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Unformatted text preview: ECE 430 Exam #2, Spring 2009 Name: g0 I ‘A ‘HOV‘
90 Minutes Section (Check One) MWF TTH 1. /25 2. /25 3. /25 4. /25 Total /100 Useﬁll information #0 = 47:.10'7 H/m fCHd1=jSJ.nda ICEdl=—a—at [SBnda 92:1; MMF:N2’=¢ER B=,uH ¢=BA A=N¢ 2=Li(if1inear)
,u :_ m 6x 6x Wm=idi Wm’2Iﬂtdf Wm+W,,’,=/tz' fe—an 6W x—w
0 fe_9Te
b I
15%;“: idl EFM=— fedx €§§+EFM=erWm 1:6Wm  6W»: l :
a—>b 4'95
a 61' 8/7. 1. (25 points) A 2phase machine, with two stator coils and one rotor coil, has following ﬂux linkagecurrent relationship 13,, L5 0 McosB isa 2,3,, = 0 LS Msine x isb A, Moose MsinG Lr ir
a) Compute the co—energy W "'1 (10 points)
b) Compute the energy Wm (5 points)
0) Find the torque of electrical origin Te (10 points) x 1/ ’ J '7' . . u .. . t
A\ Wm :% 365’“, ‘l' lljcs‘s 4' m/dﬁQg‘F/ I’mg‘ﬂaggcr fillrc/ // a l ( {PM a 5757377“) 2. (25 points) The ﬁgure below shows a magnetic strucuture composed of an iron core and a moveable iron
plunger. The plunger is connected to a solid structure through a spring with stiffness coefﬁcient
K. The spring exerts no force when the plunger is located at x = C. The plunger is separated
from the core by a constant gap of length g above and below the plunger. The horizontal length
of the plunger is W. The plunger and the core both have a depth of D. The iron core and plunger
both have inﬁnite permeability. You should neglect fringing in the air gaps. You may neglect
the force of gravity and all friction. Depth: D [1—900 For V = det, a) Find the ﬂux linkage )L in terms of current i and position x plus no, N, V/, g, and D. b) Find the force of electric origin either in terms of ﬂux linkage 9t and position x, or in terms of
current i and position x (whichever you prefer). c) Select either ﬂux linkage 9» or current i as an independent state and write the three differential
equations that describe all of the dynamics of this electromechanical system with voltage v as the only input. P2 . N1,“ (w... 150 .
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; 4d7<rc8 2 DH?” (Wad 3. (25 points) The co—energy of a device is given by 51' 6/ z 6 Z ‘
.5 .3 . _ A ‘
W / "a = L + L. + .1. C {—— ‘l’ ‘f— + max) 24x 6x x (A iii 6* X Find: i a) The force of electrical origin f e (i, x) b) The energy stored in the coupling ﬁeld Wm as a function of i and x. (,,CC ,3”!
M\ ’F ’ mL 41" X7" 4. (25 points) An electromechanical system has a nonlinear ﬂux linkagecurrent relationship: 12
1':—
x a) Find the energy stored in the coupling ﬁeld when i = 2.0 Amps, x = 0.02 m, k = 0.2 Wan
b) Find the force of electric origin when i = 2.0 Amps, x = 0.02 In, 9» = 0.2 Wan c) Find the energy transferred from the mechanical system into the coupling ﬁeld (EFM) as the
position x changes from 0.02 m to 0.01 m along a constant ﬂux linkage (0.2 Wan) path. VA
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 Spring '12
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