1 Institute of Mechatronics and Information Systems Electric Machines.
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Transcript of 1 Institute of Mechatronics and Information Systems Electric Machines.
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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. Basic electrical quantities and dependencies2. Basic magnetic quantities and properties3. Basic mechanical quantities4. Power conversion5. 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:
(Ohm’s law)
where:
R - resistance – [Ω] (ohm)
RU
I
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Institute of Mechatronics and Information Systems
AC – alternating current
- instantaneous value
where:- angular frequency - [rad/s]
tsinUtu peak
f2
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Institute of Mechatronics and Information Systems
AC – alternating current- instantaneous value
where:- angular frequency - [rad/s]
Upeak , (Um) - peak (maximum) value
URMS , (U) - root mean square value
Uav - rectified average value
tsinUtu peak
f2
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Institute of Mechatronics and Information Systems
AC – alternating current
Ohm’s law:
where impedance Z :
ZU
I
jXRZ
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Institute of Mechatronics and Information Systems
AC – alternating currentReactance X depends on the type of reactive element.
Inductive reactance:
Capacitive reactance:
LjXL
Cj1
XC
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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
Voltage leading current
LjXL
Cj1
XC
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Institute of Mechatronics and Information Systems
Basic electrical circuits dependencies
Kirchoff’s circuit laws:
0In
1kk
0Un
1kk
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Institute of Mechatronics and Information Systems
Basic magnetic quantities
F - magnetomotive force (MMF) – [A] (ampere)
H - magnetic field strenght – [a/m] (ampere per metre)
B - magnetic flux density – [T] (tesla)
- magnetic flux – [Wb] (weber)
(Hopkinson’s law)
where:
R - reluctance – [1/h] (1/henry)
RF
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Institute of Mechatronics and Information Systems
Basic magnetic properties
Magnetisation curve in ferromagnetic materials
μ0 - permeability of vacuum [H/m] (henry per metre)
μr - relative permeability [-]
HB r0
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Institute of Mechatronics and Information Systems
Basic magnetic propertiesHysteresis in ferromagnetic materials
BR - remanence HC - coercivity
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Institute of Mechatronics and Information Systems
Basic magnetic dependencies
- magnetomotive force
- magnetic flux
- analogy to Kirchoff’s law
Sm ds B
dl H F
0n
1kk
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Institute of Mechatronics and Information Systems
Basic mechanical quantities
Linear movementF - force – [N] (newton)
x - position – [m] (metre)]
- velocity – [m/s] (metre per second)
- acceleration – [m/s2] (metre per second square)
(Newton’s law)
dtdx
v
dtdv
a
maF
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Institute of Mechatronics and Information Systems
Basic mechanical quantitiesRotational movement
- torque – [Nm] (newton metre)
α - angular position – [rad] (radian)]
- angular velocity – [rad/s] (radian per second)
- angular acceleration – [rad/s2] (radian per second
square) (analogy to Newton’s law)
dtd
dtd
FrM
IM
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Institute of Mechatronics and Information Systems
Energy conversion (transformation)
akoutin WWW
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Institute of Mechatronics and Information Systems
Power conversion
Efficiency
in
L
in
out
P
P1
PP
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Institute of Mechatronics and Information Systems
Electric power
DC – direct current
AC – alternating current, single phase
apparent power:
real power:
reactive power:
RU
RIUIP2
2
cosUIP
UIS
sinUIQ
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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:
Delta connection (Δ, D, d) Star connection ( , Y, y)
3I
Iph
UI3IU3S phph
3U
Uph
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Institute of Mechatronics and Information Systems
Mechanical power
Linear movement:
Rotational movement:
FvP
MP
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s circuital law:
k
kkSCNidS J dl H
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s circuital law:
k
kkCNidl H F
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Faraday’s law of induction:
dtd
dS B dtd
es
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Faraday’s law of induction:
dtd
Ne
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Ampere’s force
r2II
F 210
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Institute of Mechatronics and Information Systems
Fundamental principles of electromagnetism
Lorentz (Laplace) force
lBIF
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Institute of Mechatronics and Information Systems
Thank You for Your attention