EM Devices Exercise Set #1
1. A square loop of wire, with each side length L, carries a current I. Find the magnitude and
direction of the magnetic intensity at the center of the loop.
2. A long, stra
EM Devices, Solutions to Exercise Set #2
Problem 1
Assume that H is uniform in the material around r, H dL
At a radius r, r1
So since B
r2 , 2 rH
r
H, B
B dA .
NI
,
2r
L
N
r
N 2a
ln( 2 )
2
r1
d
dI
drd
EM Devices Exercise Set #8
1. Consider 3phase D.C. brushless motor with 8 poles and 6 slots. The motor is wye wound
with a salient pole winding. Hall effect switches (HES) are used for position sens
EM Devices Exercise Set #2
1. For the toroid with a rectangular crosssection, made of a material of permeability
wrapped with N turns, shown below, show that the inductance L may be given by
N 2 a r2
EM Devices Exercise Set #3
1. A piece of grade 28 neodymium is 5 mm thick and 10 mm in diameter. The material has an
intrinsic coercivity of 1300 kA/m. It is to be magnetized at the center of a wire c
EM Devices, Solutions to Exercise Set #1
Problem 1:
For example in Lecture #1, the intensity at a distance r from a length of wire is
H
Irdz
2
L / 2 4 (r
z 2 ) 3/ 2
L/2
In this case, r
z2
L/2
L
.
2
2
EM Devices Exercise Set #5
1. Consider the VCM structure you built for HOMEWORK SET #4 (0.5 Tesla field over an
airgap of 0.004 m, 0.100 m in the direction of coil travel, and with a 0.100 m effective
EM Devices Exercise Set #4
1. With a soft iron core and Ferrite 5 permanent magnets, the design of the magnet structure for
a Voice Coil Motor is shown below. It is required to produce a 0.15 Tesla fi
EM Devices, Lecture #21: Torque Calculation using a Permeance Based Model in
Hybrid Steppers
First, a qualifier for the technique presented last time. The Fourier coefficients were
based on the assump
EM Devices, Lecture # 22: Torque Calculation using a Permeance Based Model in
VR Steppers
I.
Torque calculation in a single stack VR step motor
Previously, torque calculation was for a multistack VR
ME 229 Lecture #23 : Inductance Calculation in Stepper Motors
When stepper motors are operated at high rates of speed, the effects of phase inductance and
speedance become important. As the number of
EM Devices, Solutions to Exercise Set #5
Problem 1
1 / 2 Circuit !
Bg
0.5 T
Length of 1 loop is 2(0.300) + 2(0.050) = 0.7 m.
For 100 turns, length = 70 m.
For #26 AWG copper wire (d = 0.404mm),
R = 0.
ME229 Solutions
HW#8
EM Devices, Solutions to Exercise Set #8
Problem 1
motor
Phase 1 on
6 slot, 8 pole, 3phase commutates every 15o
Power sequence, from position shown
15o
15o
15o
15o
15o
+
0
0
+
0
EM Devices, Solutions to Exercise Set #9
Problem 1
Center  tapped wye winding
V1
Vo sin( t ) ,
V2
Vo sin( t 120o ) ,
V3 Vo sin( t
240o )
k = Torque constant, R = coil resistance.
There will be a back
EM Devices, Solutions to Exercise Set #7
Problem 1
Consider 8 pole / 9 slot motor that is wye wound with pattern AaABbBCcC.
1
2
3
For a single phase (e.g. 12), current pattern is looks like
T
Torque
EM Devices, Solutions to Exercise Set #6
Problem 1
Without shorted turn,
V
N 12 ( P
12
R1 I1
k f I1
m
P)
1
dI1
dt
ke x
dx
dt
with initial conditions:
dI1
dt 0
I1 ( 0 ) 0 ,
V
N1 ( P
12
2
P)
1
, x( 0 )
EM Devices, Solutions to Exercise Set #3
Problem1
R
I
I1
I
L
C
r
t
I2
Want I to produce > 2Hci and I to produce < Hci.
Since air is a linear material, H
I , thus I1 / I 2
2.
For an underdamped circuit
EM Devices, Solutions to Exercise Set #4
Problem 1
o
Am
, Pg
Lm
o
o
Br Am , Pm
Ag
Lg
Pg
,
g
o
Pm
Pg
Pair
In this case, there is a small section of air that must be added to the permeance of the magnet
EM Devices, Solutions to Exercise Set #10
Problem 1
(1) step angle
360
# teeth # phase
s
20
(2) Permeance can be approximated using the normalized permeance formula given in the class reader;
Tp
Wv
EM Devices Exercise Set #7
1. Consider the following rotary 3phase D.C. brushless motor for a precision spindle
application. The motor has 8 poles (on the rotor) and 9 slots (on the stator). The stat
EM Devices Exercise Set #9
1. A permanent magnet DC brushless motor has 9 slots and 6 poles. It is wound with a salient
pole centertapped wye winding. The back EMF pattern (and thus also the drive to
EM Devices Exercise Set #6
1. Consider the VCM structure below. In this structure, a coil of #26 AWG magnet wire, with
100 turns, pushes a carriage of 100 grams mass (plus the mass of the wire). The m
EM Devices, Lecture #18: Thermal Protection of Motors, Insulation Rating, UL
Standards
I.
Thermal Protection of Motors
A.
Mechanical Failure
B.
Electronic Failure
C.
Magnetic Failure
D.
Thermal Failur
EM Devices, Lecture #19: Stepper Motor Operation, Permanent Magnetic Steppers,
Hybrid Steppers
I.
Stepper Motors in General
A.
Characteristics
1.
2.
3.
B.
Provide incremental motion
Provide position c
EM Devices, Lecture 17: 3Phase Drivers, Hall Effect Switches, Switch Timing
Diagrams
I. Driver for Delta and Wye Wound Motors
For a delta wound motor, we use the following controller.
V+
1
2
3
V
Thi
EM Devices, Lecture #14: 2Phase Devices, Cores and Slots, Commutation
I.
Coreless Motors
Coreless motors are characterized by the following attributes:

contain no moving iron or magnets
similar t
EM Devices, Lecture #13 : Theory of the Shorted Turn
I.
The Shorted Turn
Sometimes in a VCM, the center pole is covered by a copper or aluminum sleeve.
magnet
airgap
center pole
shorted turn
coil (fre
EM Devices, Lecture #15 : 3Phase Devices, Demagnetization, Torque Constant vs.
Motor Constant
I.
Demagnetization in a Motor
The coils in a motor can act the coils in any magnetizing device. If too mu
EM Devices, Lecture #10: Coreless (BIL) Devices, the Voice Coil Motor
Simple reluctance devices are very good in applications that require an onoff function
only. They are inexpensive and can generat
EM Devices, Lecture #12 : Design Considerations, Configuration, some NonLinear
Effects
I.
VCM's Design Tradeoffs
A.
Choose an Application
(Have the class decide on an application)
B.
Design Constrai