CUSRS10_02 FROGGER- Design and Fabrication of Pneumatically Actuated

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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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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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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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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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

Documents

CUSRS10_02 FROGGER- Design and Fabrication of Pneumatically Actuated