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 assumption of straight line and arc approximations. These are
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 step motor.
165
For a single stack VR motor, we need to
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 turns, N, increases, and the airgap decreases
in an att
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 = 0.135
/m and mass per unit length is 0.001 kg/m.
Ans
Coil
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 emf from each coil with the same frequency as the appl
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 diagram
12
23
31
12BiLN
r
5
Problem 2
If wye winding
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 ) 0 , and x( 0 ) 0 .
With shorted turn,
V
R1 I1
N12 ( P12
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
Vo
e
dL
I (t )
t
sin
Vo
e
dL
From class notes, I1
Thus
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.
Bg Ag
Ag / Lg
( Br Am )
Am / Lm
Ag / Lg
(20 50 / 40)
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
drdz ,
NIa r2
ln( ) .
2
r1
NI
drdz
2r
0 r1
NI
,
2r
NI , H
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
I.
2L
Evaluating the integral gives H
For 4 sides, H
L/
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 Wt
Lg
Wv
Wt
1
20
From the table C0=9.363, C1/C0=0.2696,
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 stator is
wye wound with the pattern AaABbBCcC. Sketch the
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 sensing of the
rotor poles. Show 4 possible locations for t
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 torque
pattern) from each phase is perfectly sinusoidal.
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 magnetic
material is Ferrite 8B with Br = 0.420 T, Hc =
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 coil
length per wire turn). Assume that h = 0.150 m. I
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
ln
2
r1
,
r1
a
r2
2. With a soft iron core and a 15 VD
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, straight conductor carries a current density (in cylindrica
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 field over an
airgap of 0.004 m (direction of flux), 0.10
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 coil
magnetizing fixture, with a coil diameter of 12 mm.
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 Failure
1.
Magnetic Failure
2.
Coil/Insulation Failure
There
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 control without feedback, HED, or HES
Provide holding to
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
This generates the following phase torque diagram.
T
+1,2
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 to the moving coil in a VCM
low moving mass, perfect for
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 (free)
This sleeve, usually the thickness of a wire diamete
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 much current is
applied, in the wrong direction, the magn
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 generate a great deal of force over a small distance.
They are
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 Constraints and Restrictions
Energy (power) must be conserved.