Master Thesis Design and Construction of the Shutter Demonstrator

Transcription

Master Thesis
Design and Construction of the Shutter
Demonstrator Model for the Mercury Radiometer
and Thermal Infrared Spectrometer
Dipl.-Ing. (FH) Andreas Hurni
from Bern, Switzerland
Thesis submitted in partial fulfillment of the requirements
for the degree of Master of Science (M.Sc.)
University of Applied Sciences Munich
Department of Precision- and Micro-Engineering, Engineering Physics
Master’s program Micro- and Nanotechnology
Examiner:
Prof. Dr. rer. nat. Rolf Heilmann
Second examier:
Prof. Dr.-Ing. Rainer Froriep
Supervisor:
Day of submission:
Dr.-Ing. Thomas Zeh, Kayser-Threde GmbH Munich
July 31, 2008
Munich 2008
We verify that this thesis satisfies the requirements of the graduate school as approved
by the graduate faculty.
———————————————
———————————————
Prof. Dr. rer. nat. Rolf Heilmann
Prof. Dr.-Ing. Rainer Froriep
Acknowledgements
Writing a thesis about a self conceived mechanism once flying to an orbit of another
planet is an amazing fortune, when I thinking about my unbroken fascination of space
flight since childhood. Furthermore, to combine it with the attained knowledge of the
basic studies in microtechnology, and improve it to culminate in a degree of Master of
Science in micro- and nanotechnology causes a big satisfaction, which I like to share
with all concerned persons.
First of all I like to thank Dr. Thomas Zeh to make this topic possible for writing
my master thesis. His support and cooperativeness was exceptionally positive during
whole the work. Special thanks go to Hans-Georg Preißler, Marion Rost, Dr. Michael
Leininger, Markus Manhart and many others from Kayser-Threde GmbH for their
design-engineering support and the profitable discussions.
Of course I like to express my gratitude to the examiners Prof. Dr. rer. nat. Rolf
Heilmann and Prof. Dr.-Ing. Rainer Froriep for their support on the part of the
University of Applied Sciences Munich.
For the discussions about the mechanical optimizations and the sometimes exhausting
encouragements to finish this work, I don’t want to miss to thank Thomas Wenger.
And of course, Anna, thank you very much for the time with you besides working on
this thesis for gaining new energy everytime.
Andreas Hurni
Munich
July 2008
i
Abstract
Exploring Mercury, the planet closest to the Sun, can offer valuable clues to the formation of the solar system and the Earth itself. However, accurate investigations must be
performed locally. This encouraged the ESA to launch the BepiColombo mission. The
on-board infrared spectrometer MERTIS will thereby globally map the mineralogical
surface. To substract disturbing radiation from the wanted spectrum, a shutter is required inside the instrument. The goal of this master thesis is to design and construct
the demonstrator model of this shutter.
Based on the results of a precedent shutter actuation principle study, just a voice
coil driven shutter guided with a flexible hinge structure can fulfill all requirements.
Besides the definition of the mechanical design, a helmholtz coil shaped setup was
determined for the voice coil actuator after theoretical analyses.
A power amplifier with a contol circuit was designed for reaching the required switching
mode of the shutter blade. Test measurements with the manufactured demonstrator
model in the closed loop system showed, that the requirements can be fulfilled with
the selected design. When the verification tests of the complete instrument will show
positive results as well, the flight model of the shutter shall finally be built based on
this demonstrator.
ii
Zusammenfassung
Durch seine Nähe zur Sonne kann die Erforschung des Merkurs Aufschlüsse über die
Entstehung des Sonnensystems und damit auch der Erde geben. Genauere Untersuchungen müssen hierfür jedoch vor Ort gemacht werden, was die ESA dazu veranlasst hat, die BepiColombo Mission ins Leben zu rufen. Das mitfliegende Infrarotspektrometer MERTIS wird dabei den Merkur auf mineralogischer Ebene kartieren.
Dazu ist ein Kameraverschluss notwendig, um Störstrahlungen zu messen, damit das
Nutzspektrum kalibriert werden kann. Ziel dieser Masterarbeit ist die Entwicklung
und Konstruktion des Demonstrator Modells dieses sogenannten Shutters.
Die Entwicklung basiert auf den Resultaten einer im Vorfeld durchgeführten Studie
über anwendbare Shutterprinzipien. Dabei hat sich als einzige Lösung, welche allen
gestellten Anforderungen gerecht werden kann, ein Voice-Coil-Antrieb geführt von
einer Festkörpergelenkstruktur herausgestellt. Nach theoretischen Analysen wurde
neben der Festlegung des Mechanik-Designs eine helmholtzartige Spulenanordnung
für den Voice-Coil-Antrieb definiert.
Zum Erreichen des geforderten Schaltzyklus wurde einhergehend mit der Endstufe eine
Regelelektronik entworfen und aufgebaut. Messungen mit dem gefertigten Demonstrator Model des Shutters, eingebaut im Regelkreis, zeigten als Resultat, dass die Anforderungen mit dem gewählten Design erfüllt werden können. Bei positiven Testergebnissen nach dem Einbau im Instrument soll zu einem späteren Zeitpunkt aufbauend
auf diesem Demonstrator letztendlich das Flugmodel gebaut werden können.
iii
Abbreviations
AlNiCo Aluminum Nickel Cobalt
DM Demonstrator Model
EDM Electrical Discharge Machining
FEM Finite Element Method
FH Flexible Hinge
MEOP MERTIS Entrance Optics
MERTIS Mercury Radiometer and Thermal Infrared Spectrometer
MMO Mercury Magnetospheric Orbiter
MPO Mercury Planetary Orbiter
MRAD MERTIS Radiometer Focal Plate and Slit
MSOP MERTIS Spectrometer Optics
MSTS MERTIS Short Term Shutter
NdFeB Neodymium Iron Boron
OPAMP Operational Amplifier
SmCo Samarium Cobalt
VCA Voice Coil Actuator
iv
Notations
aF H Aspect Ratio of the Flexible Hinge
B Magnet Field
BHmax Maximum Magnetic Energy Product
b Width of the Flexible Hinge
c Spring Constant
cH Heat Capacity
D Damping Ratio
d Helmholtz VCA Clearance
DC Coil Diameter
dC Coil Wire Diameter
dL Magnet Length
dM Magnet Diameter
E Young’s Modulus
e Error Signal
EV CA Total VCA Energy
F Dynamic Force
v
f Deflection of the Flexible Hinge
(1)
feig 1st Eigenfrequency
fres Resonant Frequency
FV CA Lorentz Force
GF H (s) Transfer Function of the Mechanical Part
GV CA (s) Transfer Function of the Electromagnetic Part
h Thickness of the Flexible Hinge
hC Coil Winding Height
I Geometrical Moment of Inertia
IC Coil Current
KF Force Factor
k Attenuation Constant
L Coil Inductance
l Length of the Flexible Hinge
LC Coil Wire Length
lC Coil Length
M Bending Moment
m Mass
N Number of Windings of the Coil
Nc Buckling Load
P Force applied on the Flexible Hinge
PC Power Dissipation of the Coil
vi
RC Coil Resistance
r Feedback Variable
Se0 Endurance Strength
TC Curie Temperature
UC Coil Voltage
w Set Point
x Control Variable
y Actuating Variable
z Disturbance Variable
∆ Oscillation Amplitude
δ Logarithmic Decrement
Thermal Efficiency
ζ Glue Thickness
λT Thermal Conductivity Coefficient
µ0 Vacuum Permeability
ξ Ratio of the Necked Down Flexure
ρ Mass Density
ρC Electrical Resitivity
τL Time Constant of the Inductance
χ Magnet Clearance
vii
Contents
page
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1
1
BepiColombo Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 About the Mission . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
1.1.2
Technological Challenges . . . . . . . . . . . . . . . . . . . . . .
2
MERTIS Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.1
1.2.2
Scientific Goals . . . . . . . . . . . . . . . . . . . . . . . . . . .
Instrument Setup . . . . . . . . . . . . . . . . . . . . . . . . . .
3
4
1.2.3
Short Term Shutter . . . . . . . . . . . . . . . . . . . . . . . . .
4
2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2
2.1
2.2
Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
7
3 Shutter Actuation Principles . . . . . . . . . . . . . . . . . . . . . . . .
9
3.1
Shutter Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3.2
Study Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
4.1
Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
4.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
4.1.2
4.1.3
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
13
4.1.4
Wire-Cut EDM . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
viii
Contents
4.1.5
Stage with two Parallel Blades . . . . . . . . . . . . . . . . . . .
15
4.1.6
Technological Limitations . . . . . . . . . . . . . . . . . . . . .
18
4.1.7 Linear Stage with Necked Down Flexures . . . . . . . . . . . . .
Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
19
4.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
4.2.2
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
Electromagnetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
21
4.3.2
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
4.3.3
Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
4.3.4
4.3.5
Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cylindric Single Coil VCA . . . . . . . . . . . . . . . . . . . . .
23
23
4.4
Interaction Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
4.5
Control
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
28
5 Analysis, Calculations and Experiments . . . . . . . . . . . . . . . . .
30
4.2
4.3
4.5.1
4.5.2
5.1
Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
5.2
Finite Element Calculations . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Electromagnetic FEM . . . . . . . . . . . . . . . . . . . . . . .
33
33
5.2.2
Mechanical FEM . . . . . . . . . . . . . . . . . . . . . . . . . .
33
5.3
Cylindric Single Coil VCA Experiments . . . . . . . . . . . . . . . . . .
34
5.4
5.5
Flexible Hinge Experiments . . . . . . . . . . . . . . . . . . . . . . . .
Parallel Blade Stage VCA . . . . . . . . . . . . . . . . . . . . . . . . .
35
36
5.6
Helmholtz VCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
6 MERTIS Short Term Shutter Demonstrator Model . . . . . . . . . .
46
6.1
6.2
6.3
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
46
6.2.1
MSTS FH Structure . . . . . . . . . . . . . . . . . . . . . . . .
48
6.2.2
Mounting Part . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
Electromagnetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
ix
Contents
6.4
Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
6.4.1
Static Measurement . . . . . . . . . . . . . . . . . . . . . . . . .
51
6.4.2
Dynamic Measurement . . . . . . . . . . . . . . . . . . . . . . .
51
7 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
7.1
Control Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
7.1.1
Power Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
7.1.2
7.1.3
Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
55
Control Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
8 Conclusions, Status and Open Work . . . . . . . . . . . . . . . . . . .
58
7.2
APPENDIX
A Deviation of the Logarithmic Decrement . . . . . . . . . . . . . . . . .
61
B MSTS DM Design Drawing . . . . . . . . . . . . . . . . . . . . . . . . .
63
C MSTS DM Breadboard Electronics Circuit Diagram . . . . . . . . .
65
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
x
Chapter 1
Introduction
1.1
1.1.1
BepiColombo Mission
About the Mission
BepiColombo1 , an ESA mission in cooperation with Japan, will explore Mercury, the
planet closest to the Sun. Europe’s space scientists have identified the mission as one of
the most challenging long-term planetary projects, because Mercury’s proximity to the
Sun makes it difficult for a spacecraft to reach and survive in the harsh environment.
The scientific interest to go to Mercury lies in the valuable clues that such a mission
can provide in understanding the planet itself as well as the formation of our Solar
System—clues which cannot be obtained with distant observations from Earth.
Only NASA’s Mariner 10 and MESSENGER have visited Mercury so far. Mariner
10 provided the first-ever close-up images of the planet when it flew past three times
in 1974 - 1975. En route to its final destination in orbit around Mercury in 2011,
MESSENGER flew past the planet on January the 14th , 2008, providing new data
and images. The information gleaned, when BepiColombo arrives in 2019, will throw
light not only on the composition and history of Mercury, but also on the history and
formation of the inner planets in general, including the Earth.
The mission will consist of two separate spacecrafts that will orbit the planet. ESA is
building one of the main spacecraft, the Mercury Planetary Orbiter (MPO) and the
1
Named after Giuseppe Colombo (October 2, 1920 - February 20, 1984), Italian scientist, mathematician and engineer. He is best known for his orbit calculations on planet Mercury.
1
1 – INTRODUCTION
Figure 1.1: Emblem of the BepiColombo mission.
Japanese space agency ISAS/JAXA will contribute the other, the Mercury Magnetospheric Orbiter (MMO). The MPO will study the surface and internal composition
of the planet and the MMO will study Mercury’s magnetosphere, the region of space
around the planet that is dominated by its magnetic field.
1.1.2
Technological Challenges
With two spacecrafts, BepiColombo is a large and costly mission, one of the cornerstones in ESA’s long-term science programme. The mission presents enormous, but
exciting challenges. All of ESA’s previous interplanetary missions have been to relatively cold parts of the solar system. BepiColombo will be the agency’s first experience
of sending a spacecraft to hot regions.
The journey from Earth to Mercury will also be a first. After launch into a geostationairy transfer orbit, the Mercury composite spacecraft will be boosted to the
phasing orbit using chemical propulsion. From here the spacecraft will be set on its
interplanetary trajectory through a flyby of the Moon. On its way to Mercury, the
spacecraft must brake against the Sun’s gravity, which increases with proximity to the
Sun, rather than accelerate away from it, as is the case with journeys to the outer Solar
System. BepiColombo will accomplish this by making clever use of the gravity of the
Earth, Venus and Mercury itself and by using solar electric propulsion. This innovative
combination of low thrust space propulsion and gravity assist has been demonstrated
by ESA’s technology mission SMART-1.
When approaching Mercury, the spacecraft will use the planet’s gravity plus conventional rocket engines to insert itself into a polar orbit. A special weak stability
boundary capturing technique is employed. This gives flexibility and is more robust
2
1 – INTRODUCTION
against failures compared to using the more traditional “big kick” approach (single
burn capture). The MMO will be released into its operational orbit, then the sunshield
and the MMO interface structure will be separated while the chemical propulsion system will bring the MPO to its lower orbit. Observations from orbit will continue for
one Earth year2 .
1.2
MERTIS Instrument
1.2.1
Scientific Goals
The scientific goal of the Mercury Radiometer and Thermal Infrared Spectrometer
(MERTIS) is to provide detailed information about the mineralogical composition of
Mercury’s surface layer by measuring the spectral emittance of different locations.
Knowledge of the mineralogical composition is crucial for choosing the best of several
competing theories, and thus for selecting the valid model for origin and evolution
of the planet. MERTIS has four main scientific objectives, building on the general
science objectives of the BepiColombo mission:
• study of Mercury‘s surface composition,
• identification of rock-forming minerals,
• global mapping of the surface mineralogy and
• study of surface temperatures and the thermal inertia.
The instrument covers the range from 7 − 14 µm at a high spectral resolution of up to
90 nm which can be adapted depending on the actual surface properties to optimize
the signal-to-noise ratio (S/N). MERTIS will globally map the planet with a spatial
resolution of 500 m and a S/N of at least 100. The flexibility of the instrumental setup
will allow to study the composition of the radar bright polar deposits for an assumed
surface temperature of 200 K.
2
http://www.esa.int/esaSC/120391_index_0_m.html accessed on June 4, 2008.
3
1 – INTRODUCTION
1.2.2
Instrument Setup
The MERTIS instrument (fig. 1.2) is an IR-imaging spectrometer based on the pushbroom principle which is located on the MPO. It is based on an uncooled microbolometer array providing spectral separation and spatial resolution according to its
two-dimensional shape. The operation concept principle is characterized by intermediate scanning of the planet surface and three different calibration targets—free space
and two on-board black body sources. Sharing the same optical path, a pushbroom
radiometer is implemented according an in-plane separation arrangement. The general
instrument architecture showed in figure 1.3 comprises two separate parts—the sensor
head (SH) including optics, detector and proximity electronics and the electronics unit
(EU) containing sensor control and driving electronics, as well as the power supply.
This highly integrated measurement system is completed by a pointing device which
orients the optical path to the planet and the calibration targets.
1.2.3
Short Term Shutter
For spectrometer data acquisitions a reference signal representing the instruments
background ratiation is necessary for on-board data processing and for on-ground calibration. This is performed by periodical acquisitions without the targets scene/planet
radiation. Therefore a shutter is foreseen, the MERTIS Short Term Shutter (MSTS),
covering the optical slit by closing the MSTS. The designated integration position of
the MSTS in the MERTIS instrument is indicated with the red dashed ellipse in figure
1.2.
Within this master thesis, the Demonstrator Model (DM) of the MSTS shall be designed and constructed, which finally shall prove its functionality after integration in
the MERTIS instrument.
4
1 – INTRODUCTION
BepiColombo
MERTIS
Reference:
MER-DLR-TN-007
Issue:
Draft
Date:
25.05.2007
Page:
2
Rev: 1
Figure 1.2: MERTIS instrument model with the MSTS integration position indicated
with the red
dashed
ellipse
[12].
The main
parameters
of the
instrument are given in table Table 2.2-1
Space View
S/C Radiator
MSBA
MRBA
MSHS
Planet View
MSTS
MLTS
MRAD
MBOL
S/C MLI
MBEL
MPOI
MBEL / MHKE
MBB3
MSOP
MRED
MEOP
MOST
MBB7
MHAR
MICU
MPSU
EU
Fig.
2.2-1 1.3:
MERTIS
structure block
diagram
Figure
MERTIS
instrument
Parameter
Focal length
F – number
Optical efficiency
Microbolometer array detector
x illuminated pixels
µRAD thermopile line array
Spectral channel width
Spectral resolution
Spectral range
Unit
block diagram [12].
Spectrometer
F
F#
Kopt
pixels
OG
O/OG
O
S/C Instrument Panel (TRP) -20 …+40°C ±5K/ Orbit
SH
Radiometer (µRAD)
50 mm
2.0
0.54
160 x 120 @ 35 µm
100 spatial
80 spectral
7 – 14 Pm
2 x 15 @ 250 µm
90 nm / pixel
78 – 156
7 – 40 µm
5
Chapter 2
Boundary Conditions
2.1
Requirements
A first requirement compilation for the MSTS was proposed from the MERTIS instrument team at the German Aerospace Center (DLR) in spring 2007. Table 2.1 lists the
reviewed requirements annotated with priorities. Further boundary conditions which
must be considered are summarized in the experiment interface documents [11] and
[12].
The shutter blade must cover the slit periodically as expressed in figure 2.1. Hereby,
the required velocities and accelerations of the blade can be estimated and used for
the selection of an applicable shutter actuation principle presented in the following
chapter.
Lifetime and fail safe are quoted as most important requirements. When multiplying
the lifetime of two years with one closing and one opening stoke in a period of 109 ms,
a total number of cycles of 1.577 · 109 results [5]. A required security factor of 1.25
for moving mechanical components [11] increases the number of cycles to around two
billion. If the MSTS will fail, the shutter blade shall never cover the infrared light
beam to guarantee at least resticted operation of the instrument. Therefore, a fail safe
mechanism shall be foreseen in the MSTS design.
It must be mentioned, that several requirements and priorities had changed during
the design phase. Some of them had to be discussed due to installation interferences
with other MERTIS components. However, table 2.1 lists the requirements which were
valid during the shutter actuation principle study.
6
Contrast ratio
tbd
tbd
Reflector surface
properties (e.g.
max. radiation
power, absorption)
tbd
tbd
2 – BOUNDARY CONDITIONS
Switching mode
10 ms
99 ms
200 ms
close
close
open
open
19,8 s
= 109
ms, f =blade
9,2 Hz
T = 20 s, f = 0,05 Hz
FigureT2.1:
Shutter
switching mode.
2.2
Table 2-1: STS and LTS requirements
Integration
As indicated in figure 1.3, the MSTS shall be integrated between the MERTIS Entrance Optics (MEOP) and the MERTIS Spectrometer Optics (MSOP). The light
beam escapes from the MEOP and then passes the MERTIS Radiometer Focal Plate
and Slit (MRAD) before it will be blocked by the MSTS blade during its closed phase.
The blade shall be placed with a distance of 0.5 mm to MRAD in direction of the beam
propagation.
C:\Dokumente und Einstellungen\Andreas Hurni\Desktop\MSTS\Papers & Presentations\MER-KTM-TN-005-Issue-1 Draft_c_Shutter_Study_05.09.2007.doc
This document
is proprietary.
dispatch
or disclosure
of content
is authorized
only after written
authorization
by Kayser-Threde.
The MRAD
consists
of aAny
tiny
silicon
plate
without
providing
space
for furter
mounting
Kayser-Threde GmbH, Wolfratshauser Str. 48, 81379 Munich, Germany, Tel.:+49 (0) 89 / 72495-0, E-Mail: [email protected], www.kayser-threde.com
screws. Therefore, the MSTS shall be mounted at the MSOP housing. Figure 2.2 shows
a bird’s eye view of the MSTS integration space.
When considering the slit dimensions (tab. 2.1), it is reasonable that the blade stroke
shall be oriented across the slit width for fast operation. Enough space for mounting
the MSTS on the MSOP housing is provided at the right side of the window (fig. 2.2).
All boundary conditions had to be considered for the study and the ultimate selection
of the shutter actuation principle.
7
2 – BOUNDARY CONDITIONS
Figure 2.2: Bird’s eye view of the MSTS integration space between the MEOP (grey)
and MSOP (light blue). The MSTS shall be placed in front of the MSOP window
close to the MRAD (wine red).
Property
Weight
Dimensions
Frequency (fig. 2.1)
Close time
Open time
Close area
Lifetime
Power consumption
Control
Mechanical robustness
EMC properties
Operation temperature range
Non operation temperature range
Space qualification
(e.g. out gassing, radiation, vacuum)
Fail safe integration
Position feedback
Temperature feedback
Applicability for IR
Value
25 g
max. 20 × 20 × 5 mm3
worst case 10 Hz,
depends on operation
max. 6 ms
max. 6 ms
slit area: ca. 1.5 × 5 mm incl.
overlap
2 years
average 0.6 W at 3.3 V (3 W peak)
3.3 V digital
nominal as specified in section
3.2.3.4 in [11]
low conducted and radiative
emission
−30 . . . 50 ◦ C without heater,
0 . . . 50 ◦ C with heater
−30 . . . 50 ◦ C
yes
yes, fail open
yes, closed / open
yes
7 − 14 µm
Priority
3
2
2
2
2
3
3
2
1
3
2
2
2
3
3
2
3
3
Table 2.1: MSTS requirements and their design priorities weighted from 1 (lowest
priority) to 3 (highest priority).
8
Chapter 3
Shutter Actuation Principles
3.1
Shutter Study
In a preliminary phase of the MSTS design, common shutter actuation principles and
mechanisms were studied and summarized in [5]. Already space qualified or even flown
actuators were particularly investigated. However, no one of these shutter mechanisms
can fulfill all boundary conditions listed in table 2.1. Nevertheless, a lot of information
about actuation principles and control electronics designs could be gathered.
The investigated actuation principles comprise
• motor driven shutters,
• electromagnetic field driven shutters,
• piezo actuator driven shutters and
• piezo motor driven shutters.
The actuation principles of these four shutters are sketched in figure 3.1. Termed as
non applicable principles for the MSTS, but listed for the sake of completeness are
• opaque fluid based optical shutters and
• liquid crystal optical shutters.
The most promising and withal space qualified shutter design considered in [5] is
the Laser Chopper Mechanism (LCM) included in the ALADIN instrument for the
ADM-Aeolus satellite which will be launched in 2009 [9]. This voice coil based shutter
mechanism persisted > 6 · 109 cycles in the testing phase.
9
3 – SHUTTER ACTUATION PRINCIPLES
a)
b)
Shutter blade
Piezo actuator
DC motor
Rotary
tubular
shutter
d)
c)
Piezo motor
VCA
Shutter
blade
Shutter
blade
Fail safe
spring
Fail safe
spring
Figure 3.1: Investigated shutter actuation principles: a) DC motor rotary tubular
shutter, b) piezo actuator driven shutter, c) piezo motor driven shutter and d) voice
coil actuator linear shutter.
3.2
Study Results
As result of the study, the piezo actuator driven shutter and the voice coil actuator
linear shutter were valuated as predestinated to fulfill all the requirements listed in
table 2.1. However, piezo actuators need high driving voltages and cannot achieve long
strokes. Designing the MSTS DM based on the Voice Coil Actuator (VCA) principle
was therefore concluded as best solution in every sense.
The shutter study was closed with the insight of combining a debris free guidance with
a fail safe mechanism in terms of a Flexible Hinge (FH) structure driven by a VCA.
10
Chapter 4
Fundamentals
4.1
4.1.1
Statics
Introduction
As a result of the shutter study presented in the previous chapter, the MSTS mechanical part shall be designed using a flexible hinge structure due to the lifetime and fail
safe requirements. To consider the basics of flexible hinges and to discuss applicable
materials and machining technologies is important for the design of the MSTS FH
structure.
A FH generally works like a spring in the elastic range described by Hooke’s law,
but additionally performs frictionless guiding and stroke amplification. Although a
FH underlies that simple mechanical principle, conception methods for their usage in
micro- and even nanotechnology just came up in the end of the 20th century. Powerful
computers for calculations with the Finite Element Method (FEM) and improved performances of the Electrical Discharge Machining (EDM) are essential for designing and
manufacturing flexible hinges in the micro- and nanotechnological range. MEMS1 accelerator sensors, today manufactured in lot of millions, contain flexible hinges etched
in silicon with lengths below one millimeter2 .
Flexible hinges are generally characterized by regions of reduced bending stiffness in
one ore more directions. They have a lot of advantages for microsystems compared to
1
Microelectromechanical systems.
http://www.panasonic-electric-works.de/pewde/en/html/23405.php? accessed on June 4,
2008.
2
11
4 – FUNDAMENTALS
bush and ball bearings or other bearing systems e.g. magnetic, hydrostatic, hydrodynamic and air guidings [4]. But they also have some disadvantages which are listed in
the following compilation.
Advantages
Frictionless guiding
No wear and therefore no wear debris
No galling
No lubrication
High transversal rigidity
No play
Monolithic piece
Disadvantages
Limited strokes
Restoring forces
Complex geometries
A conclusion of this valuation shows, that flexible hinges are ideal for the MSTS
application due to the frictionless, lubrication and wear debris free guiding3 . The
reachable stroke will be determined by the design analysis discussed in chapter 5.4.
Different translational and rotatory FH designs are presented with formulas in [4]
and [6] with improvements of the general designs in [10] and [13]. Figure 4.1 shows
three patterns of flexible hinges for getting a first impression in which direction the
design of the MSTS FH structure tends. These designs have different advantages and
disadvantages. For instance, the circular notch hinge features the highest precision due
to its stationary rotation center. However, high forces must be applied for reaching
adequate deflections.
4.1.2
Theory
The formulas for calculating the forces and deflections, presented in the above mentioned papers, are exclusively deduced form the fundamental theory of structural mechanics
M (x)
+
y =
EI(x)
00
η ∂F (x)
GA(x) ∂x
.
(4.1)
This equation describes approximately the curvature of a beam implementing the
bending moment M , Young’s modulus E and the geometrical moment of inertia I.
The term in the brackets describes the shearing, which won’t be further considered
due to its small influence on the deflection [4].
3
Applying lubricants in spacecraft mechanisms is generally problematic, especially inside optical
instruments. As well as wear debis, they can contaminate the optical components.
12
4 – FUNDAMENTALS
a)
b)
c)
Figure 4.1: General designs of flexible hinges: a) leaf spring hinge, b) circular notch
hinge and c) elliptical notch hinge [6].
The mathematical description in (4.1) bases on three assumptions named continuity, homogeneity and isotropy. Parts of the MSTS FH structure can possibly reach
dimensions where some of these assumptions loose validity due to very thin waists.
Therefore, a good knowledge about the material properties and the accuracy of the
FEM calculations is required for the MSTS FH design.
4.1.3
Materials
A lot of materials, preferably metals, are applicable for flexible hinges. Thereby,
different properties like
• density,
• Young’s modulus,
• endurance strength,
• thermal conductivity,
• space qualification and
• radiation degradation
must be evaluated.
The range of applicable materials is not only limited to metals as already shown with
the mentioned MEMS sensor. Also ceramics like silicon nitride (Si3 N4 ) or composits
13
4 – FUNDAMENTALS
containing carbon fiber show good performances for FH structures. However, a comparison of the above listed properties with the requirements (tab. 2.1) obviate their
usage, what reduces the range of applicable materials for the MSTS FH.
For a further confinement, the endurance strength is regarded as most important criterion due to the high required number of cycles of the MSTS. Some metals have an
endurance strength limit, what means that the number of cycles until a loaded FH
breaks, tends to infinity, when a certain stress limit will never be exceeded. The endurance strength of a metal depends on its crystal system. Metals with body-centered
cubic systems have an endurance strength limit, whereas metals with face-centered cubic systems do not. The S-N curve4 characterizes the magnitude of an applied cyclical
stress against the logarithmic scale of cycles until failure [8]. This fatigue test with
structural damage divides the applicable metals for the MSTS in two groups, which
are listed in table 4.1.
Beryllium copper, titanium alloys and cobalt alloys have been classified as best candidates for the MSTS FH structure. Beryllium copper (CuBe) is an excellent alloy for
springs and is space qualified. However, the high density and the missing endurance
strength limit exclude its applicability. Furthermore, the toxicity of Beryllium is a
problem during the wire-cut EDM due to emerging vapours.
R
NIVAFLEX
45/18, basically used in the watch industry, is designed especially for
long term cyclical stressed springs5 . Thus, it has an endurance strength limit. A
high elastic force is required according to the high Young’s modulus, which possibly
cannot be generated with the VCA. Missing space qualification and minimum delivR
ery quantities of several 100 kg avoid the usage of NIVAFLEX
for the MSTS FH
structure.
As most commonly used titanium alloy for space applications, Ti-6Al-4V shows ideal
properties like an existing endurance strength limit [3], a low density and a low
Young’s modulus. The influence of these properties for the MSTS FH structure
design will be discussed in chapter 5.4.
Figure 4.2 shows a collection of S-N curves of Ti-6Al-4V samples with different milling
axes and surface finishes respectively. Obviously the endurance limit depends on
the surface finish. Thus, it is crucial for the MSTS FH design, that the maximum
stress which occurs in the flexible hinges never exceeds the endurance strength limit.
4
5
Also known as Wöhler curve.
http://www.vacuumschmelze.de accessed on June 4, 2008.
14
4 – FUNDAMENTALS
Otherwise, a nondestructive operation cannot be guaranteed over several billion cycles.
For the most demanding applications e.g. aerospace, lifetime and fatigue tests must
be perforemd at any rate [2].
Alloy
Ti-6Al-4V
R
NIVAFLEX
45/5
Beryllium Copper (CuBe)
ρ / mkg3
4420
8500
8260
E / GPa
114
220
131
Se0 / MPa
≈ 350
n/a
-
W
λT / Km
7.2
n/a
106
Table 4.1: Properties of the investigated materials for the MSTS FH structure. Listed
are the mass density ρ, the Youngs’s modulus E, the endurance strength Se0 and the
coefficient of thermal conductivity λT . The table is separated in two parts characterized by the endurance strength limit.
4.1.4
Wire-Cut EDM
EDM allows very high precision and arbitrary shaped machining of electrical conductive materials. There are two main types of EDM called sinker EDM and wire-cut
EDM. Flexible hinges with one degree of freedom will be ideally machined by wire-cut
EDM. Reasons for selecting this method are the simpler machine setup, because no
special matrices must be prepared, and the lower costs.
A maximum precision of 5 µm and an average roughness height of Ra ≈ 0.18 µm are
obtainable by wire-cut EDM [4]. The average roughness height has an influence on
the endurance strength limit as shown in figure 4.2. Thus, a roughness measurement
on the surface of the manufactured MSTS FH structure should be performed before
the flight model will be constructed. The wire diameters are generally in the range of
a few hundred microns. The MSTS FH design must be optimized for the applied wire
diameter. For example, with a diameter of 0.2 mm no radii smaller than 0.3 mm can
be cut. Repeated passages with reduced cutting velocities improve the surface finish,
but increase the machining costs [4].
4.1.5
Stage with two Parallel Blades
Since the movement of the shutter blade will be performed just in one direction, a
FH structre variant called stage with two parallel blades presented in [4] should be
discussed in detail.
15
4 – FUNDAMENTALS
700
600
σ / MPa
500
400
300
200
100
0
104
105
Number of Cycles
106
107
Figure 4.2: Ti-6Al-4V fatigue tests [4].
Figure 4.3 (left) shows the main principle of the stage with two parallel blades. The
formulas for calculating the deflection, the rigidity and the buckling load for this FH
structure are deduced in [4] using the approximated Euler-Bernoulli beam theory.
The formula for the deflection f thereby follows to
f=
P l3
.
2Ebh3
(4.2)
It is obvious that the length l and the thickness h have the highest significance for
the blade dimensioning, because they raise to the power of three. P characterizes the
force applied on the FH and is reasonably equal to the force generated by the VCA,
which will be introduced in chapter 4.3. The rigidity, which is represented by the
spring constant c, can be calculated with
c=
and the buckling load Nc with
Nc =
24EI
,
l3
(4.3)
8π 2 EI
.
l2
(4.4)
16
4 – FUNDAMENTALS
Linear stage with necked down flexu
Parallel Spring Stage
Mobile
block
Bloc mobile
Parabolic Translation (1 Degree-of-Freedom (DOF))
f
f
f
M
N
λ
Mobile Block
l
d
B
b
b
l
B
l
d
l/2
lc
h
A
P
A
C
h
e
l/2
P
λ
P
S. Henein, Slide 3.8
e
Bloc debase
base
Fixed
Figure 4.3: Stage with two parallel blades (left) and linear stage with necked down
flexures (right) [4].
2l
ξ= c
l
0 <ξ ≤1
ξ =1
ξ →0
For a given stroke f and given outer dimension
what is the optimal hinge length lc ?
Figure 4.4: Occuring blade deflections during the wire-cut EDM process limit the
maximum aspect ratio aF H = l/h [4].
17
4 – FUNDAMENTALS
4.1.6
Technological Limitations
When estimating the parameters in (4.2) for the MSTS design, it becomes obvious,
that especially the thickness h of the FH blades can achieve very small dimensions.
Therefore, it is reasonable to check the technological limitations of the applied manufacturing methode.
Wire-cut EDM is a swarf-free machining method, because the electric discharges melt
and vaporize the metal for cutting. Nevertheless, vibrations occur due to electrical
arcs and busts, electrostatic forces and due to the jet of the dielectric fluid for rinsing.
This limits the aspect ratio of machined blades and therefore affects the MSTS FH
structure design. A maximum aspect ratio of aF H = l/h ≈ 60 was defined for steel
based on manufacturing experiments [4]. Figure 4.4 sketches occuring blade deflections
during the wire-cut EDM process due to the above mentioned disturbances.
The minimum notch thickness depends on the material and the EDM quality. Circular
notch hinges can reach values of a few microns. For blades as in leaf spring hinges,
a minimum thickness of at least 50 µm is reasonable. In this dimension range no
violation of the three basic assumptions noted in subsection 4.1.2 shall occur.
4.1.7
Linear Stage with Necked Down Flexures
To avoid the technological limitations for extending the dimensioning range of the FH
structure shown in figure 4.3 (left), an improved variant called linear stage with necked
down flexures is presented in [4]. As sketched in figure 4.3 (right), both blades carry
a segment considered as infinitely rigid. A parameter ξ defines the ratio between the
flexible and rigid parts to
2lc
with 0 < ξ ≤ 1.
(4.5)
l
A multidimensional optimization including the rigidity, the blade thickness and the
ξ=
critical load yields an ideal ratio for the necked down flexure of ξopt ≈ 0.3 [4].
An adequate aspect ratio shall be optained for the MSTS FH stucture design using
ξopt . The required force in this setup will be higher due to the augmented translational
rigidity, but increases as well the eigenfrequencies, what is highly desired for the control
as discussed in section 4.5.
The formula for the deflection can be deduced to
P l3 ξ(3 − 3ξ + ξ 2 )
f=
.
2Ebh3
(4.6)
18
4 – FUNDAMENTALS
Analogously follows for the rigidity
2bh3 E
c=
ξ(3 − 3ξ + ξ 2 )l3
(4.7)
and the buckling load
Nc =
4.2
4.2.1
8π 2 EI
.
ξ 2 l2
(4.8)
Dynamics
Introduction
The design of the MSTS FH structure shall be optimized in terms of dimensions and
weight to achieve the requirements listed in table 2.1. To fulfill the shutting frequency
and especially the maximum open/close time, an optimization in consideration of the
MSTS dynamics is essential.
4.2.2
Theory
A mathematical model for the MSTS FH structure design as proposed in figure 4.3 is
required to optimize the mentioned parameters. The sketch 4.10 (left) allows to deduce
the mathematical description for a driven damped spring-mass system satisfying the
equation
dx
d2 x
+ cx = F (x, t),
(4.9)
m 2 +k
dt
dt
whereas m is the mass, k the attenuation constant, c the spring constant and F the
applied dynamic force.
The mass and the spring constant are coupled with the system’s first eigenfrequency
r
c
1
(1)
feig =
.
(4.10)
2π m
The parameters in (4.10) can be determined by means of FEM calculations. However, determing the attenuation constant is virtually impossible with simple calculation methods. Measurements at a manufactured FH structure must be performed for
disclosing the attenuation constant.
The required open/close time is in the range of a few milliseconds. A relatively high
first eigenfrequency of the FH structure shall therefore be achieved to guarantee fast
19
4 – FUNDAMENTALS
shutting. Furthermore, controlling a mechanical system is much simpler in a frequency
range considerably below its first resonant peak. The system’s resonant frequency fres
and its eigenfrequency nearly coincide for weakly damped mechanical systems. They
(1) √
are coupled with the damping ratio D to fres = feig 1 − D2 .
Analog to (4.10), the first eigenfrequency can be written in terms of
(1)
feig =
k
.
4πDm
(4.11)
Dynamical step response measurements of the mechanical system allow to determine
the damping ratio.
Weakly damped systems show approximately PT2 behaviour in words of the control
theory. Thus, several decaying oscillations occur before reaching a stationary state
after a step or Dirac delta excitation respectively. Neighboring amplitudes ∆ of
these oscillations peaks define the logarithmic decrement6 δ to
δ = ln
∆i
.
∆i+1
(4.12)
Hereafter, D can be calculated with
δ
D=√
.
π2 + δ2
(4.13)
In the verification phase of the MERTIS project, the MSTS shall persist several shaking
tests simulating the launch phase. It is appropriate to maximize the damping ratio
for avoiding high resonant peaks, which can destroy the MSTS. However, a high first
eigenfrequency is required for fast shutting. These parameters obviously interact in
an reciprocal manner when analyzing (4.11).
The force generated by the VCA is equal to the dynamic force F in (4.9) and must
counteract the totalized acceleration force, attenuation force and spring force. The
goal for the MSTS FH design is therefore to minimize these forces by finding adequate
values for the parameters m, k and c.
6
Consider the associatied graphic and the mathematical derivation of the logarithmic decrement
for unknown stationary amplitudes presented in appendix A.
20
4 – FUNDAMENTALS
4.3
Electromagnetics
4.3.1
Introduction
As applicable actuation principle, a voice coil actuator was disclosed in the shutter
study. This electromagnetic actuator is capable to perform linear or rotary movements
comparable to electric motors. The configuration of a VCA is in general a cylindric
coil, which plunges into a setup of a centered magnet surrounded by a ferrite ring, like
it can be found in conventional loudspeakers. The application of rotary VCAs is well
established in hard disk drive heads.
4.3.2
Theory
To introduce the relevant electromechanic parameters, a loudspeaker VCA shall be
considered as shown in fig. 4.5 (left). The stroke of the coil will be generated by the
Lorentz force FV CA induced by the coil current IC and the magnet field B of the
centered permanent magnet. The Lorentz force can be written as
Z
~
~ C × B,
~
FV CA = IC dL
(4.14)
~ C indicates the differential of the coil wire cross section normal.
whereas dL
The right hand grip rule defines the direction of F~V CA . Due to the axisymmetric setup
~ is always perpendicular to dL
~ C . Therefore (4.14) can be
of the considered VCA, B
simplified to
FV CA = IC LC B.
(4.15)
When assuming a homogeneous magnetic field within the coil region, a force factor
KF can be determined written as
KF =
FV CA
= LC B,
IC
(4.16)
which characterizes every VCA7 . Loudspeaker VCAs usually have a heavy magnet
setup compared to the coil’s mass. So, it is obvious that normally the coil is moved for
optaining high accelations. However, moving the magnet has significant advantages
when its mass is in the same range as the mass of the coil. Here, the coil’s power leads
do not move and possibly break after a high number of performed cycles. Thus, two
VCA concepts can be deduced and will be named as
7
www.beikimco.com accessed on June 4, 2008.
21
4 – FUNDAMENTALS
FVCA
z
dLC
y
B
x,
r
FVCA
Figure 4.5: Loudspeaker VCA model with the indicated vectors of the Lorentz
~ and the coil wire cross section normal dL
~ C building
force F~V CA , the magnet field B
an orthonormal system (left). Cylindric single coil VCA model with some indicated
magnet field lines (right).
• moving coil concept and
• moving magnet concept.
This concepts shall be evaluated for the MSTS application. However, when reminding
the lifetime requirement, it must be said, that the selection shall tend towards the
moving magnet concept to avoid a power lead breakage.
4.3.3
Coil
An axisymmetric coil setup allows to generate the highest possible FV CA due to the
~C × B
~ =⇒ max when dL
~ C ⊥ B.
~ Since the induced field in
cross product identity dL
the coil does not remarkably influence the magnet field B, FV CA mainly depends on
the current IC and the coil wire length LC . Ohm’s law couples these parameters in a
reciprocal way to
RC =
8ρC LC
UC
,
= 2
IC
dC π
(4.17)
whereas RC represents the coil resistance, ρC the electrical resistivity, UC the applied
coil voltage and dC the coil wire diameter8 . RC shall be minimized due to the low
supply voltage (tab. 2.1). However, to maximize the Lorentz force a high LC is
required.
8
Note that dC is considered as the the overall wire diameter including its isolation, whereby the
calculated RC is smaller than the measured value.
22
4 – FUNDAMENTALS
4.3.4
Magnet
Nowadays several new combinations of materials are used for permanent magnets,
which replace more and more the common ferrite magnets. They mainly differ in
terms of the maximum magnetic energy product BHmax .
Three permanent magnet materials can be taken into account for the MSTS VCA
known as
• Aluminum Nickel Cobalt (AlNiCo),
• Samarium Cobalt (SmCo) and
• Neodymium Iron Boron (NdFeB).
SmCo and NdFeB are rare earth element magnets with the today highest possible
energy products. The theoretical maximum of NdFeB amounts to 64 MGOe [1]. Table
4.2 lists the most important parameters of these materials.
Material
AlNiCo
SmCo
NdFeB†
ρ / mkg3
7300
8000 - 8500
7400
BHmax / MGOe
7.5 - 9.0
28
64
TC / ◦ C
≈ 800
700 - 800
310 - 370
Table 4.2: Properties of the investigated permanent magnet materials. Listed are
the mass density ρ, the maximum magnetic energy product BHmax and the Curie
temperature TC . † www.ndfebmagnets.de accessed on June 4, 2008.
The restricted MSTS dimension requirements ask for applying a NdFeB magnet due
to its high BHmax . The VCA concept in terms of moving magnet or moving coil has
a direct influence to the magnet selection concerning its dimensions and mass. Furthermore, the Curie temperature TC must be well above the operating temperature
of the MSTS to avoid demagnetization.
4.3.5
Cylindric Single Coil VCA
VCAs generally consist of a cylindric permanent magnet and an ambiant cylindric coil.
An optional ferrite ring, which is directly coupled to the magnet, encases the coil to
concentrate the magnetic field lines for achieving higher Lorentz forces.
23
4 – FUNDAMENTALS
Figure 4.5 (right) shows a model of a cylindric single coil VCA without ferrite ring.
The x-axis indicates the direction of the translational movement and coincides with
F~V CA , which follows with (4.15) to
FV CA (x) = IC LC Bx (x).
(4.18)
The coil’s magnet field Bx (x) induced by the current shows the same distribution like
the field of the permanent magnet (fig. 4.6). Thus, the Lorentz force pushes or pulls
the coil9 on the x-axis depending on the current flow direction. It is reasonable that no
force will be generated when the axial centers of the magnet and the coil conincides,
because the magnet fields cannot cause a magnetic attraction or repulsion respectively.
An axial displacement of this two components is necessary for optaining a functional
cylindric single coil VCA.
The magnet field distribution on the x-axis of a cylindric coil can be derived to


lC
lC
−
x̂
+
x̂
µ0 N 
2
2
,
q
BxC (x̂) =
+q
(4.19)
2
2
2
2lC
lC
DC
lC
DC 2
−
x̂
+
+
x̂
+
2
2
2
2
whereas µ0 indicates the vacuum permeability, N the number of windings of the coil,
lC the coil length and DC the coil diameter.
Due to the same field line distribution, the magnet’s field BxM (x∗ ) will be defined
analogously to (4.19) with the translation x∗ = x + a. Note that x̂ = x − a. The force
distribution of a cylindric single coil VCA can now be calculated with the superposition
of the two B-fields depending on the shifting parameter a, to
FV CA (x, a) = IC LC (BxC (x̂) − BxM (x∗ )).
(4.20)
Anticipating to the following chapter, figure 4.7 shows a calculated force distribution
for arbitrary defined values, which won’t be discussed here. In fact, the characteristic
of the FV CA curve interests in terms of the optimal coil positioning relative to the
magnet. The goal is to maximize the VCA force. The two optimal displacement
positions can be calculted using the first derivative
∂FV CA (x, a)
= 0.
(4.21)
∂x
It must be noted, that the this displacement optimization must be considered dynamically due to the stroke, which the VCA shall perform for operation. Further
investigations will be presented in chapter 5.
9
Evidentially, the magnet will be pushed or pulled when applying the moving magnet concept.
24
4 – FUNDAMENTALS
1.5
Bx / a.u.
1
0.5
0
−5
−4
−3
−2
−1
0
x / a.u.
1
2
3
4
5
Figure 4.6: Calculated |Bx (x)| distribution of a cylindric single coil.
0.2
0.15
0.1
F/N
0.05
0
−0.05
−0.1
−0.15
−0.2
−8
−6
−4
−2
0
x/m
2
4
6
8
−3
x 10
Figure 4.7: Calculated Lorentz force distribution of a cylindric single coil VCA.
25
4 – FUNDAMENTALS
Interaction Map
Electromagnetic
Magnet properties
Coil properties
Back-EMF damping
Mechanical
1
31.10.2007
Thermal
FH properties
ti
Heat conduction
Eigenfrequencies
Thermal radiation
Shutter installation
Glue heat conductivity
Figure 4.8: Map of the physical interactions separated in the mechanical, electromagnetic and thermal branches.
DIVISION Science & Earth Observation
Short Term Shutter and Long Term Shutter
4.4
Interaction Map
In the previous sections, the mechanical and electromagnetic basics for the MSTS
design were discussed. However, no introduction in the thermal basics is given due to
its reduced significance for the DM during the preliminary design phase. Nevertheless,
a thermal analysis, which served its purpose, was performed and will be discussed in
chapter 5.1.
As a summary of the physical interactions, which lead the MSTS design, figure 4.8
shows an interaction map with indicated parameters of the concerning physical branches.
This figure shall point the designing difficulties for fulfilling all requirements. Reciprocal relations of different parameters in the electromechanical equations do not allow
a straightforward design approach, but rather require good optimizations.
26
4 – FUNDAMENTALS
4.5
4.5.1
Control
Introduction
A shutter blade switching mode with a maximum close/open time for the MSTS
movement is defined in table 2.1. Thus, an adequate electronics which controls the
blade stroke is required to achieve this mode.
Applicable fundamentals of the control theory will be introduced here in view of defining the control parameters, which must be finally converted into electric resistances
and capacitances respectively.
z
w
e
y
Controller
x
Control Path
-
Figure 4.9: Standard closed loop system [7].
Figure 4.9 shows the standard closed loop system subdivided in the controller, the control path and its characterizing feedback comparator. The parameters are well known
as
x control variable,
w set point,
e error signal,
y actuating variable and
z disturbance variable.
The electronics shall perform all parts of the standard closed loop system excepting
the control path, which is composed by the FH and the VCA.
27
4 – FUNDAMENTALS
4.5.2
Theory
The first step in control theory is to build a physical model of the control path and then
to describe it mathematically. For simplifying the physical model of an electromechanical system, the mechanical and electrical part shall be considered separately. Their
models are sketched in figure 4.10, whereof the applicable formulas can be deduced.
UR
UL
x
k
m
IC
c
RC
UC
L
Figure 4.10: Models of the FH as a spring mass system (left) and the VCA as a RL
circuit (right).
The mathematical model of the mechanics and its Laplace transform follow to
mẍ + k ẋ + cx = FV CA (x, t)
(4.22)
s2 mX(s) + skX(s) + cX(s) = FV CA (s).
(4.23)
Thereof, the transfer function for the mechanical part GF H (s) can be described as
GF H (s) =
X(s)
1
= 2
.
FV CA (s)
s m + sk + c
(4.24)
Analogously follows for the mathematical model of the electric circuit and its Laplace
transform the equations
uR + uL − uC = 0
diC
RC iC + L
= uC
dt
RC IC (s) + sLIC (s) = UC (s).
(4.25)
(4.26)
(4.27)
28
4 – FUNDAMENTALS
Thus, the transfer function of the electromagnetic part GV CA (s) results in
GV CA (s) =
1
IC (s)
=
.
UC (s)
sL + RC
(4.28)
Since the VCA drives the FH, the mechancial part can be considered as connected in
series to the electromagnetical part. Thus, a multiplication of the transfer functions
results in the frequency domain. As interconnecting part, the force factor KF derived
in (4.16) must be taken into account, whereof its Laplace transformation can be
denoted by KF
figure 4.11.
KF (s) = FV CA (s)/IC (s). The extracted control path is shown in
Note that this description must be considered as a first approximation, what corresponds to the general path of modeling in control theory. Obviously, no distrubance
variable appears in figure 4.11. But when the MPO once arrives in Mercury’s orbit
and the MSTS starts working, no disturbances should occur anymore.
UC
IC
GVCA(s)
x
FVCA
KF(s)
GFH(s)
Figure 4.11: Model of the control path consisting of a serial connection of the transfer
functions GV CA (s), KF (s) and GF H (s).
29
Chapter 5
Analysis, Calculations and Experiments
5.1
Thermal Analysis
It is a fact, that a thermal analysis must be performed for every component once
reaching the outer space due to the hash conditions and, of course, the missing air.
Thus, no convection occurs which normally supports the heat dissipation mainly of
electronic components.
Two VCA concepts were presented in section 4.3.2 named as moving coil and moving
magnet. One of theses concepts shall eventually be selected with help of a thermal
analysis to proceed the MSTS design.
Figure 5.1 shows the thermal networks for the two concepts consisting of six nodes, each
coupled by heat conduction and thermal radiation respectively. The applied physical
parameters of the nodes are listed in table 5.1. They are defined in all conscience at
this project stage. The ESATAN software was applied for the calculations.
The node Housing (No. 6) shown in figure 5.1 was set to a constant temperature of
45 ◦ C acting as a boundary condition. Fixing the mangnet does obviously not allow
an efficient heat dissipation of the moving coil by conduction, but just by radiation.
This was taken into account for the definition of the thermal networks. As variables,
the temperature of the electronic board, whereof the coil will be supplied, and the
length of its power leads were defined for the moving coil concept. Analogous, the
glue thickness between the fixed coil and its mounting structure was altered for the
calculations of the moving magnet concept.
30
5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS
5
Housing
6
EL board
5
Housing
3
Fixed
part
4
Moving
part
3
Fixed
part
4
Moving
part
1
Coil
2
Magnet
2
Magnet
1
Coil
6
EL board
Figure 5.1: Thermal networks for the moving magnet concept (left) and moving coil
concept (right). Connecting lines indicate conductive couplings and thunder lines
indicate radiative couplings between the thermal nodes. The electronics board is abbreviated with EL board.
Figure 5.2 shows the calculated coil temperatures for both VCA concepts for a maximum allowed average power consumption of 0.6 W (tab. 2.1) and a maximum housing
temperature1 of 45 ◦ C. On the abscissa, the temperature of the electronics board is
plotted as undependent variable. The glue thickness is fixed to 0.1 mm and the lenght
of the power leads amounts to 40 mm.
With the moving magnet concept, the coil does apparently not heat up to temperatures
of > 50 ◦ C, whereas the coil reaches temperatures of > 110 ◦ C with the moving coil
concept. A relatively big gluing area between the fixed coil and the mounting structure
allows a high conductive heat dissipation. This can furthermore be improved when
reducing the glue thickness.
With this analysis, the design progress has definitely turned in direction of the moving
magnet concept for the MSTS VCA, what furthermore supports the postulation about
the power lead breakage discussed in section 4.3.2. Now the mass of the magnet must
be defined as small as possible to achieve the required shutter blade’s open/close time.
1
The preliminary thermal calculations of the whole MERTIS instrument show a maximum temperature for the MSOP housing of 45 ◦ C at Mercury’s subsolar point.
31
Component
Node
Material
Coil
Magnet
Fixed part
Moving part
1
2
3
4
Cu
NdFeB
Steel
Steel
cH /
J
kgK
385
9†
444
444
λT /
W
mK
393
502‡
67
67
m / kg
/-
0.2 · 10−3
0.31 · 10−3
6 · 10−3
4 · 10−3
0.6
0.5
0.5
0.5
Table 5.1: Thermal and material properties of the nodes 1 to 4 of the thermal network
configuration (fig. 5.1). Listed are the heat capacity cH , the coefficient of thermal
conductivity λT , the mass m and the defined thermal efficiency .
†
www.johnsonmag.com, ‡ www.shnfb.com accessed on June 8, 2008.
120
110
Coil Temperature / °C
100
90
80
70
60
50
40
30
40
50
60
70
Electronic Board Temperature / °C
80
90
Figure 5.2: Thermal analysis curves of the moving coil concept (red) and the moving
magnet concept (blue). The average power dissipation of the coil is set to PC = 0.6 W
and a MSOP temperature to 45 ◦ C.
32
5.2
5.2.1
Finite Element Calculations
Electromagnetic FEM
First estimations of FV CA for the coil dimensioning were performed with (4.15). However, force measurements of different loadspeaker VCAs and voice coil motors showed,
that this simple mathematical model cannot be applied for the dimensioning of the
MSTS VCA. As a powerful tool, the FEMM2 electromagnetic simulation software was
used for the design progress. FEMM solves planar and axisymmetric problems for
electro- and magnetostatic setups. The results of the FEM calculations are in good
agreement with the performed test measurements.
The left part of figure 5.3 shows a cylindic single coil VCA setup meshed with triangles.
Since FEMM solves axisymmetric problem in 2D, just the half of a cylindrical VCA’s
cross section must be sketched. The parameters of the magnet, the coil and the
surrounding air3 are directly indicated inside of the corresponding countours. As result
of the calculation, the right part of the figure shows the field lines and the magnet
field distribution represented with graded colors. The generated Lorentz force will
be determined by integrating the coil area and results as a planar vector.
5.2.2
Mechanical FEM
Applying the mathematical model for the mechanical deflection calculation presented
in (4.2) shows results, which are in a good agreement with the FEM calculations
performed with NASTRAN. Therefore, this formula was mainly applied for the dimensioning of the FH structure.
For experimenting with more complicated FH shapes, the calculations must be performed with FEM. The mechanical FEM model was generally meshed with tetrahedrons of an adequate mesh size for reducing the calculation time.
2
The Finite Element Methode Magnetics (FEMM) solver is a freeware tool an can be downloaded
at http://femm.foster-miller.net accessed on June 8, 2008.
3
Air must be defined as surrounding medium for the DM. The permeability and permittivity of
air and vacuum (space condition) almost conicide, that this fact practically can be disregarded for
the flight model.
33
Air
NdFeB 40 MGOe
0.125mm
[Coil:500]
Figure 5.3: A meshed cylindrical single coil VCA (left) and the corresponding FEMM
calcualtion result (right). The left vertical border of both images indicates the rotation
axis of the half of the cross section. Integrating the magnet field in the green coil area
and multiplying it with the defined current results in the Lorentz force.
5.3
Cylindric Single Coil VCA Experiments
As first performed experiments, three test VCAs with different self wound coils were
constructed and measured for verifying the calculations and simulations. A single
point load cell with strain gauges4 was applied for the force measurement after calibrating it with reference weights. Fixed on a linear positioning table, the load cell
carried the magnet, which penetrated into the fixed coil on its x-axis. First of all,
the linear force to displacement characteristic FV CA (x) ∝ x was verified by linearly
augmenting the coil current IC . A good correlation was established for currents up to
IC = 500 mA. However, during the steady state with IC > 0.5 A, the coil was heating
up to temperatures of > 100 ◦ C. This caused unlinearities in the FV CA (x) relation due
to the coil resistance changement.
For all VCA setups, the static force distribution FV CA (x) along the coil axis was
measured and compared with the simulations. Figure 5.4 shows the measurement
results of a VCA setup with the parameters listed in table 5.2. The cruxes in the
negativ x-domain in the mentioned figure indicate the measured values. Due to the
test setup, no forces for x > −1.5 mm could be measured. However, when considering
4
www.vishay.com/docs/12002/1004.pdf accessed on June 8, 2008.
34
(4.20) and its curve plotted in figure 4.7, the characteristic for the positive x-domain
can be anticipated. Therefore, the curve in figure 5.2 is rotational symmetric mirrored
for easier interpretation. All measurement results are in good agreement with the
analytic and FEM calculations.
Coil
Material MULTOGAN†
dC
0.1 mm
hC
1.75 mm
lC
4.2 mm
N
500
IC
0.2 A
Magnet
Material
NdFeB
dM
2 mm
dL
3 mm
BHmax 38 MGOe
Table 5.2: Parameters of the test VCA setup for the static measurements, whereas hC
represents the coil winding height, dM the magnet diameter and dL the magnet length
(see fig. 6.2). † www.isodraht.de/MHflachd.pdf accessed on June 8, 2008.
The MSTS switching mode characterized in figure 2.1 allows to estimate the induced
voltage in the coil, which depends on the magnet’s velocity expressed as
Uind ∝ −Bx (x)ẋ.
(5.1)
High induction voltage peaks possibly disturbe the power supply and furthermore
complicates the control of the MSTS. However, as an advantage of the induction, the
transient period of a weakly damped spring-mass system can be shortened due to the
eddy current brake effect. This damping effect shall be utilized during the launch by
short-circuiting the coil for achieving lower FH deflections forced by structure shakings.
5.4
Flexible Hinge Experiments
The calculations and measurements of the test VCAs confined the range of generateable Lorentz forces to FV CA ≈ 130 mN. This value was applied for estimating the
FH dimensions starting with a blade thickness of h = 50 µm. Its width was defined to
b = 5 mm according to the maximum dimension requirement. The following calculation shows the necessary FH blade length of a stage with two parallel blades presented
in section 4.1.5. At this stage, Ti-6Al-4V was definitely selected for the MSTS FH
structure. Thus, with its Young’s modulus, the required deflection of f = 1.5 mm
35
and the equality FV CA = P , the resulting FH length can be calculated with (4.2) to
r
3 2f Eb
l=h
≈ 13 mm.
(5.2)
P
This length does not exceed the MSTS dimension requirement. But the defined thickness reaches the limit for blades manufactured by wire-cut EDM. Considering the
technological limitations, the aspect ratio for l ≈ 13 mm follows to
l
≈ 260.
(5.3)
h
However, this ratio distinctly exceeds the maximum allowed ratio of aF H ≈ 60 discussed in section 4.1.6. The MSTS design shall therefore be progressed in terms of the
aF H =
linear stage with necked down flexures.
5.5
Parallel Blade Stage VCA
Based on the presented calculations, a test shutter consisting of a cylindrical single
coil VCA and a stage with two parallel blades was constructed. The VCA parameters
correspond to the values listed in table 5.2. As FH structure, a steel band with a
thickness of 50 µm was cutted, folded and glued. Figure 5.5 shows the test shutter,
where the cylindric magnet can be identified on the right side of the coil.
The performed static measurements confirmed the calculated parameters. Furthermore, the damping ratio could be measured, which is laborious to determine by means
of FEM calculations. The test shutter setup shows a very weak damping ratio. This
causes dozens of decaying oscillations of the FH structure when measuring the step
response. So, a control electronics with well adjusted parameters will be inevitable for
the MSTS.
Albeit the simple construction of this test shutter, a lot of useful measurement data
could be gathered and used for the MSTS design progress. Furthermore, the study an
analysis results in terms of using a flexible hinge structure driven by a moving magnet
VCA could be physically proved.
A necessary step of improvement is to increase the first eigenfrequency for achieving the required switching mode by broadening the blade thickness. Therefore, a
higher Lorentz force will be needed for reaching an adequate stroke. Optimizing the
different VCA parameters however rapidly voilated the requirements and boundary
conditions. Thus, an alternative to the single coil VCA had to be found for the MSTS.
36
50
40
30
FVCA / mN
20
10
0
−10
−20
−30
−40
−50
−6
−4
−2
0
x / mm
2
4
6
Figure 5.4: Result of the single coil VCA force distribution measurement. A maximum
Lorentz force of FV CA ≈ 43 mN can be generated with IC = 0.2 A. The magnet’s
axial center must therefore be displaced to x ≈ ±2 mm relative to the coil’s axial
center (x = 0).
Figure 5.5: Photo of the test shutter consisting of a cylindrical single coil VCA and a
stage with two parallel blades.
37
5.6
Helmholtz VCA
A first idea for optimizing the VCA based on the well known Helmholtz coil setup.
The goal there is to elongate the magnet field’s peak for achieving an extended region
with a constant field along the x-axis (compare fig. 4.6). This can be realized by two
axially oriented coils separated in a particular distance. The reason for experimenting
with a Helmholtz coil setup was the fact, that the generated force no longer depends
on the magnet’s position expressed as
FV CA (x) ∝ Bx (x) ⇒ FV CA ∝ Bx .
(5.4)
Since it was clear that the magnet’s and the coil’s axial origins must be displaced
for a cylindric single coil VCA, its optimal positions had to be figured out for the
Helmholtz VCA. This was mainly performed with means of the FEMM simulation
software.
Obviously, four variants are possible for wiring and coupling the coils of the Helmholtz
VCA named as
1. serial – equal coupled,
2. serial – anti-coupled,
3. parallel – equal coupled,
4. parallel – anti-coupled.
The terms serial and parallel point to the electrical wiring of the coils. Equal coupled
and anti-coupled define, whether the coils are wound in the same or in the opposite
orientation relative to the x-axis. Elongating the constant B-field will be optained with
an equal coupled setup. The two coils thereby act as a long cylindric coil. But since it
was clear, that the required coil lenght must exceed the magnet length for generating
the required Lorentz force, no improvements can be achieved with a equal coupled
Helmholtz coil compared to a single coil setup. However, the simulation shows, that
an anti-coupled setup is capable to augment the generated force by approximately 80 %
compared to a corresponding equal coupled coil. The |Bx (x)| distribution of an equal
coupled Helmholtz coil has a behaviour comparable to that of a single coil with an
extended summit. But for the anti-coupled Helmholtz coil, the |Bx (x)| distribution
corresponds to the curve shown in figure 4.7.
38
Coils
Material MULTOGAN
dC
0.125 mm
hC
1.8 mm
lC
2.1 mm
N
2 × 250
IC
0.5 A
Magnet
Material
NdFeB
dM
2 mm
dL
3 mm
BHmax 40 MGOe
Table 5.3: Parameters of the Helmholtz VCA simulation.
A formula for calculating the force can be deduced using (4.20). However, the force can
be directly determined with the FEMM software. A free parameter of a Helmholtz
VCA is the clearance d between the coils. The figures 5.6 to 5.8 show the simulated
curves for three different clearances comparing the forces of an equal coupled VCA
(blue) and an anti-coupled VCA (red) with the parameters listed in table 5.3.
The maximum force of the anti-coupled VCA will be reached when the magnet is
precisely positioned in the middle of the coils. Compared to the maximum force of the
equal coupled VCA, an absolute augmentation of 80 % can be achieved in the best case.
This can be explaned when considering each coil as a single magnet. One pushes the
permanent magnet and the other one pulls it respectively. The maximum force depends
on the clearance when considering the negative peaks of the red curves5 . Figure 5.9
shows the simulation result of Fmax (d). The optimal clearance was calculated with the
Taylor approximation to dopt ≈ 1.3 mm.
The highest mechanical force appears at the maximum deflection of the FH structure
due to the spring force F (x) = cx according to (4.9). Therefore, it is reasonable that
the axial magnet center shall then coincide with Fmax of the anti-coupled Helmholtz
VCA. However, high acceleration forces occur during the deflection phase because of
the fast switching mode requirement. These forces may exceed the spring force. Hence,
an optimization of the total VCA energy EV CA was performed in terms of
x
Z 2
EV CA = FV CA (x)dx .
(5.5)
x1
The required stroke for the MSTS amounts to f = 1.5 mm. Two cases of the magnet’s
end points were analyzed for optimizing EV CA . For the first, Fmax shall be achieved
5
The negative force peak results of the magnet’s B-field orientation defined in the simulation.
Thus, the magnet must be correctly oriented in the MSTS to achieve the desired movement.
39
Coils
Material MULTOGAN
dC
0.1 mm
hC
2.0 mm
lC
2.2 mm
d
1.7 mm
N
2 × 400
IC
0.15 A
Magnet
Material
NdFeB
dM
1.5 mm
dL
5.0 mm
BHmax 38 MGOe
Table 5.4: Parameters of the Helmholtz VCA test setup.
at the full stoke expressed in (5.6). For the second, Fmax shall be achieved at the half
stroke expressed in (5.7).
Fmax = FV CA (fˆ)
⇒
EV CA
!
fˆ
2
⇒
EV CA
Fmax = FV CA
1.5 mm
Z
= FV CA (x)dx
mm
0 0.75
Z mm
= FV CA (x)dx
(5.6)
(5.7)
−0.75 mm
The optimization curves in relation to the coil clearance are shown in figure 5.10. A
coil energy improvement of around 22 % will be optained for the second case (blue)
compared to the first case (red). Furthermore, the maximum coil energy occurs approximately at dopt like in the maximum force simulation of the anti-coupled Helmholtz
VCA shown in figure 5.9.
The same static measurement as described in subsection 5.3 was performed for a
Helmholtz VCA setup with the parameters listed in table 5.4. The current was
set to a low value to suppress the coil heating. The test setup did also not allow to
measure the force at x > −1.5 mm. Figure 5.11 shows the measured force distribution,
whereas the curves in the positive x-domain are rotational symmetric mirored as well.
The measured curve characteristics are in good agreement with the simulated results
plotted in figure 5.7.
With the same Helmholtz VCA setup, several dynamic measurements were performed to gain conculsions about the eddy current brake effect and the induction with
the different coil wirings and couplings. The magnet was thereby moved along the
x-axis inside the fixed coils driven by a loudspeaker VCA, which was excited with
different shaped signals.
40
Considering the step response measurements showed in figure 5.12, distinct statements
about the different wiring of the coils can be made. The anti-coupled setup shows a
considerably better damping behaviour and smaller induction voltage peaks. Due to
the same winding number of the coils and the opposite axial orientation, the induction
peaks will be almost completely suppressed. Furthermore, the eddy current brake
effect occurs in both movement directions, what can be deduced from the falling edge
of the upper curve in figure 5.12 (right). Thus, this measurement results confirm the
selection of the favoured Helmholtz VCA setup for applying it in the MSTS.
41
150
100
50
F / mN
0
−50
−100
−150
−200
−250
−5
−4
−3
−2
−1
0
x / mm
1
2
3
4
5
Figure 5.6: Helmholtz VCA simulation with d = 0.5 mm.
150
100
50
F / mN
0
−50
−100
−150
−200
−250
−5
−4
−3
−2
−1
0
x / mm
1
2
3
4
5
42
150
100
50
F / mN
0
−50
−100
−150
−200
−250
−5
−4
−3
−2
−1
0
x / mm
1
2
3
4
5
−170
−175
−180
Fmax / mN
−185
−190
−195
−200
−205
−210
0
0.5
1
1.5
d / mm
2
2.5
3
Figure 5.9: Maximum force to clearance characteristic of the simulated Helmholtz
VCA.
43
300
290
280
270
ECoil / µ J
260
250
240
230
220
210
200
190
0
0.5
1
1.5
d / mm
2
2.5
3
Figure 5.10: Helmholtz VCA energy optimization curves.
30
20
10
F / mN
0
−10
−20
−30
−40
−50
−10
−8
−6
−4
−2
0
x / mm
2
4
6
8
10
Figure 5.11: Result of the Helmholtz VCA force distribution measurement with
d = 1.7 mm.
44
Figure 5.12: Step response oscillograms of the equal coupled (left) and the anti-coupled
(right) Helmholtz VCA. The upper curves show the magnet’s step responses of the
stroke x measured with a capacitve sensor in USensor = 2 V/DIV and the lower curves
show the induction voltages measured in Uind = 10 mV/DIV. The abscissa is measured
in t = 20 ms/DIV.
45
Chapter 6
MERTIS Short Term Shutter Demonstrator Model
6.1
Design
This chapter discloses the finally realized MSTS DM design with its mechanical and
electromagnetic components. To highlight the parameters and their interactions summarized in figure 4.8 shall make this design solution comprehensible.
The MSTS design had to bear several requirement adaptions during the work period.
Here, the clearance between the MSOP and the MEOP structure (fig. 2.2), where
the MSTS will be embedded, shall be mentioned. The dimension requirement firstly
allowed an overall width of 5 mm. Due to calculation corrections of the optical path,
the width was eventually confined to 4.5 mm. This influenced the MSTS FH design,
which had to be adapted several times.
6.2
Mechanics
The mechanical part can be devided in two parts, even when it is monolithically
manufactured. These are the moving FH structure and the non moving mounting
part discussed in the following sections. Figure 6.1 shows the CAD model of the
MSTS mechanics with the mounted coils and magnet. Table 6.1 lists the defined
and calculated mechanical parameters. A comparison of these parameters with the
manufactured MSTS test sample is essential for the construction of the Engineering
Model (EM) and, ultimately, the Flight Model (FM). The design drawing of the MSTS
DM can be found in appendix B.
46
6 – MERTIS SHORT TERM SHUTTER DEMONSTRATOR MODEL
Figure 6.1: MSTS DM CAD model which shows the mechanical part (grey), the
mounted coils (green), the magnet (red) and the support pin (voilet).
Parameter
Material
l
b
h
m
ρ
E
c
(1)
feig
Value
Ti-6Al-4V
20 mm
4 mm
80 µm
1.782 g
4430 kgm−3
113.8 GPa
83.0 Nm−1
110.4 Hz
Table 6.1: Defined and calculated design parameters of the MSTS DM mechanical
part.
47
6.2.1
MSTS FH Structure
The maximum force generated from the Helmholtz VCA and the required first
eigenfrequency determined by the switching mode (fig. 2.1) define the dimension
parameters of the FH. They result from the FEM simulations to FV CA = 124 mN and
(1)
feig = 110.4 Hz. The leaf width was defined to b = 4 mm and its length1 to l = 20 mm.
For reaching an adequate spring constant c, the leaf thickness amounts to h = 80 µm.
Thus, a necked down flexures design is necessary. With ξ = 0.5, the length of the
flexible hinges results to lc = 5 mm for each leaf. With a thickness of 0.5 mm, the rigid
part is around 250 times stiffer than the leafs.
The parallel stage avoids canting and rotary movements of the magnet and increases
the eigenfrequency due to the higher stiffness. However, this will be counteracted by
the higher mass, what forced the implementation of three mass reducing cavities in
the rigid parts.
The infrared light beam exits the slit with a divergence of ≈ 30 ◦ and passes the
MSOP window afterwards. So, the blade will be placed as close as possible to the slit
for reducing the blade width.
The force should be induced in the middle of the FH structure to avoid tensile and
compressive stress in the leafs [4]. This would require an additional rigid bar and a
changement of the VCA positioning. But FEM calculations showed maximum stress
amplitudes in the leafs far below the endurance strenght limit when inducing the
force at the bottom of the FH structure. Thus, the Helmholtz VCA is positioned
centered to the half round magnet mounting area (fig. 6.1). Since the magnet must
be placed axially centered between the coils, an additional support pin with the same
diameter and a resulting length of 4.7 mm is required to connect the magnet with the
FH structure. Aluminum was selected as material to keep down the moving mass.
6.2.2
Mounting Part
The MSTS DM will be fixed at the MSOP structure with two M2 screws. The MSOP
window and the milling slot for the grating adjustment screws (fig. 2.2) restrict the
bore placement for the MSTS screws. Because the VCA must be placed towards the
grating and, therefore, interfere with its screw, an additional knob at the MSOP is
1
The height of the MSTS obviously exceeds the dimension requirement with the defined leaf
length. However, this was approved by the instrument prime.
48
Coils
Material MULTOGAN
dC
0.1 mm
hC
1.75 mm
lC
3.85 mm
d
1.3 mm
N
2 × 232
ζ
0.1 mm
Magnet
Material
NdFeB
dM
2 mm
dL
3 mm
χ
0.15 mm
BHmax 38 MGOe
Table 6.2: Electromagnetic parameters of the MSTS DM design.
necessary. The bores are designed as long holes for adjusting the shutter blade relative
to the light beam. The mounting part supports the coils of the Helmholtz VCA.
Due to the coils’ diameter of ≈ 6 mm, a slot must be milled in the MSOP to let insert
the MSTS VCA support.
6.3
Electromagnetics
As confirmed with test constructions, the Helmholtz VCA is capable to achieve an
around 1.8 times higher FV CA than a VCA with an equivalent coil, without necessitating more installation space. Listed in table 6.2 are the magnet and coil parameters.
Figure 6.2 shows the VCA cross section with the corresponding dimension parameters.
A glue thickness of ζ= 0.1 mm was defined.
The coils were hand-crafted and glued with epoxy after every winding layer to optain
self-supporting air-core coils. The magnet was glued on the support pin, which itself
was glued on the junction of the FH structure. A small vertical displacement of the
magnet relative to the coils occurs at maximum deflection because of the parallel FH
structure setup. However, the displacement for the required stroke of f = 1.5 mm
amounts to approximately 56 µm. With a magnet clearance of χ= 0.15 mm, enough
space between the magnet and the coils is foreseen, even for longer strokes possibly
provoked by launch shakings.
6.4
Measurements
Static and dynamic measurements were performed with the constructed MSTS DM to
determine the mechanical and electromagnetic parameters, which are required for the
49
Coil Dimension
ζ
hC
χ
NdFeB
lC
2
d
lC
lM
Figure 6.2: Helmholtz VCA dimension parameters shown in the axisymmetric cross
section.
hC
n=
m=
dD
lC
dD
N tot = 2mn
L = 2δ + 2l C + l S
R = rM + ε + hC + ζ
Boundary Conditions
l S = 1.3mm
(due optimization)
δ = 0.25mm (adjustment clearance)
L = 9mm
(boundary condition)
R = 3mm
(boundary condition)
ζ = 0.1mm ( glue thickness)
ε = 0.15mm (magnet clearance)
Coil wire diameter dD with insulation and copper thickness of 0.15mm.
1. single coating
2. double coating fineFigure 6.3: Photo of the MSTS DM.
3. double coating thick
No.
1
2
3
dD / mm
0.164
0.174
0.185
Comments
•
•
⎣n⎦
10
10
9
⎡m⎤
22
21
20
Ntot
440
420
360
Rtot / Ω
5.46
5.21
4.47
Imax / mA
495
518
604
Fmax / mN
127.9
127.8
127.7
P/W
1.34
1.4
1.63
50
UC=2.7V as maximum output voltage of an applicable H-bridge amplifier.
Increasing the wire thickness lowers the resistance, thus increases the force and, however, the dissipated
power.
Parameter
fres
m
c
k
RC
L
Value
109.1 Hz
194.6 mg
91.46 Nm−1
1.652 · 10−3 kgs−1
1.712 Ω
38 µH
Table 6.3: Measured mechanical and electromagnetic parameters of the MSTS DM.
Note that the spring constant c was not measured for the MSTS DM, but was deduced
from the step response and, therefore, slightly differs to the value listed in table 6.1
design of the control electronics. Since the MSTS builds a electromechanical system,
the calculated parameters resulting from the separated considerations discussed in the
previous sections must slightly differ to the measured parameters. Table 6.3 lists the
measured parameters of the MSTS DM.
6.4.1
Static Measurement
The spring constant can be determined by a force measurement at static deflections.
Figure 6.4 shows the resulting linear characteristic of the MSTS FH structure, whereas
its slope corresponds to the spring constant, which can be calculated to c = 82.3 Nm−1 .
This value almost coincides with the simulated value (tab. 6.1). Thus, it can be concluded, that the leafs of MSTS FH structure were accurately cut by the manufacturer.
6.4.2
Dynamic Measurement
Figure 6.5 shows the measured step response of the MSTS DM VCA excited by a
symmetric rectangular signal with f = 0.9 Hz. Due to the weak damping ratio D, the
highest peak reaches almost the double value of the steady state amplitude. The system’s resonant frequency can be determined to fres = 109.1 Hz. With (4.11) to (4.13),
the attenuation constant can be calculated to k = 1.652·10−3 kgs−1 . When considering
this measurement result, it becomes obvious, that the MSTS control electronics must
be very well adjusted to reach the required open/close time.
The spring mass can be calculated with (4.10) to m = 194.6 mg considering the measured spring constant c and the attenuation constant k. These values will be used to
define the experimental model of the control path.
51
140
120
P / mN
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
f / mm
1
1.2
1.4
1.6
Figure 6.4: Static force measurement of the MSTS FH structure which results in a
spring constant of c = 82.3 Nm−1 .
1.2
1
0.8
0.6
f / mm
0.4
0.2
0
-0.2
-0.4
-0.6
0
0.5
1
1.5
2
2.5
t/s
Figure 6.5: Measured step response of the MSTS DM VCA. The VCA was excited by
a symmetric rectangular signal with f = 0.9 Hz. Because of the weak damping ratio
D, the transient period is relatively long.
52
Chapter 7
Electronics
7.1
7.1.1
Control Electronics
Power Amplifier
The design of the control electronics for the DM was mainly driven by the selection
of an adequate power amplifier for the Helmholtz VCA. Two possibilities were discussed named as
• push pull Operational Amplifier (OPAMP) and
• bridge amplifier.
Due to the small attenuation constant of the FH structure and the resulting blade
oscillations, relatively high braking currents are required to guarantee the switching
mode (fig. 2.1). Therefore, the power amplifier must drive currents in both directions
through the coil, which can be realized by a push pull OPAMP. The low required
supply voltage of 3.4 V allows maximum driving voltages of ±1.5 V even with rail-torail amplifiers1 . Thus, the coil resistance must be kept small for reaching high driving
currents. The coils can favorably be connected in parallel in the Helmholtz VCA
setup, which halves the total coil resistance.
With the MSTS DM’s Helmholtz coil resistance of RC = 1.712 Ω (tab. 6.3) and the
minimum driving current of IC = 1.2 A, a minimum driving voltage of UC = 2.05 V
results. Therefore, it is necessary to select a bridge amplifer for the MSTS DM control
1
Note that the supply voltage requirement (tab. 2.1) was changed to 3.4 V during the design
phase.
53
7 – ELECTRONICS
D
I
P
w
P
+
r
y
x
_
Sensor
Figure 7.1: Functional schematic of the control electronics. The operational amplifier compares w with the feedback variable r. Directly implemented in the OPAMP
circuit are the P-, I- and D-contributions indicated with dashes rectangles. A second
P-contribution is implemented in the bridge amplifier, which consists of two power amplifiers. The position of the MSTS DM, replaced by the coil symbol, will be contactless
measured with the sensor and returned as feedback signal to the comparator.
electronics, because a push pull OPAMP circuit cannot reach this minimum driving
voltage.
7.1.2
Controller
When considering the measured step response of the MSTS DM (fig. 6.5), it is reasonable to define PT2 behaviour for the control path. For the DM, a classical PID
controller based on an operational amplifier as shown in [7] was applied. Since no sensor was definitly selected for the position feedback, the controller had to be designed
for fulfilling all wiring possibilities of the P-, I- and D-contributions. Figure 7.1 shows
the functional schematic of the realized control electronics. This figure is leaned on the
standard closed loop system (fig. 4.9). An operational amplifier compares w with x,
which is conditioned with an additional circuit. The control contributions are directly
implemented in the OPAMP circuit indicated with dashed rectangles.
In the circuit diagram (appendix C), the feedback signal conditioning circuit consists
of three additional OPAMPs to compensate the offset, adjust the gain and invert the
signal if needed. This circuit diagram shows the breadboard electronics design, which
offers a large range for adaption.
54
7 – ELECTRONICS
7.1.3
Sensor
The laser triangulator optoNCDT 1700 from MICRO-EPSILON2 was applied as
position measuring sensor for the static and dynamic measurements. Furthermore,
it was used as feedback sensor for the control electronics breadboard, whereas the
conditioning circuit was adjusted to compensate the sensor’s output signal range of
0 . . . 10 V. It must be mentioned that the optoNCDT 1700 causes a dead time of
1.2 . . . 1.6 ms due to the internal analog-to-digital conversion. However, this seems to
be useful at the first glance and will be discussed in the following section.
A sensor for the position feedback must be found which is
• small,
• lightweight,
• shows a linear input to output characteristic,
• operates with a maximum supply voltage of +3.4 V and
• causes virtually no dead time.
Different sensor systems were evaluated e.g. inductive, capacitive, optical and Hall
effect sensors. Thereby, the latter turned out as most promising because of the already
existing moving magnet in the MSTS VCA, which can directly stimulate the sensor.
An applicable space qualified sensor was not found up to the day of submission of this
thesis, but is to be determined for the further project phase.
7.2
Control Results
For closing the design and construction part within this thesis, the first achieved results
of the controlled MSTS DM presented in figure 7.2 will be discussed. When focussing
on the lower curve in the right part of this figure, it becomes clear, that the switching
mode requirement can be satisfied with the controlled MSTS DM. The open/close time
can be measured to < 5 ms and is therefore shorter than the value listed in table 2.1.
In the right part of figure 7.2, a switching period of ≈ 100 ms is identifiable. Note the
almost entirely suppression of the decaying oscillations, which otherwise occur in the
2
http://www.me-us.com/laser-sensor/ accessed on July 5, 2008.
55
7 – ELECTRONICS
step response measurement of the uncontrolled MSTS (fig. 6.5). The stroke amplitude
amounts to f ≈ 1.2 mm and is slightly below the required stroke. Therefor a peak
current of IC ≈ 1.3 A must be applied, what can be deduced from the upper curve.
As stimulus, a rectangular LVTTL signal was applied with a frequency of 10 Hz and a
duty cycle of 20 %. The controller only consists of a P-contribution, what surprises at
the first glance when considering the stroke measurements. Now the fact of the dead
time in the feedback path, caused by the laser triangulator, must be discussed. This
dead time is directly discoverable as the time shift of the two measured curves. Therefore, the set point (IC ) spurts to around the half amplitude and then stays constant
for ≈ 2 ms until the feedback signal reaches the comparator. The time constant of
the Helmholtz coil can be calculated to τL = L/R ≈ 22 µs and has an insignificant
influence to the blades open/close time.
The control variable x, which corresponds to the blade stroke f , shall follow the set
point as accurate as possible to reduce the error signal e to a minimum. Here, just a
proportional controller3 was applied, what typically does not suffices for well controlling a control path with PT2 behaviour. Hence, undetermined capacitives occuring in
the whole control loop optimize the controller, that the required behaviour just can
be achieved. Further investigations must be performed for the controller design when
an adequate sensor will be applied.
3
Note that the P-contribution was manually adjusted with help of a potentiometer until the
required behaviour was achieved.
56
STS
7 – ELECTRONICS
P-Control
25.05.2008
Figure 7.2: Results of the controlled MSTS DM, which fulfills the required switching
mode. The left part shows one cycle measured in t = 20 ms/DIV, whereas the right
part is zoomed in to t = 5 ms/DIV. The lower curves of both parts show the stroke of
the blade measured with the optoNCDT 1700 represented in f = 0.4 mm/DIV. The
upper curves show the controlled current IC measured in 0.5 A/DIV.
H:\MERTIS_HUA\MSTS DM Control Electronics\Measurements
57
Chapter 8
Conclusions, Status and Open Work
A voice coil actuator driven shutter based on a flexible hinge structure was concluded
in the study [5] for the design of the MERTIS short term shutter. Within this master
thesis, it could be showed, that the implementation of this selection is capable to fulfill
all requirements. The electromagnetic and mechanical parts were designed with help
of analytic and FEM calculations in view of harmonizing all parameters and resulted in
the construction of the MSTS DM. To reach this goal, investigations in the fundamentals of material properties, flexible hinges and electromagnetics had to be performed.
The parameters were adjusted to minimize the power consumption, the dimensions
and the mass of the MSTS DM. However, this couldn’t be performed staightforward
due to reciprocal relations, what rather caused a parameter optimization.
The mechanical structure with the flexible hinges was deviated from a the linear stage
with necked down flexures presented in [4]. But for the voice coil actuator, an unconventional design based on two anti-coupled coil was proposed, realized and labeled
as Helmholtz VCA. This VCA design shows an improvement of the generated
Lorentz force of around 80 % compared to an equivalent single coil VCA. Theoretic
considerations of this electromagnetic design let assume a lot of advantages, which
could be proved with adequate measurements.
The low damping ratio of the MSTS DM is a result of the force reducing sanctions for
fulfilling the power and open/close time requirements. Therefore, a control electronics
was designed to achieve the required blade switching mode. A laser triangulator was
applied as feedback sensor, whereby satisfying results of the closed loop system could
be optained.
58
8 – CONCLUSIONS, STATUS AND OPEN WORK
As a result from the MERTIS shutter study, life time and fail safe are quoted as
most important requirements, which can be met with the designed and constructed
MSTS DM. Up to the day of submission of this thesis, the constructed MSTS DM
performed almost 50 million cycles without identifiable damage. However, this must
be investigated in regard to occuring microcracks in the thin FH blades. Detailed
material and lifetime tests must be noted as open work, as well as the definition of a
space qualified sensor and control electronics.
Albeit the MSTS DM must be sligthly adpated for the ultimate integration in the
MERTIS instrument due to continual structur and optics changements, a solid base
was achieved with the presented construction, whereon the following engineering and
flight models can be built.
It is still a long way to go until the scheduled launch of BepiColombo in 2013. So, let’s
use the time for upgradings and—as free side effect—to learn from every performed
step.
59
APPENDIX
60
Appendix A
Deviation of the Logarithmic Decrement
Calculating the logarithmic decrement δ is important for the determination of the
damping ratio D of a mechanical system. The formulas presented in [7] allow to
calculate D when the stationary amplitude x0 is known, to which ∆1 and ∆2 can be
related. When the system cannot reach a steady state due to a periodical excitation,
the amplitude of a third peak is required for calculating δ. In the following part, the
required formulas will be derivated refering to figure A.1.
With
∆1
∆2
=
∆2
∆3
and a simple geometrical consideration follows
δ=
(A.1)
∆1 ∆3 = ∆22
(A.2)
∆1 + ∆2 = x1 − x2
(A.3)
x 3 = x2 + ∆ 2 + ∆ 3 .
(A.4)
When substituting (A.2) with (A.3), the quadratic equation
∆22 + ∆2 ∆3 − ∆3 (x1 − x2 ) = 0
(A.5)
results with the roots
∆2(1,2) =
−∆3 ±
p
∆23 + 4∆3 (x1 − x2 )
.
2
(A.6)
(A.4) can now be written as
2x3 = 2x2 + (−∆3 ±
q
∆23 + 4∆3 (x1 − x2 )) + 2∆2
(A.7)
61
A – DEVIATION OF THE LOGARITHMIC DECREMENT
T0
x1
Δ3
x / a.u.
Δ1
Δ2
x3
x2
t / a.u.
Figure A.1: Step response function with the indicated parameters.
and solved to
−x23 + 2x2 x3 − x22
.
(A.8)
2x2 − x3 − x1
Finally a set of three reqursive formulas can be defined for the calculation of the
∆3 =
logarithmic decrement with three absolute peak amplitudes to
(x2 − x3 )2
2x2 − x3 − x1
∆2 = x3 − x2 − ∆3
(A.10)
∆1 = x1 − x2 − ∆2 .
(A.11)
∆3 = −
(A.9)
62
Appendix B
MSTS DM Design Drawing
63
Appendix C
MSTS DM Breadboard Electronics Circuit
Diagram
65
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A
A
STS_+3V4
STS_+3V4
R42
10R
Header
D-Sub
+2V5
+3V0
C44
C45
C42
220uF
100nF
100nF
100nF
100nF
(U20)
(U21)
(U70)
R40
220R
A
VR40
TL431
4
C43
C
C40
R41
56R
C
9
8
7
6
5
4
3
2
1
LVTTL_GND
C41
(U10)
(U30)
X10
SV10
100nF
11
11
(U70)
R
+
4
B
R43
0R
(U10)
SENSOR_OUT
+3V0
RTN_+3V4
1
2
3
4
5
6
7
8
STS_+3V4
RTN_+3V4
MSTS_CLOSE_NOM
MSTS_POS_DIG
COIL+
COIL-
B
9
10
11
12
13
14
15
MSTS_TEMP_MAIN+
MSTS_TEMP_MAINLVTTL_GND
MSTS_POS_ANA_MAIN
MSTS_CLOSE_EME
MSTS_TEMP_RED+
MSTS_TEMP_REDC
RTN_+3V4
RTN_+3V4
RTN_+3V4
RTN_+3V4
C101
C100
MSTS_CLOSE_STAB
Control
D
Emergency
R93
U10A
R90
1
R95
STS_+3V4
STS_+3V4
STS_+3V4
R22
1k
TLV2764
U10B
5
R91
7
9
13
R19
F
U20
OPA567
U21
OPA567
8
COIL_NOM+
2
3
1k
TLV2764
R97
R94
R25
14
TLV2764
TLV2764
U10D
12
0R
6
R18
R98
8
R92
9
R96
+1V0
8
2
3
9
COIL_NOM-
1k
RTN_+3V4
R60
F
T60
BFS20
10k
R24
6.8k
R23
6.8k
RTN_+3V4
E
+1V5
MSTS_CLOSE_EME
RTN_+3V4
K60
G6A-274P-ST_US
D60
MLC1N4148
6
5
4
R17
1
12
U10C
10
4
5
6
R15
RTN_+3V4
1k
1
R16
2k2
SENSOR_MOD
2
E
R21
16
3
R20
12
1
R14
SENSOR_OUT
D
+3V0
R13
R12
+3V0
Bridge Amplifier
R103
R102
R101
R100
C103
C102
R61
STS_+3V4
RTN_+3V4
RTN_+3V4
RTN_+3V4
RTN_+3V4
G
G
Signal Conditioning
STS_+3V4
R73
R75
Ur
Constant Current Regulator
Vref
R50
10R
R71
STS_+3V4
+2V5
H
U30
LT1086
IN
+1V5
RTN_+3V4
3
SENSOR_OUT
U70A
1
U70B
5
7
R74
2
R54
10k
+1V5
TLV2764
R30
1R / 2W
ADJ
R51
20k
MSTS_POS_DIG
6
S1
OUT
COIL_NOM+
O1
S2
K60
COIL+
COIL_NOM-
O2
P2
R72
P1
R70
H
K60
COIL-
R
R52
10k
STS_+3V4
A
STS_+3V4
C
TLV2764
I
RTN_+3V4
LVTTL Stabilization
VR50
TL431
I
+1V0
MSTS_CLOSE_STAB
R87
R81
R53
20k
U70D
+1V5 10
R83
K
U70C
8
12
14
R86
MSTS_POS_ANA_MAIN
Tag
R55
7.5k
13
9
Bearb.
RTN_+3V4
RTN_+3V4
TLV2764
SENSOR_MOD
R84
TLV2764
R85
Name
20.03.08 HUA
R89
MSTS_CLOSE_NOM
R88
R57
R56
10k
zu Gerät
MSTS DM Control Electronics
MERTIS
10k
R82
K
Benennung
Gepr.
Q50
BSS123
R58
zu Anlage
Zeichnungs-Nr.
1
L
RTN_+3V4
RTN_+3V4
RTN_+3V4
RTN_+3V4
1
RTN_+3V4
Rev
1
2
3
4
5
6
7
8
9
10
11
First Issue
Änderungs-Nr.
12
L
05.03.08 HUA
Tag
13
Name
MSTS_DM_V1_0
14
Blatt 1/1
15
02.04.2008 11:46:29
16
List of Figures
Figure
page
1.1
BepiColombo emblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
MERTIS instrument model . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.3
MERTIS instrument block diagram . . . . . . . . . . . . . . . . . . . . . .
5
2.1
Shutter blade switching mode . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
MSTS integration space . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.1
Shutter actuation principles . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4.1
Flexible hinge patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
4.2
Ti-6Al-4V fatigue tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
4.3
Parallel blade stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
4.4
Technological limitations of wire-cut EDM . . . . . . . . . . . . . . . . . .
17
4.5
VCA models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
4.6
Calculated magnet field distribution of a cylindric single coil . . . . . . . .
25
4.7
Calculated Lorentz force distribution of a single coil VCA . . . . . . . . .
25
67
List of Figures
4.8
Interaction map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
4.9
Standard closed loop system . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.10 Models of the spring mass system and the RL circuit . . . . . . . . . . . .
28
4.11 Model of the control path . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
5.1
Thermal networks for moving coil and moving magnet . . . . . . . . . . .
31
5.2
Thermal analysis curves . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
5.3
FEMM meshing and calculation result . . . . . . . . . . . . . . . . . . . .
34
5.4
Single coil VCA force distribution measurement result . . . . . . . . . . .
37
5.5
Photo of the test shutter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
5.6
Helmholtz VCA simulation with d = 0.5 mm . . . . . . . . . . . . . . . . .
42
5.7
42
5.8
43
5.9
Maximum force to clearance of the simulated Helmholtz VCA . . . . . . .
43
5.10 Helmholtz VCA energy optimization . . . . . . . . . . . . . . . . . . . . .
44
5.11 Helmholtz force dirstribution measurement . . . . . . . . . . . . . . . . .
44
5.12 Step responses of the equal coupled and the anti-coupled Helmholtz VCA
45
6.1
MSTS DM CAD model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
6.2
Helmholtz VCA dimension parameters . . . . . . . . . . . . . . . . . . . .
50
6.3
Photo of the MSTS DM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
6.4
Static force measurement of the MSTS FH structure . . . . . . . . . . . .
52
68
List of Figures
6.5
Measured step response of the MSTS DM VCA . . . . . . . . . . . . . . .
52
7.1
Control electronics principle . . . . . . . . . . . . . . . . . . . . . . . . . .
54
7.2
Results of the controlled MSTS DM . . . . . . . . . . . . . . . . . . . . .
57
A.1 Step response function . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
69
List of Tables
Table
page
2.1
MSTS requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
4.1
FH material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
4.2
Magnet material properties . . . . . . . . . . . . . . . . . . . . . . . . . .
23
5.1
Thermal model properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
5.2
Test VCA parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
5.3
Helmholtz VCA simulation parameters . . . . . . . . . . . . . . . . . .
39
5.4
Helmholtz VCA test setup parameters . . . . . . . . . . . . . . . . . . .
40
6.1
MSTS DM mechanical design parameters . . . . . . . . . . . . . . . . . .
47
6.2
MSTS DM electromagnetic design parameters . . . . . . . . . . . . . . . .
49
6.3
Measured MSTS DM mechanical and electromagnetic parameters . . . . .
51
70
Bibliography
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72
Name
Andreas Hurni
geb.
30.11.1982
Matr. Nr. 83766088017
06MNM
im SS 2008
Erklärung
gemäß § 13 Abs. 5 RaPO
Hiermit erkläre ich, dass ich die Masterarbeit selbständig verfasst, noch nicht anderweitig für Prüfungszwecke vorgelegt, keine anderen als die angegebenen Quellen oder
Hilfsmittel benützt sowie wörtliche und sinngemäße Zitate als solche gekennzeichnet
habe.
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Ort, Datum
Unterschrift

Master Thesis Design and Construction of the Shutter Demonstrator

Transcription

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