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DEPARTMENT OF ELECTRICAL AND COMPUTING ENGINEERING
FINAL EXAMINATION
ELECTROMECHANICAL ENERGY CONVERSION
304462B
Examiner:
Professor B.T.Ooi
Date:
December 14,2002
Time
: PM (3 hours)
INSTRUCTIONS:
•
OPEN BOOK EXAMINATION
•
Answer all six questions.
Trigonometric Identities
cos(A+B)=cosAcosBsinAsinB
cos(AB)=cosAcosB+sinAsinB
sin(A+B)=sinAcosB+cosAsinB
sin(AB)=sinAcosBcosAsinB
[All dimensions are in meters. Field vectors are represented by bold letters, for example
B
and
K
. The directional vectors in cylindrical coordinates are:
u
r
,
u
ϕ
and
u
z
. The
superscript
T
denotes “transpose”.]
An electric machine consists of a cylindrical rotor inside an annular stator. They are
separated by an airgap “g” at a mean radius “R”. The stack length is “L”. The
permeability of the iron is infinite and the permeability of the airgap is
μ
o
.
Question 1
Two
4
pole stator windings carrying currents i
α
and i
β
produce sheet currents:
K
α
=
u
z
i
α
B
s
sin(
2
ϕ
) and
K
β
=
u
z
i
β
B
s
sin(
2
ϕ
90
0
)
respectively, where B
S
is the Fourier
coefficient of the fundamental space harmonic.
(a)
What are their magnetic density distributions
B
α
and
B
β
around the airgap?
(b)
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 Spring '09
 BonTekOoi

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