ME 108: Mechanical Behavior of Engineering Materials
Professor Grace OConnell, 5122 EH, g.oconnell@berkeley.edu.
Office Hours M & W 3-4:30pm or by appointment
Lectures: MWF 2-3pm, 277 Cory Hall
DESCRIPTION
This course covers elastic and plastic deformatio
Assigned: Week of Aug. 29
Fall 2016
Due: Week of Sept. 5
ME108 Laboratory Assignment 0:
Teaming with Diversity
The purpose of this laboratory assignment is to get to know your teammate, identify your teams goal,
and your own personal goal for ME108.
You h
ME108: Materials Overview
ME108, Fall 2016
Professor Grace OConnell
Copyright @ 2016 Grace D. OConnell
Announcements
Due today - Results from Learning Style Inventory
Upload onto bCourses
Next Week Lab 0
Bring your individual profile to lab
Sign safe
ME108: Lecture 2 - Overview of Materials
Professor Grace OConnell
August 26, 2016
Learning Objectives
Overview of types of material failure that affect mechanical and structural design
Cite three criteria that are important in the material selection pro
Math 108b Problem set 1 due: Friday January 16th, 2015 4:00 P.M
1. Wheeden-Zygmund pp. 11-12 gives two equivalent denitions for the Riemann
integral of a bounded function on an interval in Rn . One denition is that
inf U (f ) = sup L (f ),
where U (f ) an
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 multi-stack 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. 1-2), current pattern is looks like
T
Torque diagram
1-2
2-3
3-1
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 3-phase 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 3-phase 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 center-tapped 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 cross-section, 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