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Proceedings of the Bennett Conference on Mechanical Engineering
April 20, 2012, Pittsburgh, PA, USA
LANDING GEAR DESIGN AND STABILITY EVALUATION OF A LUNAR LANDER
FOR SOFT LANDING
Ahmet Sahinoz Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213
ABSTRACT A stable soft landing is crucial for a lunar roving mission to
maintain structural integrity of the lander to enable payload
operation as well as rover egress. This research develops legs
and evaluates energy absorption methods for an 800kg lander to
maximize landing capabilities for various touchdown scenarios.
Four telescoping legs with aluminum honeycomb cartridges are
utilized for energy absorption to limit the g-force experienced
by the spacecraft, where legs support the lander structure and
provide clearance to avoid impact with rocks.
Full scale landing on the moon is dynamically similar to 1/6
scale on Earth due to similar acceleration/gravity ratios. Drop
tests with a 1/6 scale model are performed in a motion capture
room to verify stability and required honeycomb stroke. A good
correlation is achieved between simulations and experiments.
The design provides a stable landing under the worst case
scenarios that are based on previous lunar missions.
1 INTRODUCTION
Planetary landers require compliant legs to touchdown
undamaged in a stable position, ready for operation. The proper
understanding of the mission requirements, reduced gravity
forces, lander mass properties, worst case touchdown scenarios
and the stowing space limitations of the launch vehicle are of
great importance in order to design an optimal landing system.
Challenges are to design for uncertain landing conditions and to
perform tests on Earth to simulate lunar gravity. Landing gear
must cope with the expected mass, velocity and orientation of
the lander at touchdown, in the expected range of terrains, and
doing so with minimal mass and a margin of safety.
Uncertainties include the mechanical properties of regolith,
slope of the surface and rock distribution.
Fig 1: Scaled model with Astrobotic Griffin lander (mock up
legs) and Red rover
The vertical velocity of the lander will be reduced nearly to
zero as a result of the deceleration provided by the main engine
during descent. Hazard detection identifies obstacles larger than
a threshold value, and finds a landing site. A horizontal velocity
component may be present due to targeting or hazard
avoidance. The main engine cuts off at a predetermined altitude
in the order of a few meters to prevent instability due to surface
effects. The touchdown occurs following a short free fall phase.
The resulting kinetic energy has to be dissipated over a finite
distance while providing sufficient clearance and a stable
landing [4].
A bottom-up design and test approach is utilized, starting
with the characterization of energy absorption materials,
proceeding with leg design and stability simulation, and
concluding with scaled drop experiments.
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2 BACKGROUND
The main configuration types are legged and pod landers.
Pod landers are not viable for the moon because there is no
atmosphere. Griffin lander utilizes four legs due to the geometry
and available connection points of the primary structure.
Energy absorption approaches include spring-damper
systems, airbags, and crushable materials. Any system including
fluids or gases would need hermetic sealing at vacuum. In this
project, crushable materials are considered due to their rigid (no
spring-back), simple, efficient and cost effective nature. Closed
cell materials such as synthetic foams cannot be used since the
air must escape from the crush material during flight as the
atmosphere density rapidly decreases. Aluminum honeycomb
and aluminum foam are available open cell crush materials,
where honeycomb is directional and foam is isotropic. Crush
materials can be incorporated into the struts of the legs, under
the footpads and/or the base of the lander. Force-stroke
characteristics can be adjusted to specific needs by stacking
crushable materials with different densities or cross sections.
Fig 2: Honeycomb, aluminum foam and synthetic foam
Surveyor landers used an inverted tripod leg design with
shock absorbers, where honeycomb under the footpad would
reduce the load if the foot lands on a rock, and the block under
the base provided extra energy absorption capability in case the
shock absorber reaches its limit. The landed mass of Surveyor
landers was about 300kg.
Fig 3: Surveyor landing gear design (one of three legs)
Deformation of the soil is an important aspect for footpad
design. Size of the footpad and the bearing strength of the
regolith determine the penetration distance. Surveyor had a
30cm footpad and penetrated 2 to 10cm with 1 to 4m/s vertical
velocity. Landing conditions are listed in Table 1 [1, 2].
Table 1: Surveyor landing conditions summary [2]
Apollo utilized a cantilever leg design with aluminum
honeycomb cartridges in all three struts of each leg. The main
strut has a compressive stroke only, whereas lower struts
incorporate a tensile stroke because they can experience both
types of loading. Due to space restrictions, legs have a folding
mechanism and they are stowed during launch and flight, and
deployed after separation from the launch vehicle [3].
The cantilever design creates a torque on the telescoping
interface that increases friction force and the design loads
significantly. The inverted tripod configuration eliminates the
bending torque, minimizing the design loads by creating almost
pure axial forces on all struts, but increasing the length of the
lower struts compared to cantilever design. Apollo used
cantilever design to achieve compactness when the legs are
stowed, due to the space restrictions of the launch vehicle [5].
Fig 4: Apollo landing gear and main strut design
Materials used in the design of landing structure are usually
high grades of aluminum such as 6061-T6 and 7075-T6, or
aluminum/titanium alloys. Although carbon fiber composite
structures are available, the brittle nature of these structures
may not be well suited for an application that requires
compensation for uncertainty, possibly with plastic deformation.
In addition, due to extreme temperature conditions, the
difference between the thermal expansion coefficients of
composite and metallic structures would have to be addressed.
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3 DESIGN CONSIDERATIONS
The design problem is defined by the specific requirements
for the mission, including lander properties and lunar
conditions. Landed mass of the spacecraft is in the range of
650-850kg depending on the fuel leftover and payloads. The
vertical acceleration limit of the structure is defined to be 10g’s
for Earth gravity (9.8m/s2). No strict limitation is put on the
horizontal component. Dynamic envelope of the launch vehicle
(Falcon 9) is 4.6 meters in diameter, which means the legs must
be contained within this circle. The hazard avoidance system
can detect rocks larger than 25cm with some error, so the
minimum clearance required is selected to be 30cm. Therefore,
the bottom of the lander is required to stand at least 30cm
higher than the ground after the landing. Slopes that are larger
than 10deg can be detected, so the lander may have a 10deg
angle with respect to the ground during touchdown. Angular
velocity is assumed to be negligible. Although nominal landing
velocities are 2m/s vertical with zero horizontal component, to
be conservative, the worst case scenarios are selected as 4m/s
vertical with 1m/s horizontal velocity, considering Surveyor
landings as a reference. Target mass for one leg is 5kg with a
safety factor of 2 [6].
Fig 5: Lander primary structure (from above and below)
The primary structure of the lander consists of a deck (3x3
meters), upper cone, lower cone and bulkheads illustrated in
gold. A rover sits on top of the upper cone; fuel tanks are
located within four holes on the deck; weight of the tanks is
transferred to the bottom ring through bulkheads, and the lander
is connected to the launch vehicle with a clamp band from the
bottom ring. Rectangular plates near the bottom ring between
the bulkheads alleviate stress concentration at the vertices
where bulkheads are touching the lower cone. They also
provide potential connection points for legs.
Lunar gravity is 1.63m/s2, 1/6 of Earth. Temperature has a
wide range from -100 to 120oC depending on the day time and
the region. The effect of temperature is neglected in this study.
Soil bearing strength increases with depth, starting from
0.2N/cm2 at 1-2mm and reaching 5.5N/cm
2 about 5cm. Friction
coefficient is reported being in the range of 0.3-0.7 [2, 3].
4 LANDING GEAR
Landing gear design concepts are evaluated starting from
the simplest configuration and proceeding to more complex
designs. Integrating crush material under the body is not
feasible because the bottom ring is not wide enough to provide
a stable landing.
The simplest form of landing gear would be four rigid legs
with crush material under the footpads. The novelty of this
design is simplicity, strength and rigidity. Welded connections
between the struts and the footpad eliminate the mass of any
type of connectors and/or hinges.
Fig 6: Rigid leg with crush pad design
Up strut is bolted to the lander via a welded plate at the tip.
Lower struts from two different legs share a triangular bracket
that is welded to them, and the bracket is bolted to the
rectangular plates. 10g acceleration requirement for a 650kg
lander results in an approximate total maximum force of 64kN,
16kN for each leg. The energy that needs to be absorbed is
equal to the kinetic energy of an 850kg (upper limit) lander with
4m/s velocity, and the absorbed energy is equal to the integral
of force-displacement curve of the crush material. Assuming
constant force is applied during the crush, for an ideal vertical
landing parallel to the ground, the stroke required to absorb the
energy would be 10cm.
The up strut is designed to be connected to the edge of the
deck, coming straight down to the footpad, while lower struts
connect to the rectangular plates. Thus, the base width is equal
to 3.5m, the diagonal across the deck. The up strut transfers the
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vertical force from the deck to the honeycomb where lower
struts provide stiffness in the lateral plane. Each footpad is
located 30cm below the bottom ring, providing the required
clearance. The material used in design is AL 6061-T6 due to
availability. Legs are analyzed in Solidworks for static yield and
buckling.
Fig 7: Solidworks static, buckling, modal analysis results
There are two options for materials, aluminum foam and
aluminum honeycomb. Detailed characteristics of these
materials and formulations are illustrated in [7, 8, 10].
Aluminum honeycomb is a directional lightweight energy
absorption material which provides constant force during the
stroke. It can compact as much as 70-80% of its original length.
Since the force is constant, the absorbed energy is equal to the
crush force times the stroke. The major disadvantage of
honeycomb is the drastic loss of strength with increasing crush
angle. When incorporated under the footpad, the energy
absorbed heavily depends on the horizontal velocity, and the
orientation of the lander which determine the crush angle. The
advantage of aluminum foam is its isotropic structure, but the
energy absorption efficiency is much less than honeycomb
which makes the foam significantly heavier [10, 11].
Fig 8: Honeycomb strength vs. crush angle [7]
Considering the bearing strength of the soil, diameter of the
footpad is chosen to be 45cm. In order to achieve 16kN of crush
force, honeycomb with crush strength of 15psi (~0.1MPa) must
be used. This is one of the lowest crush strength honeycombs
available in the market. It is inefficient to use low strength
honeycomb because the specific energy absorption
(energy/mass) increases with crush strength [9]. This design is
also sensitive to the rock distribution. If the footpad lands on a
20cm rock, the engaged cross-section is smaller, and loss of
absorption capacity will be more than 50%. These uncertainties
increase the required stroke from 10cm up to 25cm. There are
two potential issues if the footpad diameter is decreased to use a
higher strength material for efficiency. First, increased
penetration into the soil cuts from the clearance. Second, as the
honeycomb gets taller in height and smaller in diameter, it
becomes prone to breaking off from the footpad. The achieved
mass for one leg was 4.5kg with the crush angle limited to
20deg which is combination of the orientation and the angle of
the velocity vector.
Fig 9: Illustration of lander parameters vx (horizontal
velocity), vy (vertical velocity), planar landing scenarios (2-2
and 1-2-1), center of mass height (h), base width (b),
stability triangle (β), and sample velocity vectors v1 and v2
The higher the ratio between the base width of the landing
gear and the height of the center of mass, the more stable the
lander is against toppling over in the presence of horizontal
velocity and orientation errors. The additional honeycomb
height due to uncertain conditions increase the height and
decreases stability, which will also lead to a higher stance after
the landing, requiring the ramps to be longer to provide a safe
rover egress angle. For the rigid leg design, a rough stability
criterion is defined to give a baseline. The worst case is the
pads getting stuck to the soil. Defining the origin of the velocity
vector as the center of mass, if the vector lies within the stability
triangle illustrated in Fig 9 as v2, the landing is stable. If the
vector is aligned with the side of the stability triangle, the
vehicle is critically stable. If it is above the triangle (v1), the
tailing leg would lift from the ground. The energy required to
reach tip over angle is calculated from the resulting increase in
center of mass height due to the motion. If the energy from
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horizontal velocity is larger than this value, the landing might
be unstable. Assumptions include infinite friction and no
rotational energy absorbed by crush pads which is not realistic.
But since the crush of honeycomb depends on the angle, the
system cannot be evaluated in a realistic way with a simple
model. Issues such as the inefficiency of low strength
honeycomb, high sensitivity to landing conditions and footpad
diameter being tied to the crush force, led to the exploration of
other design options.
A telescoping leg design with honeycomb insert in the main
strut is an option that enables the use of high strength efficient
honeycomb. It also constrains the honeycomb to be crushed
along its main axis, eliminating all the variables that affect the
crush angle. The mechanical difference of this configuration
from the rigid leg is introduction of moving parts. The main
strut consists of two parts sliding in each other, has pin joints at
the top and bottom, with a bushing and a honeycomb insert
incorporated inside the upper part. The material for the bushing
is plastic and the structure is AL 6061-T6. For the lower struts
to rotate about the same axis, pin joints with a 15deg bend are
utilized, and they are connected to the rectangular plates on the
lander. Lower struts are welded to the footpad. All connections
at the strut ends are plugs, and these are designed to be bonded
to the struts with space approved adhesives.
Fig 10: Telescoping leg design (transparent main struts)
Previous missions either used crush materials inside, or
load limiters at the ends of the lower struts to limit horizontal
accelerations. The footpad is designed to be deformable in
order to absorb impact if excessive side loadings are present,
for example hitting a rock while sliding on the ground.
Fig 11: Footpad, lower strut hinge connection, main strut
honeycomb integration and cross section sketch
Center part of the footpad is thicker to keep three struts
connected to each other while the rest of it deforms. The top
section of the footpad is a dome, providing remarkable strength
with the same mass compared to a flat surface. A high strength
honeycomb is placed under the dome and a thin sheet of
aluminum is bonded at the bottom of the honeycomb to
minimize penetration and friction. The honeycomb stays intact
if the landing is on regolith, but partially deforms if there are
rocks on the contact surface, creating a deformable structure.
Fig 12: Footpad cross sections (w/o honeycomb)
Kinematic analysis is performed to determine the required
honeycomb stroke and crush force to produce a vertical
resultant force of 16kN and a displacement of 10cm for each
footpad. The stroke is only related to the leg geometry. But the
crush force is also dependent on the friction coefficient because
as the honeycomb crushes, legs move outward and this creates a
horizontal force, a resistance to the outward movement. The
acceleration experiences by the lander increases with friction.
Honeycomb should provide sufficient energy absorption at the
minimum friction expected and the acceleration should be kept
below 10g at the maximum expected friction. The inside
diameter of the main strut is set to be 63.5mm which provides
the desired forces with 750psi honeycomb, one of the highest
strength values available. It is 5 times more efficient than using
a low strength honeycomb under the footpad. This telescoping
leg configuration enables the footpad design to be independent
from the energy absorption design, and the system is less
sensitive to the uncertainties. Assuming that the lower struts
provide sufficient stiffness in the lateral plane, the main strut is
under pure axial loading. The connection of the main strut to
deck is shifted towards the tank to because when the deck is
loaded at the edge, it acts as a cantilever beam starting from
where the bulkhead ends. Thickness of the strut is reduced to
6
0.6mm since the welding consideration does not exist, and the
overall design is optimized to 4.5kg with a safety factor of 2.
6 STABILITY
Tip-over stability and honeycomb stroke are investigated
for telescoping legs in a motion simulation program, Working
Model 2D. The honeycomb crush depending on the crush angle
could not be simulated, but honeycomb inside the strut is
modeled utilizing a constant force spring which displaces under
compression and doesn’t extend. Two separate models are
created to simulate 2-2 and 1-2-1 scenarios, as shown in Fig 13.
Fig 13: Working Model 2D simulations (2-2 and 1-2-1)
The structure is rigid and the ground is an anchored block
with adjustable slope and position. Leg geometry is the same as
the lander. Mass, center of mass and rotational inertia of the
block are defined. The trick to imitate the behavior of
honeycomb is the combination of spring, rope and rod elements
that are available in the program with the right activation
conditions. The spring provides constant force during flight
where the rope holds the leg in place under tension. As long as a
leg hits the ground, spring is decompressed by some amount,
but it should stop acting as a spring as soon as the crush is over
to prevent bouncing. To do that, a rod element overrides the
spring at the instant when the length of the spring is below its
initial length and the velocity crosses zero and enters into the
extension region. The limit is tuned to be 0.05m/s because
setting it very close to zero causes chattering due to numerical
errors. Rods are coincident with the springs, and the ropes are
connected to the body for 2-2 and to the deck for 1-2-1.
Variables including the slope, initial velocity of the lander,
mass, inertia, friction coefficient and the spring force can be
altered. In 2-2 configuration, the springs provide 32kN force as
they are the combination of two legs. The middle leg of 1-2-1 is
also modeled with a 32kN spring, and ropes are placed in a way
that resembles struts. Single legs have 16kN springs. Run time
of each simulation is about 10 seconds at 1000Hz and 0.001m
accuracy.
In the simulation environment, linear and rotational
position, velocity and acceleration of each element, normal and
friction forces acting at the contacts, and reaction forces at pin
joints can be measured and recorded. These values can be
exported to a file which can be imported into Matlab for post
processing. The simulations provided valuable insight on the
kinematics and dynamics of the problem. The lander is proven
to be stable in the worst case conditions, and it is shown that the
honeycomb strokes are sufficient, but physical testing is
required to validate the results.
A full scale test is the most realistic option but it requires
extensive use of resources. Creating a scaled drop test platform
is representative and viable. An Apollo era study proved that the
free body drop tests of a 1/6 scale model on Earth produces
dynamically similar results with a full scale landing on the
moon. This similarity is achieved by adjusting the results from
the experiments with scaling factors (Appendix A). The reason
behind the perfect match of the results is the similarity of
acceleration/gravity ratios of each scenario [12]. Drop tests with
a 1/6 scale model of the lander is a feasible method to validate
simulation results. The parameters that must be considered are
leg geometry, total mass, center of mass height and rotational
inertia.
The inner diameter of the scaled main strut is equal to
12.7mm in which the crush material must be inserted. For this
purpose, samples from three different materials are prepared
and crushed with an Instron compression tester to obtain the
force-displacement curves. A total number of 9 samples, three
from each material are tested for statistical significance.
Fig 14: Instron tester and crush samples
7
Materials are 360psi and 690psi aluminum honeycomb
from Plascore, and 215psi Rohacell foam. Honeycomb samples
have a small number of unit cells, 7 cells for 690psi and 3 cells
for 360psi. The foam is tested to use it as a backup plan if the
honeycomb samples crush inconsistently. Samples are inserted
in a piston and the speed of the tester was set to 20mm/min.
Test results showed that the 360psi samples crushed with an
average constant force of 325N (400N expected) and the 690psi
samples crushed with 650N (700N expected), both by 70% of
their initial length (31.75mm) before the force increases rapidly.
Foam crushed with an average force of 185N (240N expected)
with a 60% stroke. Other plots are located in Appendix B.
Fig 15: Force-displacement plots of pre-crushed samples
The time frame of the landing is about 10ms for the scaled
drop with 690psi honeycomb cartridges that are equivalent to
10g on the full scale lander. To extend the time period of crush
for the purpose of having more data points with a finite
resolution measurement method, 360psi honeycomb is chosen
which would create about 5g’s on the full scale lander.
Fig 16: Scaled lander sketch and Solidworks model
The scaled lander is designed to satisfy the desired mass
property values within ±20% error. Legs and the body are made
of aluminum with bronze bushings and plastic footpads. The
body is a 275x275mm square which corresponds to the height
of the deck. Center of mass should be located 2cm above the
top surface of the body. The lower struts are solid rods that are
bolted to the footpad. The maximum available honeycomb
stroke is 45mm. The top part of the main strut is threaded onto
the clevis plug for quick honeycomb reload.
Fig 17: Scaled lander leg parts and assembly
Preliminary drop tests are done with springs, foam and
honeycomb. After the telescoping legs are proven to be strong
enough and the crush material is sufficient for energy
absorption, a counterweight is designed and positioned to
achieve desired mass properties.
Fig 18: Scaled lander (first version) with real lander
Desired mass properties of the scaled lander are calculated
with the scaling factors presented evaluated in Solidworks.
Large diameter holes are drilled to the body of the lander to
achieve desired inertia values with a total mass which falls
between 3-4kg that corresponds to a 650-850kg landing mass.
8
There are venting holes at the top of the main strut plug which
lets the air escape to minimize the force increase due to viscous
damping. After the counterweight is mounted, the total mass is
measured. The final form of the prototype is 4kg. Other
properties are evaluated only in Solidworks.
Fig 19: Scaled lander final version (w/o holes on prototype)
The drop rig consists of a stand with an adjustable height,
and a four bar mechanism with pitch adjustment to give an
initial angle and a horizontal velocity to the lander while
keeping the orientation the same throughout the swing. An
electromagnet with a switch is attached to the four bar swing as
a quick release to drop the lander.
Fig 20: Four bar illustration
Fig 21: Drop rig with the scaled lander attached
The experiments are conducted in CMU’s Motion Capture
Room, equipped with 15 high speed infrared cameras
distributed around the room that can track coordinates of the
markers on the lander at 480fps with 0.1mm resolution.
Cameras can be seen in Fig 22 as blue light emitting objects.
The shiny surfaces of the lander are covered with a blue tape to
eliminate reflections. Bolt heads are also covered to prevent
errors because the system is trained to detect spherical surfaces.
Fig 22: CMU Motion Capture Room (MOCAP)
Friction coefficient on the ground is measured by dragging
the lander with a spring scale. It is 0.5 on the ground and 0.3 on
plywood. The floor of the lab is plastic and has compliance.
Structural elasticity is present, different from the simulation.
9
9 markers are placed on the lander: 4 on each footpad, 4 at
the corners of the body and 1 on the counterweight in an
asymmetric position. Legs on the lander are named on the blue
tape from I to IV in a clockwise order.
Fig 23: Marker locations (note the asymmetry on top)
Honeycomb cartridges are pre-crushed to a desired length
in order to eliminate the peak load (Appendix B) and achieve a
tight fit. They are inserted into the main struts and the strut is
threaded onto the clevis plug which can be seen in Fig 24 as a
part sticking out diagonally from the corner of the deck.
Fig 24: Honeycomb reloading into the main strut
Honeycomb inserts are crushed with variable heights as can
be seen in Fig 25, depending on the landing configuration (2-2
or 1-2-1), velocity and orientation. A few of the cartridges
crushed significantly less than the expected value during the
experiments. The presumed reason is the lack of pre-crush.
The markers on the footpads are used to determine the
contact instant since they instantly stop when they hit the
ground. Markers on the body is utilized to extract the height,
velocity and acceleration of each corner, and to calculate the
center of mass accelerations by taking the average. Although the
center of mass is located 2cm above the surface of the body, this
method provides very close results and is sufficient. The marker
on the counterweight is used to identify the orientation of the
lander, and it can be used to calculate accelerations around the
rover if desired.
Fig 25: Leg view, crushed honeycomb samples, a marker
Pitch angle is calculated from two markers on the body
using the height difference and the known distance, between the
footpads (different for 2-2 and 1-2-1 orientations). Angular
velocity and acceleration are derived from the pitch angle with a
finite difference method. Presence of roll and yaw angles due to
the imperfect structure of the drop mechanism are neglected in
all calculations for practical purposes.
A total number of 10 landing scenarios with different
configurations, velocities and pitch angles are tested. Pitch
angles are disturbed at release due to the imperfection of the
swing mechanism. The predetermined angles are different than
real values. Thus, experiment results are generated, and pitch
angle and velocities are imitated in the simulations to compare
the results. Scenarios listed in the table below show the actual
touchdown conditions of five selected experiments.
Table 2: Landing conditions achieved in experiments
10
Fig 26: Result comparison for Landing 5
The time scale of the experiment is multiplied by 6, the
linear accelerations and the angular velocity are divided by 6,
and the angular acceleration is divided by 36 due to scaling
factors in order to correlate with the full scale simulation
results. Results are plotted, the continuous line being the
experiment where the discrete line shows the simulation results.
The comparison of simulations results to the drop test for
Landing 5 is illustrated above. Comparison values include pitch
angle (deg), angular velocity (deg/s), angular acceleration
(deg/s2); horizontal velocity (m/s) and acceleration (m/s
2);
vertical velocity (m/s) and acceleration (m/s2). The acceleration
values are lightly filtered in MATLAB to reduce cripples.
A full list of drop experiment landing conditions and the
results of other selected scenarios are in Appendix A.
7 CONCLUSION
Two landing gear configurations are designed, analyzed
and evaluated. Telescoping legs are preferred to rigid legs due
to energy absorption efficiency and robustness against uncertain
landing conditions.
Stability of the landing is investigated by a 2D motion
simulation. The lander is stable and the honeycomb strokes are
sufficient in worst case conditions. A scaled model of the lander
is prototyped and drop tests are conducted with various landing
conditions to verify the simulation results. Pitching motions,
center of mass velocities and accelerations were in good
agreement. The scaled prototype adequately reproduces 2D
landing dynamics and it is suitable for detailed studies.
Future work includes scaled drops on a lunar simulant with
high velocities to determine the bounds of stability. The effect
of structural elasticity could also be investigated. Manufacturing
full scale legs and performing drop tests with the real lander
would verify the structural integrity of the landing gear.
ACKNOWLEDGMENTS
The author thanks Red Whittaker, Uriel Eisen, Justin
Macey, Steve Huber, Kevin Peterson, Jason Calaiaro, William
Pingitore, Jason Hallack, Eric Benson, Kevin Fulton and Katy
McKeough for their support.
REFERENCES
[1] A. Ball, J. Garry, R. Lorenz and V. Kerzhanovich, 2007,
Planetary Landers and Entry Probes, Part I, Chap. 7.
[2] NASA, Surveyor Program Results, pp. 141-163
[3] Bryan, C., Strasburger, W., “Lunar Module Structures
Handout IM-5”, NASA LSG 770-154-10, May 1969
[4]Buchwald, R., Witte, L., Schroder, S., “Verification of
Landing System Touchdown Dynamics”, IAC-11.A.3.1.3, 2011
[5] Rogers, W.F., “Apollo Experience Report - Lunar Module
Landing Gear Subsystem”, NASA TN D-6850, June 1972
[6] Astrobotic Technology, “System Definition Review”, 2010
[7] Hexcel, “HexWeb Honeycomb Energy Absorption Systems
Design Data”, March 2005
[8] Hexcel, “Honeycomb Attributes and Properties”, 1999
[9] Plascore, 2012, “Crushlite Lightweight Energy Absorption”,
http://www.plascore.com/pdf/Plascore_CrushLite.pdf
[10] ERG Aerospace, “Duocel Foam Energy Absorption”,
http://www.ergaerospace.com/Energy-Absorbtion.html
[11] Chu, B., Jetson, O., Parkhurst, N., “Crash Absorption
Structure for Formula Ford, Use of ROHACELL in Motosport
Crash Worthiness”
[12] Blanchard, U., “Evaluation of a Full-Scale Lunar-Gravity
Simulator by Comparison of Landing-Impact Tests of a Full-
Scale and a1/6-Scale Model”, NASA TN D-4474, June 1968
11
APPENDIX A: SCALED DROP EXPERIMENT
Table 3: Scaling factors [2]
λ = Geometric model scale, β = Gravitational ratio
Table 4: Lander parameters (1/6 scale model, corresponding full scale, real lander values)
12
Table 5: Landing scenarios of all drop tests (pitch angle is affected by drop rig)
Test Results
- Accelerations are filtered; this enables the reader to see clear output, but decreases correlation at peak points
- Flat tests do not show correlation at angular and horizontal plots (on the left hand side) due to low signal/noise ratio
- Oscillations occur in real experiment due to compliance of ground and structure, simulations are rigid
- Position and height are shown as a reference, not compared with simulation
Fig 27: Landing 1 (Flat, µ = 0.5, Vx = 0, Vy = 3.3m/s)
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Fig 28: Landing 2 (Flat, µ = 0.3, Vx = 0, Vy = 3.3m/s)
Fig 29: Landing 3 (Configuration: 2-2, Pitch = 7.5deg, µ = 0.5, Vx = 0, Vy = 3.25m/s)
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Fig 30: Landing 4 (Configuration: 1-2-1, Pitch = 7.5deg, µ = 0.5, Vx = 0, Vy = 3.25m/s)
Fig 31: Landing 5 (Configuration: 2-2, Pitch = 11deg, µ = 0.5, Vx = 0.4, Vy = 3.25m/s)
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APPENDIX B: CRUSH MATERIALS
Fig 32: Representative aluminum honeycomb behavior [9]
Fig 33: Representative aluminum foam behavior [10]
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In-strut Crush Test Results
Initial length: 31.5mm
Units: Force (N), Displacement (mm)
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