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Unformatted text preview: EE321 Exam 2
Spring 2011 Notes: You must show work for credit on Problems 14.
The last page of exam has a piece of extra paper if needed. Good luck! 1.) 20 pts. Consider the magnetic system below. The permeability of the cores is inﬁnite,
and you may neglect fringing and leakage flux. The air gap g =3.14159 mm, w: 2.5
cm, and the depth into the page is 10 cm. Coil 1 has 100 turns (with a direction such that
positive current tends to cause ﬂux to go up in the leftmost leg) and a current of 10 A. Coil 2 has 100 turns (with a direction such that positive current tends to cause positive
flux to travel to the left through the coil) and a current of 40 A. What is the total ﬂux linkage for winding 2 (i.e. 22) ? SideView
/l 5 wet = ZEXWKlOKL’ —: 29’x10“5m"
R9 2 L = I “Ora : log H"
MA 47f x:o“7x252<I0'3
(VFC KCL a} Mood/Q A
FA 0*”000 74 £4 +F4+1+000 :0
(000,4 40004 a : ~3000//29 : 4000;? 3/129 452 = /0007L4000 c gar/0'3 Nb
429
22 2' Ajz¢2 1 0‘31/5 2.) 20 pts. Consider a four—phase multistack stepper motor. All phase currents are zero
except for the dsphase. The ds—phase inductance is given by L43. = 0.005 — 0.003 cos(49,. —7r/12) The machine is at a equilibrium point at 6,. = 0.5 rad under a load torque of 0.1 Nm. What is the dsphase current (you may assume it is positive)? Is this equilibrium point
stable or unstable? 4% Wtinl‘L/m far/“n #5" (Keg/Q f: 120‘le Wu: 24mm: 7&2 9%
Ear
A l 2;
: 5% 0003 gm C467“ ’T/Il) (0L3
>> (a? _~_ Mgr :5 0‘45 : 441/3 4
0006 gm (2»7f/r9.)
7” .
~27; = 4(0‘006) La? 49¢ wa/m) <0
7 :> 5mm eavz‘um‘vm MW" 3.) 20 pts. Consider a permanent magnet dc machine being fed from the one quadrant
chopper (buck converter) we discussed at length in class. The armature resistance is 100 mg), and kv = 0.1 Vs. It is desired to operate the machine so at to satisfy a load of l Nm at a speed of 3000 rpm. You may assume that the switching frequency is such that
operation is in continuous mode. If the dc voltage is 50 V, the forward switch voltage
drop is 1.5 V, and the forward diode voltage drop is 1 V, compute the system efﬁciency
of the buck converter / motor system at this operating point. L05: 3000 may at m 33/4. WMM 71:55"? Kev we ’a =1 IE, .2 ._L a m
Kv 0'!
Va 2 mm»; + 0~IX/007f 2: 32mm v
3 Va “WM a 67/5
VOLL”¥£M+VIAQ(
(’3: Oil; “ 6375A
Pout w VEWyQ /)(/oo7{” : 3/645W 4.) 10 pts. Consider a machine where Nm.=[01100—1—1001100—1—1001100—~1—10]T ( f g I 2
Find the winding function. P
m 2 am 52> W y 3 :6
Pct/ME?” Mae! 2
Nam L24
W/ 3 :1? é/Ug: :(WI+(+0>2/
M9, 1 /~@ a! » Waé 1{(104440) \IO"1“1~\O’,lkal~lw\oi] 5.) 6.) 7.) 8.) 9.) 10.) 11.) 12.) 13.) 14.) 3 pts, Suppose you are given a variable reluctance stepper motor. What technique can
you use to increase its advance torque? Hail; a (if if)me
3 pts. What it the chief di ference (it terms of the magnetics) between single and multi
stack stepper motors (even though we tend to ignore it)? MM trim/Q Lev}: Lang
3 pts. What is the chief advantage of the twotransistor per phase drive circuit over the
onetransistor per phase drive circuit we looked at? Lemma Masai. 3 pts. For a dc machine operated from a buck converter, for a given switching frequency
what duty cycle give the worst case current ripple? pi '; 0 ‘ ’5“
3 pts. In our derivations concerning discontinuous mode diode conduction time, what
value did we use to approximate the armature current? (q 2 {MK /2_
3 pts. What is a capability curve? é
\ .~ 1 WW Ce. ma Wm Cam. Q
QQQ’CQM. m Té VQUJ'D’ W at 3 pts. Which dc machine configuration is more apt to be suitable for very highspeed
operation — a shunt connected dc machine or a series connected dc machine? JWQQ» Carin <2 0552/ DC MW
3 pts. Consider the conductor distribution mm. = 500 COS(6¢S,,,). How many poles does
this machine have? 9/23: a 25 ﬁzz/2. 3 pts. In distributed winding machines, what is the purpose of the stator teeth? 75 Wat/(106' ﬂoat
3 pts. Consider a 4 pole machine. At an instant of time, the air gap ﬂux density from the
rotor to the stator has a value of 0.5 T at a position of 0.1 rad. At what position is the air
gap ﬂux density 0.5 T? (multiple correct answers are possible, you only need to name
one of these) 04+ “((2): vagt: a“ (67fo M
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