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8/2/2019 CUSRS10_02 FROGGER- Design and Fabrication of Pneumatically Actuated
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2010 COSGC Space Research Symposium Page 1
FROGGER: Design and Fabrication of Pneumatically Actuated
Mars Exploration Rover
Stacy Jonett, Joseph Kennedy, Tim Schneider, Ian Smith
Colorado State University
Dr. Azar Yalin; Grant [email protected]
April 17th, 2010
AbstractOwing to the difficulties encountered by NASA in trying to
liberate the Mars rover Spirit, which had become stuck in
sand earlier last summer, a Colorado State University
DemoSAT team elected to design, fabricate and test a
jumping Mars rover. The goal was to demonstrate
pneumatic actuators as a viable method for the
dislodgment of rovers in unpredictable terrain. The team
focused on a hybrid rover having wheels to navigate
terrain but also with an on board pneumatic system to
launch itself to a height of approximately one meter as
could be needed in precarious situations. A preliminary
design was developed and fabricated from the results of
calculations and experiments. The initial Frogger unit
with weight of thirty pounds could jump to a height of 2.5
feet with a gage air pressure of ninety psi. Currently,
Frogger is undergoing major redesign in an attempt to
reduce mass and improve reliability.
1. Introduction
The purpose of this Mars rover prototype is to prove
that pneumatic actuators are a viable option for dislodging
Mars rovers in unpredictable terrain. The idea of
developing a pneumatically actuated Mars rover was
selected after learning of the difficulties encountered by
NASA in trying to liberate the Mars rover Spirit, which
had become stuck in sand during the summer of 2008 The
group decided to look into the possibility of using the thin
Martian atmosphere, consisting of mainly carbon dioxide,
as a resource to benefit the rovers. On Mars, a rover could
use solar or nuclear power to compress the thin CO2
atmosphere, as shown in figure 1, into large pressure
reservoirs. These pressure tanks could then be used to
power pneumatic actuators that would dislodge a rover ifit were to become stuck like Spirit.
2. Project Requirements
To design a pneumatic prototype the DemoSAT team
first had to develop and define realistic requirements in
order to define concept viability and they were as follows:
PRIMARY OBJECTIVE
The rover will jump a minimum of 1 meter on earth: This requirement will sufficiently demonstrate that
the pneumatics system is capable of propelling the
rover to a height many times higher than what isnecessary to simply dislodge the rover if it were to
become stuck. It will also show that the rover design
is capable of withstanding the impacts from landing.
SECONDARY OBJECTIVES
The rover will drive at least mile on a singlebattery charge: The budget for this prototype did not
allow for solar panel integration or other alternative
power generation. A DC motor driven system was
used because the rover will not consume excessive
amounts of power during normal operation.
The rover will navigate inclines of at least 45degrees: This was to measure the rovers ability to
navigate through tough terrain. By designing therover with enough torque and traction to lift itself up
steep inclines, it is more likely to be able to navigate
over obstacles, such as rocks, without difficulty.
The rover will drive at a minimum speed of 3 in/s onflat ground: This specification was chosen based on
the top speed of the current Mars rovers, Spirit and
Opportunity, which travel at 2 in/s. A 50% increase
in speed was chosen due to the reduced size and lack
of additional payload of the prototype.
Figure 1: Mars with thin CO2 atmosphere visible
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2010 COSGC Space Research Symposium Page 2
3. Original Rover Design
In the original rover design the team focused on the
development of five major systems in order to meet all
criteria. These systems were categorized as the
pneumatic system, the electronic control system, the drive
train system, the suspension system, and the frame andbalance system.
The pneumatic system dealt primarily with the
placement, size, and quantity of the actuators. Electronic
systems focused primarily on the integration and timing
of the drive systems and pneumatic systems into a remote
control unit. The drive system focused on the number of
motors and type of wheel motion. Both a tank tread and
conventional wheel design were considered with tank
treads being the final choice in the original design due to
the rough Martian terrain. In addition to the rough terrain,
the impact forces that are associated with a jumping
rover dictated that the rover has a robust internal
suspension system in all three axes in order to support themore sensitive components such as the electronics and
pneumatics. All of these systems need to be
accommodated in a strong, but relatively lightweight and
compact frame. Given the possibility that after the launch
the rover could land either right side up or upside down, it
was decided to design the rover to work in either
orientation.
During the design process, weight was a large
concern. Many of the simple components could only be
purchased as-is, restricting weight control. To
compensate, most of the parts were custom manufactured,
including the wheels and pneumatic actuators, to reduce
weight in those areas.
Due to the lack of an external suspension system, the
frame, wheels, and two drive motors received the majority
of the impact forces during landing. To compensate,
these components were made larger and stronger, but also
heavier. A table of the original rovers major components
and their weight allocations can be seen in Table 1.
After a weight estimate was calculated, the actuators
force, drive motor torque, suspension spring stiffness, and
component strength was adjusted accordingly. This was
mostly an iterative process, but detailed calculations of
actuator design, suspension spring selection, motor and
battery selection, and frame strength can be found in the
appendices.
3.1. Pneumatic Actuator Design
Actuator orientations were analyzed base on a one,
two, or four actuator system. Using only one centralized
actuator, launch stability had a high probability of being
sacrificed, and four corner pinned actuators would
significantly complicate the design and manufacturing as
well as add unnecessary weight.
Therefore, a two in-line actuator system was
developed along the center of the rover, with the center of
gravity at the approximant midpoint. The actuators were
designed to fit an arbitrarily set rover size. This design
attempted to maximize the stroke length and bore sizegiven the set size of the rover. The largest size actuator
that could be accommodated was a 1.875 inch diameter
cylinder with a stroke length of four inches. At that size,
a calculated pressure of about 90 psi would be required to
launch the rover 1 meter. Taking these values as
constants, failure modes were determined and
components were sized and given relatively large safety
factors to prevent possibly dangerous failures of the high
pressure actuators. The actuators were then manufactured
and assembled for preliminary testing to verify they
functioned as predicted. The original design can be seen
in Figure 2.
Component Weight (lbs)
Center Support Bars and
Actuator Tilt Drive Assy.
6.1
Wheels (4) 4.3
Frame 4.2Pneumatic Actuators (2) 3.1
Batteries 2.7
Valves and Fittings 2.2
Suspension Springs 1.9
Drive Motors (2) 1.6
Compressor 1.0
Drive Belts (2) 0.4
Tank 0.3
Roller Chain 0.1
Total Weight 27.9
Table 1: Component Weight Budget
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2010 COSGC Space Research Symposium Page 3
3.2. Electronics Design
The main emphasis of the project was to demonstratethe use of pneumatics in a Mars rover therefore the
electrical design was kept relatively simple. While the
rover was not made to be autonomous, electrical
components were still needed to interface the rovers
functions to a remote control. For each motor, high
current H-bridges were designed and built by soldering
four bipolar junction transistors (BJT) onto custom etched
circuit board. The two valves are also triggered using
high-current BJTs. Short programs were written in Basic
to interface these functions with the remote allowing for
drive, actuator tilt, and actuator launch controls. Figure 3
shows a functional block diagram.
3.3. Power train Design
Two designs were investigated for the power train
design; a track-and-wheel combination verses a 2-wheel
drive system. The track-and-wheel combination was the
preferred driving method because of the ability to utilize
slip steering and the added benefit of increased traction.After several tests using gears, belts, and a chain and
sprocket driven system, the chain drive proved to be the
most effective option for power transmission providing a
reliable and durable way to transmit power to the wheels,
without slip, while allowing for a gear reduction. An
example of the chain and sprocket transmission system
can be seen in Figure 4.
A two motor combination was selected, as opposed to
four motors because of cost and weight efficiency. The
motors were selected using three criteria: weight, current
draw, and stall torque. The weight and nominal current
draw was to be kept as low as possible for the purpose of
long range use and power efficiency. A torque largeenough to theoretically drive the rover up a 90 degree
incline was chosen so that the rover would have plenty of
power to climb hills. Matching the speed of 3 in/s was
not a limiting factor and was easily surpassed.
Power was supplied by three-eight AA packs battery
packs wired in parallel due to ease of replacement and its
light weight.
Figure 3: Functional Block Diagram Figure 4: Picture of the rovers motor, chain
drive, and wheel with the track removed.
Figure 2: CAD model of the pneumatic actuator
design to launch the rover to a height of 1 meter.
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2010 COSGC Space Research Symposium Page 4
3.4. Suspension Design
To provide suspension to critical components in all
three axes, a three dimensional mass and spring design
was adapted. Several variations of this design were
discussed with the final consensus being that an internal
system would be better than having an external system.This decision was based on the fact that if the springs
were on the frame, they would be subject to direct impact
during some landing scenarios, possibly damaging the
springs and impairing their functionality. The tradeoff
was that the pneumatics and electronics systems must
now be separated into two separate bays on each side of
a suspension component that goes directly down the
middle of the rover (See Figure 5), while avoiding the
actuators that are also in this area. The springs were sized
according to the estimated weight so that the suspended
components would be cushioned by the springs for any
fall under 3 feet without the springs fully compressing.
3.5. Frame and System Layout Design
The original frame design was developed to maximize
the frames strength while minimizing its weight. Again,
due to no external suspension system the frame needed a
high level of strength to endure impact forces. The wheels
were slightly offset from the frame for a more compact
design as shown above in Figure 5.The pneumatic and electronic components are mounted
together, and suspended by springs and designed to
translate in any direction. Extra space is necessary to
prevent these components from colliding with the ground
or with the frame during spring compression. In addition,
these components also need to be positioned to keep the
keep the center of gravity directly between the two
actuators.
4. Testing Results
Repeated testing was performed in parallel with
manufacturing to ensure manufactured components and
systems functioned as planned.
Testing was first performed on the pneumatic
actuators to obtain performance capabilities needed to setother design criteria. Testing consisted of manufacturing
a rough model functionally identical to the actual design.
Numerous tests were performed with the actuator model
by launching various weights at varying pressures and
recording the varying launch heights. The test data
formed a consistent linear fit, and the required pressure to
reach the required height of 1 meter was predicted. The
required pressure predicted from experimentation
consistently read about 30% above the calculated values,
likely due to fluid flow inefficiencies and friction. Figure
6 shows this test data.
Drive testing was done to verify that power could
successfully be transmitted from the batteries to the track
system. The three AA battery packs were found to supply
the motors with sufficient current, and a fourth battery
pack did not add any visual benefit.
The three different power transmission systems were
also tested: gears, belt drive, and chain drive. Gears
required high precision to mesh properly, and there were
concerns that the plastic gears teeth might shatter during
impact. The belt drive worked, but did not provide the
necessary grip when placed under high-torque situations.
The chain drive was selected after numerous successful
tests.
The track system for the wheels was also fine tuned
during the drive test. It was noticed that minute changes
in the wheel placement had dramatic effects on the
tracking system alignment. Spacers were added to either
side of the wheel to aid in keeping the tracks aligned and
seated.
The climb tests were performed to find the rovers
maximum angle of attack. After each successful test, the
angled surface was set to a steeper angle. Discrepancies
Figure 5: CAD model of the rover with select
components removed to show the frame details
Fi ure 6: Pneumatic Actuator test data and
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between the measured motor torque and the manufactures
claim, along with a heavier than expected rover weight
limited the climbing angle to between 15 and 20; far
short of the goal of 45.
Pressure testing was performed on the air tanks to
ensure that they could withstand pressure up to 100 psi
and possible impact loading. Testing was carried out by
inflating the pressure tanks to excessive pressures, and
subjecting the tanks to significant impact loads by
repeatedly hitting the bottle with a 10 foot steel rod. The
bottle never exploded, but the cap failed at higher
pressures as seen in Figure 7. Epoxy has since been
added to the cap to increase strength.
Post-assembly tests consisted of drop testing,climbing, and jumping. The drop test consisted of a three
foot drop with the rover at varying orientation onto a tile
floor. With the exception of minor frame deformation
when landing from its known worst possible orientation,
all tests were successful. The deformation was minor,
and future landings in this orientation are extremely
unlikely.
The jump test reached just over two feet at ninety-
five psi shown in Figure 8. While the expected height
was closer to 3 feet, the jump tests were preliminary and
minor modifications between the initial tests and final
assembly should increase the jump height about six more
inches, bringing us closer to the one meter (three foot)goal.
5. Conclusions
During the designing, manufacturing, and testing of
the rover, much was learned about what it takes to employ
a pneumatic jumping mechanism. After completing the
project, there is enough empirical evidence to argue that
pneumatics actuators are indeed a practical means of
dislodging Mars rovers. With the budget and time
allotted, this rover prototype is a simplified demonstration
of how such a system would work. By demonstrating
how a thirty pound rover can jump over two feet on earth
with one hundred psi and two actuators, it can be
extrapolated and inferred what a similar system would
look like on larger applications. By making a few
hypothetical design decisions, the mass a rover that could
successfully employ a pneumatics system on Mars could
be estimated. Assume the following occurs in order to
accommodate a larger rover:1) A rover only needs to jump 6 inches to
become dislodged.
2) The rover is jumping on planet Mars, with 1/3the gravity of earth.
3) Four actuators are used, instead of two.4) Each actuator is double the size of the current
actuators.
5) The tank pressure is 4500 psi (the pressure ofmany carbon fiber high pressure tanks)
With these assumptions in addition to the
experimental tests that yielded a linear relationship, the
allowable rover weight to successfully use this setup can
be extrapolated to over 60,000 lbs. That is,
(4 times less jump height) * (3 times less gravity) * (2
times the number of actuators) * (2 times the size of
the actuators) * (45 time the pressure) = 2160 times
experimental rovers weight! That comes out to
2160*30 lbs = 64800 lbs.
Figure 8: Rover beginning to lift off the ground
during a jump test.
Figure 7: Air tank trajectory for the first quarter
second after ca failure.
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2010 COSGC Space Research Symposium Page 6
The basic design without modifications could propel
the 400 lb Sprit and Opportunity rovers to a height of just
over 5 inches with the help of Mars low gravity. Such a
jump would likely be enough to dislodge the rover from a
stuck position.
(3 times less gravity) * (24 inches on earth) * (30lbs
experimental rover / 400lbs Spirit Rover) = 5.4
inches
6. Improvement Suggestions Based on Tests
After the completion of experiments and the design
process, the original design was not the most ideal option
for employing a pneumatically actuated system in a Mars
rover. The original design has shown that using
pneumatic actuators to launch the rover is a viable option,
which was the purpose of this prototype, but in order to
get a feel of real applications, a new prototype would
need to be manufactured utilizing the followingimprovements:
1. Lighter weight, non-electrical conductivematerials. A lighter design would be more
beneficial in reducing required inputs to get the
desired output, which would allow for the
addition of payloads to the chassis.
2. A new chassis design consisting of an improvedsuspension system. The current system doesnt
protect the drive motors at all. In addition to the
motor issues, testing results yielded that the
rover lands approximately flat relative to the
launch surface 90% of the time. The majority of
the current suspension system was designed to
allow for in flight reorientation and landing,
which means the majority of the current
suspension system is rarely utilized.
3. The containment area used in housing electronicsand pneumatics would need to be enclosed and
ideally combined into one unit instead of two. It
would be beneficial to the pneumatic system if
the majority of the pneumatics could be run
inline instead of jumping to odd orientations in
order to minimize tubing necessary to transport
high pressure air.
4. The application and use of CO2 gas should beemployed instead of compressed air, with
possible research into liquid CO2 or dry ice aspropellant, which means introducing thermal
insulation or even thermal heating, into the
pneumatic line to keep the CO2 from freezing
when released from a pressurized container.
5. Large improvements can be made to theelectrical system including the addition of solar
panels to charge batteries, use of pressure and
temperature sensors to regulate gas pressure and
consistency, range, tilt, and acceleration sensors
to better control pneumatic launches and
landings, and integrating all of this into an
autonomous system.
7. Benefits to NASA Community
The completion of this objective has shown that
pneumatic systems could be practically employed in
larger applications with the use of higher tank pressure in
conjunction with more and/or larger actuators. In
addition to the ability to get rovers dislodged from rough
terrain, the ability to trigger a pneumatic launch while in
driving motion and clear obstacles also has certain
appealing aspects such as the ability to gain access to low
level mesas, plateaus and buttes currently inaccessible to
present day rovers. Looking beyond the rover
application, the integration of pneumatic actuators into
new Mars missions would be advantageous. Making
pneumatic actuators an addition into human controlledspace suits would allow the controller the ability to gain
access to and explore low level or large obstacles with a
couple of well placed jumps instead of trying to hike
around and find a suitable climbing path, which would
increase exploration range and better utilize exploration
time.
8. Lessons Learned
If the opportunity to redo this experience was
presented, less weight would provide more options with
better results. Carbon fiber and high density polyethylene
were not used for the frame, which would havesignificantly reduced the weight, due to a lack of
knowledge and experience with these materials. Given a
10 week project schedule, it was not feasible to gain the
required knowledge of the materials or the skill set to
work with the materials. With a lower frame weight the
team could have employed smaller motors, actuators,
used smaller, low pressure tubing, producing an overall
smaller product thus reducing the weight and increasing
performance. The reduction in weight would allow for a
reduction in required air pressure to achieve the desired
results along with a reduction of impact forces on landing
which would have been extremely beneficial.
Another lesson learned would be to design thesubsystems layout for the pneumatic system and electrical
systems before or at least in conjunction with the design
of the chassis. One of the largest problems we
encountered was trying to integrate subsystems into an
arbitrarily set amount of space when the parts ordered
after design didnt fit well into the allotted volume.
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9. Rover Upgrades to DateSince the completion of the original prototype shown
in figure 9, Frogger, in comparison, has seen a complete
redesign as seen in figure 10. The steel and aluminum
frame has been replaced with high density polyethylene
and ultra high molecular weight polyethylene. These
plastics were chosen due to their relatively high tensilestrength as well as their flexural strength. The increased
flexibility of the frame allows it to work as the suspension
system. This allows the internal systems to be directly
attached to the frame. See figure 11. In addition the track
system has been removed and replaced with a four wheel
drive system. Figure 12 shows the redesigned pneumatics
system which has been modified to run inline utilizing
pipes instead of tubing to increase the reliability of the
system as well as the functionality of the cylinder
rotation. Figure 13 show the updated cylinders
themselves, which have been redesign using UHMWPE
instead of stainless steel for the casing. A half inch
diameter titanium piston rod replaced the old quarter inch
1018 steel rod, and again the piping replaces the old
tubing. The electronics use a fully digital remote control
to reduce the number of misfires that occurred from using
a mixed digital/analog controller. The principal
components have been removed from the original rover
and are ready to be mounted in the newly upgraded
Frogger which is currently in the process of being
machined.
Figure 9: The origanal rover assembly.
Figure 10: The current Frogger design.
Figure 11: Notice the four wheel drive system and the
three point corner braces for the suspension system.
Figure 12: The pneumatics system is now run inline
improving efficiency, and actuator motion.
Figure 13: Upgraded pneumatic cylinder. Utilizing
pipe instead of tubing, and a titanium pistion for a
better weight to strength ratio.
10. References
[1] E.Oberg, F.D. Jones, H.L. Horton, and H.H. Ryffel,
27Machinerys Handbook, Industrial Press, New York,
2004.
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11. Appendices
Frame Strength:
Assumptions:
Dtube 0.75in ttube 0.0625in Ltot 16in Fmax 151lbf Lbeam 20in
Calculate the Bending Stress:
Mbend ymax
I
Find Bending Moment:
Mbend
Fmax
2
Lbeam
2
Mbend 755 lbf in
Find Moment of Inertia:
I
64Dtube
4Dtube 2 ttube
4
I 0.008041in4
Find "y max":
ymax
Dtube
2
ymax 0.375in
Determine Bending Stress:
y_alum 21000psi y_steel 63250psi
max
Mbend ymax
I
max 3.521 10
4 psi
0.931 0.593 0.338
SFalum
y_alum
max
SFsteel
y_steel
max
SFalum
0.596
SFsteel
1.796
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Determine Weight:
steel 0.23lbm
in3
alum 0.0975lbm
in3
Find Cross Sectional Area:
Across_sec_tube
4Dtube
2Dtube 2 ttube
2
Across_sec_tube 0.135in
2
Find the Total Frame Weight:
Wtot_alum alum Across_sec_tube Ltot Wtot_steel steel Across_sec_tube Ltot
Wtot_alum 0.211lb Wtot_steel 0.497lb
Determine Strength To Weight Ratio:
SWRalum
y_alum
alum
SWRsteel
y_steel
steel
SWRalum 5.775 105
ft
2
s2
SWRsteel 7.373 105
ft
2
s2
Spring Calculations:
Longitudinal Springs Calculation:
Assumptions:
k 51lbf
in
xfree 4.18in xsolid 2.1in mtot 12lbm
Nsprings
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Calculate Drop Height (Using Energy Method):
*** There will be a "limiter" that prevents the opposing spring from pushing in the direction of impact. (Undesirable).
m g h1
2k xf
2xi
2 2.5 g h
1
2k xfree xsolid
2xfree xprecomp
2
h
1
2k xfree xsolid
2xfree xprecomp
2
mper_spring g h 2.577 ft
Calculate Drop Height (Using Kinematic Equations):
Favg
kxf xi 2
Favg
k xfree xsolid xfree xprecomp 2
Favg m aavg Favg 74.205lbf
aavg
Favg
mper_spring
aavg 795.825ft
s2
aavg_spring aavg aavg_spring 242.567m
s2
V 2 a s Vspring Vfall
2 aavg_spring sspring 2 agravity sfall aavg_spring xprecomp xsolid g sfall
sfall
aavg_spring xprecomp xsolid g
sfall 2.577ft
Calculate Maximum G-Forces
Frebound k xfree xsolid Frebound 106.08lbf
F m a
arebound
Frebound
mper_spring
arebound 1.138 103
ft
s2
Gsarebound
g Gs 35.36
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Actuator Pressure Calculations:
xfall 1m "Fall" height and/or jump height
g 9.807m
s2
Force of gravity
xtakeoff 4in Stroke of the actuator (length of acceleration)
mass 20lbm Mass launched per actuator per cylinder
Dpiston 1.875in Actuator piston diameter
x xo v0 t1
2a t
2 General Kinematic Equation Eqn. 1
xfall1
2
g tfall2
Initial x and v equal zero, and are removed. a = gravity
tfall
2xfall
g Previous equation (Eqn. 1) rearranged
tfall 0.452s The time it would take to fall from the "fall" height and/or jump
height
v a t General Kinematic Equation Eqn. 2
Vfall g tfall Equation 2 with gravity substituted for the acceleration
Vtakeoff Vfall The initial velocity of launch will equal the velocity at the end of the
fall
Vtakeoff 4.429m
s The required takeoff velocity to reach the predetermined jump
height
v2
v02
2 a General Kinematic Equation Eqn. 3
Vtakeoff2
2 atakeoff xtakeoff The initial velocity is equal to zero and was removed
atakeoff
Vtakeoff2
2 xtakeoff The previous equation (Eqn. 3) rearranged
This is the acceleration required to achieve the required velocity in
the predetermined actuator stroke distance.
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atakeoff 96.522m
s2
F ma Newton's Second Law Eqn. 4
Ftakeoff mass atakeoff Substitution of Variables into Eqn. 4This is the constant force required to accelerate the predetermined
mass to the calculated force in order to achieve the predetermined
height.
Ftakeoff 875.634N
Factuator Ftakeoff mass g The actuator force must also overcome the Force of gravity to lift
the predetermined mass against gravity.
Factuator 964.599N This is the force that the actuator must supply to accelerate the
predetermined mass to the calculated force in order to achieve thepredetermined height.
A D
2
4 Equation for the area of a Circle Eqn.5
Apiston
Dpiston2
4 Eqn. 5 rearranged
Apiston 2.761in2
This is the area of the piston
Pactuator
Factuator
Apiston
Pressure Equation Eqn. 6
Pactuator 5.415 105
Pa This is the pressure required to launch the predetermined mass to
the predetermined height. (With experimental actuator's specs)
Pactuator 78.536psi
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Pneumatic Cylinder Failure Calculations:
Goal: Verify the structural integrity of the pneumatic actuator by performing failure analysis calculations for all
anticipated modes of failure.
Possible Modes of Failure:1) Cylinder Bursts
2) Tie Rod Yielding Due to Tension
3) Top of Cylinder Shears Due to Impact
4) Threads Strip
*Fatigue is taken into account in the safety factor. Under 1000 cycles, 90% of the initial strength of the material is
retained, making fatigue calculations negligible.
CylinderTop
FAxialMax
Ashear
Impulse Calculations (to be used in failure analysis):
Assumptions (worst case):
mLaunchStructure 0.5lb Per cylinder.
hjump 1m
xaccel1
8in 1 1/8in washer and one 1/16in washer (assuming not fully
compressed, that is why we use 1/8, not 1/8 + 1/16)
Find Takeoff Velocity:
Vtakeoff2
2 g hjump
Vtakeoff 2 g hjump
Vtakeoff 4.429m
s
Find Acceleration of Launch Structure:
Vtakeoff
22 a
LaunchStructure x
accel
aLaunchStructure
Vtakeoff2
2 xaccel
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aLaunchStructure 3.089 103
m
s2
Find the Force (per cylinder) Due to Impulse of Launch:
FAxialMax mLaunchStructure aLaunchStructure
FAxialMax 0.701kN
FAxialMax 157 lbf PER CYLINDER
1) Cylinder Burst - Failure Analysis:
Assumptions (worst case): Cylinder will initially be under compression; however, this was neglected because the worst
case will occur when the cylinder is loaded in tension.
twall1
16in
SteelYield 234MPa
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Von Mises Stress:
1 hoop Defined Above
Force Per Rod Using the Maximum Axial Force Due to Impulse from Takeoff:2 times the maximum axial load because the rod will initially be preset in tension to a value that is near the maximum
axial load in order to avoid leakage during the small periods of time when the actual load is applied. Ideally, the value
would be at least 2x, but it is unlikely that this will actually be true. 2x is probably a safe number, it will likely have lower
initial tension.
FRodMax
2FAxialMax
NumberOfRods FRodMax 0.35 kN
Cross Sectional Area of the Tie Rods:
Arod Drod
2
4
Arod 7.917 106
m2
Maximum Axial Stress of the Tie Rods:
rods
FRodMax
Arod
rods 44.239MPa
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Calculate the Safety Factor of the Tie Rods:
SFrods
SteelYield
rods SFrods 5.289
3) Top of Cylinder Shear Yielding - Failure Analysis:Assumptions (worst case):
AlumYield 110MPa Aluminum Alloy 6061-T4
tshear1
8in
Shear Strength of Aluminum:
AlumYield 0.55 AlumYiel AlumYield 60.5 MPa
Shear Area:
Ashear 2 rcylinder tshear Ashear 4.75 104 m
2
Shear Stress:
CylinderTop 1.475MPa
Calculate the Safety Factor of the Top of the Cylinder:
SFshear
AlumYield
CylinderTop SFshear 41.027
4) Thread Stripping - Failure Analysis:Similar to Tie Rod calculations, we will use a value of 2x the maximum axial force to represent a static force on the
threads. This value is chosen because the rod will be under an initial tensile force in addition to the maximum axial force
from the impulse of takeoff.
Assumptions (worst case):
Stainless Steel 302A Rods and Nuts ---> Defined Above
Nrods 4
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Stress on threads:
threads
4 2FAxialMax
Nrods
do2 di2
pcoarse
tnut
Eqn. 10.10 in Machines Book
The "2" is explained above.
threads 136.538MPa
Calculate the Safety Factor of the Threads:
SFthreads
SteelYield
threads SFthreads 1.714
Conclusion (Before changes of launch structure weight and extra rubber washer thickness):
The chosen materials and thicknesses are probably sufficient; however, to maximize strength, the following should be
done (in order of importance).
1) Add extra-thick rubber washers to minimize the maximum axial force! (VERY IMPORTANT)
2) Minimize the weight of the launch structure to minimize axial force.
3) Increase the shear thickness on the top of the cylinder.
4) Increase the thickness of the tie rods if need be (however, this will add weight).
5) Increase the threaded thickness (or number of nuts) if need be.
6) Using higher quality materials or adhering to more realistic assumptions will help the safety factors all around. Thesafety factors shown are Worst Case.
THICK RUBBER WASHERS IS, BY FAR, THE MOST IMPORTANT!
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Motor Calculations:
Design Constraints:
Wtot 30lbf Dwheel 8in
Calculate Stall Torque Required to Climb a Vertical Wall:
We are calculating this unrealistic situation so that we can be positive that the rover will not be short of the requiredtorque.
Assumptions:
Nmotors