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BOSTON UNIVERSITY

COLLEGE OF ENGINEERING

Thesis

DESIGN ND

TESTING o F A

NOVEL MODUL R

N NOS TELLITE STRUCTUR L

BUS

by

N TH N

THOM S

D RLING

B.A. , Saint Michael s College, Colchester , Vermont, 2004

Submitted in partial fulfillment of the

requirements for

the

degree of

aster of Science

2013



First

Reader

Second Reader

Third Reader

Approved by

Raymond Na gem

Ph

Professor of Mechanical Engineering

Theodore A F r i t z Y n

~ · -

Professor of Astronomy



©

opyright by

Nathan

Thomas arling

2 13



Es verdad; pues reprimamos

esta fiera condici6n

esta furia esta ambici6n

por si alguna vez soiiamos;

s{ haremos pues estamos

en mundo tan singular

que el vivir solo

es

sonar;

la experiencia

m

enseiia

que el hombre que vive sueiia

lo que es hasta despertar.

Pedro Calderon de la arca



cknowledgments

hanks to Professor Theodore A. Fritz, who offered me enough rope on the first

day

of the job, as he has done

with

great success for a great many students. Also to

the many

undergraduate and graduate

students

(past and present) who have worked

harder

than most anyone I know

to

juggle a huge course load nd long hours on

hardware development, design review posters, and whatever else it takes

to

get the

project out the

door on time. Finally, I would like to thank Krista, who doesn't like

satellites very much, for supporting me when I really needed it.

Figure ·1: Sipping from the fire hose.



DESIGN ND TESTING OF

NOVEL

MODUL R

N NOS TELLITE STRUCTUR L BUS

N TH N THOM S D RLING

ABSTRACT

Launch cost per unit mass is the most consistent and largest cost driver for any

modern

spaceflight mission,

with

quoted per-kilogram launch f s in

the

thousands

or

tens

of thousands of dollars. This is followed

by the

costs associated with long

development schedules, shifting mission requirements, radiation-hardened electron

ics

and

other similar systems engineering constraints common to satellite develop

ment

efforts. The Boston University

Student

satellite for Applications and Training

(BUSAT) responds directly to these issues by providing a modular satellite

bus

archi

tecture addressing

the

early hardware lifecycle from concept development

to launch

.

BUSAT s novel approach to

the

logistics of satellite structural integration supports

a novel plug-and-play software and physical-layer architecture. Unique pressure-lock

fastening techniques not only allow very fast integration but also display excellent

frequency response characteristics when subjected

to

stringent vibration tests. The

unique cubic geometry of BUSAT s modular structure allows mission

planners

better

control over cost and risk before launch, including the ability to predict features of

the structure s frequency response over a variety of payload configurations.

vi



Contents

Introduction

1.1 Small Satellites and Scientific Space . 1

1.2 B

oston

University and Scientific Space 3

1.2.1 Background:

The

University

Nanosat

Pro

gram

UNP)

4

2 Requirements

Development

5

2.1 Requirements Identifi

cation

and Flow-down . . . . . . . . . . . . . . 5

2.1.1

The

BUSAT

Primary

Science Mission: Ionosphere-

Magnetosphere

Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Space Plug-

and-Pla

y

Proto

col

Operationally

Responsive Space

ORS)

and the

Getting to

Space . . . . . . . . . . . .

2.3 Mission Overview

and Concept

of

Operations

2.4 High-level Mechanical Bus R

eq

uir

ements

2.5 Low-level Design R

eq

uirements

2.6 Solar

Panel

Deployment . .

2.7 Nanosat-5

Inherited

Design

Featur

es

3

Structural Design

3.1

Components

3.1.1

Hub

3.1.2

Cube

Stack

3.1.3 Endoskeleton

3.1.4 Exoskeleton .

vii

7

1

11

13

13

14

7

18

18

23

24

25



301 5 Deployables

302

~ s s e n a b l y

0 0

303

Mass Budget

Vibration

Testing

401

Background 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

401 1 Vibration Testing for Snaall Satellites

401.2 Mechanical Vibration Testing

5 Data

Analysis

50003

Observations

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

500 4 Sunanaary of

ata

Gathered and Conclusion

6

Analytical Model

601

Introduction 0 0 0 0 0 0 0 0 0 0 0

602 Danaped Mechanical Oscillators

603 Multiple Degrees of Freedona 0 0

6.4 Danaped Frequency Response for Multiple Degrees of Freedona

605 Spring Coefficients

and

Forcing

Input o t i o n ~

606 Three Degree of Freedona Model 0 0 0 0 0 0

6 7 Nine Degree of Freedona Model Coupled)

608 Twenty-seven Degree of Freedona Model Coupled)

609 Franaework of ~ n a l y s i s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

609

01 Building Mass, Spring and Danaping Matrices

6010

Initial Results

6011 Discussion 0 0

7

Results

and Conclusion

701

Design 0 0 0 0 0 0 0 0 0

Vlll

26

29

30

4

34

34

36

44

44

59

6

60

61

64

64

66

69

74

77

78

85

86

92

95

95



7 2 Testing . .

. . .

. . . . . . . . . . 95

7 3 Thned

27

Degree of Free

dom

Model and Comparison to Vibration T

est

Dat a .

.

.

.

96

A

MATLAB Script

for 1 DOF

Model

98

B

MATLAB Script

for

3 DOF Model

102

MATLAB Script

for

9 DOF Model

107

D

MATLAB Script

for 27 DOF

Model

115

References

130

E Vita

132

lX



List of igures

0·1

Sipping from the fire hose. . . .

1·1

The

Pumpkin CubeSatKit 1U picosatellite structure, commercially

available and used widely accross academia, industry and even the

v

military. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1·2

The

ANDESITE mission, a Boston University 3U CubeSat currently

approved for funding from the Air Force Office of Scientific Research.

Andesite will explore fine-scale filamentation in the Earth s magneto-

sphere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2·1 Requirements originate from the Principal Investigator via high-level

mission definition, the University Nanosat Program via industry stan-

dards for safety

and

best practices. Additionally, BUSAT has identified

a niche opportunity in the pico- and nanosatellite indust ry from which

requirements are sourced. . . . . . . . . . . . . . . . . . . . . . . . . . 5

2·2 The Space Experiments Review Board (SERB) 2012 rankings include a

total CubeSat volume of over 40U in experimentation awaiting launch

opportunities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2·3 BUSAT seeks

to

optimize

the

pre-launch lifecycle,

with particular

em

phasis on tolerance

to

late, game-changing requirements shifts and the

lengthy integration process. . . . . . . . . . . . . . . . . . 9

2·4 The BUSAT Low-Earth orbit (LEO) concept of operations.



2·5 BUSAT's 1U solar panel design costs

about

150 in

parts and takes

less

than three

hours

to

build using refiow solder techniques but do

not

perform as well as more expensive cells.

PCB substrate

is shown at

left, finished component is shown at right. . . . . . . . . . . . . . . . 14

2·6 Nanosat-5 model

structural

spacers (not

to

scale). From left: exterior

spacers arranged in

top

panel configuration, interior spacer (original

model, unmodified), hexagonal spacer. 15

2·7 1-U, 2-U

and

3-U Cube Structures. . . 16

3·1 Early concept sketch of

the

BUSAT mechanical architecture. 17

3·2

The

BUSAT satellite shown before solar panels are deployed. 18

3·3 Exploded views of

the

BUSAT Hub (upper assembly) and Endoskele-

ton

showing

the

hub

PC\

104 printed circuit

board

stack, connectors,

and four routing boards. . . . . . . . . . . . . . . . . . . . . . . . . . 19

3·4 Detail from

the PC\1 4

embedded systems

standard

showing fastener

placement , header (right) and keep-out areas.

3·5 Detail view of

the

hub stack assembly showing

three

midplane stand-

offs Each standoff fastens

to the

external

hub

walls in a slotted groove

that

allows variations in

hub

stack height

due to

non-standard

PC\1 4

20

overhead height in

COTS

components. . . . . . . . . . . . . . . . . . 21

3·6 Detail view of

bottom cap

and

three hub

walls integrated.

Aper

t ures

for 25-pin and SMA connectors are shown, as well as a tongue-and

groove fastening technique

that

minimizes

the

need for fasteners along

the

entire length of the hub, and the labeled

PC\

104

bolt

pattern. . . 21

Xl



3· 7 Top left : schematic

top

view of

the

BUSAT wiring harness. Composed

of several standardized

short

cable harnesses, this wiring method alle

viates the need for costly and time-consuming one-off harness design

and

allows the hub to be removed from the satellite at any time during

integration. Top right: side vew of the harnessing scheme from the

payload (left)

to

endoskeleton to hub (right) . . . . 22

3·8 The

hub

. Inset: A 45° filet fixes

the hub

in place.

3

3·9 The Birtcher WedgeLok is

the

principal fastener used in BUSAT s eas-

ily integrable design. A torque applied to the tension bar results

in

a

lateral

pressure applied to the

cube

stack.

3·10 Twelve

WedgeLok™s are distributed around

the cubestack and pro

vide sufficient clamping force to restrain BUSAT s payload bay during

launch . . . .

3·11 The BUSAT exoskeleton.

3·12 The BUSAT-NMT Langmuir Probe shown

protruding

through the ex

oskeleton

top

panel. . . . . . . . . . . . . . . . . . . . . . . . .

3·13 The BUSAT satellite showing modular solar panels deployed

3·14 The TINI Aerospace Frangibolt (shown

in

red)

with

associat

ed

housing

3

24

5

5

6

and custom

titanium

flange for heat isolation. . . . . . . . . . . . . 27

3·15 Cross-sectional view of the cup-cone kinematic mounting structure. 27

3·16

Th

e BUSAT deployable

panel

stowed and completely

constrained

(at

left) by the TINI Aerospace 4 Frangibolt and

(at

right) by a titanium

groove (to avoid cold-welding under extreme vibration. . . 28

3·17 The tongue-and-groove kinematic mount after deployment. 28

Xll



3·18

The

BUSAT assembly procedure (top left

to

bottom right) begin

ning with

the

exoskeleton bottom plate, endoskeleteon, cube stack,

WedgeLok™s and hub. . . . . . . . . . . . . . . . 29

3·19 BUSAT s mass breakdown arranged by subsystem. 30

4·1 Nanosat-5 integration and test flow (from NS-7 User s Guide) 34

4·2 Mechanical Test Flow (from NS-7 User s Guide). . . . . . . . . 35

4·3 Concept schematic of Thermotron vibration

table

control loop. (5) . 36

4·4 Schematic view of the structural test as performed at the Draper ETF

showing control accelerometer

mounted

on the

shake table

armature.

37

4·5 Conceptual representation of SRS plot generation

and

vibration table

control showing (in red) control accelerometer input

to

a virtual mass

spring-oscillator array implemented within the control software. The

model simulates a system response based on

the

control accelerometer

input , and this signal is plotted (red). Control software commands

based on

this

simulation are

then

passed to a power amplifier which

sends current to the

table

s inductive coils, imparting an acceleration

to

the table and again causing the control accelerometer to feed back to

the

software oscillator model. The number of oscillators in the software

model (n) determines resolution (5) . . . . . . . . . . . . . . . . . . . 38

4·6 Typical plot of sine sweep acceleration vs. frequency. This is an in-axis

response. . . . . . . . . . . . . . . . . . . . ·. . . . . . . . . . . . . . . 39

4· 7 Typical plot of sine burst acceleration as a function of

time

. This is an

in-axis response. . . . . . . . . . . . . . . . . . . . . . . . . .

4

4·8 Random vibration response raw

data

from 20Hz

to

2000Hz 42

xiii



4·9 Typical

time

history of shock test.

This

is an in-axis response. Ramp

up and ramp down motion can be seen from 0.00 ms

to

0.04 ms

and

from 0.06 ms

and

0.09 ms. . . . . . . . . . . . . . . . . . . . . . . 43

5·1

C-channel assembly. . . . . .

46

5·2 First Diagnostic Sine Sweep. Run 1: Z-Axis. 48

5·3 Channel 4 only. Diagnostic Sine Sweep Runs 1, 3 5 and 9.: Z-Axis. 49

5·4 Diagnostic Sine Sweep, Run

14:

X-Axis. All Channels.

5·5 Diagnostic Sine Sweep,

Run 19:

Y-Axis. All Channels.

5·6 Sine Burs t,

Run

02:

Z-Axis. All Channels.

5·7 Sine Burst , Run 11: X-Axis. All Channels.

5·8 While still within specifications, the BUSAT structure does display

some shift in lowest

natural

frequency. Generally, the peak shifted

lower by

around

10 to 20 z after each subsequent test (frequency

51

51

53

53

and

magnitude are labeled for each of the four response curves). 56

5·9 Elastic modulus as a function of

temperature.

. . . . 56

5·10 Evidence of wear on

the

anodized surfaces of a cube. 59

6·1 The model developed in this section seeks to determine the BUSAT

satellite's frequency response based on the characteristics of

the

pay-

load bay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6·2 A basic mass, spring,

and

damper system where the motion of mass

min

response

to

an excitation .;(t) is described by the

state

variable x

measured from

the

origin in

the

upper

left

hand

corner of

the

diagram

. 61

6·3 A single degree of freedom mass, spring and

damper

system with two

points of coupling to the oscillating platform. . . . . . . . . . . . . . . 63

6·4 Single degree of freedom mass-spring-damper system displacement re-

sponse plotted over frequency.

68

xiv



6·5 Single degree of freedom mass-spring-damper system acceleratation fre-

quency response

plotted

over frequency. . . . . . . . . . . . . . . . . . 69

6·6 A three degree of freedom mass, spring and

damper

system

with

four

points of coupling to the oscillating platform. . . . . . . . . . . . . . . 70

6·7 Generalized free-body diagram for the three degree of freedom system. 71

6·8 Three degree of freedom forced mass-spring-damper acceleration re

sponse

plotted

over frequency.

Undamped

natural frequencies

are

marked by vertical lines. .

73

6·9 Schematic representat ion of a general planar cube array element sur-

rounded

by

four masses, four springs

and

four dampers. . . . . . . . . 74

6·10 Masses 1-3 of a nine degree of freedom forced mass-spring-damper fre

quency response plotted over frequency. Undamped natural frequencies

for each mass are marked by vertical lines. . . . . . . . . . . . . . . .

75

6·11 Masses 4-6 of a nine degree of freedom forced mass-spring-damper fre

quency response plotted over frequency. Undamped natural frequencies

for each mass are marked

by

vertical lines. . . . . . . . . . . . . . . . 76

6·12 Masses 7 9 of a nine degree of freedom forced mass-spring-damper fre

quency response

plotted

over frequency. Undamped natural frequencies

for each mass are marked by vertical lines. . . . . . . . . . . . . . . . 77

6·13 The BUSAT

standard

satellite-fixed reference frame. The unit vectors

i

3

and are assigned

to

the

x

y and

z

axes, respectively. . . . . . . 79

6·14 A one-to-one transformation between payload cube position and state

variable subscript, as shown in Table 6.2. . . . . . . . . 80

6·15 Two-dimensional representation of the satellite cell array. 82

6·16 SolidWorks FE displacement analysis of Top Plate. . . 87

X



6·17

Acceleration response for masses XI x

2

and x

3

.

Subscripted mass

notation can be converted using Table 6.2

• • 0 • •

88

6·18

Acceleration response for masses x

4

x

5

and x

6

.

Subscripted mass

notation can be converted using Table 6.2 • • • •

88

6·19


7

x

8

and x

9

.

Subscripted mass

notation can be converted using Tab le 6.2 • • • • •

89

6·20

Acceleration response for masses

x

10

x

11

and xi

2

.

Subscripted mass

notation

can

be converted using Table 6.2

89

6·21 Acceleration response for masses

XI

3

XI

4

and

5

. Subscripted mass


90

6·22 Acceleration response for masses

6

XI

7

and XIs· Subscripted mass

notation

can

be converted using Tab le 6.2

90

6·23 Acceleration response for masses x

19

x

20

and x

2

·

Subscripted mass

notation can

be

converted using Table 6.2

91


22

x

3

and x

24

. Subscripted mass

notation can

be

converted using Table 6.2 91


5

x

26

and x

27

. Subscripted mass


92

6·26 Acceleration response for mass XI3 located in the center of the top

layer of the satellite cube stack. . . . . . . . . . . . . . . . . . . . . . 93

6·27 Acceleration response for mass x

1

9

located

at

a corner of the top layer

of the satellite cube stack.

6·28

xvi

93

94



List of bbreviations

AIAA . .

AFOSR

.

AFRL/RV

BU NSP . .

BUARC .

COG .

COTS .

EPS .

ETF

. . .

FCR .

IES .

MGSE .

PCB

.

PSD

.

RMS .

RPI

.

SIF . .

SIP . . .

.

SRS . . . . . .

TID . . .

UNP

. . .

VLF .

American Institute of Aeronautics and Astronautics

Air Force Office of Scientific Research

Air Force Research Laboratory s Space Vehicles

Directorate

Boston University Near Space

Program

Boston University Amateur Radio Club

Center of Gravity

Commercial Off-The-Shelf

Electronic Power Supply

Environmental Test Facility

Final Competition Review

Imaging Electron Spectrometer

Mechanical Ground Support Equipment

Printed Circuit Board

Power Spectral Density

Root Mean Square

Remote Polar Imager

Scientific Instruments Facility

Satellite Interface Plane

Shock Response Spectrum

Total Ionizing Dose

University Nanosat Program

Very Low Frequency

xvn



hapter

Introduction

1 1 Small

Satellites and

Scientific

Space

Since 1957

and

the launch of the Russian

Sputnik

1, the first Earth-orbiting artificial

satellite, the concept of spaceflight has

taken

a superlative position in the politics,

technology, education

and

cultural psyche of

the

United States of America. Despite

budget

cuts

to

spaceflight programs within NASA, the Air Force and elsewhere, names

like Yuri Gagarin, Neil Armstrong and now Elon Musk resonate even with people who

are unfamilar with engineering and space physics.

Scientific exploration was integral

to

the first successful US attempts

to

fly a satel

lite-

James Van Allen s inclusion of a Geiger counter on

the

Explorer I mission (1958)

enabled discovery of the Earth s radiation belts

that

now

bear

his name. As would be

expected from early, ground-breaking missions developed under the political pressure

of the early Cold War, these early

US

satellite missions were

o

ne-off engineering

concepts.

More recent trends in spaceflight hardware (and especially in the funding avail

able for space missions) indicate an industry shift towards cheaper spaceflight plat

forms. Perhaps

the

single biggest game-changer in

the

small satellite

industry

has

been

the CubeSat, a containerized satellite concept originated

at

California Polytech

nic

State

University. The core concepts

that

have enabled the CubeSat

standard to

tally roughly 75 successful launches since 2003 are miniaturization, containerization,

interface standardization, and open-source development.



2

igure

· :

The Pumpkin CubeSatKit

1U picosatellite

structure,

com

mercially available and used widely accross academia, industry and even

the military.

Weighing

under

2 kilograms at a volume of 1 liter, the basic single-unit 1U)

CubeSat contains all modifications to the satellite structure within an external stan-

dard,

allowing any

CubeSat

rideshare on a launch vehicle

via

the

standardized

Pol

y-Picosatellite Orbital Deployer (P-POD). This gives

greater

freedom to the

pay

load developer by relieving the paperwork, cost, risk and

time spent

interfacing

to

the

l

aunch

vehicle.

igure ·2: The ANDESITE

mission, a Boston University 3U

CubeSat

currently

approved for funding from

the

Air Force Office of Scientific

Research. Andesite will explore fine-scale filamentation

in

the Earth s

magnetosphere.



3

1 2

Boston University and

Scientific Space

The Boston University Student satellite for Applications and Training (BUSAT)

program is a grassroots spaceflight hardware development program entirely staffed

and

directed by students of engineering, physics, astronomy, and computer science.

BUSAT was initially formed in 2007 in response to the University Nanosat Pro-

gram (UNP) Nanosat-5 competition for the purpose of delivering a completed space

we

ather

nanosatellite. Since

that

time, the BUSAT program has grown to include

the

Boston University Near Space

Program

(BU NSP, a scientific high-altitude bal

looning program for

the

Boston University community

and the

local MATCH

charter

public high school) , the Boston University Amateur Radio Club (BUARC) ,

and

ul

timately

a new space weather satellite design for the

UNP

Nanosat-7 competition.

While professional and academic mentorship is essential to the program, BUSAT is

entirely staffed and directed by students of Boston University and Boston Univer

sity Academy. Cooperat ive efforts by

students

at Georgia

Institute

of Technology

and New Mexico Institute of Mining and Technology also contribute considerably

to

the

BUSAT effort . BUSAT s programmatic goals include

the

laying

the

groundwork

for future spaceflight hardware and general sensor development programs at Boston

University.

BUSAT s current scientific space weather satellite effort seeks

to

characterize mag

netosphere ionosphere interactions from low-Earth orbit by simultaneously measuring

energetic electron flux and subsequent light emissions in the polar

latitude

s. Comple

mentary information about the local magnetic field, plasma environment, and internal

system

health

will also be collected

and

telemetered to ground, along with structural

health monitoring and total radiation dose

data



4

1.2.1

Background:

The University Nanosat Program UNP)

The

University Nanosat

Program

is a joint program between

the

Air Force Research

Laboratory s Space Vehicles Directorate AFRL/RV), the Air Force Office of Scien

tific Research (AFOSR)

and

the American

Institute

of Aeronautics and Astronautics

(AIAA).

The

objectives of the program are to educate and train the future workforce

through

a national

student

satellite design and fabrication competition

and

to enable

small satellite research and development, payload development , integration, and flight

testing.

The

N anosat

Program

has two distinct stages.

The

first stage is a design

and

proto-flight build phase, which lasts approximately two years

and

culminates

in the

AIAA Student Satellite Flight Competition Review (FCR). During this first phase the

universities are partially funded by the AFOSR and construct a proto-flight satellite

while participating in various design reviews and program-sponsored hands-on activ

ities and workshops over a two-year period. Teams are evaluated based on criteria

including program

maturity

, hardware

maturity

and flight readiness. FCR judges are

a distinguished panel of government and industry professionals.

The UNP is currently in its seventh competition cycle. Boston University

and

BUSAT participated in Nanosat-5; currently the BUSAT program is a

participant

in

Nanosat-7.



5

Chapter 2

Requirements Development

2.1

Requirements

Identification and

Flow down

In

a

project

as complex

and

long-lived

as

the

development of a satellite

it

is essen

tial to ground truth development at regular intervals to keep the

project

progressing

efficiently towards the originally stated goal. The process of requirements identifica

tion

is complicated

by

the fact

that there are at

least

three

customers:

the BUSAT

Principal

Investigator,

the

satellite

industry

represented

by

the

Air Force),

and the

UNP

whose

dual

mission is

education

and technology development)

Figure

2· : Requirements

originate from

the Principal Investigator

via

high-level mission definition,

the

University

Nanosat Program via

industry standards

for safety

and best

practices. Additionally,

BUSAT

has identified a niche opportunity in

the

pico- and nanosatellite industry

from which

requirements are

sourced.



6

2.1.1 The

BUSAT Primary

Science

Mission: Ionosphere-Magnetosphere

Coupling

BUSAT s primary scientific instrumentation includes the Remote Polar Imager (RPI),

a pushbroom-style geographically resolved spectrometer sensitive to visible light at

391.4 nm, 427.8

nm

, 557.7 nm,

and

630.0 nm. These wavelengths correspond

to

auro

ral

phenomena produced by energetic particle interactions with oxygen

and nitrogen

in

the ionosphere. Imaging is accomplished using several off-the-shelf components

mounted to an optical bench, including the Lippert Cool Space Runner single-board

computer , an ATIK 314L+ astronomical camera, and a sophisticated arrangement of

customized commercially available mirrors, lenses and a diffraction

grating

. Together

these components provide the ability

to

bend

the

required focal length into a 3U form

factor , the sensitivity required for low-light measurements,

and

the processing power

needed

to

compress, buffer

and translate data to

BUSATs native SPA-1 I

2

C

data

protocol.

Working in tandem with the RPI is the Compact Half-Unit IES for Cubesat

Operations

(CHICO) . Complementing

the RPI s

data

, CHICO allows simultaneous

in-situ measurement of energetic electron flux.

CHICO

is based

on

a line of legacy

hardware

flown on

the

Cluster (launched 2000) and

Polar

(launched 1996) missions, as

well as the Fixed Sensor Head (FSH) , currently awaiting launch on

the Demonstration

and Science Experiments (DSX) mission (Gunda, 2008). Filling a total CubeSat

volume of less that 0.5U, CHICO represents a powerful new adaptation of this line of

legacy hardware, capable of detecting particles

with

energies between 30keV

and

500

keV and resolving pitch angle to within 10 degrees in a plug and play s nsor package

Originally developed for Boston University s

Twin

Imaging of the Moving Ele

ctron

trapping boundary (TIME) mission, CHICOs uti lity is demonstrated by its ability to

be

integrat ed into

the

BUSAT

bus

with a minimum of redesign.



7

The RPI s requirement for pointing and stability is the primary scientific con

straint on the mechanical satellite bus design. These requirements are satisfied by

the

BUSAT bus three-axis torque coil control and

an

on-orbit

attitude

control scheme

that matches

the

satellites rotational period to its orbital period (described as a

Thomson Spinner ). In this way, the auroral imager points towards the earth and

CHICO points towards zenith

at

all times.

It

is interesting

to

note that future spec

trographic imaging missions with higher resolution

and

much finer pointing would

be

possible with minimal recurring engineering cost if several reaction wheels were

included in Mission Group A A further requirement levied on the current BUSAT

mission by the space weather instrumentation is the need for a low-Earth orbit in

sertion. Additionally,

both

RPI

and

CHICO require direct access

to

open space for

measurement.

2.2 Space Plug-and-Play

Protocol,

Operationally Responsive

Space ORS) and the Getting

to

Space

The

Space Test

Program (STP)

has been

the

primary

provider of

Department

of

Defense (DoD) integration and launch services for almost 50 years since it was char

tered

in 1965,

and

had over 200 missions

to

its name as of 2010 (Galliand). Serving

the entire DoD, the STP coordinates the Space Experiments Review Board (SERB),

which meets on

an

annual basis with the Air Force, AFRL, the Navy,

the

Army,

DARPA,

the

NRO and

the

MDA. The panel hears a series of 15-minute briefs from

spaceflight mission representatives and a ranking is then assigned based on percieved

military relevance and DoD interest in providing access

to

space via sounding rocket,

the

International Space Station or a launch vehicle to orbit. While this process

may

seem challenging at best, current plans for the U.S. fiscal year 2013 budget have in

dicated that both

STP

and the Operationally Responsive Space (ORS)

program

may



8

be closed altogether.

Against this background, small scientific spaceflight systems that actively seek to

op timize t he massive cost of

sate

llite development and

laun

ch are abso

lutel

y essen

tial

for t he U.S. to

maintain its current

level of industrial, educational, scientific and

defense activity

beyond

t he lower atmosphere.

Figur

e (2·2) shows a portion of the

2012 SERB list, showing rankings for programs currently seeking launch opportuni-

t ies. Twelve CubeSat missions are included on the

ranked

list,

with

a total volume

of 42.5U.

With

appropriate

funding for development, BUS T could el

iminate

more

than 20

of

the CubeSat missions on the SERB list in just two deployments, with

room to spare. This co

uld

very eas

il

y be accomplished wit h

ju

st one launch.

:

-

I I

-

.

-

-

.

- I - I ·-··

-

-

~ ;

-

--

_

.

· .. dl.AN Product

o..

- _::_

-

-

-

-·

· n v : r ~ 1 i ;

-·

-

- -·

-

-

- ·/

NPS Solar (@II Arrav

T@ster

-

-

•'

-

·-

Operationally Responsive

1\

.

;

-

-

~

Space Enabler Satellite

- -

..

Peregrine

'

- ·-

ParkingsonSat Remote Data

-

7

.

Relav

----

Pica Satellite Solar Cell

Testbed

-

-·

v

-

-

....

,

Rapidprototyped

..

.

\

Mlcroelectromechanlcalsyste

·-

' ~ , ;

7

·--

-

\

m Propulsion and

Rad

iation

:::: ::=:::

· -

..

Test Cubeflow Satellite i

-

-

-

-

..

SMOC n o s t e l l i t e ~

-

--

_ ;:--...

--

-·

.

l>ro«ram

/f-:: :

-

·-

·

- I

- I ·

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-·

-

-

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--

-

-·

. .

.

.

.

-

igure

2·2: Th

e Space Exp

er

iments Review Board (SERB) 2012 rank-

ings include a

total

CubeSat volume of over 40U in experimentation

awaiting launch opportunities.

The cost of launch is not t he only

problem in

need of engineering in the cur

rently challenging fiscal environment.

Many

satelli

te

development programs follow



9

a one-of-a-kind design

path

in which a unique satellite is developed specifically to

support the needs of a

distinct

set

of instrumentation. This method

is both expen

sive and time-consuming [4] . Because of the complexity and variability of

satellite

missions, a universal satellite has yet to develop fully,

although

at least one modular

demonstration

mission has received

substantial

support [2] BUSATs novel

satellite

nanosatellite

bus

provides

both

the general utility of a multi-mission structure while

at the same

time

retaining mission-specific adaptability to a wide range of in

strument

requirements.

igure 2·3: BUSAT seeks to optimize

the

pre-launch lifecycle, with

particular emphasis on tolerance to late, game-changing requirements

shifts and the lengthy integration process.

While BUSAT strives

to

optimize

the

design cycle

by

reducing

recurring

engineer

ing costs, the superlative and elegant universal satellite

bus

is

not

possible, especially

on

a university budget.

This

is supported

by

the fact

that programs such

as Space

Plug and Play

SPA) , developed

at

AFRL and in the

ORS

program

, have

met with

limited success operating under much more favorable budgetary constraints. How

ever, while the concept of universality is unwieldy in its most general form, it can be

effectively applied to a slightly narrowed subset of spacecraft missions,

namely

those

requ

iring only basic

system

support functions.

The broad

satellite

bus

functionalities



10

required by

this

subset include

rough

pointing, low

data

rate

telemetry an

d

tolerance

of

duty

cycling,

and

are achievable on a university budget.

In other

words,

the

elegant

solution s practical if properly constrained.

BUSATs

target

role in the spaceflight

industry

is

that

of a mission broker for small

scientific

instrumentation.

By adhering

to standardized

interfaces

in

a

star

network,

taking

advantage of symmetries

that

exist

in

software, hardware, mission design and

even documentation, and

by

arranging

the

misssion around a centralized bus,

BUSAT

facilitates mission sharing

and

drives down cost for payload developers

and

overall

risk for launch providers.

2 3 Mission Overview and

Concept

of Operations

The

dual

design

intent that

drives BUSAT s requi rements addresses both the geo

physical environment of the

upper

atmosphere

as much as

it

addresses

the

economic

and

technical environments

in

which a small sate llite develops. Initially,

BUSAT

was

planned

as a scientific

platform

for space weather research. As

the

design

ma-

tured budget and

personnel

constraints stimulated

the

development of a parallel

engineering mission

in

order to optimize the pre-launch lifecycle. The

two

missions

are

co-dependent and fully

supported by

the satellite s mechanical

architecture.



11

OIII NTIITION

Separation from ESPA rln1vi•

PSC U1htbond Adapter.

Detumble (3 weeks max.)

Fine

Polnlinc(lwoek

.)

lleain hea lth beacon

lleain Hub Initio- on Mode

- GIOCI ID OfiERAJIOfVS

S IIIINtll around stlltlon

at BU

Cno rles Rver campus

func liOM

oullonomously to own I

nk

dato .

f ll 0 O L I ~

sate lli

te or

ien

ted for max

i

mum drae:

durlna:de-orb ft phase .

Al l systems poM

red

d

own

.

Pav load health

assessed

poss ib

le

new sc iencemisslonsstarted.

Amateur repeater fun ction enabled.

Soler panels depl

oy

Bec ln

pa

yl

oad

boy

lnitiolizotlon

1

week

)

I

·0

NOIIMAI.

Of fiiATIONS

SCifflCE MODE)

Ill

.

CH

I

CO

.

Ma1nt tommr.

SHM takl

nedateo

v r

po l

es

{

La

titude > 50 ' .

Opti

on

to

duty cy

cl

e

Instrumentation at anv

location in orb it

OUTY CYCLING

Low-power

or

sleep mode

dependi

n a

on stlllte of

charp. SHM and

Ma10etometer tokin1

data

Figure

2·4: The

BUSAT

Low-Earth orbit

(LEO) concept

of opera

tions.

2.4

High level Mechanical Bus Requirements

Modularity

, scalability,

limited

resources

and

a robust science mission

ar

e

the

four

mam themes

to

BUSAT s

mission. Science

requirements

have

been

introduced

and

have

little

direct effect

on the

structure of the satellite

(other than

what was

mentioned

in Section 2.1.1).

The

following list of high-level

requirments

pertaining to the satellite

mechanical

bus

fall

under

the remaining three headings.



12

Modularity

1. Any 1 U BUSAT payload shall be capable of integrating with the spacecraft in

at

least two different angular orientations.

n. Any 1U BUSAT payload shall have at least one to three open look-directions into

space.

m. Any BUSAT payload shall interface to

the

mechanical bus via a single

standard-

ized connector and harness.

iv. Integration shall take less

than

6 hours nominal) for any given payload bay

configuration.

v. Integration shall be repeatable i.e., several build up/ take-down sequences

must

be possible without new machining, fabrication, or undue effort.

Scalability

i

The

final flight configuration shall

be

scalable from a single central module

to

a

larger, more capable aggregate spacecraft.

ii. The avionics module shall be capable of removal and use in

other

compatible

satellites.

iii. BUSAT compatible payloads shall be capable of flying in multiple configurations

on multiple missions.

Low

Cost

i Hardware should be radiation tolerant wherever possible, but BUSAT shall pro

vide enough shielding to

protect

off-the-shelf

radiation

sensitive electronics.



13

n. BUSAT shall be compatible with Commercial Off-The-Shelf (COTS) components

commonly available to the satellite developer, thereby eliminating the cost of in

house development.

iii. Payloads shall require no more than 30 seconds between plug and play (i.e.,

physical layer integration completed and functionl testing commenced

within

that

time).

1v

Payload structural raw materials shall

be

sourced from commonly available and

affordable stock.

v. Machining tolerances specified in engineering drawings shall be 0.005 inches or

greater wherever possible.

v1

Locking helicoils shall only be used in final integration phases. Alternative meth-

ods shall be used during early build/ rebuild sessions.

2.5 Low level

Design

Requirements

The

process of requirements identification is iterative and new design specifications

generate new dependencies

and

new design requirements arise.

The

following design

constraints are more evolved than

the

requirements listed in Section (2.3) and begin to

suggest

the

actual design specifications and choices described later

in

this document.

2.6 Solar Panel Deployment

While a single side panel covered with conventional satellite solar cells (such as the

Spectrolab Ultra Triple Junction UTJ) Solar Cell) would provide power for the en

tire satellite, a cheaper modular solar panel based on Triangular Advanced Solar

Cells (TASCs, also from Spectrolab) was chosen instead.

The

TASCs are custom

manufactured at Boston University using a solder refl ow oven

and

are therefore very



4

cheap

to

manufacture, install

and

replace. Because they do not produce sufficient

power for a comfortable margin of error (one side of BUSAT s exoskeleton can pro

duce

approximately

20 W

with

TASCs

- which leaves a power

budget margin

of only

8 W without considering

the

power

draw

from

the payload

bay.

The

power budget,

therefore, drives a requirement for BUSAT to deploy

additional

solar

panels

once in

orbit.

Figure

·5:

BUSAT's 1U solar

panel

design costs

about

150

in

parts

and takes less

than three

hours

to build

using refiow solder techniques

but do not perform as well as more expensive cells.

PCB substrate

is

shown at left, finished component is shown at right.

2.

7 N

anosat 5

Inherited

Design Features

Even given

the

geometric

and

conceptual simplicity of BUSAT's cube stack, it has

proven very difficult for both the Nanosat-5 and Nanosat-7 teams to provide an

elegant solution to more advanced design issues

such

as cabling, integration

and

access to key electrical components

after

assembly. As more

information

about the

original development of the Nanosat-5 structure

became

available, it was clear that

requirements for easy assembly of the structure were compromised late in the design



15

process because of a break down in modularity. The spacers became specific

to

the

geometry of adjacent cubes, removing

the

ability to reorient or reposition payloads

as

originally intended. As

the

design evolved incrementally,

with

new modifications

to both machine drawings and fabricated parts , each spacer was

edited

in such a way

that many distinct modifications to the original part were necessary.

Due to these

non standard spacers, as well as the sheer number of unique

parts

and attachments,

the

assembly process

became

very difficult.

igure

2·6: Nanosat-5 model

structural

spacers not to scale). From

left: exterior spacers arranged in top panel configuration, interior spacer

original model, unmodified), hexagonal spacer.

Interior, exterior and· hexagonal standoff) spacers

ultimately made

up 15 dis

tinctly modified manufactured parts. Since

the

N anosat -5 part naming scheme lacked

enumeration and because there was no intuitive way to quickly assemble components,

build up

was

belabored

and slow.

Each

assembly step was not ·necessarily

intuitive

and

would

not

have been possible to rebuild without a working CAD model. The

CAD

model was

not without

its own challenges, however.

Due

to

revision control

issues

during

Nanosat-5, even the SolidWorks structural model lacked coherence and

did not reflect

the

fabricated

structure

, leaving ample room for interpretation as

the

NS-7 team assembled the structure.



6

igure ·7:

1-U, 2-U and 3-U Cube Structures.

Once a UNP satellite passes the Final Competition Review (wins the competi

tion), the satellite and the team are supported for a further two years of integration

and testing in preparation for launch. Integration,

the

process of forming a single co

hesive unit (electrically, mechanically

and

in software) from

the

satellite s substems, is

undertaken by professional technicians at AFRL s in-house facility. One ofthe largest

challenges to

the

Nanosat-5 structure would have been

in the integration

phase. Even

with

a very good assembly manual to explain the complex assembly procedure, tech

nicians working

to integrate

the

satellite

with

a

launch

vehicle would

be

challenged

by cabling and by the inevitable need to assemble and disassemble the structure re

peatedly

for troubleshooting.

This

is especially important for centralized subsystems

like the data processing unit or the communications system. Since the Nanosat-5

structure

provides no re-usable means of restraining cabling, some semi-p

ermanent

solution such as epoxy staking would have to be adopted, effectively locking sub

systems

into

a complicated mechanical puzzle. Though the intent and

end

goal of

the design was novel and impressive, the actual prototype did

not

satisfy original

requirements for ease of use and modularity.



7

hapter 3

Structural Design

Figure

3· :

Early concept sketch of

the

BUSAT mechanical architec

ture.

With

a total payload bay of 27U, BUSAT reserves

the

core 3U volume for its cen

tral avionics unit, leaving a total of 24U open for payloads seeking a mission-of

opportunity launch into space. One of the best advertising points for future BUSAT

missions is the centralized electrical

bus

architecture. While conventional 1U, 2U

and 3U satellites must necessarily use substantial portions of their meager mass and

payload allotments on support subsystems like radios and batteries, BUSAT payloads

optimize the ''rideshare launch opportunity

and

can use entire mission resource bud-

gets (mass, volume, power, time, and fiscal) on the payload and the mission itself.



8

Figure

3· :

The BUSAT satellite shown before solar

pan

els are de

ployed.

The BUSAT bus is organized into five specific groups of hardware: Hub ,

En

doskeleton, Exoskeleton, Deployables

and

Cubestack. An explanation of each is nec

essary to fully understand BUSATs

intended

function and mechanical design.

3 1 Components

3 1 1 Hub

The Hub Figure 3·3) is literally and figuratively the core of the satellite

bu

s, hold-

ing all of

the

subsystems essential for supporting a satellite mission. This includes

command and data handling, communications, power generation and

regulation

at -

titude determination

and

control,

and

a single magnetometer implemented

on

fifteen

standard printed circuit boards using a

standard

set of stack-through connectors.

The Hub

is completely enclosed in 6061-T6 aluminium

to

shield

the

satellite

bus

subsystems.



19

Figure 3·3:

Exploded

views of the BUSAT Hub

(upper

assembly)

and Endoskeleton showing the hub PC\104 printed circuit board stack,

connectors, and four

routing

boards.

The PC\104

embedded

systems standard defines printed circuit board dimensions

as

seen in Figure 3·4). Following

suit with

much of

the industry

that

has

developed

surrounding

the

CubeSat

standard

such as hardware manufacturers AstroDev

and

Clyde Space) , BUSAT

s hub

includes

5 printed

circuit

boards that

conform

to the

PC\ 104 standard. Also in line with common practice in

the

embedded systems in

dustry, the BUSAT design rejects some features of the PC\104 standard, including

the

use of several specified electrical headers. While the

modularity

of

the standard

s beneficial in lowering non-recurring engineering costs i.e. every

student

designer

begins from the same

template), mating and de-mating

PC\104 headers is

very

dif

ficult

without damaging

components

and there must

certainly

be

a

better

solution

for

modular

circuit design

in

small satellites. Additionally, standard PC\104 circuit

board dimensions as shown in Figure 3·4) are within press-fit tolerances of the inner

diameter

of BUSAT s 4-inch

extruded aluminum cube

design,

meaning that either

the standard

must be

compromised or that other

materials must be

used for

payload



20

cube design

(t

he hub

ca

n a

ll

ow standard P C

\1

04 dimensions because it is machi

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from four pieces of a

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Figure 3·4: Detail from

the

P C\104

embedded

systems standard

showing fastener placement, h

eader

(right) and keep-out areas.

The PC\104 circuit

board

stack wit hin the hub is supported by t hree sets of four

mid-plane standoffs

that

fasten directly

to

t he four wa

ll

s of t he hub

(Figure

3·5) ,

which allow each of t he avionics subsystems to be fully integrated (with standoffs)

before enclosing them in the

structure.

This allows for easy trouble

shooting

should a



2

component

within

the

hub

stack

fail as often happens

during

satellite

environmental

testing and integration.

igure

·5:

Detail view of

the hub stack

assembly showing

three

mid

plane standoffs.

Each

standoff fastens to

the external

hub walls in a

slotted

groove that allows variations in hub

stack

height due to non

standard PC\104 overhead height

in COTS

components.

igure ·6:

Detail view of

bottom cap and

three hub walls inte

grated . Apertures for 25-pin and .SMA connectors are shown as well

as a tongue-and-groove fastening technique that minimizes

the need

for

fasteners along

the

entire length of

the

hub and

the

labeled

PC\104

bolt pattern



22

The hub interfaces electrically to the payload bay via four axially symmetric walls

of the Endoskeleton (Figure 3·3) . Both data and power are routed

through

four 25-

line wire harnesses

that

connect at the

hub

's

top

cap

and run

to one of the four

Endoskeleton walls (Figure 3·7). As shown in Figure (3·6), the hub bottom cap

allows

routing

to

the

external components of

the

BUSAT bus, including solar

arrays

,

external

sensors and radio

antennas

.

igure

·7:

Top left: schematic

top

view

of the

BUSAT wiring

har-

ness. Composed of several standardized short cable harnesses,

this

wiring method alleviates the need for costly

and

time-consuming one

off harness design and allows

the hub to be

removed from

the satellite

at

any time during integration. Top right: side vew of the harnessing

scheme from

the

payload (left) to endoskeleton to

hub

(right).

In order to satisfy low-cost requirements for the satellite

that in

a structural

design, translate

to

judicious use

of

machining tolerances, a 45° surface has

been

included in

the

hub

bottom

cap

to

provide regis tration

and

a

lateral restraint. When

the hub

is pressed down

into the

satellite structure

by the

exoskeleton

top plate

this surface alleviates the need to access the bottom of the hub for fastening (Figure

3·8).



3

Figure

3·8:

The hub. Inset: A 45° filet fixes the hub in place.

3 1 2 Cube

Stack

BUSAT s containerized structure is based on a broad interpretation of the CubeSat

standard Due to

the

availability

and

price of extruded aluminum

tubing

(4-inch

outer

diameter, 0.125-inch wall) as well as

the

relative ease with which it is machined, the

BUSAT standard 1U cube is 4 inches on edge and contains a volume of 64 in

2

. The

Birtcher WedgeLok™provides a novel

and

effective means of fixing the cube

stack

in

place (Figure 3·9).

Compressive

movement

Lateral movement

Figure 3·9: The Birtcher WedgeLok is the principal fastener

used

in

BUSAT s easily integrable design. A

torque

applied

to

the

tension bar

results in a lateral pressure applied to

the

cube stack.



5

3 1 4 Exoskeleton

Figure 3· : The

BUSAT exoskeleton.

The

Exoskeleton fastens directly

to

the Endoskeleton

s

four identical side walls

s

the

satellite is assembled. Deceptively simple

in

concept,

the

Exoskeletons primary

purpose

is

that

of a space-born shipping container. The external

stru

ctures two

key features are its ability

to

allow standard

(and

customized

apertures

for

payload

instrumentation and the

ability

to support the

forces associated

with launch and later

solar

panel

deployment .

Figure 3· 2: The

BUSAT-NMT

Langmuir Probe

shown

protruding

through

the exoskeleton top panel.



6

3 1 5 Deployables

Since BUSAT will

be

sun-facing under normal operating conditions

but

will begin

its

operational

life in a

tumbling

state, solar panels that begin the mission arranged

around

the satellite and are moved to face

the sun

are optimal.

This deployment

configuration is easily realized in

the

form of a simple door, as seen in Figure 3·13).

Figure 3· 3: The BUSAT satellite showing

modular

solar

panels

de

ployed.

While the spring-loaded hinge and

latch

concept is

not

challenging to design, cer

tain features of the deployment mechanism requi red sufficient design effort and

testing

due

to

the

risky

nature

of deployable

structures in the

eyes

of

past UNP competition

reviewers. Because the deployment hinge was

predicted to

be the weakest part of

the

design all analysis was completed

s i

the hinge pin were not

in

place Actuation

is accomplished using the TINI Aerospace Frangibolt Figure 3·14), a non-explosive

actuator NEA)

that

functions

by heating

a

shape-memory

alloy

to expand and break

a pre-scored 4 bolt. While the Frangibolt has flight heritage on many successful

spaceflight missions,

any

moving parts designed by

Boston

University students no

matter how good) will not be as well trusted. t is therefore necessary

to

find a

method of allowing the

Frangibolt to

completely

constrain the

deployment

without

the use of additional moving

parts

in this case, hinges).



27

Figure

3· 4: The TINI

Aerospace

Frangibolt

(shown in red) with

associated housing and

custom

titanium flange for

heat

isolation.

The

Frangibolt itself required

that no

shear

force

be transmitted to the

breakable

bolt at

any time

before deployment

at the

risk of early

actuation

at the test facility

not

dangerous)

or on

launch (very dangerous) . A cup-cone kinematic

mount

was

employed (Figure 3·15)

with

five

mated

conic surfaces of slightly

interfer

i

ng dimen-

sions (i.e. the male cone was very slightly more oblique than the female cup and

guarunteed

zero shear at

the

interface). Titanium was chosen for

the

female fixture

in order

to

isolate

the actuator during its

15 second

heating

phase.

Figure

3· 5:

Cross-sectional view

of

the

cup-cone

kinematic

mounting

structure.

This heat

isolation was shown

to be particularly important

for successful de

ployments during microgravity

testing, and the addition

of a titanium

washer

was

necessary

to

ensure

that

the titanium

pad did not act

as a

heat

sink

and

delay

or



8

even deny actuation.

igure 3· 6: The BUSAT deployable

panel

stowed and completely

constrained (at left) by the TINI Aerospace 4 Frangibolt and (at

right)

by

a titanium groove

(to

avoid cold-welding

under extreme

vi

bration.

While the cup-cone assemblly is able to produce

contact

forces in any direction

radially from or along the axis of the Frangibolt,

there

is only friction at

the

cup-cone

interfaces to keep it from

rotating.

For

this

reason a tongue-and-groove

feature

was

added to hinged end of the deployment

panel

to provide further support

(Figure

3·16).

Because of an offset hinge, the deployment

naturally de-mates

the tongue-and-groove

before allowing

the panel

to

swing free Figure 3·17).

igure 3· 7: The tongue-and-groove kinematic mount

after

deploy

ment.

It

is

important to note that

the tongue-and-groove feature allows all structural

analysis of the assembly

to

exclude

the

hinge. In other words, the only functional



9

reason for

the

hinge is

to

guide

the

solar panel into

the

correct position after deploy

ment.

3.2 Assembly

.

~

Figure 3·18:

The BUSAT assembly procedure (top left to bottom

right) beginning with

the

exoskeleton bottom plate, endoskeleteon,

cube stack, WedgeLok™s,

and

hub.

BUSATs assembly procedure is shown in Figure (3·18) , and demonstrates the de-

sign s minimization of non-recurring engineering by exploiting symmetry about

the

vertical axis. Four vertical Exoskeleton walls (identical

with

small modifications

post-

fabrication) are assembled

with

a bottom panel

to

form

an

aluminium (6061-

T6

box.

The

central component of the satellite is the Endoskeleton, a routing node that pro

vides power and data transfer to each of up to 24 payload modules. The Birtcher

WedgeLok™is

used

to

compress

the internal structure

(center). Once

the

Exoskele

ton panels have been fully fastened,

the

WedgeLok™assemblies are tightened

and

torque

coils are installed. Solar panels

and

antennas

are then

installed

and

connected

to the power system and

the

deployable mechanism is ready for testing, as shown

from a top view in Figures (3·16)

and

(3·17).



3

3 3

Mass Budget

The

cost of launch is directly related

to

a system s mass as it

is

acceler

ated

into

orbit,

with

per-kilogram cost of launch to low-Earth orbit ranging from

thousands

of dollars

to

tens of

thousands

of dollars, depending on

the

launch vehicle. Like

any

other

satellite, BUSAT s structural mass is closely tracked. The tables in

this

section

summarize BUSAT s mass budget and are organized by major assemblies.

Margin

Exoskeleton

Central Routing Cube

ommunications

- -

Magnetometer

CHICO

Auroral Imager

C DH

Figure 3·19:

BUSAT s mass breakdown arranged

by

subsystem.



31

Name

Mass (g)

Qty.

Total (g)

Hu

Outer Structure

Hu

b B

ottom Cap

405.83 1 405.83

Hub Top Cap

263.65

1

263.65

Side Hub Wall

33

0.38

2

660.76

Front/Back Hub Wall 194.26

2

388.52

P C s and Components

Fl

ex

UEP

S

3

1.

31

1

3

1.

31

30 Whr CubeSat St andalone Batt ery 1

03

.51

1

103 .51

Helium 100

Ra

dio

33

.00

1

33.00

I

nter

face,

Vo

ltage Regul

ato

r Stack

45

.

36

1

45 .36

RF Sw itching PCB

22 .68

1

22.68

Magnetometer Small Pl

ate

3.79 1 3.79

Magnetometer Large

Pl

ate

5.80

1

5.80

Magnetometer PCB

22.68

1

22.68

AD&C PCB

22.68

2

45

.36

C&DH

22 .68

1

22

.68

Na

noCDH

6.

02

1

6.02

Expa

nsion PCB

22 .68

4

90

.

72

Rout ing Node PCB

22 .68

1

22 .68

Right Angle Cable Plug

0.87 2

1. 75

Right Angle Jack

0.61

2

1.21

Stando s

0.25in Stando

ff

0.

13

24 3

.1

2

1524 Standoff

0.29

48

13.92

2200 Standoff

1.11 4

4.44

Midplane

Sta

nd

o

ff

1

0.41

3 1.23

Midplane

Sta

ndoff 2

0.66

3

1. 98

Midplane Standoff 3

0.59

3

1.

77

Midplane Standoff 4

0.41

3 1.23

Other Components

AirBorn Connector

1. 29

4

5.16

Fasteners

Washer

0.01

20

0.2

40

-40 1/

4

Bu

tto

n Head

Ca

p Screw 0.06 8 0.50

4

-40

3/

16

Bu

tton Head Screw 0.05 4

0. 18

6-32 1

/4

Bu

tton Head Cap Screw 0. 1 12

1.13

4-

40

Machine Hex Nut

0.07 4

0.28

Total ub

Mass

(g)

2212.38



32

continued)

Mass g) Qty.

Total g)

Endoskeleton

Endo Wall 512.88 4 2051.52

Endo Routing

PCB

44.31

4

177.24

Endo AirBorn Connector

17.0109

24

408.26

Endoskeleton Spacers

Bottom

Spacer

55.53

8 444.24

Interior Spacer

47.72

4

190.88

Half Interior Spacer

56.4

1

56.4

Total Endoskeleton Mass

3328.54

xoskeleton

Bottom

Plate

2532.

1

1

2532.

1

Top

Plate

2611.81

1

2611.81

Back

Plate

1776.07

1

1776.07

Side Plate 1

1755.73

1

1755.73

Side Plate 2

1754.01

1

1754.01

Front Plate

1755.12

1

1755.12

Total Exoskeleton Mass

12184.84

Empty Payload Cubes

Single Cube Assembly 295.10 1 295.10

Double Cube Assembly

260.75

3 782.25

Triple Cube Assembly

654.64

5

3273.2

Total

Empty

Payload Cube Mass

4350.55

Payloads

CHICO

295.10

1

295.10

. LPP-SHM Assembly

755.47

1

755.47

Total Payload

Mass g)

1050.57

We eLoks

WedgeLok Corner

Pad

196.03

4

784.12

WedgeLok Side Pad

207.2

10

2072

Total

WedgeLoks

Mass

2856.12



33

continued)

Mass g) Qty.

Total g)

FrangiBolt ssembly

X-Wing EXO

197.45

2

394.9

Cup

Attachment for X-Wing EXO 21.87 2 43.74

MiniActuator Housing

2.67

2

5.34

MiniActuator Bolt

1.59

2

3.18

MiniActuator FD04

10.62

2

21.24

X-Wing SOL

74.35

2

148.7

Total

FrangiBolt Mass

617.1

Torque Coil ssembly

TCH Bottom Side

72.19

3 216.57

TCH

Left Side

72.24

3 216.72

TCH Right Side

72.24

3 216.72

TCH

Top Side

72.24

3 216.72

TCH Standoff Special

4.62

24

110.88

TCH

Standoff Corner

5.92

12

71.04

Total Torque

Coil Assembly

Mass

1048.65

Solar Panel ssembly

Solar Panel

Plate

295.91

2

591.82

Support Flange

433.95

2

867.9

Spring Hinge Mounting Extension

39.15

2

78.3

Dowel

Pin

1.74

4

6.

96

Setscrew

0.21

4

0.84

Spring

0.03

4

0.12

Solar Panel PCB

17.46

18

314.28

Total Solar Panel Assembly

Mass

1860.22

MGS

ssembly

MGSE Vertical Support

1354.5

2

2709

MGSE Corner Plate

188.7

4

754.8

MSGE Corner Fixture

93.01

4

372. 4

Total

MSGE Assembly

Mass

3835.84

Total Mass g)

33344.80

Total

Mass

kg)

33.34



4

Chapter

4

Vibration Testing

4 1

Background

4 1 1

Vibration Testing for Small Satellites

Integrated

environmental

testing

makes

up

one part of the overall lifecycle of a small

satellite and occurs

after

fabrication and before launch. For BUSAT, environmental

test procedures including cleaning, functional testing, mass and volume verification,

and

final review will likely occur at

the

AFRL High Bay facility

at Kirtland

Air Force

Base in Albuquerque, NM (see Figure 4·1).

Integrated

environmental testing is one

part of this process and includes several mechanical vibration tests (usually performed

on a shake

table and

shock

testing apparatus

interspersed

with

electronics testing.

Figure 4· : N anosat-5 integration

and test

flow (from NS-7 User s

Guide)



35

This

is followed

by

a bake

out test,

during which

time

the satellite is

subjected to

temperatures

high enough

to

vaporize many of the volatiles that would

othe

rwise later

contaminate the vacuum chamber the volatiles will also boil

out

at low pressure).

Thermal and vacuum testing then ensues, followed by electromagnetic interference

and

electromagnetic compatibility

testing

(see Figure 4·2). These

last tests

ensure

that

the

satellite can function within the ambient electromagnetic environment

of

low-Earth orbit, as well as perform all electronic tasks without adversely affecting its

own circuitry.

Repea

te

d

ro

r X Y and Z

Axes

Pre-Test Sine

Si

ne Bur

st

Intra- Test Si

ne

1

sweep

Sweep Al iveness

Te

st

n

L

Random

Intra-Test Si

ne

1

VIOratlan

Test

Sweep Al tvene

ss T

es

t

n

L

Bal<eO

U

Sha

ck

Test

Past-Te

st Si

ne

Fu

Fun

ctional

Therma l vacuum

sweep

Te st

1

Therma l Balance

EM

VE

MC

igure 4· : Mechanical Test Flow (from NS-7 User s Guide).



36

4.1.2

Mechanical Vibration

Testing

r { R

~

~

Cl - CONTliOL 1:5POtiSC

D -

DRM:

0 - VTPUT

Figure 4·3: Concept schematic of

Thermotron

vibration table control

loop. 5)

Mechanical testing (the main focus of the testing described in this document in

cludes four categories of vibration testing. All four can be administered on a shake

table

, although other apparatus are also used such as centrifuges, drop

test

machines

and Hopkinson bar or hammer blow test rigs. A shake table can

be

explained as

a very large audio speaker or solenoid connected to a large power

supply

and con

trolled by a software system with closed-loop feedback from a control accelerometer

(see Figure 4·3, Figure 4·5). The software package models

an

incremental series of

mass-spring-damper oscillators. Control software causes an initial vibration

in

the

shake

table

by commanding the power supply to deliver an electrical oscillation to

the

coils in

the

vibration table, which in

turn

induces a mechanical oscillation in

the

armature, test object

and

control accelerometer.

The

control accelerometer provides

confirmation of the

actual

vibration induced

in

the armature to the control software,

which is then able

to

change the properties of the actual mechanical oscillation de-

livered

to

the

armature

.

In

this way, the control accelerometer becomes an active



37

part of the test equipment and at the same time provides a means of estimating the

forcing function

that

excites

the

test object

Control

ccelerometer

Channell)

Fasteners

Shake Table

Figure

4·4: Schematic view of

the structural

test as performed at

the

Draper

TF

showing control accelerometer mounted on

the

shake table

armature



8

F t)

mplifier

F t)

Figure 4·5:

onceptual

representation

of SRS

plot

generation

and

vi

bration table

control showing (in red) control accelerometer input

to

a

virtual

mass-spring-oscillator

array

implemented

within the

control

software.

The

model simulates a

system

response

based

on

the

control

accelerometer

input

,

and this

signal is

plotted

(red). Control software

commands

based

on this

simulation

are then passed to

a power

am-

plifier which sends

current

to the table

s

inductive

coils,

imparting an

acceleration

to the table and again

causing

the


to

feed back

to the

software oscillator model.

The

number

of oscillators

in

the

software model (n)

determines

resolution (5)

Sine Sweep

The sine sweep

test

is

performed on

a shake

table and subjects the test object to

sinusoidal

motion

from 20 Hz

to

2 kHz, keeping

maximum

acceleration values very

low.

This

is

meant

to

identify

any resonant

frequencies

that the satellite may

have

without subjecting the

satellite to

potentially destructive

forces. When a sine sweep

is administered, several accelerometers around the structure

monitor

the vibration

response of various mechanical elements

of the

satellite.

When plotted against

fre-



39

quency, the resulting acceleration data clearly identifies resonant responses at each

accelerometer location.

In

the normal test flow, the sine sweep is

performed

first

to

establish a baseline response, and then again after each random vibration, sine burst

and shock test It can

be

assumed that any

structural

change such as a loosening

bolt

or plastic deformation) will result in some shift in

the

baseline sine sweep acceleration

responses.

-

r

0

·;:::;

ro

_

(IJ

(IJ

u

u

4:

ro

_

J

ro

z

Channel2

4

3

2

1

0.6

0.4

0.3

0.2

0.1

0.06

0.04

0.03

0.02

0 01

0.006

0.004

0.003

0.002

0.001

20

30 40 50 60 70809 ]00 200 300 400 500600 800100 0 1500 2000

Frequency (Hz)

Figure

4·6:

Typical plot of sine sweep acceleration vs. frequency. T his

is an in-axis response.

Sine Burst

The sine burst test is meant to expose

the

structure to inertial loading similar to

that experienced

on

a launch vehicle.

The

number

of actual

strokes

of the

table

as



40

it delivers the sine burst is very low (around 50 cycles), and the test is over very

quickly (around 5 seconds). Typically, sine burst

tests

are performed at a frequency

of

at

least one third the lowest identified natural frequency of the structure. In

the

case of the BUSAT structure, this lowest resonance occurred

at

relatively high

frequencies (rv300 Hz and rv500 Hz). Based on recommendations from UNP staff,

the BUSAT sine

burst test

was performed

at

50 Hz to more accurately recreate

the

launch environment, a lthough future sine burst testing would likely be performed

at

levels as low as 20Hz. Acceleration levels were set

at

24 G, as specified by the UNP

User s Guide.

Because the main purpose of

the

sine burst

test

is to simulate inertial loading

not

necesarily oscillatory loading), similar testing can also

be

performed in a centrifuge.



41

Burst Run 2

25

l

channe12l

20

15

10

c:

c

5

0

h

< J

Q

Q

u

u

<

-5

ro

::J

z

10

-15

-20

-25

0

0.1 0.2 0.3

0.4 0.5

0.6

0.7

Frequency (Hz)

Figure

4-7:

Ty

pi

ca

l

plot

of

sine

bur

st

acceler

at

ion

as

a fun

ct

ion of

t ime. This is an in

-ax

is response.

Random Vibration

Rather t han

ta

king its

inpu

t cont rol from an oscillatory s

in

e wave, t he random vib ra

t ion test is gen

erated

by a whi

te

noise source (4) and provides a

better

a

pp

roximation

of t he launch environment . Random vibrat ion data is plotted as a root mean square

(RMS)

va

lue

a

lso referred

to

as

Power

Sp

ectra

l Density

or

P SD) over fr

equen

cy.

This

prov

ides a quali

tat

ive com

pari

son between t he n

at

ural fre

qu

encies (re

pr

esented

by

p

ea

ks) in bo t h t he di

ag

nostic s

in

e sweep

test

and the ran

do

m v

ib

ra t ion

test,

al

though t he va

lu

es

are

shown in Gs in the former and G

2

z in the latter (see

Fig

ure

4·8 .



42

I

10.0000

· ·-·- • -----

--

-

c : : : _ ' ~ ~ ~ = · o c ~ : : = ± c F . = : ~ ¥ · ~ ~ ~ ~ ~ ~ ~

~ = = = · = = , ' = = = = -

1.0000

0.1000

0.0100

0.0010

0.00 1

20.00

100.00 1000.

2000.00

Frequen y (Hz

)

igure

4·8: Random

vibration

response raw data from 20Hz

to

2000Hz.

Shock

The

effect of

transient

events

that

are not

emphasized

in the random vibration and

sine burst

tests

are

measured

directly in

the

shock

test.

Shock,

or

a

sudden

forcing over

a very short

time period,

often affects stiff

or brittle

satellite

components (components

with higher natural frequencies) like circuit boards and solder joints. Shock tests

are

delivered very quickly and therefore require

testing

apparatus capable of rapid and

large accelerations. Consequently, shock

tests

for large objects are

not often

delivered

on shake tables. Instead, hammer blow tests, Hopkinson bar

tests, or

drop tests

apparatus are

employed.

Because cost and time were test

constraints

on

BUSAT s

three days at the ETF,

shock tests were delivered

at

the maximum possible acceleration values that the vi-

bration

table

and power

supply

could deliver. This

amounted to

around 60 of

the

given UNP test specification for shock tests

in

the Z-axis, and 40 of the

same

for



4

those delivered in the X andY axes (the difference is accounted for by the use of a

large slip plate

and

air bearing in

the latter

two tests, adding to

the

effective mass of

the

objects driven

by the

shake table) . Additionally, shock tests delivered on a shake

table include some amount of ramp up and ramp down motion before and after

the delivered shock (see Figure 4·9).

Shock Run 25

100

80

60

40

20

( )

0

-20

-40

-60

-60

0

0. 1 0.02

0.03 0.04 0.05 0.06 0.07 0.08 0.09

Time Milliseconds)

igure

·9:

Typical

time

history of shock test. This is an in-axis

response.

Ramp

up

and ramp

down motion

can

be seen from 0.00

ms to 0.04 ms

and

from 0.06 ms

and

0.09 ms.



44

Chapter

5

Data Analysis

5 0 3

Observations

Meeting the

100

Hz Stiffness

Requirement

The first

natural

frequency was higher

than 100Hz

consistently in all diagnostic sine

sweep

and random vibration tests, thus passing the minimum design

criteria

from

the UNP. Not only did the natural frequency remain higher

than

100 Hz

during

all

sine sweep and

random

vibration tests, but

it

occurred along a very clear and

distinct

curve toward the first peak above the 60 Hz noise, which can be seen in Figure 5·2.

All comparative graphs can be found in Appendix C

The

dominant first natural frequencies were found as an average of peak response

frequency values over each successive diagnostic sine sweep. Using this

method

a

good approximation of the exact lowest resonance frequency in each axis

can

be seen

in Table

5

.

1)

Random vibration data plots are qualitatively very similar to the diagnostic sine

sweep plots. This similarity could

be

indicative of a structurally resilient design - even

under the

more stressful

random

vibration test the N anosat-5 structure responds to

. z

233.61 Hz

221.16 Hz

Table

5 1:

BUSAT s lowest natural frequencies when subjected to a

sine sweep

test at

a fixed base in each of three orthogonal directions

described in Figure6·13



45

vibration inputs in the same way it did under the low-stress diagnostic sine sweep.

The

interplay between WedgeLoks ™ normal and friction forces in all three axes could

be one cause of

this

trend

and

a more thorough treatment of the

test data and

ana-

lytical models would likely yield proof of this.

omain

Peak

Shifts

Data analysis of

the

graphs from before and after each diagnostic sine sweep shows

a progressive shift toward a lower frequency with each successive

run

. Though the

shift signifies a decrease in stiffness, the changes are relatively small. Because

the

shifts are no more than 5 for each comparative diagnostic sine sweep, the use of

the WedgeLok™ proves to be promising for a flight-ready structure. It

maintains

a

level of stiffness

that

would not have been possible without strict tolerancing

and an

increase in manufacturing costs of the cubes.

Table 5 2: Percent change between Runs 3 and 5 Before

and

after

the random vibration tests in the Z- Axis)

and Run 12

and 14 before

and after

the random

vibration

tests in

theY-Axis .

Range Peak

Shifts

The

amplitude of the acceleration associated with the first natural frequency varies

greatly between runs and channels. As seen in Table 5.3, the greatest percent change



46

between any two runs and among all channels occurs between Runs 3 and 5 and

Runs 12 and 14. Each pair is separated by a random vibration test in t he

Z-

Axis and

X-Axis, respectively.

T he outliers in t he percent shift are Channel 4 along the Z-Axis (which is discussed

in a later section) and

Channe

l 6 along theY-

Ax

is. However t he Ch

anne

l 6 response

amplitude is so small along

the

Y-Axi

s,

the large percent (197.69 ) be lies the sig

nificance of the shift in acceleration. In Run 19, Channel 6 has a 0.024

gn

response,

wh ile in Run 22 , it has a 0.073

gn

response.

O lam el

Rill

2

3

4

5

6

7

z

Axis

(gn)

X Ax is (gn) Y Ax is ( )

1

3

5

•

1 2

•

•

22 3

9.13249 9.385m 15.10611

14.16861

1.237602

1.194257 1.412469 1.383674 0.225371

0.248292 0.248292

14.26768 14.70858

21.57141 18.62549 0.138114 0.

11

9972 0.041706 0.07677 0.710027

0.803721 0.803721

0.335918

0.432391 1.167563 1.207651 0.743424 0.711831 0.721749 0.770507 10.24388 10.59418

10 .59418

0.209738 0.198381

0.314879

0.106336

7.306512 7.06328 8.580392 a 194292

0.608061

0.657268

0.657268

11 .65426

11 .87445 18.46641 15.95839 0.663216 0.654204 0.923633 0.833619 0.024359

0.072515 0.072515

0.680448

0.676037 0.77299 0.425868 11 .06-493

10.71398

13.14629 12.52688 0.941785 1.010123

1.010123

Ta

bl

e 5 3 : Response amplitude measured in uni

ts

of Normal Accel

eration gn= 9.80665 m/s

2

) . Run 24 is a

dup

li

cate

of Run 22

due

to

human error.

Data Outlier: Th

e

C Channel

--

Figu

re 5·

:

C-channel assembly.

3

0.216734

0.738183

10.17026

0.782798

0.063465

1.18017



7

Ol

a

nn

el

z

x is( )

X

- Axis ( ) Y

- Ax is ( )

RW I 1 3

3 5

5 9

10 12

12 14 14 19 22 22 a4

24 26

2

277

-

60

.96

6.21 3.

50

-18.

27

2.02

10.17 0.00

3

-

295

-46.66

13.66 13.14

65.24 -84.

08 11

.93 0.00

4 -28.72 -

17

4.65 -1.69 4.25 -1.39 -6.76 3.42 0.00

5

5.41

-58.72 66.23 3.33

-21.48 4.50

8.

09

0.00

6

-1.89

-55.51

13.

58

1.

36

-41.18 9.75 197 .69 0.00

7

0.

65

-14.

34

44.91

3.17

-22.70

4.71 7.26 0.00

a.nge

30 10

-12.44

-.3.08

CN•axis

Table 5.4:

Percent change in acceleration

amplitude

for each succes

sive diagnostic sine sweep test according to axes. Run 24 is a duplicate

of

Run

22 due to

an

unrecorded

test

run, hence the

0

change.

Change

over axis is a comparison of averaged

peak

shift for

the

first

and last

diagnostic sweep in each axis.

Table

5.5:

Percent change in acceleration

amplitude

between Runs 3

and

5 Before

and

after the random vibration

tests

in

the

Z- Axis)

and

Run

12 and 14 Before and after the

random

vibration tests in the

Y-Axis).

12.71

8.15

4.00

19.10

12.48

16.83

Channel

4 was attached to a c-channel WedgeLok™ retainer see Figure 5·1)

and

showed the most discrepancy in relation

to

other

channels, with peaks well below

the

first natural frequency of the rest of the structure Figure 5·2) . However, since the

c-channel was

not

well constrained

it had

more degrees of freedom

than

most other

structural

elements.

This

allowed different acceleration

and

lower resonance peaks

than

in data from other channels.



48

n

39 .8107 ------------;------------------

10000

0.1000

0.0010

~ ~

f t ~

~

~

~

W J \ n

l l . \ inpu16 Q

inpu17 Q

0.0006 ------------------ ---- --------- -------- ------- -

20.

00

100.00 1000.00 2000.00

Fre uency l-Iz)

igure

5·2:

First Diagnostic Sine Sweep. Run 1: Z-Axis.

Off-axis accelerometers reflect more

variation in

the

plotted data than

on axis

channels for the

same

sine sweep,

as

seen in

Figure

5·2.

Note

the curves on

channels

4, 5 and

7.

Channels 5

and

7 have noticeable

peaks

before the on-axis

channels reach

the

first

natural

frequency

at approximately

590 Hz.

Channel

4

has

two

noticeable

peaks,

although neither of those peaks can be

definitively established

as

first

natural

frequencies for this channel. It is also important to

note that

most

of the

activity

in

the

off-axis channels is occurring below

the

0.25

gn


read-

ing

Channel

plotted in

blue

as a relatively straight horizontal line from 20 Hz to

2000 Hz .

This

suggests

that

the channels

in

question are experiencing a lower level

of

acceleration than

the

forcing that is applied

by

the shake

table

,

indicating damping.



49

Channel4

25

18

12

8

6

4

3

2

run1

i

'

l

- · - · -

- - run3

i

i

i

'

i I

i

runS

·l

r- i

.

--------

---

--·

--- -----

· : i -i-

-· -

run9

i

I

i

i

'

i

i

I

i

I I

i

I

I

'

I I I

I

I

'

I

'

i

i

i

i

i

i

I I

i

I I I

0.6

0

.4

0.3

0.2

( )

0.1

0

.0

6

0.04

0.03

0.

02

0.01

0.006

0.004

'

'

i

i

'

i i

i

i

i

i I i

I '

i

'

-

·

r---- i

1·

--· -

i-

i - '- - - --

-- - i

1

i

---

· · ·

I

I I

I

~ ~

·--

---

--

i--

·

---:

·-

~ l .

1-P

~

--

--

··_

:.....:

-

r---

,-

- ---

I

--

I

'

I

I , / . . /

i

r

·'

: .. ;j

-V-

R

----·

-- · 1

--.----l

i .

i

I

'

l"" .t/

rr

-- --

---- -

: i

I I

-i-

I I I

i

_;_

: - -

r-·-·---

------

--- --

--·-- -

-----.

------

r -

0.003

0.002

i i i i i

i

:

i

i

: : l i

0 0 ~ 0

30 40 50 60 70 8090 00 200 300 400 500600 8001000 1500 2000

Hz

igure 5·3: Channel 4 only. Diagnostic Sine Sweep Runs

1

3 5

and

9.: Z-Axis.

While mostly below the 0.25 Gn control level, Channel 4 does exhibit some res

onance amplitude values

that

rise above this level, indicating a lower first natural

frequency than the rest of

the

satellite

structure

.

An

isol

ated

view of

Channel

4

during all runs along the Z-Axis shows that there are multiple peaks before

the

en

tire system's overall first

natural

frequency

at

approximately 590 Hz. Aside from

this channel's disparity with the first natural frequency of all other channels, the

WedgeLok

™

maintained a level of stiffness in

the

structure

that

was

not

catas

trophic , but rather consistent with the design goals.

In

spite of all

the

questionable

and numerous

structural

elements that were continually edited up until

test

date , the

structure held up well and maintained a high natural frequency.



50

On Axis

Versus Off Axis

Data

urther analysis of data from X and Y axis vibration tests show that the anomalies

can

be greatly attributed to

the

axis of vibration.

The

on-axis sensors have higher

acceleration for all diagnostic sine sweep and

random

vibration tests, while

the off-

axis sensors reflect fluctuant responses, relative to the on-axis curves.

In Figure 5·4, the two X-axis channels, 5 and 7 have

the

highest acceleration

and

the

most congruous curves, while all

the other

channels are off-axis

and

have lower

acceleration,

but

more erratic curvature. All

the

channels except 5

and

7 have

at

least

one, but frequently more,

maxima

and minima prior to

the

system natural frequency

at 237 Hz. For example, Channel 3 in Run 14 has four maxima

and

fo

ur minima

between the 200 and 300 Hz range. This behavior is analogous to the behavior of

Channel 4 in the Z-Axis Figure 5·3).

Similarly, Figure 5·5 shows

that

the only Y-axis channel, Channel 4 now

has the

highest acceleration response and a smooth curve as it approaches the first natural

frequency

at

222 Hz. Whereas Channel 4 was the outlier in previous runs here it is

the only curve

with

a distinct resonant frequency.



51

gn

40.0000

------------------------------------

10.0000

1.0000

0.1000

0.0010

1.00E-04

20.00

20111020 BUSATronH x-oxls busat01 dillgnostlc-

si l

e

sw

eep· -

pr

ofile( )

. o - = o : · , : c c : ~ · = - · - - · - . : : : c ;

- c ' ~ ' : : : ' _ . . : . - . _ _ , 0 : . . . : : _ : ; - . : - c . ~ - = : . . ~ - : - ~ - : : : = - ~ - = - ~ ; , _ . . . : . - : . : : : : . .

- = . . - · n

high-abort( )

- 1

- - - - .. - 1 t- - low-abort( )

input2

1)

inp

ut3 1)

input4 1)

100.00

1000.00

2000.00

Frequency (Hz)

igure 5· : Diagnostic Sine Sweep, Run 14: X-Axis. All Channels.

gn

40.0000-.----------------------------------

-20111020 BUSAT run19 y-IXis-busatOi·dlllgnos ic

si e

sweep

10.0000

1.0000

0.0010

1

OOE 04

L---- ----- -- --- -------------- -----------__J

profile( )

high-abort( )

low-abort( )

inp

ut2 1)

inp

ut3 1)

input4 1)

input5 1)

input6 1)

lnp

ut7 1)

control( )

20.00 100.00 1000.00

2000.00

igure 5· : Diagnostic Sine Sweep, Run 19: Y-Axis. All Cha

nn

els.



52

rumheading and

Separation

Sine

urst

graphs show

out

of phase acceleration in all axes. In

the

Z-Axis,

Channel

3

is out of phase

with

Channel 2 and 6 Because accelerometers are located on different

surfaces, all with

the

potential of drumheading,

it

is likely that Channel 3, attached

to

the End Cap of the center 3U Auroral Imager cube, was drumheading out of phase

with the

Top Panel of

the

Exoskeleton (Channel 6). Since Channel 2 and

Channel

6 were very close,

though

slightly

out

of line in

the

Z-Axis, the in-phase sinusoidal

waves indicate

that

they were accelerating in the same direction at all times during

the

Sine Burst

test

.

There is no evidence of separation within the system because the on-axis sensors

reflect a clean sinusoidal curve that does not have any aberrations throughout the

time domain. f separation had been an issue, the resultant chatter or knocking

would have shown up in

the

sine burst

data

as transient , shock-like waves . The sine

burst test displayed only smooth sinusoidal curves indicating that separation was

probably not an issue.



53

on

32.0000

28.0000

control( )

24.0000

20.0000

16.0000

12.0000

8.0000

4.0000

0

-4.0000

-8.0000

-12.0000

-16.0000

-20.0000

-24.0000

-- 1

inpu12 1

: _ _ _ ~ ---

l_ftMl r·:- inpU1

4

(t)

J

- inputS( )

'iJVIvv --:-- inpU16 t)

i\f N

" input7(1

tv re-

- ·

-

I

i

npU13

(1)

~

l

j

J

__

_ ____

-28.0000

-32.0000

-34.0000

-41

0

100 200 300

400

500 600 700 758.594

n me (Milliseconds

igure 5·6: Sine Burst

Run

02 : Z-Axis. All Channels.

gn

34.0000

. . . · · ·

- - -

control( )

28.0000

..

24.0000

· ·· ·

input2

1

)

20.0000

-

input3

1

)

16.0000

12

.00

00

input4

1

)

8.0000

input5(1)

4.0000

~

input6(t)

0

F

input7(1)

-4.00 00

-8.0000

-12.0000

-16.0000

-20.0000

-24.0000

-28.0000

-32.0000

-34.0000

-41 0 1

00

200 300 400 500 600 700 758 .594

Time

igure ·7: Sine Burst Run 11: X-Axis. All Channels.



54

WedgeLok

™

Loosening

Any significant decrease in n

at

ural fre

qu

ency is indica

tiv

e of a decrease in

st

iffness,

system components loosening, or

st ru

c

tur

al elemen

ts

reaching a plas tic limit. An

in

cremental decrease in the lowest na tural frequency of every channel, alt hough small,

l

ea

ds to a h

ypot

hesis that there was loose

nin

g in t he WedgeLoks™over t he t hree

day

test pe

riod . The data in Table 5.6 is a list of the p

ea

ks along t he curve of all

diagnostic sine sweep test s. A comp

ar

ison of the frequencies shows a progressive

decrease in magnitude with cont inued vibration testing. However Tab le 5. 7 reflects

an overall

stab

ili

za t

ion toward the l

ast

few tests.

Th

e decrease in

st

iffness for the

Y-Axis is much smaller in relation to

both

t he X-Axis and Z-Axis.

Th

e apparent

st iffening between runs 14 and 18 is an anomaly and any conjecture

to

the cause or

effect

wo

uld be unfounded.

Channel

A..

2

3

4

5

6

7

n Ja

Torque

Z - Axis (Hz) xis z) Y Axis (Hz)

(

111-32

)

1

3

•

1D

12 4 11

•

22

a

16: : 1 589.03

582.45 556.63 541 .39 237.42

236

.35 229.60

230

.32 221 .93 220.43 220.

43

220.68

16: :1 569.03 582.

45

556.63 541 .39 237.68 236.35 234.76 230.32 221 .68 220.43

220.43

220

.68

6:t

569.03

561 .79 556.83 541 .39 236.88 235.82 229.54 229 .60 221 .68 220.43 220.43

220.68

6:t

592.35

589.03 565.66 568.85 237.42 236.35

229.60 230 .32 22243

221 .43 221 .43 221.43

6 :t

589.03 582.45 556.63 541 .39 237.42 236.35 229.60

230

.32 224.« 219.

94

219.94 220.19

6:t

569.03

582.45

5.. 0

.63 541 .39 237.42 236.35 229.60

230 .32 222.43

221 .43

22

1.43

22

1.43

Table 5.6: Na

tural frequencies for each channel determined by

th

e

first peak along the curves of t he diagnostic sine sweep tests. Run 24

is a duplicate of Run

22

due to human e

rr

or .

Frequency

Shift:

Analysis

Jna

Torque

0-32)

in-lb)

7: : 1

7:t

7: :1

7: :1

7: :1

7: :1

While not outside of the specifica tions given

by

t he UNP for st ru

ctur

al

test

ing, some

shifting was obse

rv

ed

in

th

e lowest na

tur

al

fr

e

qu

ency of

th

e BUSAT

st

ruc

tu r

e over

t he t hree-day

spa

n of testing. Shown in Figure

5-8

are t he four diagnostic s

in

e sweeps

th

at

were interspersed between shock, r

an

dom vi

brat

ion and sine bur

st

tests. There

is a clear

and

somewhat regul

ar

pe

ak

shift from Run 1 (blue, at right) to Run 9 teal,

at left ). Addit ionally, t he quality of the peaks appear to indicate decreasing damping



55

Channel

Z -Alcis ( ) X -Alds (%)

y - Alcis (% )

Torque

(%)

im 1 3

sas

sa•

1t1 1Z

ZA 4

,..,.

••:zz

:ZZA:M

....

o Il

2 1.12

4.40 2.77 0.45 2.77 -0.23 0.

67

0.00

0.

11

56.25

3 1.12

4.40 2.77 0 .56 0.67 1.89 0.56

0.

00

0.11 56.25

4 1.23 4.29 2.77 0 .45 2.66

-0

.

11

0.56 0.00 0.

11

56.25

5 0.56 3.97

-0.56 0 .45

2.77

-0.23 0.45

0.00 0.00

56.25

6 1.12

4.40 2.77 0 .45 2.77 -0.23 2.00 0.00

0.

11

56.25

7 1.12 4.40 2.77

0 .45

2.77

-0.23 0.45

0.00 0.00

56.25

::.::.

7

U 1 1 ?1

• .25

Table 5. 7: Percent change of natural frequencies for each succes

sive diagnostic sine sweep t est acco

rdin

g to axes. Change in nat ural

fre

qu

encies are c

ompar

ed to percent change in t orque r

ea

dings from

Wedge Lok

s™

.

Run 24

is a duplicat e of

Run 22 du

e to errors in record

keepin

g,

hence t he 0% change.

Ch

ange over axis (last row) is a com

par ison of t he average p

ea

k of all cha

nn

els for t he fir

st

and last run

along each

ax

i

s.

with each subsequent test .

One possible explana

tion

of t his phenomenon is that

th

e WedgeLoks™ co

uld

be

loosening over t ime

du

e to relaxation of shear st resses in the

we

dges t hemselves, due

to t hermal cyclin

g,

or due to t hreaded tension rods vibrating loose. This would in

t urn cause an overall loose

nin

g of the structure a

nd

therefore a lower fundamental

frequency.



0.1

0.06

0.04

0. 3

56

Channel

0.02

------ -------- ----- ----- --

- ----------- ------ ----

520 530

540 550 560

Hz

590

600

igure

5·8: While still within specifications, the BUSAT structure

does display some shift in lowest natural frequency. Generally, the

peak shifted lower by around

1 to

2 z after each subsequent test

frequency and magnitude are labeled for each of the four response

curves).



3

;

:

25

i

20

i

15

0

;

'Z

10

Iii

w

5

0

57

-

--eng ineeringtoolbox.com

1

Carbon Steel, C < 0.3'4

Nickel Steels, Ni 2 4- 9'4

Cr

-Mo Steels,

Cr

2'4.3'4

Copper

leaded Ni-Bronze

Nickel Alloys - Monel

400

Titanium

Aluminium

-500

.300

-100 100 300 500 700 900 1100 1300 1500

Temperature (deg F)

Figure 5·9: Elastic modulus as a function of temperature

(www. engineeringtoolbox.com) .

The regularity of the peaks, however, suggests that

at

least one

other

hypothesis

is warranted . While

temperature

was not controlled or measured during testing, it

can be assumed that the climate inside the Draper

test

facility was relatively

stable

with

fluctuations of only a few degrees

and

that

the test

facility

heating system

was

sufficient to offset the chilly New England fall weather.

For a two-dimensional solid in which both transverse and longitudinal waves are

possible, the lowest

natural

frequency can

be

~ r i t t n as a function of

the

speed of

sound in the solid (aluminum,

in this

case):

5 .

1)

where n and are mode numbers, N and M represent characteristic lengths of

the

solid,

r

is the speed of transverse waves in aluminum and

£

is the speed of

longitudinal waves in aluminum. If n = and N = M



58

Inserting the Lame constants, (5.2) becomes

f

_ _': -J :_ 11

2N p p

·

Simplifying and using the definitions 1-" = l ~ v ) and A

Poisson s ratio,

5

.2)

(5.3)

v

where

v

is

( l+v)( l-2v) '

(5.4)

Given that p

~

2 7 ~ and

v ~

0.35 for Aluminum, natural frequency as a function

of the elastic modulus

E

is given as

fn = (.021) V (5.5)

Since the elastic modulus E varies inversely with temperature (see Figure 5·9) , a rough

relationship between temperature change and elastic modulus can

be

established.

From Figure (5·9), this corresponds

to

a reduction of

about

2.75

GPa

for an increase

of 35°C. Assuming an inverse linear relationship, this corresponds to about 0.078 GPa

per degree. Substitution into (5.5) reveals

that

even a small change in temperature

can produce a large shift in natural frequency:

n n n

:lfn

=

2

N.021yi :lE(T)

=

2N .021

X

V0

.

78

X

10

9

~

2

N186H

z) (5.6)

Therefore, for values of

n

and N near unity, response frequency is very sensitive

to

changes in temperature. Additionally, since the elastic modulus decreases with in-

creasing

temperature

, the lowest natural frequency also displays

an

inverse relation-

ship with temperature , suggesting that future testing efforts should include either



9

precise temperature monitoring or fine temperature control.

Wear

Figure 5·10 shows an example of surface wear that was found after testing and disas

sembly. The pressure exerted by the Wedgeloks and the frictional forces

acting

along

the surface was large enough to remove

portions

of the anodized material.

Results

showed less evidence of wear

than

expected.

Figure

5·1 :

Evidence of wear on the anodized surfaces of a cube.

5 0 4 Summary of Data Gathered and Conclusion

The

vibration

tests supplied proof that the

WedgeLok™

concept

upholds

UNP vi

brational specifications and suggests that a redesign of the Exoskeleton Cubes

and

Spacers while necessary

may

need

to

include more features of the original structural

design than previously thought Considering the positive results of the vibration t ests

the

WedgeLok™ may be

used

with

the

right design

constraints

for

the

cube

arrange

ments in

the

next engineering design unit . Structurally the NS-5 prototype exceeded

the requirements from

the

UNP thus

the

primary objectives of the new design should

be modifications geared

toward

modularity ease of assembly

and

accommodations for

integrating new ideas in

the

other subsystems.



6

Chapter

6

Analytical Model

6 1 Introduction

Because

vibration testing presents

a

potential point of

failure for

many aspects of

a

satellite mission,

it

is desirable for

the systems

engineer

to

have tools

at

hand

that

will accurately

predict whether

a given satellite structural will fail when subjected

to the sine sweep and other tests described in Section 4.1) . Additionally,

prediction

of the vibration environment within subsystem

component housings is valuable in

identifying critical

points

of failure

within

payloads. In other words an excellent sys

tems engineering model would

produce

frequency response charts from

characteristic

information

about

a variable configuration

of

mission payloads.

Figure

6· :

The

model developed

in this

section seeks

to determine

the BUSAT satellite s frequency response based on

the

characteristics

of the payload bay.

Due to the cubic and

modular

nature of the BUSAT mechanical bus , an iterated

mass-spring-oscillator model can be developed to assess the frequency

response

of



6

the

system

for a given

payload

configuration. This is accomplished by recognizing

that each of

the

satellite payloads

can be

modeled as an assembly of masses, springs

and

dampers.

The

model developed in this section houses 27 1U point masses in a

cubic matrix of springs and dampers constrained by a vibrating, rigid housing. As a

mesh of relatively simple oscillatory systems, the primary challenge is organizing the

hundreds of variables so that control of

the

model is retained

throughou

t . or

the

remainder of this section,

it

is noted that

the terms

mass , cube

and

payload

are analagous and interchangeable.

6 2

Damped

Mechanical Oscillators

Development of

the

equations of motion for a coupled 27 degree of freedom mass,

spring, and damper system starts with

an

elementary model.

The

most basic model

of a vibrating sy

stem

has three basic elements arranged as in Figure (6·2) .

Figure

6· :

A basic mass, spring,

and damper

system where

the

mo

tion of mass m in response to

an

excitation ~ t ) is described

by

the

state variable measured from the origin in the

upper

left hand corner

of

the

diagram.

The

equations of motion are found

by

considering

the

free-body

diagram

for m ,



62

using Newton s second law

x

-

: ;, = ~ ) , where is the sum of forces applied

to the mass m and f

)

= f )) is the periodic forcing delivered

to the

mass via

damper and

spring and caused by

the

periodic motion of the platform:

mx

ex kx =

~ t ) +

~ ( t ) (6.1)

and

~ t ) is the motion of the rigid platform. Written in

standard

notation for a

second-order system

x

+

2 wnX

+

~ x

=

. : _ ~ ( t )

+

} 5 _ ~ t )

m m

(6.2)

with

forcing terms from the platform motion placed in the right hand side of the

equation. The

undamped

natural frequency of

the

system is

(6.3)

which can be solved immediately upon inspecting the single spring

and

mass.

The

damped natural

frequency is given

by

6.4)

where

the

damping ratio, ( can

be

solved from quation (6.2)

and

is

c

=

2Vkm

(6.5)

f

the

mass is placed inside a vibrating box

with

more

than

one coupling

to

the

input motion

x t)

as in Figure (6·3), the equations do not differ greatly, but deserve

mention as the next

step

in evolving the model to a larger system.



63

igure

6· : A single degree of freedom mass, spring

and damper

sys

tem

with two points of coupling

to the

oscillating platform.

The equations of

motion

for m

3

are

(6.6)

Several comments can

be

made about

the

utility of the enclosed single-mass system

shown in Figure (6·3).

irst

,

it

is recognized as

the

same

system as

the

one

represented

in

igure

(6·2) with c

=

c

2

c

4

and

=

k

2

k

4

. Second, while redundant , this

system will prove

to

be a useful simplification in the larger model.

It

is also

noted

that

the

subscript convention used to describe masses, springs and

dampe

rs captures

an element s position

with

respect

to

the origin. Finally, the vertical motion of the

platform is a very good model for the shaking of

the

vibration table, which can only

impart vibrations in one axis at a time.



64

6 3 Multiple Degrees of

Freedom

In

general,

the

equations of motion for a vibrating system with more

than

one degree

of freedom can be

written

in matrix form as

Mx +Cx + Kx =

f t)

(6.7)

where M and K are symmetric matrices representing the mass, damping

and

stiffness of

the

system,

and f

) some forcing function affecting

the motion

of the

system. In

the

case of

Equation

(6.6),

the

forcing

term

is dependent on

the motion

of

the rigid supporting platform as well as

the

connecting dampers and springs, therefore

j t) =

c ~ : 4 ~ t )

+ k 4 ~ t ) .

Undamped natural frequencies are found by solving the eigenvalue problem

Kx=

.Ax

(6.8)

where

the

system s natural frequencies Wn and mode shapes are recovered from the

eigenvalues

and

eigenvectors of Equation (6.8) .

6 4 Damped

Frequency

Response

or Multiple

Degrees

of

Freedom

In the case of the BUSAT

structure

undergoing a sine sweep over a range of frequencies

with

the magnitude of acceleration held constant, the forcing function is sinusoidal

by

definition and

can be

represented

with

complex exponentials:

(6.9)

Taking the real

part

of

f t)

can be expressed as a function of

f t) and

its complex



65

conjugate yielding:

6.10)

Similarly, one

can

assume a steady-state displacement

Xp

t) of

the

matching form:

6.11)

Taking the real part of Xp t) yields:

6.12)

Substituting f t) and xp t) into quation

6. 7)

and reorganizing terms yields:

-w

2

M + iwC + K) Xpeiwt

-w

2

M + iwC +

K)

~ X = ~ F e i w t F - i w t

2

p

2 2

This can be separated into two equations - one real and one imaginary:

-w

2

M + iwC + K) ~ X

iwt

= ~ F e i w t

2 p 2

-w

2

M iwC + K)

~ X e - i

=

~ F e i w t

2 p 2

6.13)

6.14)

6.15)

Because

8)

is the complex conjugate of 7), they are redundant equations.

The

term

-w

M iwC K) is a matrix, and can

be

inverted

to

find Xp w):

Xp w) = -w

2

M+ iwC

K -

1

F

Xp w) = G w))-

1

F,

6.16)

6.17)



66

where Equation (6.17) is the complex displacement frequency response,

and

is

valid for oscillating systems of any size and configuration for which

G w)

can be

inverted, including a single degree of freedom damped oscillator in Section (6.2).

Since acceleration frequency response plots are desired (based on the

data

collected

during shake testing

and

based on industry standards , Equation (6.17) is differenti

ated twice and the magnitude is taken. Since

taking

the second time derivative

in

the

time domain is equivalent

to

multiplying by a factor of w

2

in the complex frequency

domain

, the final

quantity

to be

plotted

is

(6.18)

6 5

Spring Coefficients

and Forcing Input

o t i o n ~

Initial values of mass are then set

at

1

k

and spring constants k are calculated using

Hooke s law

(6.19)

where the cross-sectional area is based on

the

dimensions of 4-inch

extruded

alu-

minum

tube with a 0.0032 m (0.125-inch) wall, modulus of elasticity

E

is taken to

be 69 x

1

9

Pa (Aluminum 6061-T6), and Lis O.lm.

Looking again at Equations (6.9) and (6.5),

the

forcing term is written as

(6.20)

Since the motion of the vibration table discussed in Section (

4

, is the sinusoidal

displacement

that

will drive the network of masses,



67

~ t )

=

iwAeiwt

~ t ) = -w2Aeiwt,

6.21)

6.22)

6.23)

where A is the magnitude of displacement and w is the frequency sweep over which

the

frequency response is plotted.

By definition of

the

sine sweep test , the forcing magnitude is a constant 0.25G

0

,

where G

0

is 9.8 From Equation 6.23) ,

6.24)

and

therefore, A= A w) = Now Equation 6.20) is written

=

t w - - e

+

e

(

. 0.25G

iwt C2 +

C4) 0.25G

iwt k2 + k4

w

2

m

3

w

2

m3

6.25)

and the

magnitude

can be

recovered as

JSRJ +

<;Sj or

6.26)

Next,

the

magnitude of the complex displacement response

JXP

is pl

otted

over

frequency for a range of damping constants using

quation

6.17) , as seen

in

Figure

6·4). Qualitatively, the plot is similar to the test

data

in Section 4), but displays

far higher resonance frequencies because of

the

low mass

to

spring coefficient ratio.



68

10°

Single DOF model

10-

2

10 .

10 '

110 '

0

3

1 ·1

;

$

§

1 ·12

c.

i l

0::

10· 4

10

1 ·18

10-

20

10°

10 '

10

2

10' 10

10

5

10°

10

7

10'

Frequency

(Hz)

igure 6·4: Single degree of freedom mass-spring-damper system dis

placement response

plotted

over frequency.

I t

is also noted that this is a plot of displ cement over frequency that , while not

directly applicable

to

the test

data

discussed in Section

4),

does illustrate

the

effect

of

Equation 6.24

which constrains

the

sine sweep

to

a constant

cceler tion input.

Finally, the system's acceleration frequency response is

plotted

, as shown in Figure

(6·5).

As in Figure

(6·4), the

high resonance frequency response reflects the relatively

low mass of the system when compared

to the

spring constants applied.



10

1

3

10 '

10°

10

1

10

2

69

Single DOF model

\

0

3

10

4

10

5

10°

10

8

Frequency (Hz)

Figure 6·5: Single degree of freedom mass-spring-damper system ac

celeratation frequency response plotted over frequency.

6 6 Three

Degree

of Freedom

Model

Extrapolating the vibrating single-mass system into a three-mass system, position

vectors x

1

to x

3

are assigned to each of

the three

masses and the system is driven

by the

motion

x t),

as in Figure 6.6). It is also

noted

that in Figure 6·6), the

simple numbering scheme

adopted

in Figure 6.6) has been extended to the larger

system. Proceeding vertically down from

the

origin

at

the top left (at k

=

0 springs

and

dampers appear

at

even positions beginning at k

=

2 while masses only occupy

positions k = 1, k = 2 and k =

3.

Since

the

model does not

extend

in

the

i or

direction, there is no subscript applied.



70

igure · :

A three degree of freedom mass spring

and damper system

with

four

points

of coupling to

the

oscillating platform.

The equations of

motion

are again

obtained

from free-body diagrams of each mass

however a general method of analyzing

the diagram can be

used.

y noting that

any mass m is connected to other mass elements by springs or dampers in positions

1 a general formula for the

kth

mass is found.



7

•

l

igure

·7:

Generalized free-body

diagram

for the

three

degree of

freedom system.

and finally, rearranging quation ??) according to state variable,

6.27)

quation

6.27) represents the generalized

equation

of motion for the three

mass



72

system, where subscripts = 3 5 7 call appropriate values for each of

the

masses,

springs

and

dampers

that

are relevant

to the kth

equation of motion for

the

system.

Since the three-mass system is bounded above and below the three masses m

3

, m

5

and m

7

,

the general equation for state variables

±

2

will result in

state

variables

x

1

and

x

9

entering

the

equation. Looking again

at

Figure 6·6),

the

position values

k = 1 and k = 9 indicate the rigid structure surrounding the system and are therefore

variables of motion associated

with the

forcing term. Therefore, the full equations of

motion for th is system are

c

2

c

4

• C4 .

X - [ 0 ] + X - X5

m3

m3

k2 + k k c2 · k2

- [ 0]

+ X3

x5

= - ~ t ) +

- ~ t )

m

3

m

3

m

3

m

3

.. C4 • C4 C5 . C5 .

X5 -

X3

+ X5 - X7

m

5

m

5

m

5

k k + k6 k6

- X3 X5 - X7 =

0

m

5

m5 m5

.. C5 • C5 + Cg . [ O

X7

X5

+

X7

m7 m7

k6 k6 ks

cs ·

ks

- x5 + X7 [ 0] = - ~ t ) ~ t )

m

7

m

7

m7 m7

6.28)

Where

the

terms on

the

right hand side of Equations 6.28) are the motion x

1

=

x

9

= and ±

1

= ±

9

= of

the

rigid enclosure. he equations of motion

are

therefore

shown in Equations 6.30)

and the

normalized) frequency response is shown

in

Figure

6·8).



73

Where

[

1

0

~ ] ,

=

m2

0

m3

[k

+

4

K = -k4

k +

k6

0 k6

10

2

s

~ ~

-

C4

0

C =

-

c4

C4

+

C5

~

0

- C6

C5 + Cs

0

{ ~ t )

+

}

~ ]

j t)

= 0

k6 + ks

c s ~ t )

+

s ~ t )

3DOF System in Rigid Enclosure

1) 1

10

4

Frequency Hz)


1)2

\

'

Cll

'

:

0

a.

'

ll

::

10°

10

2

10

3

1) 1

10

4

Frequency Hz)


10

4

Frequency Hz)

y

}_[\

P

-.....:::::::::

Figure

6 ·8: Three degree of freedom forced mass-spring-damper accel-

eration

response plotted over frequency. Undamped

natural

frequencies

ar

e marked by vertical lines.

(6.29)

(6.30)



7

6.

7

Nine Degree of Freedom

Model

Coupled)

Figure ·9: Schematic

representation

of a general planar

cube

array

element

surrounded by

four masses, four springs and four dampers .

As

the

image in

Figure

6·14) shows, a nine degree of freedom model is also

simply

constructed

using a slightly more complex version of the

three

degree of freedom

method, as

shown

in Figure

6·9) , and the general

equation

of mot ion that describes

any

of the nine state variables is

C i+1,k) C i-1,k)

C i,k+l)

C i,k-1) .

X i,k) X i,k)

m i,k)

C i+1,k)

. C i-1,k) .

X i+2,k)

- X i-2 ,k)

m i,k,k) m i,k,k)

C i,k)

.

C i,k)

.

X i,k) - X i,k)

m i,k,k)

m i,k,k)

C i,k+1) . C i,k-1) .

X i,k+2) - X i,k-2)

m i,k,k) m i,k,k)

k i

,k+1)

k i

,k-1)

X i,k)

m i,k)

k i,k+l) k i,k-1)

m

X i,k+2)

- m X i,k-2) = 0

i,k,k)

i,k,k)

6.31)

Using

Equations

6.31) and

this time

varying

mass

values for the

system, Figures



75

(6

·1

0) through 6· 1

2)

we re generat ed to show qualitatively t hat t he model develop

ment model reflects a real system. Simul

at

ing a system wit h one very heavy (around

50 kg) node, the lowered first n

at

ural frequency verifies

that

the system behaves

s

it should . Before cont inuing to t he full model, it is also useful

to

note that

the

sig

nificant asymmetry of a large mass in

on

ly one node of t he system generates very

different high-frequency e

ff

ects in each of the 9 degrees of freedom (as expected).

10

5

I

~

i

i

)

10°

/)

<

0

0..

/)

Q)

0:::

10-

5

10

3

10

5

I

/)

:§_

Q)

10°

---------

----

/)

<

0

0..

/)

Q)

0:::

10-5

10

3

~

10

5

N

Q)

10°

/)

I

0

0..

/)

Q)

0:::

10-

5

10

3

- -- -- - ---1--------

1 o 9DOF System in Rigid Enclosure

i [ I ' l I '

i I :

j

1

i

i 1

2 ~ 1

i

~

~ ~ ~

~

t

:

10

4

Frequency (Hz)


10

4

Frequency (Hz)

3 of 9DOF System in Rigid Enclosure

' j '.

)

: I

i

i

I I

1

I : '

I I ' : I I

I

---f -

-+-

- :T.: .

---

:

-

l

10

4

Frequency (Hz)

Figure

6·1 :

Masses

1-

3 of a nine degree of freedom forced mass

spring-

damper

frequency response pl

otte

d over frequency. Un

da

m

pe

d

natural frequencies for each mass are marked by vert i

ca

l lines.



i

l

l

i

I

T

;

76


i

i

I

_.1.

I

- -----

I

10

4

Frequency (Hz)

[


I

I

i

1

I

T

'

I

~

i

i

10

4

Frequency (Hz)

)

I

'

.

A

i

Y

'

'

i

i

)

i

'

I

i

I

I

I

i

i

-

A

I

I

1

--·

f--

~

i

i

I


. ~ . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . ~ ~

s

~

f = = = = = = = i = = =

~

= = = f = = f = i =

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ . l k d

i

0-5 L_____________j___

----'-------l_____J_______L_j_

j l_____

____

______

__ __

_____1_-- --------i.__

i

10

3

10

4

Frequency (Hz)

Figure

6· :

Masses 4-6 of a nine degree of freedom forced

mass-

spring damper frequency response plotted over frequency. Undamped

natural frequencies for each mass

are

marked by vertical lines.



77

7 of 9DOF System n Rigid Enclosure

- - - - - - - - - - - - - - ~ - - - - - - - - - - - . - - - - - - - - - - ~

f

'

=

= t = = r = = =

~

~

~

y

r

F = 4 ±

±=b

iiJ

I l y .

I

o:: 1

o·s - - - - - - - - - - - ~ - - ~ __ _ _ _ _ _ - - - - - - - ~ - - - - - - - - - - - - - - - - ~ - - L . J _ ~ _ , _ ~ _ . _ _ _ _ . _ j

10

3

10

4

l

· ---·-

Frequency (Hz)


I

i

i

I

:

i

I

I

I

I

-----

- -

:

10

4

Frequency (Hz)

J

iY

i

i

I

I

i

i

I

i}

I

'

i

"i"" '

I

I

i

1

Figure

6 12:

Masses 7-9

of

a nine degree of freedom forced mass

spring-damper frequency response plotted over frequency. Undamped

natural

frequencies for each

mass

are

marked by

vertical lines.

6.8 Twenty-seven Degree

of

Freedom Model Coupled)

This model being developed is essentially a matrix that organizes all masses, springs,

and

dampers

within

a framework that reflects the orthogonal modularity of the

BUSAT

structure

itself. Because the models components are

distributed

regularly

about a 10x10x10

matrix,

they can be manipulated

in

a regular fashion using itera

tive loops in

MATLAB, and a generalized

method

for dealing

with the

rather large

(27

-DOF

system becomes more manageable.

In

the full model

the

subscripts i, j know run from 1 to 10

in order

to accomodate



8

all masses, dampers and springs within the model.

It

is notable

that

positions

i, j

k

0, 10 are empty, that masses occupy the

odd

position values i, j k 3, 5, 7 only, and

that

dampers

and

springs occupy even position values

i,

j

k

2, 4, 6, 8 only.

Thus

the model contains 27 masses, 108 dampers and

36

springs.

Only

motion

in

the

vertical z) direction will be considered in this model

6 9

Framework of Analysis

In order to predict frequency response, an equation of motion must first

be

developed.

The standard

notation

for this system is

Mx + C±+

Kx

f t)

(6.32)

where M, C and K are diagonal matrices representing the mass, damping

and

stiffness

of the system, and

j t)

some forcing function affecting

the

motion of t he system.

Since the BUSAT satellite has up

to

27 mass elements of interest (excluding the

exoskeleton, which is considered a rigid external

structure to

which forcing motion is

applied), there must necessarily be 27 degrees of freedom (one for each mass) and M,

C and K are therefore square

27

x 27 matrices.

Due to the high number of discrete elements (high for an analytical model, at

least) in the system, a regular and easily accessed data structure is needed for storage

of the satellite's spring, mass

and

damping characteristics. These characteristics will

also be the knobs

to

be adjusted in order to tune the model

and

calibrate it to

reflect

the data

described in Section (4.

1

, so

they must

also

be stored

in

a logical

manner for ease of access. The most intuitive structure reflects

the

cubic nature of

the satellite itself: a

10

x

10

x

10

MATLAB cell array holds values for the system's

dampers, springs and masses, allowing intuitive access by the systems engineer as well

as indexed access by

the

frequency response algorithm implemented in MATLAB.



79

Subscripts for

the

discrete modelling elements placed within

the

cell array will be

governed

by

the following rules:

• Masses will occupy odd subscript combinations of 3 5 and 7 only.

• Springs and dampers will occupy indexes within the cell array that have at least

one even value.

• Any mass subscripted with a single value of 1 or 9 will indicate the position of

the

rigid

external

frame.

Further

simplifications

are brought about by setting

all spring

constants

to

zero

except those that are subscripted with

odd

integer values of 3 5 or 7 Physically

this reflects the fact that damping will likely occur only between cubes or

between

the cubes

and the

structure

but

that spring forces are likely

to

be important only

in

the

vertical direction. In other words because

the

system is clamped primarily

in the lateral direction because of the placement of WedgeLoks vertically around the

perimeter of the cube stack it is assumed that

the

vertically mated surfaces of the

wedgeloks exoskeleton

and

endoskeleton will

be

better

by

use of friction forces

than

spring forces.

igure

6· 3: The BUSAT standard satellite-fixed reference frame.

The

unit vectors

i J and

k are assigned to the x y

and

z axes respec

tively.



8

A

method

of

naming

each variable for

tracking throughout the

model is also essen

tial. While

the

numbering

system is

arbitrary,

strict adherence to the identifications

given in Table 6.2) is absolutely necessary. Additionally, a frame of reference for the

structure to

be

reflected in

the subscripted

indices

of

the MATLAB cell

array

will

ensure

fidelity

in

the model. The frame of reference is shown in

Figure

6·13) .

igure 6· 4: A one-to-one transformation

between

payload cube po-

sition and state variable subscript, as shown

in

Table 6.2.

Because each

point mass

is

arranged in

a

regular

network,

the motion of

any given

mass

is coupled

with

the

motion

of

as many as

six different masses

surrounding it

four

lateral

adjacent,

two

vertical

adjacent .

Since

the

forces applied by dampers

and

springs to a given

mass are

a function

of

both

the

motion of that mass and

the

surrounding

ones,

it

is important

to establish

the positional relationship

between

mass

values in the

MATLAB

cell

array

and their corresponding values within

the

M , C and K matrix equivalents.

In

other words, a

regular

relationship

between

the

position

of a

mass

in

the

MATLAB cell

array and

the

subscript of

its

state

variable in

the

equations of

motion must be established. This relationship is given by the linear

function

f i , j, k =

4.5i

1.5j 0.5k-

18.5, 6.33)



81

ube Mass

--+

~ t t e Variable

X333

xl

X335

- t

X2

X337

- t

X3

X353

t

X4

X355

_-r.

xs

X357

- t

x6

X373

t

X7

X375

t Xg

X377

Xg

X533

- t XlQ

X535

- t

X n

X537

t

X12

X553

- t

X13

X555

- t

X14

X557

t

X15

Xsn X15

X575

- t

X17

X577

t

X18

X733

t

X19

Xns

- t

X2o

Xn7 t X21

X753

t

X22

X755

- t

X23

X757

- t

X24

X773

t

X25

X775

- t

X26

X777

t

X27

Table

6.1:

State

variable conversion from

the

satellite matrix

to

sub

scripts used to describe

the

27 equations of motion.

where j k) are the positions of each mass value within

the

MATLAB cell array

and

f i

j

k) gives

the

index of

the

mass within

the

mass

matrix

, also

the

subscript

value in Table 6 .2) . f a relationship is discussed between a mass mi j k and the mass

mi, j ,k

2

directly below it,

the

index of the lower mass is

f i j k + 2) = 4.5i + 1 5j +

0.5 k

+ 2) -

18

.5

= 4.5i

+ 1 5j + 0.5k

- 17.5

=

f i

j k

+

1

6.34)

6 .35)

6.36)

indicating a net motion of + in the mass matrix index value for degree of freedom

,

j

k

+

2)

in the

downward or

k

direction within

the

MATLAB cell array model.

In

the following sections this convention will be used to developed a series of analyses



8

starting with

simplified one and

three

degree of freedom models.

n illustration of

the

satellite

matrix

is shown in

Figure

(6·15) .

0

igure

6· 5:

Two-dimensional

representation

of the satellite cell array.

Intuitively,

this

is

the

equivalent of beginning

at

the

cube

3

,

3

,

3

)

and progressing

first down

the

column of cubes in

the

positive k-direction,

then

shifting one

column

in the

positive i-direction and progressing down

that

column. Once

the fi

rst row

of

columns is complete, the process starts over

with

the

adjacent

row of columns in the

positive j-direction.



83

Th

e generalized

equation

of motion for the mass mi,j,k is

.. + C(i+1,j,k) +

C i

,j,k)

+ C i,j+ l ,k) + C(i,j

,k)

+ C i,j,k+l) +

C i,j ,k-1) .

X i,j,k)

X i, j

,k)

m i , j

,k)

C i+l, j ,k) . C(i-1

,j ,k) .

X i

+2

,j,k)

-

X i

- 2,j,k)

m i,j ,k)

m i,j,k)

C i,j

+ l ,k) . C(i,j-1,k)

.

X i,j+2,k)

-

X i

,

j -2

,k)

ffi(i

,

j,k) ffi(i,j,k)

C i,j,k+ l ) .

C(i,

j,k-1)

.

X i,j,k+2)

-

X i,j ,k-2)

ffi(i,j,k) ffi(i,j,k)

+ k i, j,k+l) + k i, j,k-1)

X i,j,k)

m i ,j,k)

k i , j

,

k+l)

X . . _

k i

,

j ,k-1)

X . .

=

Q

(t,J,k

+2

) t, ]

,

k-2)

m i,j ,k)

m i,j,k)

where

i , j ,

k = 3,

5, 7.

As stated

in

Rule (6.9), any state variables xi, j ,k where

i = 1 o r 9, j = 1 o r 9 or k = 1 or 9 then = 1

Xi,j,k

= ~ t and it is

expressed as a forcing term on

the

right side of

the

equation. Additional simplifica-

tions

ca

n be made for Ci,j,k where (i,

j

k) is equal to (2, j k), (i, 2, k

,

(i, j 2), (8, j k) ,

(i,

8,

k , (i,j, 8)-

these values

can be

simplified to a group of

outer

dampin

g values

and

separated from the inner damping values between cubes. Additionally,

the

three

dampers

installed at the

extreme

faces of each corner cube all depend on the

motion

between

the

rigid

outer structure and that

corner cube,

and can be

combined

into one value.

The

above equation can

be

re-written as



84

X(·

k)

+Ax

·

k)

,J, t,J,

+Ex ·

·k)

J

where the coefficients

are

matched with indexed with state variables according

to

Table

(6.2).

C:oethcient

---

::;tate Vanable

--- X i,i,k)

lh

--- X i+2

,j ,k)

H2

--- X i-2

,j ,

k)

G\

---

X i,i+2 k)

G 2

---

X i,.i-2,k)

l

---

X i,j,k+2)

l

---

X i,j,k-2)

.b

---

X i,.i,k)

1 1

---

X i,j,k+2)

1 2

---

X i,i,k-2)

able

6.2: Coefficients of the

i,

j, kth

equation

of motion. Since the

acceleration term always

has

a coefficient of 1,

there

is no letter as-

signed.

It

is recognized

that

while

the

coefficients

of the

velocity

and position

terms will

vary

with values of i, j,

k,

the shifting subscripts also indicate an

interdependence on

the adjacent cube

motions, i.e.,

the motion

of

cube m i,j,k)

is coupled

to

the

motion

of the two cubes above and below m i,j ,k±2) and the four laterally adjacent

cubes

m i±2,j,k)

and m

,j±2,k)·

In

addition to the

linear

Equation

(6.33) that governs

transformations

from the



85

MATLAB cell array

to the

equations of motion,

it

is also useful

to

note that

f i

± 2 j k f i

,j,

k ± 9

f i

, j ± 2 k

f i

, j, k ±

3

f i,j,

k ±

2) f i,j, k

±

1

6 9 1 Building

Mass Spring

and

Damping

Matrices

f

is the newly indexed position of variable ±i,j,k in the 27-DOF velocity vector

X.

then PA

= g ± i,j,

k

=

f i

,j,

k

and

PA 4.5i + 1.5j +

0.5k-

18.5

6.37)

This means that when X. is multiplied with the damping matrix

C

the PAth

term

of X. will multiply the PAth term of the rows of

C and

PA therefore dictates the

position of the damping coefficients within

the

rows of C:

c1 1 c1 2

c

PA

c1 21

Xl

C2,1 C2,2

C2 PA

c2 21

X2

X

6.38)

XpA

C27,27

X27

In this way the coefficient A which, as above, is multiplied by velocity ±i,j,k) is

appropriately indexed to the PAth position in the rows of

C.

Similarly, the positions

of the remaining damping coefficients are



86

Ps

1 ,2

=

g i: i±2,j

,k))

=

f i,j,

k

±

9

=

4.5i 1.5i

0.

k

18.5

±

9

Pc

1

,

2

=

g i:

(i ,

j±2

,k)) = f i

, j k ± 3

=

4.5i + 1.5i + 0. k 18.5 ± 3

l 2 = g i: i ,j,k±2)) = f i , j , k

±

1 = 4.5i 1.5i 0.5k -18.5

±

1

and the

position of each of the stiffness terms are

P

= g X

i

j k))

=

f i

,

j

k

=

4.5i 1.5i

0.5k-

18.5

1

,

2

= g x i ,j ,k±2)) = f i, j

, k ±

1 = 4.5i

+

1.5i

+ 0. k 18

.5

±

1

Therefore, one may build both

the

stiffness and damping matrices K

and

C by

placing the coefficients A through in the

Pth

positions along each row.

6 10 Initial Results

Created using the MATLAB scripts included in Appendix ??), Figures (6·17) (6·25)

show

the

frequency response for each of 27 payloads. The plots shown here

are based

on a model that assumes the following characteristics:

1.

A 3U cube is placed

at

the center of the satellite matrix . This is accomplished

by

fusing the central column of cubes by increasing the spring constants between

them

by

a factor of 100 (line 145) .

2. Drumheading of the otherwise rigid exoskeleton top plate is assumed

to

play

a role, so spring constant values at the top and bottom plate are lowered by

just over an order of magnitude (lines 163, 170).

The

value used is based on a

SolidWorks Finite Element Analysis of

the

top

plate

under 1N loading

at

the



87

center. Hooke's law was used to solve for

the

equivalent spring const

an

t using

the displacement from

the FEA

plot (Figure 6·16).

t.co4

Figure

6·16:

SolidWorks

FEA

displacement analysis of Top

Plate

3. 10 random noise is added to each ofthe values

in

the mass, spring and damping

matrices. Because the model is still very

symmetric

,

this

helps to

simulate

a

more realistic response.

4. Light damping from ( = 0 to ( = 0.3 is considered (line 316).

5.

Redundant

corner

dampers

are eliminated. For example,

the cube

at

position

(3,3,3) had three faces with dampers connecting to the cube, but is now reduced

to

just

one (lines 344, 354).



88

x1

:

g)

'

10

2

10

3

10

10

5

10.

Frequency (Hz)

x,

10

:

'

)

'

10

2

10

10

10

5

10.

Frequency

(Hz)

x3

10°

:

Q)

'

10

10

3

10

10

5

10.

Frequency (Hz)

igure

6 · 7:


1

, x

2

and x

3

. Sub-

scripted mass notation can be converted using Table 6.2

10

2

10

3

10

Frequency (Hz)

10

3

10

Frequency (Hz)

x

10

5

10.

F i

gure

6 · 8: Accel

erat

ion response for masses x

4

,

and

6

•

Sub-

scripted mass notation can be converted using Table 6.2



89

x7

rf

10

°

:

<=

8

0::

10

2

10

3

10

10

10

8

Frequency Hz}

xe

Q c

10°

:

<=

8

0::

10

2

10

Frequency Hz}

Xg

rf

100

:

<=

8

l

:

:

0::

10

2

10

3

10

10

5

10

8

Frequency Hz}

i ure 6·19: Acceleration response for masses

x

7

x

8

and

x

9

•

Sub-

scripted mass notation

can be

converted using T

ab

le 6 2

10

2

10

3

10

Frequency Hz}

x

10

Frequency Hz}

x12

10

3

10

Frequency Hz}

10

5

10

8

10

10

8

i ur

e 6 ·2 : Acceleration response for masses x

10

x and x

12

Sub-

scripted mass

notation

can be converted using Table 6 2



10

2

10

2

9

10

3

10

4

Frequency (Hz)

x

Frequency (Hz)

x s

10

5

10°

10

5

10°

J

·rt

rllll \·

lr I

, 1

tft

11

10

2

10

3

10

4

10

5

10

6

Frequency

(Hz)

Figure

6·2 :


xi

3

XI

4

and xi

5

. Sub-


can be


10

2

10

2

10

3

10

4

Frequency (Hz)

x17

10

3

10

4

Frequency (Hz)

x s

1

3

1

4

Frequency (Hz)

10

5

10°

10°

10°

Figure 6·22: Acceleration response for masses xi

6

X 7

and

XIS · Sub-

scripted mass notation can

be




91

x g

r

;

i

j

~ i

0

2

10

10

4

10

5

10

6

Frequency (Hz)

x2o

10

8.

ill

0::

10

2

10

10

5

10

6

Frequency (Hz)

21

10°

8.

ill

0::

10

2

10

3

10

4

10

5

10°

Frequency (Hz)

Figure 6· 3: Acceleration response for masses x

19

, x

20

and x

21

. Sub-


can

be converted using Table 6.2

10°

::

10

2

10

10

4

10

5

10

6

Frequency (Hz)

23

10

ll

.

ill

0::

10

4

10°

Frequency (Hz)

x24

r

10

2

10

10

4

10

10

Frequency (Hz)

Figure

6· 4:


x

22

x

23

and

x

24

. Sub-

scrip

ted

mass notation can

be

conver

ted

using Tab le 6.2



9

~

i • i l

'' ' '

: : : :

: : : : : : : ::

: : : : :

:

: : :

: : : : : : : :

:

J

l

p:;

r

:··

;,rrw

·:

:··¥ .·p,:'

vm

U L W ~

10

2

10

2

10

3

10'

Frequency (Hz)

:ze

10'

Frequency (Hz)

x27

10

3

10'

Frequency (Hz)

10

5

10°

Figure 6·25: Acceleration response for masses x

25

, x

26

and x

27

. Sub

scripted mass

notation

can be converted using Table 6.2

6 11 Discussion

t is noted that of the 27 acceleration response plots in Section (6.10), only x

13

, x

14

and

x

15

resemble what is ordinarily

thought

of as a mass-spring-damper oscillation,

with

the quality of the response smoothing

out

as damping is increased. The re

maining 4 masses also display a smoothing characteristic,

but

instead of smoothing

down from the sharp,

undamped

peak, they

smooth

up and

the

magnitude of the

damped response approaches the magnitude of the undamped response

at the

reso

nance frequency as damping is increased. This seemingly

odd

behaviour is

illustrated

by Figures (6·26) and (6·27).



93

10 ' 10

4

Frequency Hz)

igure

6· 6:

Acceleration response for mass x

1

3, located

in

the center

of the top layer of the satellite cube stack.

9

rl

10

2

10

3

10

4

10.

1

Frequency (Hz)

igure 6· 7:

Acceleration response for mass x

1

9, located

at

a corner

of

the

top layer of

the

satellite cube stack.

While this effect is

not

intuitive, it is entirely the result of the system s depen-

dence on dampers as part of the forcing term (see Section 6.5) .

In the

analytical

model presented here, mass x

13

has fewer dampers

attached

to

it

than mass x

19

and

is therefore acts more like a normal oscillatory system. This can

be

verified by

increasing the value of the forcing damper constant in the model shown

in

Figure

(6·4) by two orders of magnitude. The resulting plot is shown n Figure (6·28).



9

Single

DOF

model

~ ~ ~ ~ r ~

4

- : - - - - - - - ~ - = - - - - - - - - _ _ _ _ . . _ - = - - _ . _ _ ____ -- -::-----------

Frequency

Hz)

igure

6 28:

Single OF system experiencing variable damped forc

ing.



9

Chapter

Results

and Conclusion

7 1 Design

Developed under a requirements-based design method, the BUSAT structure is able

to respond

to

almost all of

the

structural, scientific

and

logistical ideas

that

were

introduced in

the

first BUSAT University Nanosat

Program

competition (Nanosat-5,

2007

to

2009). This is remarkable, considering

the project s

100% personnel turnover

rate and low budget ( 55,000

per

year in 2007, 2008, 2011 and 2012). In addition, if

BUSAT continues

to be

successful in

the

University Nanosat

Program

and beyond,

the concept of

an

aggregate

and

containerized nanosatellite will carry a huge impact

on

the

current scientific spaceflight industry.

The structural

system's

potential

cost

savings alone will ensure this. However,

the

development documented here is only

an

early portion of

the

potential life cycle of

the

BUSAT modular bus as an

industry

game-changer;

there

is much work to be done

in

qualifying with a first successful

launch.

7 2 Testing

Not only did the vibration testing performed

at

Draper Laboratories in October,

2011 prove that BUSAT's novel fastening technique works well, it also served as a

good

starting

point for development of a standardized , modular

testing

protocols for

potential payloads. Because strict controls must be placed at the interfaces between



9

bus and subsystems

in

the modular BUSAT system, particular care must be taken

with the mechanical interfaces to see that they will satisfy the

minimum

needs for

both

sections of the satellite.

This

includes predicting the inner

cube vibration,

radiation

and

magnetic enviroments so that potential payload providers will know

what to expect on launch

and

on orbit .

Future

testing

will necessarily include electronic

hardware

, or at least

mass

models,

as well as thermal

and electromagnetic environmental procedures

to

verify structural

performance. Due to the sensitivity of

the

system to changes in temperature, im

proved monitoring, control and modeling is necesary to ensure that any temperature-

dependent frequency shift can

be

predicted

and

removed from results.

Th

is will

ensure that marginal

test

results do not result in the need for a complete redesign of

the structure.

7 3 Tuned 27

Degree

of Freedom Model and

Comparison

to

Vibration Test Data

The

first significant result of

the

27-mass model is

that

the method

of forming equa

tions

of motion is verified. Based on the results of both

the

simplified and the final

models , the systems behave qualitatively as they should

in

the frequency response

plots

and the remaining work to be done is

in

tuning and refining

the mo

del itself.

Second, while initial simple models suggested

that

the spring coefficients were far

more important

than

damping values

in

tuning the

system

, the 27-mass model high

lights an interesting feature of the dampers. Probably because of the sheer number

of

dampers

surrounding

the

cube stack (54),

the

low-frequency peak seen

in

Figure

(6·17) ris s to

meet

the lightly damped resonance,

smoothing

it. From this it can

be

hypothesized that BUSAT s dependence on a friction force oriented in t he vertical

direction for fastening

the

WedgeLok ™) could provide an

inherent tolerance to



97

high-energy environments and may be more appropriate for aerospace applications

than

standard threaded fasteners .

The fact that the model s frequency response begins

to

approach actual data

when

the

top layer of springs is weakened suggests

that

as-built ,

the

model may need

improvement. n its current configuration,

the

model

can

only approximate the effect

of the exoskeleton top

plate

resonance feeding back into the cube stack, and a more

thorough

look

at plate

bending under vibration is

warranted

.



Appendix A

MATLAB Script for 1-DOF

Model

clc

clear

close

al l

Specify

di rec tory

to which M-f

i l

e and

subsequent

p l ots wi l l

save

dir = 'C: \Users \Nate\Documents \newschool \1000 docs \1200

c l a s s e s \

;

subdir = Thes i s \ Thesis_Finals \10

_ModeLBuilding\

' ;

subsubdir

= '100F\ ' ;

cd

( s t r ca t (

dir

,

subd

i r , subsubdi r

) ) ;

Vector of colors for p lo t t ing

co l o r s= [

'b

' , ' g ' , r ' , 'c ' , 'm' , 'y ' , 'k ' , 'b: ' ' g: ' r : ' , 'c : ' , 'rn: ' , y: ' , k : '

, g ,

r ' , ' c ' , m ,

'y

' ,

k

) ' b :

)

,

g

' , ' r ' , ' c ' , m , y

' ,

'k ) )

'b :

)

' b ' , '

g

, ,

, m ,

' y) '

'k ) )

'b :

)

s

=

1 ·

for

stepping

thro

u gh

Vo

Spring

Constant Calcula t ion

cubewidth = . 1 ;

c u

be

lengt h = . 1 ;

wal l th ickness

= . 1 25*.0254 ;

A

L

E

4*cubewidth*wal l th ickness ;

c u

bewidth;

69*10 A9 ;

Set

mass and

spring

charac te r i s t i c s

m3

k2

k4

;

A*E /L;

A*E /L;

98

'g :

)

,

r :

'g :

)

, r :

'

g:

)

, r :

colors

o/cm

n

)

)

)

) )

c:

)

, m:

)

'y :

)

c:

)

, 'm:

)

' y :

)c:

)

, 'm: 'y :

inches

* .0 2 54

m/ inch

)

k:

)

)

'

k :

)

)

k:

) ;



K =

k2

+ k4);

M= m3;

%

Find

natural

frequency

of system

omega_n = sqr t K/m3);

l ightly_damped

=

0 . 001;

cri t ical ly _damped

=

1;

%Set

ve ctor of frequencies

for

plot

domain

omega = l inspace

1

,2000000 ,1000);

%In i t ia l ize

Magnitude

Response Vector

X_p

=

zeros

1,1000);

Wo KNOBS AND BUTIDNS

%

Scal ing factor and

s

witch for second-order forcing A omega)

scal ing

=

1;

%Pr in t

Button

ppr int =

t rue;

ggrid =

fa lse ;

box = fa lse ;

ax

=

fa lse ;

omegalines t rue;

%fo r - lo o p t o

i t e ra te

plots over in teres t ing

damping

values

for zeta = l ightly _damped:

.1 :

cr i t ical ly

_damped

%Set d amping va lues

c2

=

0.5* 2* zeta*omega_n);

c4

= 0.5* 2* zeta*omega_n);

C

= (

c2

+

c4);

o fo

r - loop

to co

n

t ruct

t

he vecto

r

of ma g nitude response for the

range

%

of fr

e

qu

e

ncies

s

pecif ied

.

Note tha t

t

he forcing function

is

dep

endent

fr e quency.

for l = l length omega)



1

X_p(l) =

1/(-omega(l)h2*M+

1i*omega(l)*C +K)* · · ·

scal ing*

. . .

end

omega(l) h

2*(0.25/rrili)*

sqr t

(((k2+k4)h2/omega(l)h4

+

1000*(c2

+ c4)

2/

omega

( l ) 2) ) ;

end

Plot

log log (omega, abs (X_p) , spr in tf (colors ( s ) ) )

hold

on

s

=

s+1;

Finish Plot

i f ax

axis

([20,

2000,

.001, 25])

end

y_lim

x_lim

get

(

gca

, 'YLim ' );

get (

gca

, 'XLim ' );

if

omegalines

l ine (omega_n*[1 1J,y_lim, ' Color ' , ' k ' )

l ine (x_lim,10h0*[1

1],

' Color ' , '

k

)

end

t i t le ( ' Single OOF

model

' )

ylabel

( ' R e

sponse Magnitude

(m/ s h2) ' )

x l a bel ( ' Frequency (Hz) ' )

Block out area where we want the plot to appear

if box

end

l

ine (20*[1

1] ,y _lim , '

Color

, ' k ' )

l ine

(x_lim,10h-3*[1

1], Color ' , ' k ' )

n e ( 2 0 0 0 * [ 1 1 J , y _lim , ' Color ' , ' k ' )

l ine (x_lim,25*[1

1],

C

olor ' , ' k ' )

if ggrid

grid on

end



1 1

hold

off

if

pprint

Change

to directory for saving plots

foldername = s t rcat

( ' plo t

s\

, datest r now,

30))

mkdir (s t rcat ( dir , subdir ,subsubdir , foldername)) ;

cd

(

s t r ca t

(

dir

, subdir , subsubdir ,

foldername));

fi lename

s t rca t ( ' fi g _l ' )

pr in t (

- pa

i

nt

e

rs

' , dpng ' , ' -

r600

' , filename)

end



Appendix

B

MATLAB Script for 3 DOF Model

cl

ea

r

close al

l

clc

Specify directory

to which

M-file and subsequent plots will

save

dir =

C:

\Users \Nate\Documents\newschool \1000 docs \1200 classes

;

subdir

= '

Thesis\

Thesis_Finals

\10

_ModeLBuilding\ ' ;

subsubdir = ' 300F\ ' ;

cd ( s t rca t ( dir , subd ir , subsubdir)) ;

Vector of

co lors for plot t ing

and

color increment counter

colors=[

b ,

'

g

'

r

' '

m ,

y ' ' k ' '

'

b:

g:

' r :

c:

'm:

y:

b '

g '

r

c '

m ,

y ' ' k ' '

' b:

g:

' r:

c:

'm:

y:

k:

b '

g '

r ' '

c

'

m

,

y ' k '

'

b:

g : r :

c:

'm:

y :

k:

k

b , ' g , r ' , c ' , m , y ,

k

, b: ' g: ' r : '

c:

' , 'm: ' y: '

k:

' ] ;

s= O

;

S p r i n g Constant

Calculat ion

cubewidth

= .

1;

cu belength = . 1 ;

wa ll

th ickn e

ss

= .

125*.0254;

A =

4*cubewidth*wa ll

t

hi

c k

ness

;

L

E

cubewidth;

1 2

o/<1 11

n

i

nch

es

* .0 2

54

m/

inch

o/111

o c N m

2



1 3

%Set

in i t i a l values for

mass,

springs

m = ;

k

=

A*E/1 ;

m3 =

5

j

m5 = 3*m;

m7

=

m;

M=

[

m3,

0 ,

0

k2

k·

k4

k·

k6

k·

k8

k·

K=

[

k2+k4,

-k4

0,

0 )

0

m5, 0

0 ,

m7];

-k4 , O·

k4+k6,

-k6;

-k6

k6+k8

%kilogram

<J{Njm

];

%Find

eigenva

lues and

eigenvectors

for system

[Phi , Omega] = eig (K, M);

omega_n

=

sqrt

( d i

ag (Omega));

%Define

size

of

system (OOF)

and

number of

data

points

OOF =

length

( diag

M)) ;

X_p = zeros

(OOF,5000)

;

counter = 1;

%

Begin

for -

loop for plot t ing over

a range of

damping values

for z e t a=

0 .

001: .1 :1;

%

Construct damping matrix

based

on

range

of damping ra t ios in for

- loop

c2 =

2*zeta*

sqr t (k*m);

c4 2*zeta* sqr t (k*m) ;

c6

2*zeta* sqr t (k

*m) ;

c8

2*zeta* sqr t

(k*m);



104

C=

[ c2+c4,

- c4 ,

O·

-c4

,

c4+c6,

-c6;

0,

-c6 , c6+c8

l

%

In

c r e m en t

c olor counter for th i s

plot

s

= s +

1 ·

%Set up fr e

qu

ency range of i n t e res t for plo t t ing

omega = l inspace (1

,200000

,5000);

% fo r -lo o p to cons truct the

vector

of magnitude response for the rang e

%s p eci fied. Note

tha t

the forcing funct ion

is

dependent on fr e quency

for r = 1: length (omega)

X_p(: , r) = inv ((-omega(r) 2 ) * M +

1i*omega(r)*C

+ K) * · · ·

omega(r)

2 * [ c 2 / o m e g a r )

+ k2/omega(r)

(forcing function)

0;

end

c6/omega(r) + k 6 / o m e g a r ) ~ 2 ]*9.8*0.25; %( forcing

funct ion

%

i f

sta t ement to allow figure set up only once in this loop

i f counter = 1

scrsz

=

get

(O,

'ScreenSize

' ) ;

f igure

( ' Pos i t i o n '

,[5

5

scrsz (3) *.995 scrsz (4) *.9])

hold

on

counter =

counter

+ 1;

end

%P 1o t f i r s t OOF

sub p1o t (OOF, 1 , 1 )

z=1;

loglog

(omega,

ab s

(X_p(z

, : ) ) ,

spr in t f

(co lors (s ) ) )

t i t l e

s t r c a t s p r i n t f

OOF), 'OOF System

in

Rigid Enclosure ' ))

ylabel

( '

Response

m_3 (m/ s ' )

xlabel ( 'Freq uency (Hz) ' )

1 n e ( [ omega_n (

1)

, omega_n (

1)

] , [ 1 0 - 15 , 1 0 5])

text ( .9*omega_n(1), , ' \

omega

_{nl} ' , 'Color ' ,

'k ' ) ;

l ine ( [

omega_n (2)

,omega_n (2)], [10 - 15 ,10 5])

text ( .9*omega_n(2), 1 0 ~ 6 , ' \omega_{n2} ' , ' Color ' , ' k ' ) ;

l ine ( [

omega_n

(3) ,omega_n (3)], -15 ,10 5])



105

text

( . 9*omega_n(3), 10 ' 6 , om ega_{n3} ' ,

axis

([10

' 3 10 ' 5 10 ' -2 10 ' 2])

hold

on

C olor ' ' k ' ) ·

Plot

second OOF

subplot (OOF, 1 , 2)

z=2;

end

loglog (omega , ab s (X_p(z , : ) ) , spr in t f (co lors (s ) ) )

t i t l e

(

st rcat

( spr in t f ( 'o/;< ' ,

OOF),

'OOF System in Rigid E

ncl

osure ) )

ylabel

( ' Response m_5 (m/s A2) ' )

xlabel ( '

Fr

equenc y (Hz)

' )

1

n

e ( [omega_n ( 1) , omega_n ( 1) ] , [ 1 0 ' -15 ,1 0 A ])

text

(.9*omega_n(1), 10 ' 6 , om ega _{n1} ' , ' Color ' , ' k ' ) ;

l ine ( [omega_n

(2)

,omega_n

(2)],

[10 ' -15 ,10 ' 5])

text

(.9*omega_n(2), 10 ' 6 , '

\omega

_{n2} ' , '

Color

' ,

k ;

l ine ( [omega_n (3)

,omega_n

(3)] , [10 ' -15 ,10 ' 5])

tex t (.9*omega_n(3), 10 ' 6 ,

om

e

ga_{n3}

' , ' Color ' , k ) ;

axis ([10 A3 10 ' 5 10 ' -2 10 ' 2])

hold on

Plot

third

OOF

subplot

(OOF, 1 ,3)

z=3;

1o g 1o g (omega '· a bs ( X_p ( z , : ) ) , s p r i n t f ( co 1or s ( s ) ) )

t i t l e

( s t rca t ( spr in t f

(

o

;<

' ,

OOF),

'OOF Sy

st

em

in Rigid

Enclosure

'

))

ylabel

( ' Re sponse m_7 (m/ s A2) ' )

xlabel

( '

Frequ

ency (Hz) ' )

1 n

e ( [omega_n (

1)

, omega_n (1) ] , [ 1 0 • -

15

, 1 0 '

5])

text

(.9*omega_n(1),

10 ' 6 ,

\ om

ega-{n1} ' , C olor ' ,

' k '

);

l ine ( [omega_n

(2)

, omega_n (2)] , [10 ' -15 ,10 ' 5])

text

( . 9 * omega_n(2) , 10 ' 6 , ' \o m ga_ {n2 } ' , Co lor , ' k ' );

1

n e ( [omega_n ( 3) , omega_n ( 3) ] , [10 ' -15 ,10 A5])

tex t

(.9*omega_n(3), 10 ' 6 , ' \ om ga _{n3} ,

C

lor ' , k ) ;

a xis

([10

' 3 10 ' 5 10 '

-2

10 A

2])

hold

on

hold

off

pngname=

s p r in t f ( ' 300FBOXED ' ) ;



1 6

pr n t

(

-dpng

, -

r500

,

pngname)



p p ~ n d i x

MATLAB

Script

for 9 DOF Model

clea

r

close

a ll

c l c

<7<

LOGISTICS

Specify directory to which M-file

and

subsequent plots will save

d i r = 'C:\ Users\Nate\Documents\newschool\1000 docs\1200

classes

\ ' ;

subdir =

'

Th es is

\ Thesis_Fina l s \10

_ModeLBuilding\

' ;

subsubdir =

'9DOF

Coupled\ '

;

cd

( s t r ca t (

dir

, subdir , subsubdir ) ) ;

Vector

of

colors

for

plot t ing

and

co

l

or increment

co

u

nter

colors = [

' b ' , ' g ' , ' r ' , ' c ' ,

'm'

, ' y ' , ' k ' , ' b : ' , ' g : ' , ' r : ' , ' c : ' 'm: ' , 'y : ' , ' k

.

' b ,

g

, r ' ,

'c

' , 'm ' ,

y

, 'k ,

'b:

' 'g: ' ' r : ' , c: ' , 'm: ' y : ' ' k : '

b , g , ' r ' , 'c ' , 'm ' , y

,

' k ' , ' b: ' , 'g: ' r : ' , c : ' , 'm : ' y

: '

' k : '

' b ' ,

g ,

' r ' , c , 'm ' , y

,

' k ' , ' b: '

g: '

'

r:

' 'c : ' , 'm: ' ,

y: '

'

k:

' ];

s=O;

< < Spring Constant Calculat ion

cubewidth

= .

1 ;

cu belength = . 1;

wal l th ickness =

.125*.0254 ;

A =

4*cubewidth*wall thickness;

L

E

cubewidth;

69*10

A9;

107

11

o m

inches*

.0254

m/ inch

nA2

n

<Y<N m

A



108

<71 UNDAMP ED SYSTEM

Set

v alues

for mass, springs

m=

1·

k = A*E/L;

m33 = m;

m35 =

hm;

m37 =

hm;

m53 =

hm;

m55 =

hm;

m57 = m;

m73 = l*m;

m75 = l*m;

m77 = m;

M3=

[

m33,

0, 0

0 ,

m35 ,

0

0 0,

m37];

M5=

[

m53 ,

0,

0

0,

m55,

0

0 0 ,

m57] ;

M7=

[

m73 ,

0 ,

0

0,

m75,

0

0 0,

m77];

M = [M3, zeros (3

,3) ,

zeros (3

,3) ;

zeros

3 ,3) ,

M5

, zeros (3 ,3) ;

zeros

3 ,3) ,

zeros

3 ,3) ,

M7];

k32

k·

'

k34

k·

k36

=

k·

'

k38

k·

k52

k·

k54

k·

'

k56

= k ;

kilogram

Njm



1 9

k58 = k ;

k72 =

k;

k74 = k;

k76

=

k;

k78

=

k;

K3 =

[

k32+k34 '

-k34

-k34

k34+k36,

0,

-k36,

K5 =

[

k52+k54 '

-k54

-k54

,

k54+k56,

0,

-k56 ,

K7 =

[

k72+k74

'

-k74

,

-k74

k74+k76,

0,

-k76,

K = [K3 , zeros 3 ,

3)

, zeros 3

,3);

zero

s ( 3 , 3 ) , K5 , zeros ( 3 ,3 ) ;

zeros 3 , 3) , zeros 3 , 3) , K7] ;

0·

'

-k36 ;

k36+k38

O·

'

-k56;

k56+k58

O·

-k76;

k76+k78

%

Find eigenvalues and eigenvectors for

system

[Phi ,

Omega] =

eig

K, M);

omega_n

=

sqrt

(

diag

Omega)

) ;

DOF =

length

(

omega_n)

;

X_p = zeros (OOF,5000) ;

scrncounter

= 1 ;

%Vector

and

constants to change plot locat ions

vee

= [ 1 , 2 , 3 , 1 , 2 , 3 , 1 , 2 , 3] ;

plot1 1;

plot2

=

3;

DAMPED SYSTEM

l

l ;

l

%

Begin for

-

loop for

plot t ing

over

a range of

damping values

for z e t a =

0.001: .1:1;



110

%Construct damping matr ix based

on

range of damp i

ng

ra t ios in for - loop

c32

2*Zeta

*S

qr t

(hm) ;

c34

2 * z e t a *

s q r t k ~ ) ;

c36

2*zeta*

sqr t k*m);

c38 2 * z e t a * s q r t k ~ ) ;

c52

2*zeta* sqr t k*m)

;

c54

2*zeta*

sqr t

k*m) ;

c56 2*zeta*

sqr t k*m);

c58 2*zeta*

sqr t k*m);

c72 2*Zeta*

sqr t

(hm) ;

c74

2*zeta*

sqr t k*m);

c76

2*Zeta*

sqr t k*m);

c78

2*

zeta*

sqr t

k*m)

;

C3

=

[ c32+c34 ,

-

c34

,

-

c34,

c34

+

c36,

0 ,

-c36,

C5

[ c52+c54

,

-

c54

,

-

c54,

c54

+

c56,

0 ,

-c56

,

C7

=

[

c72

+

c74,

-c74

,

-c74 ,

c74+c76 ,

0 ,

- c76 ,

C = [C3 , zeros

3

,3) ,

zeros 3

, 3) ;

zeros 3

,

3) ,

C5 , zeros

3

,3);

zeros

( 3 ,3) ,

zeros

( 3 ,3) , C7] ;

O·

-c36;

c36

+

c38

O·

- c5 6 ;

c56+c58

O·

-

c7

6 ;

c76+c78

%

Increment co

lor counter for th is

plot

s

=

s + ;

l

j

l

l j

%

Set up frequency range of in te res t for plot t ing

omega

= l inspace ( 1 , 200000

,5

000);

%

for

-

loop to

const ruc t

the

vector

of magnitude response for the range

%speci f ied . Note that

the

forcing funct ion

is

dependent

on f requency



111

for r =

1:

length (omega)

end

X_p(: , r ) = inv ((-omega(r) A2)*M+ l i*omega( r )*C+K)*· · ·

[ c32 /

omega(

r) + k32;

(forcing function)

0 ;

c36

/ omega(r) +

k36

;

c52 / omega(r) + k52;

(forcing

funct ion)

0 ;

c56 / omega(r) +

k56

;

c72/omega(

r)

+

k72; (forc

i ng function)

0;

c76/omega(r) + k76 ]*9.8*0.25; (forcing function

%Create f i rs t figure

only

if

s crncounter == 1

end

s c rsz

=

get (0 , ' ScreenSize ' ) ;

f igure

( '

Posi t ion

' , [5 5 scrsz ( 3)*.995 scrsz(4)* .9])

hold on

scrncounter

=

4 ;

%Create three ver t i ca l ly oriented plots

within

each figure

for dl = 1 : 3

end

f igure

(1 ) ;

hold

on

subplot

(3 , l , d l )

loglog

(omega , abs (X_p(dl ,: ) ) ,

spr in t f

( color s ( s ) ) )

t i t

e ( s t

rca

( spr in t f ( o/crl ' , d 1 ) , ' { } ' , ' of ' , ' { } ' , . . .

sprint£ ( 'o/crl' , DOF), 'DOF System

in

Rigid Enclo su re ' ))

ylabel

( '

Response (m/sA2)

' )

xlabel

( F

requency

(Hz)

' )

axis ([10 A3 , 10 A5 , 10 -5 , 10 ' 5])

l ine

( [

omega_n(

dl)

,

omega_n

(

dl )]

,

[lO

A

-15

,

lO

A

5])

t ex t (homega_n(dl) , 10 ' -16 , s t rca t ( ' \omega' , spr in t f ( o/crl ' ,d l ) ) )

grid on

hold

on

hold off



112

Create

second

figure

only

if scrncounter 4

end

scrsz = get (0

, '

Screen Size

' ) ;

f igure

( '

Position

' , [5 5

scrsz (3) *.995 scrsz

(

4) *. 9])

hold on

scrncounter =

7;

Cre

ate

three

ver t i ca l ly

oriented plots

within each

figure

for

d2

= 4 :6

end

f igure

(2) ;

hold on

subplot

(3 ,1

,d2-3)

loglog

(omega

,

ab s

(X_p(d2,:)) , spr in t f (co lors (s ) ) )

t i t

e ( s t

rca

t (

spr in t

f ( 'o/

rl

' ,

d2)

, ' { } ' , '

of

' , ' { } ' ,

. . .

spr in t f ( 'o/

rl

' ,

OOF),

'OOF System in Rigid Enclosure

))

ylabel

(

Response

(m/s ' 2) ' )

xlabel

( '

Fr

equen cy

(Hz )

)

axis ([10 ' 3 , 10 A5, lO A-5 , 10 A

5])

n

e ( [

omega_n

(

d2)

,

omega_n

(

d2)

] , [ 1 0 A-

15

,1 0 A

5])

text

(homega_n(d2) ,

10 A

-16

,

s t r ca t ( omega

' , spr in t f ( 'o/

rl

'

,d2)))

grid on

hold on

hold off

Cre

at

e third figure only

if

scrncounter

7

end

scrsz

=

get (0,

' S c r

ee

nS i

ze

'

) ;

f igure

( ' Po s i t ion ' ,[5 5

scrsz(3)*

.

995

scrsz(4)*.9])

hold on

scrncounter =

8;

Create three

ver t i ca l ly or iented

plots within each f igure



e

nd

113

for d3 7:9

end

figure

(3);

hold on

subplot (3 ,1 ,d3-6)

loglog

(omega,

ab s (X_p(d3,:)) , spr in t f (co lors (s ) ) )

t i t l e (s t rca t ( spr in t f ( 'o/crl' ,

d3),

' { } ' , ' of ' , '

{}

,

. . .

spr in t f ( 'o/

crl

' ,

OOF),

'OOF System in

Rigid

Enclosure ))

ylabel ( Respons e (m/ s ' 2) ' )

xlabel

( ' Frequency

(Hz)

' )

axis ([10

'

3 , 10

'

5, 10 -5 , 10 5))

line ( [omega_n (

d3)

, omega_n (

d3)

] , [ 1 0 ' -15 , 1

0 5])

t ext

(homega_n(d3) ,

10 -16 ,

s t rca t ( \

omega ' , spr in t f ( 'o/

crl

' ,d3)))

g rid

on

hold on

hold

off

hold

off

o/c

Print

all f igures to t ime-stamped folder called PLOTS

%

Change to

directory for

saving plots

foldername

= s t rca t

( '

plots

\ ,

dates t r (now, 30))

mkdir ( s t rca t ( dir , subdir , subsubdir ,

foldername)) ;

cd ( s t rca t ( dir , subdir ,

subsubdir

,

foldername));

for f 1:3

fi g

ur

e

(f)

fi lename s t rca t ( ' fig_ ' , spr in t£ ( 'o

crl

' ,

f ) ) ;

print

(£,

'- p a in t e r

s

, ' -

dp n

g ' , '- r

600

' ,

fi lename)

end

pngname=

s print f ( '

DOFCOUPLED__I

- 3 ' ) ;

pr int ( '-£1 ' , '-dpng , r500 ' ,

pngname)



114

pngname=

s pr in t

f

' 900FCOUPLEDA-6 ' ) ;

pr int ( ' -

f2

,

dpng

' ,

r500

' ,

pngname

pngname=

s

pr in t f

' 900FCOUPLED_7- 9 ' ) ;

pr in t ( ' - f3 ' , ' - dpng ' , ' _:_r500' , pngname



Appendix D

MATLAB Script

for

27-DOF Model

clear

close

all

clc

L O G I S T I S

Specify

directory

to wh ich vl

fil

e

and

subsequent p l ots

will

save

dir = C : \Users

\Nate

\Documents\newschool \1000 docs \1200

classes

;

subdir = ' Thesis \ Thesis_Finals

\10

_ModeLBuilding\ ' ;

su

bsu

bdir = '

2700F

Coupled\ ;

cd ( s trcat ( dir , subdir , subsubdir)) ;

colors=[

c , ' k ,

' b ,

c

,

b

,

' b ' , c , b ,

b ,

c

, ' b ' ,

b ,

c

, , c , b , c , , c , ,

c

, , c

c

,

b c

b , ' c , b ,

c

, b , ' c ' , ' b , ' c '·

.

c ' b c ,

' b, ,

c , ,

'

c

'

b

' , c , b , c

.

c ,

b , c

,

'

b,

,

c

,

b

,

c b ' c ' ' b ' c ]·

s=O;

Recover

screen size

scrsz = get

(0,

Scr

nSiz '

);

Cr

e

ate

27

f igures

with

which

to

plot

27 DOFs

for

figz = 1:10

f i g ur e (

Pos i t ion

, [5 5 scrsz (3) * .995 scrsz (4) *.

9])

end

Cr eat e switch

for

figure plot t ing

f igswitch

=

1;

115

...



%

Set

log-log plot axes

xmin

=

20;

xmax

=

1000000

;

ymin

= .0 0 0 0 1 ;

ymax = 25;

%

Set

log-log plot

axes

% xmin

=

20;

%

xmax =

2000;

% ymin = 10· 2 ;

% ymax = 4 0;

116

%Create

Satel l i te

Structura l Matrix

L = ce ll

(10

,10 ,10);

Vo

INITIALIZE

ALL

MATRICES USED IN SCRIPT

M= zeros

(27);

K = zeros (27);

C = zeros (27);

F_l

zeros (27, 1)

; %

Forcing through

dampers

F_2

=

zeros (27,

1);

%

Forcing through

springs

Vo

SPRING

CONST NT

CALCULATION BASED ON AREA

AND

LENGTH

OF

CUBES

%

cubewidth =

.1;

o

on

%

c ubelength

=

.1;

o

on

%

wa ll

t hickness

=

. 125* .

0254·

%inches* .0254

m/i n ch

%

%

AA = 4*Cubewidth*wall thickness;

%n · 2

%

1

=

cubewiclth ·

%u

%

E =

69*10

. 9; m ;nt 2

%

%

Set

values

for mass sp

rings

% m =

1·

%kilogram

%

k_s

= AA*E/1 ;

m ;

m



117

10 SPRING OONSI'ANr CALCULATION BASED ON AREA

AND

LENGIH OF SPACERS

spacerwidth

= .01;

spacerlength = .01;

spacer thick = .

01;

AA

= 4*Bpacerwidth*Spacerlength;

l = spacer thick;

E = 6 9 1 0 ~ 9 ;

Set

values

for mass, springs

m 1 2;

k_s

= AA*E/ l ;

kilogram

~ / m

10 SATELLITE STRUCI'URAL MATRIX: MASSES AND SPRINGS

Create sa te l l i te

s t ruc tura l

matrix as a

10x10x10

cell

array

with mass

values in each

of

the [3 ,5 ,7]x[3 ,5

,7]

pos i t ions and 2x1 column vectors

(

<damping coeff ic ient>; <st i f fness coeff ic ient>] in o f f - d i a g o ~ a l

pos i t ions

within the matrix

i . e .

,

any odd-even index such

as

323 or

454

w i

11

cal l a

damper

or

spring

co

ef f i c i en t )

.

Springs

for x =

(2,4,6,8]

for

y = (3

,5,

7]

fo r

z= [ 3 , 5 , 7 ]

L{x ,y, z }(2) k_s;

end

end

end

for X=

(3 ,5, 7]

for

y =

(2 ,4 ,6 ,8]

for z =

(3 ,5 ,

7]

L{x

,y,

z }(2)

k_s;

end

end

end

for X=

(3

,5,

7]

for

y =

(3

,5, 7]

for z =

[2 ,4 ,6 ,8]



L{x , y , z } 2)

k s

;

end

end

end

Masses

for x = [3 ,

5,7]

end

for y = [3 , 5 , 7]

end

for z = [3,5,7]

L{x,y

,

z}

= m;

end

o dro TEST

MODUlE

118

ooFor i n

se

r t in g a

dif ferent mass size at any point in

the

sa te l l i t e

s t

ru ct ur

a l

matrix 0

ii 5 ;

JJ

= 5 ;

kk 3 ;

L{ i i , j j , kk} = 50 0 ;

teste d =

4

5* i i

+ 1.

5 *

j j + 0

5 * kk -

1 8 0

5 ;

s t r

ca

t ( '

The

OOF

being

tes ted

is :

,

spr int f ( '

d , tes ted))

o dro INSERT CUSIDM PROPERTIES:

3U CUBE

IN CENTER OF SATELLITE

Sim

u l

at

e s r ig id i t y in

center

3U

s t ructure by se t t ing

all ver t i

ca

l ly

o ri en t e d in t e rnal

values

of spring

constant

to very large numbe

rs

a ppr oac hing in f in i ty 0

for v = [4,6]

L{3

, 3,v}(2) =

lOO*k-s

;

end

Notes: no si g nific a n t shif t tow a rds lower frequenci e s

0

o dro

INS

ERT

CUSIDM PROPERTIES: ALL 3U CUBES

fo r x = [3 , 5 , 7]

fo r y = [3 ,5 , 7 ]

f

or

v = [4 , 6 ]

L{x,y , v} ( 2 ) lOOOOO * k -s ;

end

end



119

% end

%Not es : no s i gn i f i ca nt s hif t to w ar d s lower

fr e

qu e n c ies .

o/1

INS

ERT

CUSTOM

PROPERTIES : SIMULATE

DRUMHEADING

BY LOWERING S

PRIN

GS IN

o/1 CENIERMCBT CUBES ('IDP AND OOTIDM)

beta = . 11 ;

L{5 , 5 , 2} 2)

L{5,5,8} 8)

5 1

b e t a h 1

o c:NOTES:

Success

full y low e r s lowest nat u ra l fr e qu ency

o/1 INSERT CUSTOM PROPERTIES : SIMULATE DRUMHEADING BY LOWERING SP RINGS IN

o/1 PERIP

HERAL

TOP

CUBES

for

X [3 , 7]

for

y [5]

for

v = [2 , 8]

L{x , y , v} 2)

end

end

end

for

x

[5]

for

y

[3 ' 7]

for v = [2 , 8]

L{x

,y

,

v} 2)

end

end

end

for

X

[3 ' 7]

for

y

[3 ' 7]

for

v = [2 ,8]

L{x,y,v} 2)

end

end

end

o/c:N

OTES:

Succ ess

full

y

lo w

er s

lo w

e

st

natural

fr

e

qu

e n

cy

a

nd

oth

e

rs follow

o/1 INSERT CUSTOM PROPERTIES : TEST TO

SEE IF

LOvVERING SPRING UNDER OOF 1

o iDOES

WHAT IT SHOULD

%

L{3

, 3 ,4 } (2 ) = .

05

*

L s

;

% L{3 , 3 ,2} (2 ) = L{ 3 ,3 ,4 } 2) ;



120

Yo

INSERT CUSIOM PROPERTIES:

WW R

SPRING EXTERIOR

LATERAL

SPRING

CONSTANTS

% for x = [2

,8]

% for y = [2

,8]

%

for

v = [3,5 ,7]

% L{x ,y,v

} 2)

= k_s ;

% end

%

end

%

end

Yo

INSERT STRUCTURE PROPERTIES: 3U CUBES

AS

IN DRAPER TEST CONF1G

fuse

=

% for v = [

4,6]

% L{3,3,v} =

fuse*L{3,3,v};

% L{5,5,v} = fuse*L{5,5,v};

% L{7,7,v} = fuse*L{7,7,v};

% end

Yo INSERT STRUCTURE PROPERTIES:

2U

CUBES AS IN DRAPER TEST CONF1G

%

L{3

,5 ,6}

% L{4

,

7,7}

% L{3 ,7,4}

L{5

,3

,4}

%

L{6

, 3 ,7}

=

fuse*L{3

,5

,

6};

fuse*L{4 , 7 ,7};

= fuse*L{3 ,7,4};

fuse*L{5 ,3 ,4};

=

fuse*L{6,3

, 7} ;

Yo BUILD

lv IASS

AND SPRING MATRICES

for

I

=

[3, 5 ,

7]

for J = [3 , 5, 7]

for k = [3, 5, 7]

o/

<Row

is

giv

e n by

r

=

4 .

5*I + 1.5*J +

0 .5*k - 18 . 5 ;

%Populate mass

matrix:

M r , r ) =

L{I ,J ,k};



Yo

Yo

end

end

2

Coefficient va l ues :

E = (L{I ,J

,k+1}(2)+L{I

,J , k-1}(2)) ;

F1

=-L{I

, J

,k+1}(2);

F2

= -L{I ,J ,k-1}(2);

Coefficient indices i n

r th

row:

%The co e

ff

i c i en t PE

PE

= 4.5*I + 1.5*J +

0 . 5 k - 18.5;

K(r , PE) = K(r , PE) + E; o oE

will never

be out

of

bounds

PF1 =

4.5*

I + 1.5*J + 0. 5*

(k+2)

- 18.5;

if k = 7

F _2 ( r , 1) = F _2 ( r , 1) -

F1;

else K(r,

PF1) = K(r ,

PF1)+ F1;

end

PF2 = 4 .5 * I + 1. 5 * J + 0 . 5 * (k - 2) - 1 8 .5 ;

i k = 3

F _2 ( r , 1) = F _2 ( r , 1) - F2 ;

e s e K ( r ,

PF2)

= K ( r ,

PF2)

+ F2 ;

end

end

Yo KNOBS

AND

BUTIONS

force_scale = 1; %scales magnitude of plot

signal

=

false

; false

turns

off constant

accelerat ion

damping

epsilon_c . 1;

epsilon_k . 1;

epsilon_m .1;

Yo

Yo

Yo ADD NOISE TO THE SPRJNG

:NIATRIX

for

u =

1:27

for v = 1:27



122

K u,v) K(u,v)*(1 + epsilon_k*(

rand

(1)

- .5 ) ) ;

end

end

11'( ADD NOISE

ID

'lliE MASS MATRIX

for u

1:27

for v =

1:27

M(u,v)

M(u,v)*(1 +

epsilon_m*( rand

(1) - .5 ) ) ;

end

end

11'(

UNDAMPED SYSTEM

%Find eigenvalues and eigenvectors

for

system

[Phi, Omega] eig

(K,

M);

Recover all system natural frequencies

omega_n sqrt ( diag (Omega));

omega_n_sorted

·

sor t (omega_n) ;

%Set

damping

values ranging

from

undamped

to

l igh t ly damped

zeta_i

0;

zeta_f

=

.3;

D e fine region of

i n t e res t

at lowest natura l

frequency

- i .e

. ,

the

lowest

%nat

ural

fr equency of the sa te l l i t e displays a very sharp

peak

a t around

590 Hz , and ind ica tes tha t

damping

values

should be

set to

re f l ec t

l ight

o/odamping

around

the lowest natural frequency (min(omega_n))

c_i

2*zeta_i*min

(omega_n)*

min

(

diag

(M));

c_f

2*zeta_f*

min (omega_n)* min ( diag (M));

res 11;

in te rva l

plot

c _ f -

c_ i ) / r e s+ l ;

+1 i s a t r i c k

to make sure the

l

as

t

c

omes

out

dark

blue .

. .

based

on

color

,

s

for c

c_i:

i n t e rva l :

c_f; Beg in damping fo r - loop

for x

=

[2 ,4 ,6 ,8]

for y

[3,5,7]



end

end

for

z

= [3,5,7]

L{x,y,z} 1)

end

for

x

= [3,5,7]

end

for y = [2,4,6,8]

for

z

=

[3, 5, 7]

L{x,y,z} 1)

end

end

for x

=

[3,5,7]

for y

= [3

,5, 7]

c·

c·

for z = [2,4,6,8]

L{x,y,z} 1)

= c;

end

end

end

<}'( INSERT

CUSIDM

PROPERTIES :

for x =

[3,

7]

end

for

y

[3,7]

end

for

v

=

[2,8]

L{X y v

} 1

end

·

123

TURN OFF TOP AND

:oor:roM

OORNER DAMPING

<}'( INSERT CUSIDM PROPERTIES :

TURN

OFF ONE OF IW ) RENIAINING DAMPERS THAT

<}'( ATTACH TO

OORNERMCBI CUBES

for x = [2, 8]

end

for

y

[3,7]

end

for

v

=

[3,

7]

L{

X

y

v } 1

end

·

<}'( INS

ERT CUSIDM

PROPERTIES: INTERIOR DM.n:>ING ~ M E PROPORTION OF



EXTERIOR

ro

DAMPING

Scaling

factor :

alpha

=

1;

for x =

[4,6]

end

for y =

[4,6]

e

nd

for

v = [3 , 5 , 7]

L{x,y,v}(1)

end

124

otes: May

help

to i solate cubestack

as sing l e mass

ro DRIVE CUBE 5 ,5 , 8 WITH LARGE DAMPING

Scaling factor :

alpha = 1 ;

for

X

[5]

for y =

[5]

for

V =

[8]

L{x,y ,v}( l ) alpha*c;

end

end

end

Notes: May

help

to

isola te

cubestack

as single mass

ro

BUILD

DAMPING MATRJX

for

I = [3 , 5 , 7]

for J = [3, 5, 7]

for k =

[3,

5 ,

7]

o oRow

is

given

by

r = 4 .

5*1

+

1.5*J

+ 0

.5*

18.5;

Coefficient values:

A = (L{I+1,J ,k}( 1 ) +

L{I-1

,J ,k}(1)

. .

.

+L{I ,J+1,k}(1)

+ L{I , J -1 ,k} 1) . . .

+L{I , J ,k+l} l ) + L{I ,J , k-1}(1)) ;



25

B

=

-L{I+1,J

,k} 1);

B2

= -L{I-1,J

, k} 1);

C =

-L{I

,

J+1,k} 1)

;

C2

=

-L{I

,

J-1

,

k} 1)

;

D = -L{I

,J+1,k} 1);

D2 =

-L{I , J -1,k} 1) ;

Co e fficient i

ndices

in rth row:

PA

=

4.5*I

+

1.5*J

+

0.5

*

18.5

;

C r , PA) = C r , PA)

+A;

PB1

= 4.5* I+2)

+ 1.5*J + 0 . 5 * k - 18.5 ;

if I=

F _ ( r ,

1) =

F _ ( r ,

1)

-

B

;

e l se

C r , PB1) = C r, PB1) + B1;

end

PB2 = 4 . 5 * ( I -2) +

1.

5* J + 0. 5* k - 1 8 . 5 ;

i f

I

F

_

( r , 1)

=

F _ ( r ,

1)

- B2 ;

else

C r,

PB2) =

C r ,

PB2) +

B2;

end

PC1

= 4.

5 * I +

1.

5 * (

J

+ 2) + 0 . 5 * k - 18 . 5 ;

if J = 7

F

_

( r ,

1)

=

F

_

( r ,

1)

- C1;

else

C ( r , PC1)

=

C ( r , PC1) + C ;

end

PC2 = 4. 5 * I +

1.

5 * ( J - 2) + 0 .5 * k - 18 . 5 ;

i f J

=

3

F _ ( r , 1)

=

F _ ( r , 1) - C2;

else

C r,

PC2)

= C r

, PC2) +

C2;

end

PD1

=

4.5*I + 1.5*J + 0 .5* k+2) - 18.5;

i

k

=

7

F

_

( r ,

1) =

F

_

( r ,

1)

- D1;



end

end

end

126

else

C(r , PD1) =

C(r

, PD1) + D1;

end

PD2 = 4.5*1 + 1.5*J + 0.5*(k-2) -

18.5;

if k

=

3

F

_1

( r ,

1)

= F

_1

( r ,

1)

- D2 ;

else

C(r ,

PD2) =

C(r ,

PD2) + D2;

end

1o

ADD

NOISE ID THE DAMPING MATRIX

for u = 1:27

for v = 1:27

C(u,v) = C(u,v)*(1 + epsilon_c*(

rand (1)

- .5 ;

end

end

1o DAMPED SYSTEM

Set

up frequency range of i n t e res t for plot t ing

omega= linspace

(1,10'6,9000);

%Ini t ia l ize complex response vector

X_p =

zeros (27 ,5000)

;

A for

- loop to cons truct the vector

of magnitude

response

for

the

range

%

of

fr

e

qu

e

nci

e s

spec if ied.

Note

tha t

the

forcing function

is dependent

o

o0n

fr equ e ncy .

if

signal

for l = 1 :

length

(omega)

X_p( : , l ) = in v

(-omega(l)

' 2*M+ 1i*omega( l )*C+K)* · · ·

0 . 25* . . .



else

end

27

(F _homega(l) '

-1 + F_2*omega(l) ' -2)*force_scale;

end

for

l

= 1:

le

ngt

h

(omega)

end

X_p (: , l) = in v (-omega ( l ) • 2*M + 1 i *Omega ( l ) *C + K) * . . .

0. 25* . . .

omega( l ) ' 2*(F

_homega(

l ) A-1

+

F

_2*omega(

l ) A 2)dorce_sca le ;

In cre m ent the color counter s for th is plot

(corresponding

to current

lo o p e d v a

lue of damping

ra t io zeta

s

=

s

+

;

V a r ia b l e d1 for incr e menting OOF after each plot

d1

=

0;

for

fig2

= 1:9

for

plot2 = 1:3

end

f igure ( fig2) B egin f igure for

each degree of

·fr e

edom

Increment to next OOF

and plot

d1

=

d1 +

1;

subplot 3 ,1 ,p lo t2)

loglog (omega, ab s (X_p(d1

, :)

) ,

spr in t f color s s ) ) )

if

f igswitch

Block

of

code

to

print

f i r s t

gr

a

ph

on

fig10

end

figure (10)

subplot (2 ,1 ,1)

loglog (omega, ab s (X_p(d1 , : ) ) , sp r in t f

color s s ) )

f igswitch = 0; fig10

only

axis (

[xmin,

xmax, ymin,

ymax])

y label ( ' Response (G_n) ' )

xlabel (

'Frequency

(Hz) ' )

grid

on

t i t l e (

spr int f

( 'x-{%d}' ,

d1))

hold

on



128

end

Plot

natural frequ

e

ncies

as ver t ica l l ines on each figure

e1

=

0 ;

o cDOF

Counter.

ten

=

4;

for fig1

= 1:9

end

for

plot1 = 1:3

end

f igure

(

fig1)

subplot (3 ,1 ,p lo t1)

Plot

natural

frequency

for

lowest

5 DOF

for

e1

=

1 :5

end

y

_lim =

get ( gca , 'YLim ) ;

l ine

( real

(omega_n_sorted(e1))*[1 1],y_lim

,

C ol

o r ' , ' r ' )

hold on

tex t ( l .02*omega _

n_sorted(e1) ,

ten*10 ' 3,

s t r c a t ( ' \ omega ' , s p r i n t f ( ' d ' , e 1 ) ) ) ;

hold on

ten = ten

A

1 ;

Plot 0 .25G forcing magnitude for all omega

lin e ( [

xmin

, xmax ]

,[ .25

* 9 . 8 , .

25*9

. 8])

Plot 10 ' 1

peak

measure

l ine

([xmin

, xmax] ,

[10

,

10]

, '

Color

,

k

' )

end End damping for - loop

o/c FIG 10 : UNDAMPED

SYSTEM

RESPONSE WITH AT. ~

AND

PHASE

ANGIE

f igure (10)

t i t l e

( '

Un

damped R

es

po n

se

with Natur

a l

Fr

e

qu

e n

cies

a

nd

Ph

ase

Angl

e

)

subplot (2

,1

,1)

grid off

ylabel ( ' R espon se (m/ s A2) ' )

xlabel

( ' Frequen

cy

(Hz ) )

for e1

=

1:

length (omega_n)

y

_lim

=

get

(

gc a

, 'YLim ' ) ;



eferences

Avery K., et al., Total Dose Test Results for CubeSat Electronics, 2011 IEEE Radia

tion Effects Workshop {REDW),

Sevilla, Spain, 2011

Bruhn F., et al.,

QuadSatjPnP: A Space-Plug-and-play Architecture SPA) Compliant

Nanosatellite,

lnfotech@Aerospace Conference, Unleashing Unmanned Systems St.

Louis, Missouri, 29-31 March 2011

Clavier

0

and Cutler

J.,

Enabling low-cost, high-accuracy magnetic field measure

ments on Small Sats for space weather missions, Proceedings of the 25th Annual

AIAA/USU Conference on Small Satellites, Logan, Utah 2011.

Darling, Nathan T.; Harris, David. Boston University Student Proposal for Deploy

able Solar and Antenna Array Testing On Board

NASA

Parabolic Flights December

16, 2011. Available upon request from author.

Darling, Nathan T. ; Mendez, Joshua. Student Payload Integrated First Flight SPIFF)

Proposal for NASA / LSU High

Altitude

Student Payload December 16, 2011.

Available

upon

request from author.

Finlay

t

al.,

HOW DRS-

Modular Space Vehicle on the

T2E

Mission,

Proceedings

of

the

25th Annual

AIAA/USU

Conference on Small Satellites, Logan, Utah 2011.

Giurgiutiu V.,et al., Space Applications

of

Piezoelectric Wafer Active Sensors for

Structural Health Monitoring,

Journal of Intelligent Material Systems

and

Struc

tures vol.

22

no. 2 1359-1370, August 2011.

Lindstrom

C. D., et al., Characterization

of

Teledyne Microdosimeters for Space

Weather Applications, Proceedings of Solar Physics and Space Weather Instru-

mentation IV, Torino, Italy, August 2011.

Mendez J. , et al., Compact Half- Unit Imaging Electron Spectrometer for CubeSat

Operations {CHICO) ,

Proceedings of the 25th Annual AIAA/USU Conference on

Small Satellites, Logan,

Utah

2011.

Thermotron Industries 2011). Vibration Test Systems Retrieved December 18, 2011

from http:/ j www thermotron. com.

130



ppendix

Vita

32



133

Nathan Thomas arling

Center

for Space Physics

725 Commonwealth A venue

Room

506

Boston,

MA

02215

Personal

Born

1981

in

New York,

NY

Education

Phone:

Fax:

Email:

Homepage:

B.A. Spanish Language and

Literature,

2004.

M.S . Mechanical Engineering, 2013.

Graduate Coursework

61 7

353-0285

617) 353-6463

[email protected]

www.busat.org

ME 515- Vibration

of

Complex Mechanical

Structures

ME 560 - Machine Design and Instrumentation

ME 900 - Research:

Preliminary

Vibration Testing and Analysis

of

a Novel Nanosatellite Structure

Licensure

and Certification

USCG

500 Ton

Ocean Master

AB Unlimited, STCW 95

Medical person

in

charge

MPIC)

NAUI

Scuba

Diver course

completed

December, 2009)

Summary

of

Experience

NASA

project management,

proposals

rocurement and

budget

management

Personnel

management and

leadership

NASA

hardware

design cycle

and

reviews



34

Manual

and

CNC fabrication

CAD / Modeling: SolidWorks, MATLAB

Microgravity parabolic flight

testing

GIS: ArcMap 10, Agisoft PhotoScan

Rigging and heavy lifting equipment

STEM

education

and

outreach

Selected

Work

Experience:

Boston

University Center

or Space Physics (Jan. 11

to

present)

http :/ / www.bu.

edu/csp

Program Manager

Currently overseeing

the

Boston University

Student

satellite for Applications

and

Training BUSAT). Duties include personnel

and

logistics management for a 25

member

student engineering and physics team, budget oversight, as well as environ

mental testing of a scientific spaceflight structure. Familiar NASA project develop

ment

and review process, including documentation procedures and export control.

Duties include regular formal technical presentations , public relations and K-12

out-

reach. Direct experience with satellite mechanical and electronic hardware, vibration

testing, high altitude balloon flights,

and

microgravity testing on

board

parabolic

aircraft.

Boston

University Center

or

Space Physics (Jan. 11 to

present)

www.busat.org

Structures Team Lead

In charge of concept development , fabrication

and

testing of a novelmodular nanosatel

lite structure. Modeling

and

analysis performed in SolidWorks

and

MATLAB. Ex

perience with shock

and

vibration testing procedures

and

data analysis.

In

charge of

organizing a

rotating

student

team

of designers, also responsible for final documen

tation

and

design review presentations.

Scientific Instruments Facility (Oct.

10 to

Jan. 11)

sif.bu.edu Research Assistant

Assisted with general shop maintenance

and

production. Familiar with fabrication

process associated with precision scientific instrumentation. Experience

with

manual



135

lathes and mills.

National

Undersea Research

Center

(Jan. 10

to

May

10)

www.nurc. uconn.

edu

Intern

Overhauled the hydraulic manipulator valve pack for the scientific remotely operated

vehicle K2

at the North

Atlantic

and Great

Lakes National Undersea Research

Center

NURC) facility in

Groton

, CT.

The

Boat Company

(Apr.

to Sept.

06, 07, 08, 09,

Aug. 10)

www.

theboatcompany.org

Chief Mate

Stood

navigational watch, worked as wilderness guide

and

answered

to the captain

in

planning logistics of a small wooden cruise vessel. Oversaw safety

and

maintenance,

including weekly drills.

Operated

hydraulic crane

in

deployment

and

recovery of four

19-foot aluminum fishing skiffs at least twice daily. Served as skiff

captain

daily while

mother

ship was

at

anchor,

stood

wheel watch every second day while underway

and

anchoring.