
Example 8-3 cont.
DC shunt motor
377 / 412

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,
Example 8-3 cont.
DC shunt motor
378 / 412

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,
Example 8-3 cont.
DC shunt motor
379 / 412

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,
Example 8-3 cont.
DC shunt motor
380 / 412

AV-222
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1. Introduction
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- DC
- Linear
- Brushed
- AC
- Synchronous
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- Universal motor
- Reluctance motor
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3. Applications
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5. Problems
,
Example 8-3 cont.
DC shunt motor
EA1
EA2
= Kφ1ω1
Kφ2ω2
= φ1ω1
φ2ω2
. First, simple
KVL and the given fact that EA does not change, gives us
the first two lines below, while the magnetization curve gives us the
third and fourth lines:
IF 1 = 6A IF 1 = 5A
ω1 = 1103 rpm ω2 = ? rpm
EA1 = 246.4 V EA2 = 246.4 V
ω1 = 1200 rpm ω2 = 1200 rpm
EA1 = 268 V EA2 = 250 V
This question can be done in 2 steps:
1 We use the magnetization curve data (third and fourth lines) as
explained in this slide to get
EA1
EA2
= φ1ω
φ2ω
⇒ 268
250
= φ1
φ2
⇒ φ1
φ2
= 1.076
2 Now, using the KVL data (first and second lines), we get
EA1
EA2
= φ1ω1
φ2ω2
⇒ 1 = 1.0761103
ω2
⇒ ω2 = 1187 rpm
Notice that the field current ratio
IF 1
IF 2
= 6
5
= 1.2 is different from the
flux ratio φ1
φ2
= 1.076 showing the non-linearity due to saturation effects
381 / 412

AV-222
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1. Introduction
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(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-4
DC shunt motor
382 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-4 cont.
DC shunt motor
383 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-4 cont.
DC shunt motor
384 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-4 cont.
DC shunt motor
The important thing to note in this question is that although VA
changes, IA does not change as the load torque and ﬂux are constant
EA1 = VA − IARA = 250 − 120 ∗ 0.03 = 246.4V
EA2 = VA − IARA = 200 − 120 ∗ 0.03 = 196.4V
So,
EA1
EA2
= Kφ1ω1
Kφ2ω2
246.4
196.4
= 1103
ω2
⇒ ω2 = 879 rpm
Therefore, if we decrease the voltage VA on the rotor, its speed
decreases
385 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5
DC series motor
386 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5 cont.
DC series motor
387 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5 cont.
DC series motor
388 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5 cont.
DC series motor
389 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5 cont.
DC series motor
EA1
EA2
= Kφ1ω1
Kφ2ω2
= ω1
ω2
, where φ1 = φ2 since the
ﬁeld current does not change.
First, simple KVL gives us the ﬁrst two lines below, while the
magnetization curve gives us the third and fourth lines:
IA = 50A (NIA = 1250A)
ω1 = ? rpm
EA1 = 246 V
ω1 = 1200 rpm
EA1 = 80 V
This question can be done in 1 step:
1 We have
EA1
EA2
= ω1
ω2
⇒ 246
80
= ω1
1200
⇒ ω1 = 3690 rpm
390 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-5 cont.
DC series motor
Pconv = EAIA = τind ω
⇒ τind = EAIA
ω
= (246 V)(50 A)
(3690 rpm)(2π rad/rev)(1 min/60 sec)
= 31.8 NM
391 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-8
DC shunt motor: eﬃciency
392 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-8 cont.
393 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-8 cont.
394 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9
DC separately excited generator
395 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
396 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
397 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
398 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
399 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
400 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
401 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
402 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
DC generator: separately excited
(a)
IF = VF
Radj +RF
= 430
63+20
= 5.2 A
From the magnetization curve, this corresponds to EA = 430 V at
1800 rpm. However, the generator is rotating at 1600 rpm.
EA0
EA
= n0
n
derivation
430
EA
= 1800
1600
⇒ EA = 430×1600
1800
= 382 V
Since this is no-load, VT = EA = 382 V
403 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
(b)
IA = 360 A
EA = IARA + VT
382 = 360(0.05) + VT
⇒ VT = 364 V
404 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
(c) No compensating windings ⇒ armature reaction
IF = VF
Radj +RF
− 450 A turns
1000 turns
= 430
63+20
− 0.45
= 4.75 A
From the magnetization curve, this corresponds to EA = 410 V at
1800 rpm. However, the generator is rotating at 1600 rpm.
EA0
EA
= n0
n
derivation
410
EA
= 1800
1600
⇒ EA = 410×1600
1800
= 364 V
EA = IARA + VT
364 = 360(0.05) + VT
⇒ VT = 346 V (lower than before due to armature reaction)
405 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
(d) To restore VT to that in part (a), we need to increase EA.
For this, we need to increase IF .
For this, we need to decrease Radj .
406 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Example 8-9 cont.
(e) We have compensating windings, i.e., part (b) and we
want to restore VT from 364 V (part (b)) to the no-load 382 V
(part (a))
EA = IARA + VT
= (360)(0.05) + 382
= 400 V at 1600 rpm
400
EA
= 1600
1800
⇒ EA = 450 V at 1800 rpm
From the magnetization curve, this corresponds to IF = 6.15 A at
1800 rpm.
IF = VF
Radj +RF
6.15 = 430
Radj +20
⇒ Radj = 49.9Ω ≈ 50Ω
407 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Sample quiz
Questions
1 What is the difference between field and armature?
2 Draw the equivalent circuit of a DC motor.
3 In a DC machine, torque depends on which 2 quantities?
4 In a DC machine, induced voltage depends on which 2 quantities?
5 What is meant by flux?
6 What does the magnetization curve show?
7 In a transformer, what causes the voltage from the primary to
appear on the secondary?
8 Why is the startup current of a motor high?
9 If I want to develop an emf on a wire, what should i do?
10 If I want to develop a force on a wire, what should i do?
408 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Sample quiz cont.
Answers
1 What is the difference between field and armature? ”Field”
windings applies to the windings that produce the main magnetic
field in a machine, and the term ”armature” windings applies to
the windings where the main voltage is induced (Chapman, pg
267).
2 Draw the equivalent circuit of a DC motor. see here
3 In a DC machine, torque depends on which 2 quantities?
I = KφIA
4 In a DC machine, induced voltage depends on which 2 quantities?
v = Kφω
5 What is meant by flux? B field passing through a surface
6 What does the magnetization curve show? Plot of flux vs the
mmf producing it (Chapman, pg 21), or EA vs IF for a fixed speed
for a DC machine (537)
409 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Sample quiz cont.
Answers
7 In a transformer, what causes the voltage from the primary to
appear on the secondary? Refer to Chapman, pg 78
1 Voltage ep is applied on primary coil
2 Current ip flows through primary coil according to ep = ipRp
3 Flux φ is created according to Ampere’s Law which flows
through core
4 Since the flux is not changing, it does not induce a voltage
es on the secondary coil
5 Now, change voltage ep on the primary side. This causes a
changing current on the primary side, and therefore a
changing flux.
6 This changing flux causes an induced voltage s on the
secondary coil according to Faraday’s Law.
410 / 412

AV-222
readme
1. Introduction
2. Theory
(b) Power
(d) Mechanics
(e) Transformers
- DC
- Linear
- Brushed
- AC
- Synchronous
- Induction
- Other
- Universal motor
- Reluctance motor
- Hysteresis motor
- Stepper motor
- BLDC motor
- Servo motor
3. Applications
4. Labs
5. Problems
,
Sample quiz cont.
Answers
8 Why is the startup current of a motor high? Refer to Chapman,
pg 573
9 If I want to develop an emf on a wire, what should i do?
eind = (v × B). , i.e. move the wire with length at velocity v
through a magnetic ﬁeld B
10 If I want to develop a force on a wire, what should i do?
Find = i( × B), i.e. pass a current i through wire with length in
presence of magnetic ﬁeld B
411 / 412

Sample OHT
Questions
1 A 50-hp 250-V, 1200 r/min dc shunt motor with compensating windings has an armature
resistance (including brushes, compensating windings, and interpoles) of 0.06 Ω. Its field current
has a total resistance Radj + RF of 50 Ω, which produces a no-load speed of 1200 r/min. There
are 1200 turns per pole on the shunt field windings. Find the speed of this motor when its input
current is (a) 100A (b) 200A (c) 300A.
2 A 480-V, 60-Hz, ∆-connected, four-pole synchronous generator has the OCC shown below:
The generator has a synchronous reactance of 0.1Ω, and an armature resistance of 0.015Ω. At
full load, the machine supplies 1200A at 0.8PF lagging. Under full-load conditions, the friction
and windage losses are 40kW, and the core losses are 30kW. Ignore any field current losses.
(a) What is the speed of rotation? (b) How much IF must be supplied to the generator to make
VT = 480V at no load? (c) If the generator is now connected to a load and the load draws
1200A at 0.8 PF lagging, how much IF will be required to keep VT = 480V? (d) How much
power is the generator now supplying? (e) How much power is supplied by the prime mover?
3 Explain the operation of a synchronous generator operating at lagging power factor.
4 What is the difference between a DC machine, a synchronous machine and an induction machine?
,

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