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Institute of Mechatronics and Information Systems
Electric Machines
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Institute of Mechatronics and Information Systems
Witold Kubiak, Ph.D., M.Sc., Eng.
e-mail: [email protected]
www:
www.kubiak.imsi.pl
phone: 42 631 25 70
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Institute of Mechatronics and Information Systems
Fundamentals of electromagnetic phenomena
in electro-mechanic energy conversion
1.
2.
3.
4.
5.
Basic electrical quantities and dependencies
Basic magnetic quantities and properties
Basic mechanical quantities
Power conversion
Fundamental principles of electromagnetism
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Institute of Mechatronics and Information Systems
Basic electrical quantities
E - electromotive force (EMF) – [V] (volt)
U - voltage (potential difference) – [V] (volt)
I - current – [A] (ampere)
DC – direct current:
U
I
R
(Ohm’s law)
where:
R - resistance – [Ω] (ohm)
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Institute of Mechatronics and Information Systems
AC – alternating current
ut   Upeak sin t
- instantaneous value
where:
  2f
- angular frequency - [rad/s]
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Institute of Mechatronics and Information Systems
AC – alternating current
ut   Upeak sin t
- instantaneous value
where:
  2f
- angular frequency - [rad/s]
Upeak , (Um) - peak (maximum) value
URMS , (U) - root mean square value
Uav
- rectified average value
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Institute of Mechatronics and Information Systems
AC – alternating current
Ohm’s law:
U
I
Z
where impedance Z :
Z  R  jX
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Institute of Mechatronics and Information Systems
AC – alternating current
Reactance X depends on the type of reactive element.
Inductive reactance:
XL  jL
Capacitive reactance:
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XC 
jC
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Institute of Mechatronics and Information Systems
AC – alternating current
Reactance introduces a phase shift between the current and
voltage.
Voltage lagging current
XL  jL
Voltage leading current
1
XC 
jC
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Institute of Mechatronics and Information Systems
Basic electrical circuits dependencies
Kirchoff’s circuit laws:
n
U
k 1
k
0
n
I
k 1
k
0
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Institute of Mechatronics and Information Systems
Basic magnetic quantities
F
H
B
F
- magnetomotive force (MMF) – [A] (ampere)
- magnetic field strenght – [a/m] (ampere per metre)
- magnetic flux density – [T] (tesla)
- magnetic flux – [Wb] (weber)
F
F
R
(Hopkinson’s law)
where:
R - reluctance – [1/h] (1/henry)
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Institute of Mechatronics and Information Systems
Basic magnetic properties
Magnetisation curve in ferromagnetic materials
B   0r H
μ0 - permeability of vacuum [H/m] (henry per metre)
μr - relative permeability [-]
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Institute of Mechatronics and Information Systems
Basic magnetic properties
Hysteresis in ferromagnetic materials
BR - remanence
HC - coercivity
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Institute of Mechatronics and Information Systems
Basic magnetic dependencies
F   H dl
- magnetomotive force
F m   B ds - magnetic flux
S
n
F
k 1
k
0
- analogy to Kirchoff’s law
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Institute of Mechatronics and Information Systems
Basic mechanical quantities
Linear movement
F
x
- force – [N] (newton)
- position – [m] (metre)]
dx
v
dt
- velocity – [m/s] (metre per second)
dv
a
dt
- acceleration – [m/s2] (metre per second square)
F  ma
(Newton’s law)
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Institute of Mechatronics and Information Systems
Basic mechanical quantities
Rotational movement
M  Fr - torque – [Nm] (newton metre)
α
- angular position – [rad] (radian)]
d

- angular velocity – [rad/s] (radian per second)
dt
d

dt
M  I
- angular acceleration – [rad/s2] (radian per
second square)
(analogy to Newton’s law)
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Institute of Mechatronics and Information Systems
Energy conversion (transformation)
Win  Wout  Wak
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Institute of Mechatronics and Information Systems
Power conversion
Efficiency
PL
Pout


 1
Pin
Pin
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Institute of Mechatronics and Information Systems
Electric power
DC – direct current
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U
P  UI  I 2 R 
R
AC – alternating current, single phase
apparent power:
S  UI
real power:
P  UI cos 
reactive power:
Q  UI sin 
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Institute of Mechatronics and Information Systems
Electric power
AC – alternating current, three phase system
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Institute of Mechatronics and Information Systems
Electric power
AC – alternating current, three phase system
apparent power:
S  3U ph I ph  3UI
Delta connection (Δ, D, d)
I ph
I

3
Star connection ( , Y, y)
U
Uph 
3
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Institute of Mechatronics and Information Systems
Mechanical power
Linear movement:
P  Fv
Rotational movement:
P  M
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s circuital law:
 H dl   J dS   i N
C
S
k
k
k
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s circuital law:
F   H dl   i k Nk
C
k
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Faraday’s law of induction:
d
dF
e    B dS  
dt s
dt
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Faraday’s law of induction:
dF
e  N
dt
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s force
I 1I 2
F  0
2r
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Lorentz (Laplace) force
F  BIl
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Institute of Mechatronics and Information Systems
Thank You
for Your attention
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