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

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