Gravity Gradient Boom Design MIM 702 Department of Mechanical, Industrial and Manufacturing Engineering College of Engineering, Northeastern University Boston, MA 02115 The Capstone Design Course Report Format Project #9 Second-Quarter Report Design Advisor: Prof. Gregory Kowalski Design Team Jason Stricker, Arthur Inglot, Gene Rossov, Jack Rafalowski, Steve Souza
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Gravity Gradient Boom Design
MIM 702
Department of Mechanical, Industrial and Manufacturing Engineering
College of Engineering, Northeastern University
Boston, MA 02115
The Capstone Design Course Report Format Project #9
Second-Quarter Report
Design Advisor: Prof. Gregory Kowalski
Design Team Jason Stricker, Arthur Inglot,
Gene Rossov, Jack Rafalowski, Steve Souza
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Gravity Gradient Boom Design
Design Team
Art Inglot, Jack Rafalowski,
Gene Rossov, Steve Souza, Jason Stricker
Design Advisor Sponsor
Prof. Gregory Kowalski NASA, Ames Research Center
John Hines
Abstract
Attitude control systems are a very important aspect in satellite design. The Northeastern design team’s
goal is to develop a passive gravity gradient boom design that can be used on the ONYX satellite or be
adaptable to other micro satellites. The ONYX, designed by Santa Clara University in collaboration with
NASA, is a micro satellite in an Earth reconnaissance and research mission. During its intended 45 day
mission, the ONYX will operationally test autonomous computer control techniques while conducting an
Earth observing mission, providing educational services as well. Attitude control for an imaging satellite is
vital. The objective of the design team is to develop a gravity gradient boom (GGB) for passive attitude
control, while following specified design parameters set forth by NASA and Santa Clara University’s
ONYX satellite team. These design parameters are: the GGB system must not exceed a physical volume of
12cm x 12cm x 15cm, the system must stabilize the satellite to +/- 5° with respect to the Earth pointing
Nadir vector, it must be under a 10kg weight, must not hinder physical properties of the overall satellite
(ONYX), must be inexpensive, and strong enough to withstand launch vibrations. The key design features
of this system consist of space qualified materials, a tip mass, a single bolt release mechanism, a non
motorized mass launch, and a spool of specifically chosen wire.
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TABLE OF CONTENTS
Error! Bookmark not defined. 1.0.0 PROBLEM STATEMENT.................................................................................................................... 5 2.0.0 PROJECT RESEARCH ........................................................................................................................ 6
2.1.0 Micro Satellites.................................................................................................................................. 6 2.2.0 ONYX ............................................................................................................................................... 6 2.3.0 Orbital Study ..................................................................................................................................... 7
2.3.1 Orbital Paths................................................................................................................................... 8 2.3.2 Polar Orbit ...................................................................................................................................... 8 2.3.3 Sun synchronous............................................................................................................................. 8 2.3.4 Low Earth Orbit (LEO) .................................................................................................................. 9 2.4.0 Attitude Sensors and Control Devises ............................................................................................ 9
2.4.1 Sensors............................................................................................................................................. 10 Sun Sensors ........................................................................................................................................... 10 Horizon sensors..................................................................................................................................... 10 Magnetometers ...................................................................................................................................... 10 Star Sensors........................................................................................................................................... 11
2.4.2 Attitude Control Devises ................................................................................................................. 11 Active Attitude Control ............................................................................................................................ 12
2.6.1 Importance to the ONYX ................................................................................................................ 29 2.6.2 Types of Deployment Devices......................................................................................................... 30
4.0.0 The design ........................................................................................................................................... 42 4.1.0 Final Design ........................................................................................................................................ 42 5.0 Final Conclusion...................................................................................... Error! Bookmark not defined. REFERENCES...........................................................................................................................................6160 Appendix……………………………………………………………………………………………………62
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PHASE I 1.0.0 PROBLEM STATEMENT
The main objective of this project was to develop an attitude stabilization system for a small satellite. The
ONYX satellite was development by Santa Clara University with the aid of NASA’s Ames Research
Center. The ONYX is classified as a micro satellite, having a mass of 30 kilograms. It will travel in a Low
Earth Orbit (LEO) at an altitude between 500-700 kilometers taking multi-spectral images of Earth. It will
operate with the use of autonomous control techniques, through an advanced microprocessor analysis and
control system. Northeastern University’s role in this project is to create a passive attitude control system
that will be tested on the ONYX and possibly other small satellites flying similar missions.
The Northeastern team goal was to design a gravity gradient boom for passive stabilization to integrate
with the ONYX. Image capturing satellites, such as ONYX, have additional stabilization needs as well. As
a satellite orbits an image can only be taken when the target is in view. A proper stabilization device will
reduce the movements in the X, Y, and Z axis to a minimum, allowing the satellite’s camera to focus and
take clear, undisturbed pictures. There are several design classifications of deployment mechanisms for
gravity gradient booms. The Northeastern design team will strive to build a passive control system that will
be precise in its orientation over long periods of time. The goal is to implement a successful stabilization
system that directly interfaces with the Emerald Protocol Suite, conforming to the specifications of NASA
and needs of Santa Clara University.
The constraints that the designed gravity gradient boom must follow consist of mass, volume/size, and
power consumption. The final design must have a mass less than 10kg. Dimensions of the completed
system are limited to the available area inside the ONYX or the cylindrical launch envelope on the outside.
The final size of the GGB system must not exceed a 12cm x 12cm x 15cm volume. The power is limited to
30 watts. However, power consumption could be zero if system would be completely passive. Additional
requirements that the system must adhere to is to generate a pointing accuracy of +/-5 degrees with respect
to the earth pointing Nadir vector. It also must not hinder the satellites physical properties, be inexpensive,
and extremely adaptable to other satellites. The system must be small and lightweight.
The gravity gradient boom design was appealing for several reasons. A well designed device can provide
accurate control and stabilization, without the constant use of power. In addition, a correctly chosen
deployment mechanism can be compact and cost efficient. The concept behind the gravity gradient boom
has been around for several decades, and initial studies and research have shown that it is effective on small
satellites similar to the ONYX.
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Similar to all space/flight components, a prototype must be physically tested to meet space flight
requirements. This is usually done on a three dimension vibration table to simulate launch conditions.
However, similar tests regarding vibration and physics principles do to time constraints have been obtained.
Vibration tests can be obtained through CAD drawings and ANSYS simulations. Physics equations can be
calculated using excel and MATLAB.
2.0.0 PROJECT RESEARCH AND BACKGROUND As stated previously the Northeastern team will be responsible for the stabilization and attitude control of
the satellite over the course of its 45 day mission. However, before the team can design an attitude system,
certain other areas of satellite flight and operation must be researched. These areas of research include
orbital studies, launch vehicle vibration profile, and thermal effects.
2.1.0 Micro Satellites
The micro satellite is a classification of small satellites more than 10kg and less then 100kg. The micro
satellite is the most common researched satellite used in the small satellite category. The main reason
engineers try to keep the satellite mass low is due to the high cost launching to reach a low earth orbit
(LEO). A launch costs an estimated $10,000 for every kilogram that is sent into space. [ ] Micro satellites
in the past decades have provide images of Earth and Space, as well as preformed numerous tests. Since
mass is such an issue when designing a satellite, every aspect that goes into the satellite must follow strict
design considerations.
2.2.0 ONYX
The ONYX satellite is an ongoing project of Santa Clara University, headed by Chris Kitts. ONYX is
designed in collaboration with multiple departments of the United State’s government including; the Air
Force Research Lab (AFOSR), Defense Advanced Research Projects Agency (DARPA), and the NASA-
Ames Research Lab. The purpose of ONYX, short for ONboard autonomY eXperiment, is to monitor
anomalies in orbital motion and resolve them using two autonomous processing systems. The output of this
system provides two simultaneous solutions. The optimal solution is then acted upon and recorded. This
system is the first of its kind, and one of the interests the defense agencies and the AFSOR have in this
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project. The ONYX satellite is also equipped with a camera cable of capturing images in multiple ranges of
visual and non visual light. During the duration of its 45 day mission ONYX will take images of Earth in
multiple spectrums. The images captured are used for educational and research purposes. The 30kg
hexagonal ONYX has dimensions of 21cm per hexagonal side and 42cm tall. This satellite is capable of
different orbits depending on its desired mission or the mission of the launch platform it piggy backs on.
One focus of the ONYX project is to be adaptable to change its configuration for different research
purposes. These multiple trials and launches will ensure continued research and development of and in time
a more successful satellite. See Figure 1 for a CAD model of the hexagonal ONYX.
Figure 1: ONYX Satellite
2.3.0 Orbital Study
When designing a free-flying satellite one of the most important aspects is the orbit of the satellite. The
orbit of a satellite will affect the radiation and thermal control of the system. A satellite’s orbit is
determined by a combination of two forces: the earth’s gravitational pull and the satellite’s horizontal
velocity. Basic physics demonstrates that gravitational pull is the attraction of two massive objects, in this
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case the mass of the earth and the mass of the satellite. Gravitational pull prevents the satellites’ velocity
from propelling it off into deep space; the velocity of the satellite prevents the gravitational pull from
bringing the satellite crashing down to earth [5].
2.3.1 Orbital Paths
Many different types of satellite orbits may be chosen depending on the specific function of the satellite.
These different orbits depend on the path it passes over and the altitude. The three aspects that should be
explained are polar and sun synchronous orbit and low Earth orbit (LEO).
2.3.2 Polar Orbit
A polar orbit is an orbit with an inclination of 90° from the equator. A satellite with a polar orbit circles
around the earths’ poles. Polar orbits are very useful for satellites that carry out mapping, surveying, or
surveillance functions due to the fact that the rotation of the earth grants the satellite access to almost any
point on the earth [5]. A polar orbit may be used; however the satellite’s attitude and orientation would
constantly change as it orbits around the North Pole, equator, and South Pole. When over the North Pole
the satellites imaging face will be pointing towards earth. Over the equator the front face will be parallel to
the plane of the equator and over the South Pole the front face will be pointing away from earth. The use of
sensors and careful deployment of the gravity gradient boom would have to be used due to the constant
shift in satellite attitude and orientation.
2.3.3 Sun synchronous
Overexposure to the heat of the sun may be a big concern when designing a satellite. Particular instruments
and equipment may not be able to withstand the higher temperatures when the satellite is orbiting in
sunlight. This will decrease performance and hinder the mission of the satellite. A sun synchronous orbit
has an orbital plane with the same period as the planets’ solar orbit period [5]. With this type of orbit the
satellite will have a period of shade as well as sunlight. Due to extreme temperature changes the satellite
can endure thermal shock. Thermal shock will be further analyzed in the course of the project.
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2.3.4 Low Earth Orbit (LEO)
The majority of free-flying satellites are launched into a low earth orbit (LEO). A low earth orbit generally
falls into an altitude range of 100-1500km above earth. Low earth orbits are often used for free flying
small satellites that are not supposed to remain in space indefinitely. A satellite whose orbit path crosses
through earth’s magnetic gravity gradient will gradually be pulled down to earth. The satellite will then
decay due to aerodynamic frictional forces created by the earth’s atmosphere [6]. Depending on the
starting altitude, the length of time that the satellite remains in orbit can be determined. Most of the
experiments performed on free-flying small satellites are designed to last from 96 hours to a couple weeks.
The ONYX may have a LEO path.
2.4.0 Attitude Sensors and Control Devices
Figure 2: Orientation
Attitude, or orientation, is determined by the satellite’s position relative to a set location. Its orbit is
portrayed by a coordinate in the three axes: X, Y, Z. There are different levels of orientation control for
satellites. Figure 2 above shows these three axis and there term of rotation in a given axis. A satellite will
rotate in these axes randomly as it freely spins in orbit with out control. In the fifty years of space travel
multiple control systems have been successfully designed and used. The selection of attitude control
devices and systems are chosen according to the satellite’s mission and project constraints.
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2.4.1 Sensors
A satellite must use a sensor to provide a frame of reference for the satellite giving it a location as well as
attitude in the X, Y, and Z plane. With this data gathered the attitude adjustment devices can be controlled.
Five sensors that are readily used in satellites and other spacecrafts are; sun sensors, horizon sensors,
magnetometers, and star sensors. These sensors all have different methods of gathering information
regarding the satellites position and behavior.
Sun Sensors
Figure 3: Sun Sensor
Sun sensors use the suns power to determine orientation. This sensor determines this by analyzing the solar
energy gathered by the solar panels. The sun sensor can determine the angle the sun is hitting the solar
panel as well as the distance from then sun. [1] Sun sensors are the most common attitude sensor. [3]
Horizon sensors
Figure 4: Horizon Sensor
Only effective in LEO, horizon sensors measure the difference in brightness of earth compared to the
darkness of space using the infrared spectrum view. With this it can measure the satellites distance from
Earth and provides a reference point for judging attitude. [4]
Magnetometers
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Figure 5: Magnetometer
This sensor measures Earth’s magnetic field. This is another popular device due to its output in vector
components, low weight, and operating power. Once again this switch is only accurate under 1000 Km. [4]
Star Sensors
Figure 6: Star Sensor
The star sensor is known for its very high accuracy; however it is heavy and expensive.
They are mainly used for higher Earth orbits. Its accuracy works by setting up a coordinate system
between cataloged starts. [4]
2.4.2 Attitude Control Devices
There are three primary reasons to control the orientation or attitude of orbiting satellites. The first is for
communication needs. Satellites must have a connection or link to ground stations through its antennas. If
spinning and motion is uncontrolled the connection will be difficult to obtain for any period of time. The
second is in regards to positioning with respect to the Sun. A satellite must collect energy from solar panels
to recharge its batteries. However, if there is no spin and a section is in direct sunlight to long thermal
shock and deformation can occur. The third and most relevant in ONYX case is for image capturing.
Satellites equipped with camera must have some form of attitude control to obtain a deseed image. If a
satellite’s orientation in orbit is not controlled; all of these essential processes would not be possible.
Attitude control devices are classified in two main subcategories, active and passive. Active design systems
use energy in pulses or continuously from a stored power source such as batteries. The batteries in a
satellite can be recharged through energy collected by solar panels. Active control devices that are currently
in use include reaction wheels, momentum wheels, torquer coils, controlled momentum gyros, and gas
actuators. All have their benefits and draw backs and are carefully selected to optimize the mission of a
satellite. Passive design systems do not use internal energy. Instead of using energy from a stored source,
they use physics properties and theories for attitude control. The three main passive controls each use
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different principals to achieve attitude control. In many instances devices can be combined to form a
system that fits the project’s requirements. Located on the next page is the device matrix based on the
summation of this research.
Table 1: Attitude Control Device Matrix
Power Needs Cost Weight Has it been found in
30kg > satellite ATTITUDE
CONTROL
DEVICES
Active (A)
or
Passive(P) L
1
2
3
H
4
L
1
2
H
3
L
1
2
H
3 YES or NO
Controlled
momentum gyro A
4 when needed
(see sec )
3
(see sec )
3
(see sec ) NO
Gas actuators A 4 Limited supply
(see sec )
2
(see sec )
3
(see sec ) YES
Gravity gradient P 1 Deployment
(see sec )
1
(see sec )
1
(see sec ) YES
Hysteresis
Rods P
0 no power needed
(see sec )
1
(see sec )
1
(see sec ) YES
Momentum
Wheel A
3 Contrant draw
(see sec )
3
(see sec )
3
(see sec ) YES
Radiation
Pressure P
0 no power needed
(see sec )
3
(see sec )
1
(see sec ) YES
Reaction Wheel A 4 when needed
(see sec )
3
(see sec )
3
(see sec ) YES
Torquer Coils A 3 when needed
(see sec )
2
(see sec )
2
(see sec ) YES
2.4.3 Active Attitude Control
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Reaction Wheel
Figure 7:
Reaction wheels use a motor to spin a mass, creating a torque. This torque provides a moment when
needed, which controls the satellite’s attitude in orbit. This device can be extremely accurate; however, it
has two drawbacks for an active device: cost and weight. One reaction wheel can cost several thousand
dollars. For a complete control system three must be used, one for each axis of rotation. Adding to this cost
is the software, sensors, and additional batteries needed to run the system. Each device consists of a motor
and solid circular mass. This adds substantial weight to the design yet is very efficient. However because of
its high stabilization precision, the use of a reaction wheel may be justified. With this control a satellite can
point to multiple locations in space and on Earth. [1]
Momentum Wheel
Figure 8: Momentum Wheel
Momentum wheels are similar to reaction wheels, but with one difference. Momentum wheels are
continuously working as opposed to reaction wheels which only work in short bursts. This gives a constant
rotational velocity stabilizing the satellite. Since only one momentum wheel is needed and it does not
require the same computing software as the reaction wheel, the cost and weight are less. However, it does
not achieve the same precision and attitude adjustment abilities as a reaction wheel that you can choose.
Momentum wheels are used more as stabilization then axial motion. [1]
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Torquer Coils
Figure 9: Torquer Coils
This system uses the Earths magnetic field for attitude control. Torquer coils are loops of wire that current
runs through to create an adjustable magnet field. This device responds to changes of attitude and corrects
its orientation. This device is only effective in low Earth orbit, and most efficient in an equatorial orbital
trajectory. The reason for this is that Earth’s magnetic gradients are projected from its poles and at more
elevated orbits the magnetic force can not be used effectively due to weaker forces when further away from
the Earth.
Controlled Momentum Gyro
Figure 10: Momentum Gyro
The momentum gyro works by spinning on mass in multiple axes, and operates when needed, as
determined by a processor. One gyro can do the same work as three reaction wheels. Although this is a
benefit, it has a higher cost and mass than the momentum wheel system and rarely used in small satellites.
[1]
Gas Actuators Gas actuators release pressurized gas that is stored in the satellite for control. Although the force it creates
has the capability to be significantly higher then the other active control devices, its energy source is
limited. While batteries can be recharged by solar energy, propellant is limited in quantity. Gas actuators
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are classified in as either hot or cold. Hot gas actuators undergo a chemical reaction where as cold gas
actuators do not. [1]
2.4.4 Passive Attitude Control
Radiation Pressure Radiation pressure uses the energy from the sun as a passive a control device. Solar radiation pressure
exerts a force by harnessing the photons on a defined area. An effective surface must be of significant size
and directed towards the sun. This proves that solar radiation pressure can not be a stand alone passive
device. This system needs a complex active system, such as reaction wheels or a momentum gyro to insure
that its normal vector is constantly pointing towards the sun.
Hysteresis Rods Hysteresis rods use the same magnetic principle as Torquer coils, yet are completely passive. This system
aligns a desired face towards the Earth’s magnetic field. Common materials used in this system are
magnetized nickel, iron, and cobalt. The system is designed to dampen the rotation velocity. Complete
stabilization of a satellite using hysteresis rods would create a heavy control system. This attitude control
system is determined by the strength of the rod’s flux and the number used. Many satellites use this system
as a primary means of attitude control because it is passive, light, and inexpensive. Multiple satellites will
use hysteresis rods as a secondary control device along with a primary active system.
2.5.0 Gravity Gradient Boom Physics
Gravity gradient booms were first used by NASA in LEO satellites in the late 1960’s with minimal success
due to they’re complexity. Further testing in and more advance computing capabilities in the 90’s gave rise
to more accurate means of solving ordinary differential equations. This proved them to be a valuable
means of passive attitude control for one main reason. They use little or no electrical power relying mostly
on stored energy in springs for deployment and once deployed require no means of power, as they rely
heavily on astrophysics and orbital mechanics. Many small satellites have employed the use of these
booms in LEO.
The structure of a gravity gradient boom consists of a base which is attached to the satellite. This base unit
contains a deployment system which, once the satellite is in space, deploys the boom structure which holds
the tip mass. The boom can either be a rigid structure like a truss or it can be made out of wire. Boom
lengths vary from hundreds of centimeters to hundreds of meters depending on the orbit, mass of the
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satellite, and mass of the weight at the end of the boom. The mass at the tip of the boom is the last major
piece to this system. This mass can vary but is generally only a small percentage of the satellites total
mass, approximately 5 to 10 percent. [7]
A gravity gradient boom works on the basis of Newton’s Law of Universal Gravitation, equation 1, which
states that the force of gravity is inversely proportional to the distance between the two objects. Also the
satellite is in an orbit giving rise to an orbital velocity.
1) 221
RmmGFG =
The gravity gradient boom is sent into space as part of the overall satellite structure. As the satellite is
deployed from the launch vehicle the force of gravity acts on the gravity gradient boom and the satellite
equally because the boom is stowed inside the satellite during take off. The satellite and boom now have a
characteristic orbital path; it has a specific altitude, orbital velocity, and eccentricity. Next the gravity
gradient boom is deployed from the satellite toward earth.
Conservation of momentum holds true in the case of the satellite/tip mass system. A force is needed to
give the mass a velocity away from the satellite. In turn the satellite is given a resultant velocity in the
opposite direction. Equation 2 shows this relationship.
2) tiptipsatsat vmvm −=
As the two masses, the satellite and tip mass, respectively, move away from each other the systems center
of mass changes as well. Now because the masses are so far away from the center of mass of the system
the center of mass is no longer the point where the system orbits the earth. Instead because the
gravitational field is not uniform over the entire system the center of gravity is actually slightly closer to the
Earth than the center of mass and it is the new point of orbit for the system. Figure 11 depicts the difference
between the two. It also shows the different types of forces this system experiences.
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Figure 11: Gravitational Force
When the mass deploys the satellite experiences an equal and opposite reaction and moves above its orbital
plane while the mass moves below it. The two are still connected and this connection causes the tip mass
and the satellite to continue to act as one system. The tip mass now has a lower elevation than the satellite;
it experiences a higher gravitational force than the satellite. The satellite on the other hand experiences a
higher centrifugal force, similar to that of a bucket of water being spun around by the handle. The water
continues to stay in the bottom of the bucket whether it is spun horizontally or vertically. The reason the
satellite has a greater centrifugal force is due to the fact that the two masses, the satellite and the tip mass,
are traveling in the same vertical plane although the satellite is farther away from the Earth. This force,
although an artificial force, gives a good representation of how the angular momentum will cause a tension
on the connection between the satellite and the tip mass. This centrifugal force is caused by the angular
momentum.
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The system shown in figure 11 is in equilibrium, thus it is not oscillating. This is because the center of
mass of the satellite, tip mass, and Earth are all in line with each other. The gravity gradient is acting on
the satellite and the tip mass is in line. There are no horizontal vectors of the gravitational gradient in this
figure. This is almost never the case especially when the system is first deployed. When the boom is
deployed there are dynamic, vibrating, and atmospheric forces acting on the satellite, therefore it will never
be in total equilibrium. Certain sensors and other monitoring devices will show how the satellite behaves
when the boom is deployed.
Sensors on the satellite relay information on the position of the satellite relative to certain celestial bodies
such as the Sun, the Moon, or the Earth. These sensors are linked to the electronics which then make the
decision whether or not to deploy the boom. The boom must be deployed in such a way that it travels
towards the Earth if the satellite is to be oriented in that direction. If it was deployed in the direction of the
orbital path the system would be horizontal and the there would be no difference between the force of
gravity acting on satellite or the tip mass. It is crucial for the mass to be deployed when it is in the same
vertical plane as the satellite but in a lower orbit. This would allow the force of gravity to be stronger on the
tip mass, stabilizing the satellite.
Once the mass is deployed, the whole system will have similar tendencies to a pendulum. This is due to
vibration and atmospheric forces and the tip mass not being precisely aligned with the satellite and earth’s
gravitational field. In a pendulum the tip mass stops swinging once the force of gravity aligns the center of
mass with earth’s gravitational field.
The stability or tolerance of the system once it is in relative equilibrium is also a main concern. The system
will never be totally damped without oscillation due to disturbances found in space. This will be a crucial
part in case study research because the gravity gradient boom needs to develop a torque that will over come
all environment and atmospheric torques combined. When this is achieved the stabilization of the satellite
body is a maximized.
Small satellites have many different functions ranging from communications, observation, or scientific
research missions. It is vital for them to overcome any disturbances that can disrupt their mission. One such
disturbance as mentioned previously is oscillation due to the satellites angular momentum as it orbits the
earth. This oscillation can throw off the stabilization tolerance which is +/- 5 degrees along the nadir vector
pointing straight toward earth. MATLAB was used to model these oscillatory motions and select boom
-Launch assembly mount holes slotted lowering precision
- See appendix # for detailed drawing
3) Deployment System Assembly
- See Appendix # for BOM
- See appendix # for Individual drawings of machined
parts
Mass: g
Dimensions: 10cm x 10cm x 1/8”
Volume:
Material: Al 6061
Design Features: - Hole location M5 through holes
- Oversized wire opening smooth and
polished with no sharp edges
Mass: 74g
Components:
a Base
b Lower Hinge
c Upper Hinge
d Torsion Springs
e Bearings
f-g M3 Dowel Pins
h M3x.5 Nylon Screw
45
a) Launch Base:
b) Lower Hinge:
c) Upper Hinge:
d) Torsion Spring:
e) Bearings:
Mass: 31.27g
Dimensions: 40mm x 40mm
Material: Al 6061
Design Features: -x4 M5 bolt holes
-Chamfer to lock arms
-M3 Drill holes for Dowel pins
Mass: 6.5g (x4)
Dimensions: 7mm x 15mm x 41mm
Material: Al 6061
Design Features: -High precision or middle milling
-Mount for torsion spring
-Upper hinge pivots around top
Mass: 1.3g (x4)
Dimensions: 5mm x 7mm x 25mm
Material: Al 6061
Design Features: -Thread for mounting bearing
-Mount for torsion spring
-High precision on 7mm max
width
Mass: .05g
Dimensions: ID Ø 3.25mm
3rd party part: McMaster-Carr pt# 9287K62
Mass: .3 g
Dimensions: Ø6mm x Ø3mm x 2.5mm
3rd party part: VXB.com pt# Kit7032
46
f) M3 Dowel Pin:
g) M3 Dowel Pin:
h) Nylon Screw:
4) Top Seal:
- See appendix # for detailed drawing
Mass: 1.0 g
Dimensions: M3 x 16mm Lg
3rd party part: McMaster-Carr pt# 91585a065
Mass: 3.3 g
Dimensions: M3 x 40mm Lg
3rd party part: McMaster-Carr pt# 91585a076
Mass: 3.3 g
Dimensions: M3 x .5 5mm Lg
3rd party part: McMaster-Carr pt# 95280A114
Mass: 263 g
Dimensions: OD =Ø10cm
Material: Al 6061
Design Features: - 45˚ incline to lock on mass
-Removed material to accommodate
deployment system
- x4 M5 Tap to mount to base plate
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5) Mounting Ring:
- See appendix # for detailed drawing
6) Wire Guide/Bolt
Mount:
-
- See appendix # for detailed drawing
7) Frangibolt® Actuator
Mass: 32 g (x4)
Material: Delrin Plastic
Design Features: -M5 Thread through to mount with
satellite
-Inner Diameter and hole pattern has
high precision to align with other parts
Mass: 9.2 g
Material: Al 6061
Design Features: -Holds bolt in tension on
plate
- Ø2mm wire guide
48
8) Frangibolt® Fastener
9) Spool Bracket
Mass: 20 grams
Volume: 2.33 cm3
Power: 25 Watts
Material: Titanium Nickel
Vendor/Part #: TiNi Aerospace/FC2-16-31SR2
Mass: 10 grams
Bolt Size: #8 X 1.75 in
Material: Titanium
Vendor: TiNi Aerospace
Mass: 113.2 grams
Volume: 41.8 cm3
Material: 12 Gauge Aluminum 6061
Design Features M5 Clearance Holes
-The Frangibolt actuator uses a Titanium Nickel shape memory alloy that when heated expands and breaks the fastener. -The TiNi Frangibolts have excellent flight heritage and have previous been used by NASA.
-The Frangibolt fastener is a titanium bolt with a notch cut in it where you want the bolt to break. -The fastener being used is a #8 bolt that can support up to 2200 N
-See appendix # for a detailed drawing
49
10) Spool
11) Spool Rod
12) Wire
Mass: 14.7 grams
Volume: 5.42 cm3
Material: Aluminum 6061
Design Features Holes for 6mm OD Bearings
Mass: 0.931 grams
Volume: 0.34 cm3
Material: 3mm Rod Aluminum 6061
Design Features M2 Taps -See appendix # for a detailed drawing
-See appendix # for a detailed drawing
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13) Solenoid
Design Concept
All wire deployer systems contain a tip mass and wire with a set length. The mass, attached to the wire, is
deployed from the system away from the satellite. As the distance increases, the mass, which is closer to
earth, feels a greater force of gravity. After a period of time the full length of the wire is extended and the
swaying of the satellite will decrease.
Below, Figure # is a diagram of the four phases that the NEU gravity gradient device will go through in
detail.
Mass: 6.88 grams
Length: 10 meters
Material: .008 inch Copper-Beryllium Wire
Vendor: Little Falls Alloys
Mass: 24.8 grams
Volume: 3.45 cm3
Power: 4.5 Watts
Vendor/Part #: Ledex/282340-0XX
-Copper-Beryllium is flight proven and has been used on other wire deployers -Copper-Beryllium was selected because of its high tensile strength of 700 MPA
-The Ledex® low profile linear solenoid was selected because of its small size and lower power usage -The solenoid can be powered by at power source or 12 volt battery
51
Figure #
Phase 1: Launch through Deploy
During launch the gravity gradient device will be subjected to high frequency vibrations and forces nearly
twenty times Earth’s gravity. During this stage the team designed against two possible failures. These
failures would be not securing the tip mass and the wire spool.
The 3kg mass tip is secure on all sides except the top. Because of this, the bolt must secure the mass against
the 20g force with a moderate factor of safety of 1.5:
thBoltstrengFFoSamF
sma
NthBoltstrengkgm
<=
=
==
1
1
2
**
20*81.9
200,23
1
1
1
9.8825.1*20*81.9*3
FthBoltstrengNF
kgF
>==
As shown above the bolt will not yield or deform in the worst case scenario when a 1.5 factor of safety is
applied.
The wire spool, during launch, was also an area of concern. During launch, vibrations will attempt to
unravel the wire from the spool, know as blossoming. The design solution for this was adding a pulling
solenoid. With a solenoid mounted securely to the frame, its tip can be inserted into an opening located on
the spool. The addition of the solenoid did not surpass any constraints on size or power.
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Phase 2: Deployment stage 1
Stage two initiates when the satellite settles to its expected rotation and oscillation. At this time a signal
will be sent to unfasten the spool by activating 4.5 watts and 12V to the solenoid. Once this is completed,
and the satellite starts its rotation towards Earth, power will be diverted to the Frangibolt® Actuator. After
an estimated 40 seconds at 25 watts the actuator will heat the bolt causing the bolt to snap, releasing the
mass. The four arms with fully compressed torsion springs and ball bearing tips begin to propel and guide
the mass out from the satellite.
Phase 3: Deployment stage 2
The four launch springs are of the lowest torque values. However in space, were only a fraction of the
weight is felt, the four spring and their moment arms propel the mass at an initial 1.85N and .6m/s2. See
Apendix # for full calculations. This initial force will be enough to start spinning the spool and align the
wire.
Phase 4: Deployment Finished
A design concern as the mass would be reaching its given length is whether a damper would be needed to
halt acceleration. The solenoid that initial secures the spool during launch vibrations and protects it from
blossoming will serve a second purpose. When the boom is about to reach its fully extended length the
solenoid will press against the flange of the spool to slow the forward momentum of the boom and tip
mass. This will ensure safe speed and limit vibrations in the boom as it reaches a safe stop. In addition, it
will prevent the spool from spinning backwards.
THE PROTYPE
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The prototype, constructed from Northeaster’s SLA 3D printer, was assembles to better understand our
design, and as a tangible scale replica. Below, Figure #, shows our assembly with machined parts as well
as well as some purchased parts.
Tests preformed on the prototype:
Once the prototype was completed the design concepts were reestablished and tested. Two tests completed
were to confirm the strength of the springs, and test force and velocity calculations. After the calculation
for the springs were completed and checked, slight inconsistencies show from McMaster-Carr’s data. The
next step taken was to find the holding force of the four springs. From this, a third comparison could be
made on the torsion spring data. The results from this show that the actual spring’s tensional constant is
lower then what was stated on McMaster- Carr and another vendor should be found for this part. Full
results for this test can be found in the Appendix.
The next test was similar to the one with the wood block. The second test was to simulate deployment in
near weightlessness. This was accomplished by the use of a low friction pulley that connected the
prototype tip mass with the matching weight in bolts and washers. This test showed the functionality of
two key features of the design; wire and spool bearings. In addition to this it showed the similarity between
the centripetal forces of the satellite vs. the slightly stronger gravity gradient force. The test was set up as
the following. The Northeaster’s gravity gradient boom devises prototype was set up on a stool under the
pulley with the wire secured to the mass on both sides, one through the pulley the other unto the locked
spool. When the mass was released from the spring deployer it raised with a low velocity.
:
CONCLUSION
Mission Adaptability and Integration
Adaptability and proper integration to other micro satellites was an important design constraint that was set
forth by NASA and Santa Clara. The Northeastern design team designed a gravity gradient boom that is
very compact and light but produces enough torque to overcome all outside disturbance torques, combined.
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The gravity gradient booms light weight and very compact size makes it adaptable to other small satellites.
In addition, the only time the gravity gradient boom draws power is when a current is applied to the Frange
bolt to let it detach the tip mass.
The Frange bolt is a space proven part with space heritage. It can withstand +/-20g of acceleration in all
axes. The entire gravity gradient boom is built out of aluminum 6061 parts that are also space qualified
with space heritage.
Optimized Design Constraint
As mentioned earlier in the paper several strict constraints had to be followed in the design of the gravity
gradient boom. The deployment system and the boom have to be small enough and compact enough to fit
into the ONYX. More importantly the system cannot drastically change the satellite’s physical properties
such as center of gravity and moments of inertia.
The gravity gradient boom system cannot exceed a 30kg mass. Other constraints were that it cannot draw
more than 30 Watts of power and that it has to fit into a volume of 12cmx12cmx15cm which is extremely
small. The gravity gradient boom that was designed maximizes all of these constraints and actually saves
room in the satellite. Finally, a pointing accuracy of 5 degrees within the earth pointed Nadir vector must
be achieved.
The systems weight mostly comes from the tip mass that is used. The tip mass is the most essential part in
generating a torque that will be strong enough to overcome all other disturbance torques that will hinder
satellite stabilization. The overall mass of the system is 3.761kg which falls under the 5-10kg maximum
mass constraint. For space applications, every pound that is sent into space over the target weight will cost
an estimated $10,000. [ ] Such a light weight gravity gradient boom system allows for extra development of other
vital subsystems of a micro satellite without having to worry about mass budget concerns.
The gravity gradient boom also meets and exceeds size and volume constraints. The whole system, including the tip
mass can be mounted inside the satellite that takes up a volume of 10cm x 10cm x 14.2cm. For ease of design and very
tight time constraints the Northeastern design team chose to work around the targeted volume. A smaller system can be
made. However, additional space can be made to incorporate extra sensors inside the gravity gradient boom if needed.
The booms inertia properties are very small due to its compact nature and very low weight. This means that the
satellites inertia properties will be not be changed and no extra modifications need to be done to the active attitude
control system to initial stabilization as it is tumbling. A detailed design table shows all physical properties of the
gravity gradient boom system.
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Since the ONYX is an image capturing satellite it needs to have a high degree of stabilization so the camera can take
clear and precise images of the earth. The initial pointing accuracy specified by Santa Clara University was +/- 5
degrees of the Nadir vector pointing towards earth. Northeastern’s gravity gradient boom can achieve a stabilization
angle of +/- 2 degrees within the Nadir vector. With the given length of boom and given mass of the tip it will take 5
days for the satellite to stabilize to such a tight tolerance. However, this is under the assumption that the active attitude
control system will “de-tumble” the satellite to 30 degrees with respect to the Nadir. If the active control system will
de-tumble the satellite closer to the Nadir it will take less time for the gravity gradient boom to further stabilize the
satellite to a high degree of accuracy. In addition, a longer boom and heavier tip mass can be used to ensure faster
stabilization. Due to the gravity gradient boom’s design, interchanging longer booms and heavier tip masses is simple
and cost effective.
To achieve such a high degree of pointing accuracy the gravity gradient boom has to develop a torque great enough to
overcome all other disturbance torques. These disturbance torques arise from the gravity gradient, solar radiation
pressure, magnetic field, and aerodynamic drag. The table below shows the worst case disturbance torques experienced
in low earth orbit. [ ]
Table # 3
Aero dynamic Torque 1.1 x 10^-8 N-m
Gravity Gradient Torque 5.1 x 10^-8 N-m
Solar Radiation Torque 2.6 x 10^-6
Magnetic Field Torque 8.6 x 10^-4 N-m
Torque Developed by GGB 3.2 x 10^-3 N-m
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The total combined disturbance torque is 8.6 x 10-4 N-m which is smaller than the torque developed by the
gravity gradient boom. Theoretically, once the gravity gradient boom is deployed in low earth orbit it will
stabilize the satellite for the duration of the mission.
8.30 Adaptability to Electronic Subsystems
The gravity gradient boom that has been developed is also adaptable to electronic devices via the Emerald
Protocol Suite. There is enough available volume to mount a motor a have it unwind the spool, deploying
the tip mass. Sun sensors and magnetometer connections can also be fit in but the gravity gradient boom
was designed as a complete stand alone system with the assumption that all sensors will be on the satellite
already.
The initial design incorporated a DC motor that had the spool attached to its output shaft. Santa Clara
University and NASA had never given a direct requirement for retract ability so the design team
concentrated on building a small light weight system that can use a motor if needed.
The motor allows for a more controlled manner of deployment and it also allows the boom to retract in
increments if needed. Proper motor selection is essential for a gravity gradient boom that is meant to use an
electric unwinding device.
The motor has to be able to withstand strong dynamic loads of +/- 20g in all axes. It also has to withstand
the harsh vibrations of the launch. Proper calculations and design concentrates have to be made to select a
motor that will work well with the gravity gradient boom. The inertial properties of the spool have to be
known, tension in the boom wire, and optimal deployment speed. From those initial design parameters the
motor selection process can start.
The tension in the boom wire is a very small .0003N. A motor was selected based on a .003N tension to
overcome any error in power requirements. Most miniature DC motors spin at a rate of several thousand
rotations per minute. Speed and torque is a function of voltage that is applied to the motor. For the gravity
gradient boom application the motor catalogue that was used contained the slowest spinning motors with
optional gear heads and encoders to produce a desired rotation of the output shaft. Micromo Electronics
was selected as the vendor for miniature DC motors. Micromo has produced numerous DC motors that
have been on past and present space flights. Many motors have space heritage in addition to their already
small size and light weight.
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The slowest motor from Micromo can spin at 9900RPM under a 24 volt power supply. The motor would
run in a 24 volt winding using a 12 Volt connection. The desired speed is roughly 5000RPM. When
coupled to a gear head it will produce the desired output shaft speed to safely deploy the boom. The power
and speed required for the motor are given in the equations below
W = no x Torque/ 1350
Where no is the desired rotational speed of the motor, T is the torque in oz-in, 1350 is a constant, and W is
power in Watts. The motor would need to produce .425 oz-in of torque to over come a tension of .003N in
the boom wire. With a desired speed of 5000RPM, the equation above indicates that 1.57W of power is
required for the motor to overcome the tension. The power needed is well under the maximum 30W that
can be used. In a 12 Volt setting the motor will spin approximately 5000RPM, the voltage ratio is shown
below
n12volts 12 x 9900RPM = 4950RPM
24
Through the help of the engineers at Micromo, a series 1524SR motor was selected with a 24 Volt winding
help monitor and maintain deployment speed. The mass of the motor is only 21 grams with dimensions of
24mm in length and 15mm in diameter. It is robust and light weight with very strong thermal properties.
Total cost of the motor with supporting gear head and encoder is $180 from Micromo electronics.
The designed prototype does not use a motor. Due to the mounting system and the optimization of size, a
motor can be placed in the spool bracket with minimal changes to physical and inertial properties. The
gravity gradient boom is versatile enough to incorporate a motor if the application strictly requires the use
of one. All materials are space qualified with large amounts of space heritage. Micromo even supplies the
right fluids that will allow the motor to work properly in a space environment.
Cost Analysis
The initial cost analysis may be higher than the actual expected cost analysis due to rushed machining costs
and overall preliminary design considerations. The machining of precise aluminum parts and the
Frangibolt® are the most expensive design pieces. It is important to note that both of these parts and
materials are space qualified, therefore costs are expected to be higher. Below is an estimated cost analysis
of all the parts making the up the gravity gradient boom.
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Part Cost
Aluminum 6061 and machining costs $1000
FrangBolt from TiNi Aerospace, Inc. *
Part # FC2-16-31SR2 # 8 $2,550
#8 FrangiBolt Fastener TBD configuration * $85
Part# W2-32-Ti #8 FrangiBolt Washers $10
Ledex Low Profile Solenoid $80
24’ of Beryllium Copper Wire $63
Torsion springs $14
3mm x 6mm x 2.5mm Bearings $15
Dowel Pin $10
M2, M3, M5 and Alloy Metric Rod $31
Optional – Series 1524SR motor with encoder and 16/7 Gear Head $180
Total Cost $4,038*
* Prices from several vendors can be significantly discounted for University Projects
The cost for a final design is estimated due to several vendors offering discounts on University projects.
The prototype was built using plastic parts from a 3D printer due to time constraints with the machine shop
for aluminum 6061.
8.4.0 Future Considerations and Improvements
The Northeastern design team was able to meet many of the constraints that were set forth. The gravity
gradient boom is a very light weight and compact design, which can be highly adaptable to other micro
satellites.
Future improvements should consider proper CAD modeling to ensure accurate meshing in ANSYS finite
element software. This will yield accurate results for modal vibration analysis. Other design considerations
would be to improve metal on metal contact and simplifying the system even more to reduce estimated
costs.
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REFERENCES
[1] Singh, Sahjendra N., and Woosoon Yim. "Nonlinear Adaptive Spacecraft Attitude Control Using Solar
Radiation Pressure." (2005). 19 June 2006.
[2] Bong, Wie, comp. Dynamic Modeling and Attitude Control Of. 10 Jan. 2002. Arizona State University.