51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR>18th
12 - 15 April 2010, Orlando, Florida
AIAA 2010-2581
Analysis of a Segmented Compliant Deployable Boom
for CubeSat Magnetometer Missions
A. Sim∗ and M. Santer†
Imperial College London, London, SW7 2AZ, UK
This paper describes the design and analysis of a self-deploying boom which is capable
of placing a magnetometer a prescribed distance from and orientation to a CubeSat. A
segmented, concertina-folded design is adopted with the self-deployment being achieved
by means of tape spring hinges. The numerical and parametric analysis related to the
design and quantification of the boom is presented. Design metrics which enable the
characterization of the boom performance are derived, and a finalized design is constructed.
I.
Introduction
This paper presents the design and analysis of a deployable segmented boom which is required to place a
magnetometer instrument approximately one meter from a CubeSat. The project is a collaboration between
the Aeronautics and Physics Departments at Imperial College London which aims ultimately to launch a
CubeSat that is capable of accurate measurement of the Earth’s magnetic field. For this reason, the magnetometer is required to be placed sufficiently far from the spacecraft during operation to avoid interference,
yet be packaged into the tight constraints placed by the P-Pod specification1 during launch. One half a
CubeSat unit, i.e. an envelope of approximately 10 cm×10 cm×5 cm, is made available for the stowed boom
and consequently a tenfold length expansion between stowed and deployed states is required.
The operation of a magnetometer imposes several design requirements in addition to those made by
the CubeSat specification.1 Two of these are of particular importance: 1) when the magnetometer is fully
deployed it is necessary to know its exact orientation relative to the spacecraft; 2) the magnetometer must
be connected by a harness (cable) to the spacecraft to enable data transfer between the instrument and the
on-board processors. These will both be seen to have a strong influence on the final deployable boom design
that was adopted. A formal design specification will be introduced below.
The primary focus of this paper is the analytical and numerical techniques that were adopted to ensure
that the boom would behave as expected, particularly during the deployment phase. Great attention is paid
to investigating the sensitivity of the design to changes resulting both intentionally, such as alterations in
the harness density, and unintentionally, such as those resulting from manufacturing errors. The effects of
these changes are quantified in terms of dimensionless numbers.
Following this introduction, a formal design specification will be introduced. The design of a deployable
segmented boom containing compliant tape spring hinges that would satisfy these objectives is then presented. In order to carry out this design, parameterized finite element models were developed to analyze
both the local performance of the tape spring hinges, and the global performance of the boom in terms of its
deployment characteristics and vibrational stiffness. Sensitivity studies are then carried out to quantify the
effects of a change in key properties on both deployment ‘quality’ and deployed stiffness. With respect to the
deployment quality, three deployment characteristics which are indicative of a failed design are described.
Finally, the final design is presented, and conclusions are drawn in conjunction with suggestions for further
work.
∗ Masters
† Lecturer
Student, Department of Aeronautics, Imperial College London, Member AIAA.
in Aerostructures, Department of Aeronautics, Imperial College London, Member AIAA.
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II.
Specification and Design Concept
The design specification of the boom is presented in this section. These are supplemental to the general
requirements stated in the CubeSat specification.
• The boom is required to fit into an envelope of 10 cm×10 cm×5 cm;
• The total mass of the boom and payload must not exceed 500 g;
• The boom must be constructed entirely of non-ferrous material.
The restriction of the total mass to 500 g is not a significant design driver. The mass of the payload is
currently undetermined as its design is currently being refined. However it was agreed that 50 g would be
a suitable representative figure. The requirement of using non-ferrous material is to ensure that the boom
does not affect the operation of the magnetometer by generating its own magnetic field.
It was also decided that the boom should be self-deploying by means of the release of stored strain energy.
This is to remove the need for additional deployment drivers, as it was noted early in the design process that
the entire provided volume would be required for the boom. No prescribed value for the deployed natural
frequency was provided, so a maximum deployed stiffness was sought, subservient to achieving a successful
deployment.
Several deployable boom concepts were considered, of which a segmented concertina-folded design was
found best to achieve the design requirements. The configuration adopted was similar to that of the MARSIS
antenna.2 A CAD model of the boom concept in its deployed configuration is shown in Fig. 1 and in its
stowed configuration in Fig. 2. Lightweight pultruded Carbon fiber rods form the main segments, with Aluminium connector pieces at each end. These connector pieces provide the attachment points for connecting
springs. These springs that are used are the single-curved shell structure known as tape springs3 which are
advantageous for many reasons. When they are subjected to end rotation starting from a straight configuration, they exhibit an initially stiff response before buckling and exert a lower approximately-constant moment
thereafter. This constant moment results in the required self deployment when the folded boom is released
and the high stiffness when straight imparts stiffness to the boom when it is fully deployed. The properties
may also be tailored through variation of the tape spring geometry, specifically the radius of curvature and
the subtended angle of the cross-section, and the thickness of the shell. This ability to vary precisely the
deploying moment is crucial to ensure a successful deployment. The material chosen for the tape springs
is plain-weave Carbon composite fabric. It will be noted that the choice of all the materials for the boom
satisfy the non-ferrous requirement.
For clarity, the hinges are named according to their position, i.e. the hinge connected to the base plate is
referred to as the ‘base hinge’. Working from the base, the hinges are numbered 1 through 8. After this set
of hinges the remaining two hinges are denoted the ‘penultimate hinge’ and the ‘payload hinge’ respectively.
This labelling system enables the clear identification of the hinges that are found to be key to the deployment
characteristics.
magnetometer
Aluminium connector
pultruded CFRP rod
tape springs
Figure 1. CAD model of the segmented deployable boom concept in its deployed configuration
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Aluminium connector
(showing tape spring interface)
magnetometer
pultruded CFRP rod
Figure 2. CAD model of the segmented deployable boom concept in its stowed configuration
A.
Numerical Models
Having specified a boom concept, numerical analysis was carried out to achieve a functioning design. Four
different finite element models are used during the design process; a dynamic deployment model in which
idealized properties are assumed for the tape spring hinges to enable parametric studies; a quasi-static tape
spring model to determine the moment-rotation response which is then idealized in the deployment model; a
dynamic modal analysis model to evaluate vibration stiffness; and an accurate dynamic deployment model in
which the hinge stiffness is fully specified as a function resulting from the tape spring model. The commercial
SAMCEF finite element package4 is used throughout.
1.
Dynamic Deployment Models
The idealized deployment models begin with the setting up of the boom in the deployed configuration, as
shown in Fig. 3. The segments are modelled as Timoshenko beam elements and assigned the appropriate
profiles and material properties. The behaviour of the tape springs is idealized by assuming a pin joint
connecting the segments with a nonlinear torsional spring to represent the stiffness of the tape spring. It is
assumed that the tape springs would be of negligible weight in comparison to the total structure. The mass
of the connectors is modelled as concentrated masses, as was the payload. The harness leading from the
spacecraft to the payload was accounted for by changing the density of the material assigned to the boom
segments. This was done by taking the mass of the harness per meter and dividing by the cross sectional area
of the given boom section. This provides the density that must be added to the material density to account
for the harness mass. This method allowed for the harness mass to be distributed, without it contributing
to the stiffness of the boom segments.
Rigid contact with zero friction is assumed between all components. Contact between adjacent boom
segments is modelled by defining spheres, of radius 0.5 mm, located at the middle of each boom segment.
In order to minimize the number of contact definitions and speed up the analysis, contact is only defined
between a boom segment and the two adjacent segments. The contact definition between the hinges and the
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CubeSat wall
rigid contact surface
CubeSat wall
rigid contact surface
boom segment
rigid contact surface
idealized hinge:
lumped mass,
torsional spring
payload:
lumped mass,
rigid contact surface
Y
Z
Figure 3. Finite element model of the boom in its initial state prior to being stowed. Note the idealization of
the tape springs to pin joints
walls of the spacecraft are modelled by specifying the spacecraft walls as parallelepiped boxes. These may
be seen at the left hand side of Fig. 3. Contact is also defined between the first two hinges and the back
wall, with the back wall being modelled using a infinite two dimensional plane in the x-y plane. The payload
surface is also specified as a parallelepiped: contact definitions are specified between this surface and all of
the nodes in the penultimate boom segment.
From the deployed configuration, the hinges are rotated into the stowed concertina-folded configuration.
For the base hinge the angle of rotation is 90 deg. Hinges between the base and the final hinge are rotated by
±180 deg. and the rotation angle of the final hinge is left as a design variable. The hinges are only rotated
through 99.5% of the actual value required because the spheres used to define the contact between the boom
segments do not permit a full rotation, since this would violate the contact definition. Consequently, the
initial relative orientation of the segments is not parallel but this is considered to have negligible effects on the
deployment. Initial folding is carried out in an incremental manner and a quasi-static response is enforced in
order to omit any inertial, damping, and frictional terms. The Newmark implicit predictor-corrector scheme,
with automatic time stepping is employed.
The release and deployment is modelled by means of a subsequent dynamic analysis. The Hilber-HughesTaylor implicit predictor-corrector scheme is employed, again with automatic time stepping. The numerical
damping parameter associated with the Hilber-Hughes-Taylor scheme is set to α = 0.01. The maximum
solution time for the deployment is specified as 2.5 s. This value was chosen following investigation of likely
deployment times – if deployment is not achieved within this time it is indicative of failure. The maximum
time step is specified as 0.01 s to ensure sufficient dynamic resolution. Outputs requested from the analysis
were reactions from the base node in the z and y directions to enable the evaluation of shock loading, and
the position of the payload node in the structural axes to characterize the deployment.
2.
Tape Spring Model
The local model used to evaluate the properties of individual tape spring hinges is shown in Fig. 4. Four-node
Mindlin shell elements are used. The element density has been shown adequately to represent the behavior of
tape springs in bending.5 Each end is fully fixed to a master node by means of a rigid multi-point constraint
and equal and opposite quasi-static rotations are prescribed to both these master nodes. The resulting
constant bending moment is recorded.
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Z
master nodes
X
Y
Figure 4. Finite element model of an individual tape spring, used to determine moment-rotation response
payload mass
lumped connector masses
Y
X
Z
Figure 5. Finite element model used to evaluate the deployed vibrational stiffness
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3.
Dynamic Modal Analysis Model
The dynamic model, shown in Fig. 5, is set up to evaluate the frequency response of the boom when
deployed. The model combines the segments from the dynamic deployment model with accurate structural
representations of the tape springs. The boom elements are defined in exactly the same way as in the
deployment models. The position of the beam nodes, however, is defined as functions of the boom section
lengths and the tape spring lengths. The profiles and the densities are appropriately assigned. The tape
springs are specified exactly as they are in the tape spring model. The position of each tape spring along
the boom, their orientation, and the offset from the centre line of the boom are all taken into account. This
is defined as a function of the boom parameters, boom section lengths and tape spring lengths. Each tape
spring is defined using the radius of curvature and the angle subtended by the curved cross-section, and the
thickness as parameters. This allowed for ease of modification of the model. The end nodes of the beam
segments were rigidly attached to the tape spring ends. The displacement of the base is fully constrained.
The payload is represented by a concentrated mass attached at the free end of the last boom section. The
vibration modes of the deployed boom are determined by means of a Lanczos eigenvalue analysis.
4.
Deployment Model with Refined Tape Spring Stiffness
This model is identical to the idealized deployment model with the main difference being the definition of
the functions which define the stiffness of the hinges. The tape spring stiffness responses were taken directly
from the tape spring model rather than using the previous assumption of a linear and a constant region of
behaviour. This results in hinge stiffness definitions which are much more representative of how the actual
tape springs are likely to behave. The boom sections were defined in exactly the same manner and the hinges
were also defined as concentrated spring elements
5.
Tape Spring Idealization
As described above, the tape spring hinges are idealized in the dynamic deployment models as pin joints
with associated torsional stiffness. This idealization is carried out according to the process illustrated in
Fig. 6. The left hand figure shows the moment rotation response of a tapespring evaluated using the local
model described in Sec. 2. (This is the response of tape spring B introduced in Sec. B below.) The right
hand side of the figure illustrates how the response is split into linear and constant components. The linear
response consists of the portion of the moment rotation response from zero deflection up to the limit points.
The equal- and opposite-sense constant moments are assigned values equal to the average moments following
the limit points.
200
150
linear response
M (Nmm)
100
opposite-sense
constant response
50
0
equal-sense
constant response
−50
−100
−200
−150
−100
−50
0
50
rotation (deg.)
100
150
200
−200
−150
−100
−50
0
50
rotation (deg.
100
Figure 6. Tape spring idealization for parameterized dynamic deployment model
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150
200
B.
Hinge Design
The base, main hinges and the penultimate hinge of the boom all use two tape springs. This is to increase
the torsional stiffness of the boom. The final hinge uses three tape spring in order to clear the payload from
the spacecraft with the necessary speed. The final hinge designs use three different tape spring geometries
in different configurations. There are distinct tape springs used in the design, however, they all have the
same radius of curvature. This is intentionally chosen so that all tape springs may be manufactured with the
same mould, thus facilitating their manufacture. The only difference between the tape springs, therefore,
is the angle subtended by the curved cross-section. The weakest tape spring subtends an angle of 63 deg.,
the middle tape subtends an angle of 81 deg. and the stiffest tape has a subtended angle of 102 deg. These
hinges designs are subsequently referred to as A, B and C respectively.
III.
Sensitivity Studies
Parametric studies were then carried out on the models, with selected properties as variables. After
initially determining the range of tape spring properties, through a parametric study using the geometric
properties of the tape springs as variables, a parametric study of the idealized deployment model with
symmetric hinges could be set up to ascertain the extent to which manufacturing errors could affect the
deployment. In the idealized deployment models, only the main hinges and the payload hinge were taken
as variables. This was done because it was noted that since they are the most numerous and stiffest hinge,
respectively, they would have the most influence on the deployment. In the dynamic model the variables
were all the geometric properties, with the exception of the length of the tape springs and the mass of the
hinges, both of which are constrained by the stowed volume and frequency requirements.
A.
Tape Spring Sensitivity
For the tape spring parametric studies, all of the geometric properties were taken as variables except for
the length of the tape spring. To determine the tape springs’ sensitivity to possible manufacturing errors,
a deviation of approximately 20% was assumed for each geometric dimension. The assumed values for the
error can be seen in Table 1. In order to determine the largest absolute error in the tape spring properties the
model was run with the variables in combination and then the results filtered to determine what combination
would result in the weakest and stiffest tape springs. The results of the parametric study can be seen in
Table 2.
variation
R (mm)
t (mm)
α (mm)
Tape Spring
A
B
C
±0.3
±0.3
±0.3
±0.005 ±0.005 ±0.005
±3.0
±4.0
±5.0
Table 1. Range of tape spring variables used in parametric study.
Tape Spring
A
B
C
Mmax (Nmm)
97
260
810
High
Mconstant (Nmm)
51
78
130
Mmax (Nmm)
55
55
400
Low
Mconstant (Nmm)
35
37
70
Table 2. Range of tape spring properties resulting from parametric study.
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B.
Effect of Tape Spring Manufacturing Errors on Idealized Symmetric Hinge Deployment
In this section, the parametric study that was carried out on the idealized deployment is described. As
mentioned above, only the main hinges and the payload hinge stiffness are used as variables, i.e. the constant
and maximum moment values. Having a large number of parameters means that it is necessary to condense
the deployment information into a single metric to enable meaningful comparison between the different
design cases. This metric is developed as follows. A high-quality deployment is defined as one for which
the payload trajectory is as straight as possible, i.e. the deviation in the ±y-direction must be minimized.
Slow deployments are also desirable as shock loading on the spacecraft when the hinges lock is reduced. It is
strongly desirable to penalize motion of the payload towards the spacecraft as this increases the likelihood
of impact and wrap-around behavior (as described in Sec. IV below.) It is desirable to penalize deployments
which occur over long time durations as this is indicative of a wayward deployment.
These requirements are combined in the design metric denoted Q – the deployment quality.
2
max (|ymax |, |ymin |)vmax vmin
τ3
(1)
4
L
in which ymax and ymin are the displacements of the payload in the y-axis in the positive and negative direction respectively, indicating a deviation from a straight deployment; vmax and vmin are the payload velocities
in the z-direction in the positive and negative directions respectively, indicating rapidity of deployment; L
is the z-displacement of the payload when it is fully-deployed which is included to make Q non-dimensional;
and τ is the time taken to reach this fully-deployed distance.
Deployment quality is observed to improve as Q is minimized as expected, although it is not able to
predict impact between the payload and the boom during deployment. The presence of such an impact must
therefore be determined by further observation of a deployment having a low Q-value. For the parameters
investigated, values of this number ranged from 1.54 to 0.05. A summary of five example design iterations
can be seen in Table 3. For comparison, the deployment quality for the final design, introduced in Sec. V
below, is included in the last column of the table. This is evaluated using the full functional representation
of the tape spring properties.
Q=
Main Hinge
Payload Hinge
Payload y-displacement
Payload z-velocity
Extension Time τ
Deployment Quality
Constant (Nm)
Linear (Nm)
Constant (Nm)
Linear (Nm)
min. (m)
max. (m)
min. (m/s)
max. (m/s)
(s)
Q
(i)
0.195
1.175
0.360
1.700
0.094
0.000
5.763
-1.883
0.60
1.54
(ii)
0.260
0.750
0.285
1.000
0.255
-0.253
6.353
-0.797
0.44
0.33
(iii)
0.130
1.160
0.360
2.400
0.017
-0.052
7.188
-2.953
0.16
0.05
(iv)
0.130
0.750
0.285
1.000
0.092
-0.381
6.705
-5.932
0.15
1.13
(v)
0.130
1.175
0.360
1.000
0.484
-0.537
7.286
-6.121
0.13
1.20
final
—
—
—
—
0.135
-0.120
6.600
-1.200
0.20
0.04
Table 3. Deployment quality number Q for example design parameters
C.
Effect of Tape Spring Geometry and Hinge Weights on Natural Frequency
A parametric study was also carried out using the tape spring geometry and the hinge masses as variables
to determine the effect on deployed natural frequency. The ratio of the first mode frequency to that of a
cantilevered beam was used to define the vibration characteristics of the deployed configuration as a function
of a non-dimensional number containing the tape spring properties and main connector mass. This reference
is chosen as it represents the best vibrational stiffness that could be achieved without the presence of tape
spring hinges. The natural frequency of a cantilever with distributed mass and a point mass at the end is
µ
¶1/2
1
3EI
f=
(2)
2π L3 (m + 0.24mb )
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where E and I are the Young’s Modulus and second moment of area respectively, L is the length of the beam,
m is the tip mass, and mb is the mass of the beam.6 The natural frequency ratio is plotted as a function of
an additional non-dimensional number S, where
µ
¶µ
¶µ
¶
αmain
Rmain
mconnector
S=
(3)
αbase
Rbase
mtotal
in which the subscripts main and base signify the values for the main and base tape spring hinges respectively,
mconnector is the mass of a single connector piece, and mtotal is the total mass of the boom and magnetometer
assembly. S is indicative of the distribution of stiffness and mass, and is denoted the ‘structural coefficient’.
For the calculation of the natural frequency of the cantilevered beam the following properties were used.
The Young’s Modulus was taken to be that of carbon fibre, 130 GPa, the length was 0.923 m, the boom
profile was assumed to be circular with a radius of 1.5 mm, giving a moment of inertia of the section as
1.82 × 10−6 m4 . The boom mass was 0.077 kg and the tip mass was taken as 0.05 kg. This gives a reference
natural frequency of 0.86 Hz. The structural coefficient was a ratio of the properties, radius of curvature
and thickness, of the two tape springs by the ratio of the connector masses to the total weight of only the
boom assembly, i.e. not including the payload. The first resonant frequency ratio is plotted with respect to
the structural coefficient S in Fig.7.
It can be seen that there are three distinct bands of frequencies. The highest band corresponds to the
deployed boom’s normal mode being the cantilever mode. This is the best vibrational stiffness that can
be achieved for the chosen concept. The middle frequency band occurs when the tape spring stiffness falls
below a critical amount. The first mode then switches from the cantilever mode to local modes where
individual segments vibrate. Even in the absence of a minimum frequency requirement, this behavior is
highly undesirable and to be avoided. Both frequency bands do not vary significantly with respect to the
structural coefficient. The third band indicates the possibility of structures with extremely low vibrational
stiffness. These are all associated with low stiffness of the base hinge at the extremes of the parametric
variation. It is important to be aware of this possibility, but it is unlikely that it would occur in practice.
0.1
0.09
cantilever mode
0.08
frequency ratio
0.07
0.06
0.05
odes
local m
0.04
0.03
0.02
local modes associated with a weak base hinge
0.01
0
200
300
400
500
600
700
S
Figure 7. Frequency ratio versus structural coefficient showing banding of frequency response into characteristic modes
D.
Conclusions on Sensitivity Study
The tape spring sensitivity investigation showed that the properties of the tape springs can vary a significant
amount although the idealized boom deployment with the asymmetrical tape spring assumption showed that
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even the worst case of deviation in the main hinges and payload hinge would not be significant enough to
cause the deployment to fail. This means that as long as the hinges are tuned to give a deployment which
does not suffer from any undesirable characteristics, then even with the worst assumed manufacturing error
the boom should still end up in the fully deployed, locked configuration eventually. With increasing error,
the probability of the deployment containing some undesirable characteristics, such as the payload impacting
the boom or severe whiplash (described below), also increases.
The resonance parametric study showed that there are three well defined bands which the natural frequency of the final structure could fall into, with manufacturing errors. It is difficult, however, to determine
which band the natural frequency will fall into since manufacturing errors can both increase the natural
frequency and decrease it depending on the particular combination. This indicates the great care that must
be taken with respect to the tolerances of the tape springs.
IV.
Deployment Characteristics
A high-quality deployment, characterized by a small Q-value as defined by Eq. 1 is defined, amongst other
factors, as one for which the off-axis displacement of the payload is minimized. In the course of designing
the boom and performing the sensitivity investigations it was noted that undesirable deployments could be
classified in a number of representative ways. In particular there are three types of deployment that are
undesirable: whiplash, drift and wrap-around. These are described and elaborated below.
A.
Whiplash
Whiplash occurs when the payload is ejected from the satellite with a forward velocity that is too high. The
high velocity results in the boom violently whipping as it reaches its maximum extension. The payload is
then pulled rapidly back towards the spacecraft, usually buckling hinges that have already locked behind it.
Whiplash is also associated with high shock loads and sometimes results in the payload impacting upon the
boom.
This characteristic is more likely to occur when the hinges are too stiff, particularly the payload hinge.
The excess stiffness results in the payload being ejected with a high forward velocity. A plot of the payload
trajectory of a boom configuration illustration the whiplash effect is shown in Fig. 8. It can be seen that in
this case, after an initially promising deployment with minimal off-axis payload motion, the whiplash effect
causes the payload to reverse direction and swing around to a point behind the spacecraft before swinging
round towards the desired location.
B.
Wrap-around
Wrap-around is a special case of whiplash. If the deployment is not straight, i.e. the payload is ejected at
an angle rather than directly away from the spacecraft, and the forward velocity is too high, the payload
will pull the boom around the spacecraft as it whips and moves backwards. As with whiplash, the shock
loads associated with wrap-around are very high. This, however, is not the most concerning aspect of these
deployments. Although the boom is designed so that there is only one stable deployed configuration, i.e. all
the hinges locked, if the payload or some component of the boom were to become caught on the satellite
exterior, as it wraps around, the boom may become jammed in this configuration and thus render the payload
useless.
This characteristic is more likely to occur when the payload hinge is overly stiff, as in whiplash. Wraparound
is also more likely to take place when the main body of hinges are significantly weaker than the payload
hinge. This lack of stiffness means that as the payload whips, the main body of hinges re-buckle and do not
arrest the payload’s negative velocity.
C.
Drift
Drift is when the payload is not ejected with enough forward velocity. There are two possible deployment
dynamics which are possible from this circumstance, both of which result in the payload impacting on the
deploying boom. One possibility is that while the payload slowly drifts away from the spacecraft, the rest
of the boom deploys explosively and impacts on the payload as it extends. The other possibility is one
where the payload is pulled back towards the spacecraft before it reaches the full extension. In this case, the
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t = 0.58 s
y (m)
t=0s
x (m)
Figure 8. Payload trajectory plot characteristic of a ‘whiplash’ deployment failure
sections behind the payload take time to settle and as they as they overshoot the locked position they pull
the payload back towards the satellite. While the shock loads are not high when drift occurs the probability
of the payload impacting on the deploying boom is high, which is undesirable.
A plot of the payload trajectory of a boom configuration illustrating the drift effect is shown in Fig. 9.
Here it can be seen that the deployment envelope, represented by a dotted line in the figure, is only 31 degrees
in the positive y-direction and 15 degrees down in the negative y-direction, would indicate an acceptable
deployment. However, there is contact which is not captured by the payload trace. Drift is usually present
when the stiffness of the main body of hinges comparable to or larger than the payload hinge. Since the
payload hinge needs to accelerate a larger mass, i.e. the payload, it will move slower than the hinges behind
it which are significantly lighter.
V.
Final Design
By taking into consideration all the requirements and results from analyses a final design was reached
which is described in this section. It consists of the base hinge, the 1st, 2nd, 6th, 7th, 8th hinges from the
base, and the payload hinge all using tape spring B. The penultimate hinge consists of two A tape springs,
and hinges 3, 4, and 5 make use of tape spring C. All hinges consist of two tape springs with the exception
of the payload hinge which has three.
The spring elements in the hinges are tape springs made from a single ply woven carbon fibre composite
of thickness 0.127 mm. The rod elements of the boom are a combination of pultruded carbon fiber rods and
hollow Aluminium rods. The pultruded carbon fibre rods are bonded to the connector pieces using Scotch
WeldTM 9323 B/A structural adhesive while the hollow Aluminium rods are pinned. The pultruded carbon
fiber rods are chosen because they introduce some structural compliance which allows less stiff tape springs
to be used. For the last two sections, however, hollow aluminium rods were chosen because of the need to
eject the payload from the space craft as quickly. The stiffness of the Aluminium results in less flexure in the
section as the hinges accelerate the payload from rest. The boom is attached to the base plate by screws.
Spacers are also attached to the base plate. These spacers are put in place to ensure that when the boom
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deployment envelope
y (m)
t=0s
t = 0.88 s
x (m)
Figure 9. Payload trajectory plot characteristic of a ‘driftback’ deployment failure
is folded the connectors for the second and third hinges have a contact area with the base plate. The final
connector is also machined with an angled face so that the angle required by the particular hinge can be
set. All of the connectors, except those of the last hinge have small holes to allow for the harness to pass
through. There are two holes, despite there only being one harness, in order to maintain symmetry in the
components.
A photograph of the manufactured boom and magnetometer in its deployed configuration is shown
in Fig. 10. A US quarter coin is included in the bottom left hand corner as an indication of scale. Key
components – the Aluminium connectors, pultruded CFRP rods, and the magnetometer itself – are indicated.
The magnetometer harness is not included as its specification is still in the process of being determined. The
predicted payload trajectory plot is shown in Fig. 11. It can be seen that the off-axis deviation is small:
8 deg. in the positive y-direction and 7 deg. in the negative y-direction, and that by the end of the analysis
time, the boom is oscillating in its first normal mode. From the payload trajectory, this can be seen to be
the cantilever mode. The quality of deployment, as assessed using Eq. 1, is Q = 0.04.
VI.
Conclusions and Further Work
This paper has presented the design process of a segmented deployable boom to place a magnetometer
approximately 1 m from a CubeSat. This was carried out by means of several linked finite element models
which were used to determine the deployment characteristics and the deployed stiffness. Key design parameters were determined and used to perform sensitivity studies to indicate the effect on predicted performance
of manufacturing and assembly errors. Dimensionless variables were developed in order to quantify the effect
of the parameters on the deployment quality and deployed frequency. A final design was reached which was
shown to meet the design specification; to be relatively insensitive to property variation; and to achieve a
high-quality deployment and adequate deployed stiffness.
It was observed, in trying to replicate the achieved deployment seen in the accurate model as closely
as possible in the idealized models that there were some particular shortcomings of the idealized models.
The most notable issue was that of idealizing the ‘constant’ region of the tape spring, i.e. the post-buckling
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Aluminium connector
pultruded CFRP rod
tape springs
magnetometer
Figure 10. Photograph of the fabricated boom and payload in its fully-deployed configuration
deployment envelope
y (m)
t=0s
t =1.5s
x (m)
Figure 11. Payload trajectory plot of the final design illustrating the straightness of deployment
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behaviour. Comparing the plot of moment vs. rotation, which can be seen in Fig. 6, it can be seen that at
180 deg. the difference between the actual moment and the assumed constant is quite significant. This turns
out to be critical to the deployment and results in very notable differences in the deployments.
When comparing the idealized models to the accurate model it was observed that the trajectories of the
payload and the individual hinges was not comparable. Since the mass of the payload is very large, with
respect to the entire assembly, the initial force required to eject it from the spacecraft is very important.
When idealizing the hinge, however, the constant is taken as the average value in this post-buckle region and
is therefore smaller, usually resulting in a deployment that experiences drift. In the accurate model the main
body of the boom was trailing behind the payload as it is ejected but while this happens for the initial phase
of the idealized deployment the main body of the boom soon bunches up behind the advancing payload.
Since they are still rotated through a large angle these hinges therefore still posses large amounts of potential
energy in a phase of the deployment which requires most of the hinges to be close to the locked position
in order to achieve an orderly deployment without any of the undesirable characteristics. In the accurate
model, the moment-rotation function can be seen to be ideal for this configuration. The initial moment is
high, setting the deployment in motion, but then begins to decay. This decay means that not too much
momentum is built up as the hinge approaches the locked position and reduces the chance of overshoot.
It is possible to compensate for the simplifications made in idealized models but modifying the value of
the constant moment assumed. Rather than taking the average, depending on the hinge being idealized,
the maximum or the minimum moment in this post-buckled region should be taken instead. For example,
by taking the payload hinge moment at 180 deg. and inputting this value as the constant for the idealized
payload hinge, the z-position of the payload replicates that of the payload in accurate model more closely.
For the main body of hinges, however, the opposite should be done. The minimum from the post-buckling
region, usually the moment reaction immediately after the peak, should be used since this gives a hinge
which is does not carry too much momentum as it rotates. Having completed the design and fabrication
of an initial test specimen, work is currently in progress to develop an air-bearing-based gravity offload rig.
This will be used to carry out deployment tests under representative conditions, and to measure the deployed
stiffness. It will also be noted that no consideration has been given to holding the boom in its high strain
energy stowed configuration. This will be the subject of future work.
References
1 CubeSat Design Specifications, California Polytechnic State University at San Louis Obispo, Revision 12, URL (accessed
12th March 2010) http://cubesat.org/images/developers/cds rev12.pdf.
2 Mobrem, M. and Adams, D., “Analysis of the Lenticular Jointed MARSIS Antenna Deployment,” In Proc. 47th AIAA
Structures, Structural Dynamics, and Materials Conference, 2006, AIAA Paper No. AIAA 2006-1683.
3 Seffen, K. and Pellegrino, S., “Deployment dynamics of tape springs,” Proc. R. Soc. Lond., Vol. 455, 1999, pp. 1003–1048.
4 SAMCEF v12.0-03 Finite Element Package, Samtech S.A., LIEGE science park, Rue des Chasseurs-Ardennais 8B-4031
Liège (Angleur), BELGIUM.
5 Yee, J., Soykasap, O., and Pellegrino, S., “Carbon Fibre Reinforced Plastic Tape Springs,” In Proc. 45th AIAA Structures,
Structural Dynamics, and Materials Conference, 2004, AIAA Paper No. AIAA 2006-1819.
6 Blevins, R., Formulas for natural frequency and mode shape, Van Nostrand Reinhold, 1979.
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