Loads, Structures, and Mechanisms Design Project

Team C4Jason Burr, Rebecca Foust, Samantha Johnson, Kiran

Patel, and Dennis Sanchez

Mission Objectives• Structural Analysis:

– Crew Vehicle– Lunar Landing Vehicle

• Crew Vehicle– Earth Launch

• Pressurization Loads• Docking Loads• Lunar Landing Loads• Earth EDL

• Landing Vehicle – Basic design

• Inert mass: 2199 kg• Propellant Mass (N2O4/MMH): 9914 kg• Payload: 12,110 kg

– Landing Gear Analysis• Touchdown velocity 3 m/s vertical, 1.5 m/s horizontal

Crew Capsule Selection

• Jason’s crew capsule was selected because it has no external elements like radiators or solar arrays

• It also has the highest mass margin, so we have the most mass available for our structural design

CREW VEHICLE

Pressurization Stresses in a Conical Head

“Analogous to the maximum stresses in the cylinder, there are maximum stresses in the conical head…However, in contrast to the

cylinder, it is not possible to establish simple expressions for the three stress indexes…”

Stresses in a Pressure Vessel With a Conical Head

For this reason we will model our cone as a cylinder to find pressurization loads.

Pressurization Loads• Cabin Pressure throughout mission = 59.77kPa

• Hoop stress on cabin = 1.067 MPa• Longitudinal stress on cabin = 533 kPa

– Hoop stress will cause the structure to fail before longitudinal stress can cause failure

Total Pressurization Stress = 1.067 MPa

Pressurization stress will occur at all times and is added into all total stress values

Earth Launch

• Use Falcon Heavy to launch to LEO– Can carry 53,000 kg to LEO

• Max Thrust = 11,200 kN– Force at payload = 587 kN

• Stress from thrust = 538 kPa• Random Vibrational Stress = 181 kPa

Temperature Variation in Atmosphere

Earth Launch

• Thermal loading occurs as payload travels through different layers of the atmosphere.– Max temperature difference = 80 K

• Thermal stress = 122.5 MPa

Total Stress at Launch = 124.3 MPa

Lunar Landing Loads

• Maximum G force that our capsule will undergo is 1.125g– This is determined from the maximum G force the

astronauts can undergo while standing • Force from Lunar Landing = 186 kN

Total Lunar Stress = 1.24 MPa

International Docking System Standard (IDSS)

Maximum force exerted during seal closure

Total Docking Stress = 1.16 MPa

Earth EDL - Heat Shielding

• AVCOAT ablative heat shield

• Total Thermal Loading: 2597.9 MPa

• Used on Apollo crew modules

• Will diffuse heat into the air as opposed to the structure

AVCOAT Shielding

• Will withstand total thermal loading for EDL

• Epoxy resin in fiberglass honeycomb matrix

• Above – before EDL• Below – after EDL

Earth EDL

• Maximum G force that our capsule will undergo is 7.19g

• Force during EDL = 493 kN

• Thermal Stress = 122.5 MPa– This is from fluctuations in the atmosphere. The heat

shield takes all of the thermal stress during EDL

Total Stress during EDL = 126 MPa

Safety Factors

NASA Technical Standard: STRUCTURAL DESIGN AND TEST FACTORS OF SAFETYFOR SPACEFLIGHT HARDWARE

Need a safety factor of at least 1.25 to fall under NASA standards

Highest Stress on Lander

• During EDL the stress reaches 126 MPa

• Based off of the yield stress of different materials, aluminum will be the best material for our structure

• With a safety factor of 1.25 the stress is still well under the yield strength of aluminum, 386 MPa

Yield Stress vs. Density

1000 2000 3000 4000 5000 6000 7000 8000 90000

100200300400500600700800900

1000

AluminumSteelCarbonTitanium

Density (kg/m^3)

Yiel

d St

ress

(Mpa

)

Total StressesCase Design Stress with SF (MPa)

Pressure 1.33Launch 155.3Lunar Land 1.55Docking 1.45Earth EDL 157.5

MOS 145.0%

MOS is based off of case of maximum load

LANDING VEHICLE

Lander Strut Configurations

• Three Distinct Design Possibilities1. Rigid Structure2. Spring and Damper Attenuation3. One-Time Energy Dissipation

Lander Strut - Rigid Structure

• Advantages– Simple analysis– Re-usable– Easy deployment

• Disadvantages– Large loads

• “Crash” landing scenario– Large magnitude accelerations

• Potentially fatal to astronauts

Lander Strut – Spring and Damper

• Advantages– Re-usable– Adjustable maximum

accelerations

• Disadvantages– Complicated analysis– Challenging deployment technique

• Springs act to move the struts to their equilibrium positions

Lander Strut – Energy Dissipation

• Advantages– Relatively simple analysis– Easy deployment• Comparable to rigid strut

– Low accelerations

• Disadvantages– One-time use

Design Choice – Energy Dissipation

• Honeycomb Energy Dissipation– Wide range of strengths available– Constant force during crushing– Reliable energy dissipation

Honeycomb – Energy Dissipation

• Energy Conservation– Kinetic Energy to Crushing Work– Lcrush is the total length of

Honeycomb required to dissipate all of the energy from landing

– Acceleration increases with decreasing stroke length

12mv 2 PcrushVcrush

Pcrush maAcrush

Vcrush AcrushLcrushv 2 vx

2 vy2

Lcrush vx2 vy

2

2a

Honeycomb – Acceleration Limits

• Maximum Acceleration – 1.125g– Limit imposed on elevators– Provides low enough acceleration that astronauts

can remain standing in lunar descent• Maximum Stroke Length – 1.75 m– Limit to easily store struts in descent stage– Assume all energy is dissipated in a single strut

(worst case)• Results in minimum acceleration of 0.328g

Honeycomb – Strength Selection

• Various Honeycombs of different strengths and densities

• Performing the worst case landing, we can determine the Honeycomb mass and diameter to meet our constraints

Strength Selection Continued

Optimum Honeycomb: p=8.1 lb/ft3 Pcrush=750psiNote: All designs from this point on use this Honeycomb

Honeycomb – Landing Scenarios

• Three likely scenarios to arise are:1. Landing on a single strut• Landing on extremely uneven surfaces (rock)

2. Landing on a constant incline• Assumed smooth planar surface

3. Landing on a flat surface• Specific type of incline

Case 1: Uneven Landing

Landing Scenario – Single Strut

• Worst case – all energy dissipation is in a single strut

• As before, the length of the crushed section is:

Lcrush vx2 vy

2

2a

Case 2: Sloped Landing

Landing Scenario – Sloped Landing

• More complicated• Total length required for energy dissipation

remains the same• Maximum crushing occurs in the “leading strut”

of the lander, minimum in the “trailing” oneAssumptions:

– Lander remains horizontal to the surface during descent– Maximum landing slope is determined where the trailing leg

does not need to absorb any additional energy

Sloped Landing – First Pass

Note: assume the lander must make contact with all four struts – any other configuration is unstable! (This is the cause of the curves ending)

*Maximum crushing occurs in the “leading strut”. It never reaches the maximum crush length because the two struts between the leading and trailing one absorb some of the energy.

Sloped Landing – Refined Pass• Considering only the data points that maximize the slope at

any given acceleration, we can produce the following plot:

•Possible landing slope is maximized at the lowest acceleration, 8.07ᵒ and 0.328g’s, respectively

Case 3: Zero-Slope Landing

Landing Scenario – Flat Surface

• Subset of the previous scenario where the slope is equal to 0

• Energy is dissipated evenly between the four struts – thus the crush length is as well

Lcrush,strut vx2 vy

2

8a

Summary of Landing Crush Lengths

Strut Single Strut Landing Max. Slope Landing (8.07ᵒ) Min. Slope Landing (0ᵒ)

Leading Strut 1.75 m 1.56 m 0.438 m

Mid-Strut 0 m 0.970 m 0.438 m

Mid-Strut 0 m 0.970 m 0.438 m

Trailing Strut 0 m 0 m 0.438 m

The following table represents the worst crush lengths for the three main landing scenarios:

*Honeycomb Mass= 2.62 kg/strut

Where:a = 0.378g’s Pcrush = 5.17 kPa Acrush = 0.011 m2

m = 16905 kg Lcrush = 1.75 m ρcrush = 130 kg/m3

Landing Strut Analysis

• Source of loads on the landing struts:1. Earth launch loads2. Lunar landing loads3. Thermal loads

• Landing struts are 6 m long before crushing– Minimum of 4.25 m after crushing

• Model the struts as hollow tubes– Design varied to minimized margin of safety

• Neglect joint forces

Strut Analysis – Earth Launch

• Stress due to launch forces and moments• Iteratively solved to minimized mass with:

ax = 8.5g ay = 5.8g az = 4.85gL = 6 m

earth ax 2 ay 2

gALI

azL

A rout2 rin

2 I

4 rout4 rin

4

Strut Analysis – Lunar Landing

• Stress due to landing force and moment• Assumed the landing force is purely axial and

purely rotational– Physically impossible to occur at once, but creates

an extreme-upper bound on loading• Iteratively solved to minimized mass with:

a = 0.328gL = 6 m

moon agL

AI

1

Strut Analysis - Thermal

• Rapidly changing temperatures while during Earth launch– Greatest temperature variation ~80 K

• Iteratively solved to minimized mass with:ΔT = 80 KL = 6 m

thermal ELL TL

Strut Analysis – Combined Loading

• Consider Earth and thermal loading combined, as well as lunar landing and thermal loading

• All cases use factors of safety (SF) of 1.4• Iteratively design with various radii to

minimize mass and the margin of safety

14.1

thermalmoon

yieldMoS

1

4.1

thermalearth

yieldMoS

or

Depending on which is the limiting (lower) value

Strut Analysis – Analyzed Materials

Material E (GPa) p (g/cm3) α (μm/m*K) σ (MPa)

Aluminum 2024 72 2.78 22.2 324

Aluminum 7075 71 2.78 22.2 490

Titanium Ti-6Al-4V 110 4.46 8.6 869

Steel AISI4340 200 7.8 13 1483

Steel 300M 200 7.8 13 1520

•Consider the following metals for our struts:

•These materials are used with the preceding formulas to find the optimum strut design that

1. Minimizes strut mass2. Keeps an external strut diameter below 20 cm3. Has a MoS = 0

Strut Analysis – Optimization

Titanium appears to be the best metal, but…

Strut Analysis – Optimization Cont.

When we consider the constraint of less than 20 cm (external) diameter, we see that Steel 300M at this point is 68.24 kg/strut, whereas titanium at an external diameter of 20 cm is 72.78 kg/strut

Strut Analysis – SummaryLanding Strut• Total length 6 m• Outer radius 10 cm• Inner radius 9.5 cm• Material Steel 300M• MoS 0• Strut Mass 68.24 kg/strut

Honeycomb• Max crush length 1.75 m• Min crush length 0 m• Honeycomb Mass 2.62 kg/strut

Strut Storage and Articulation

• The landing struts are divided into three 2-meter segments: two hollow tubes and one honeycomb piston

• During launch, the three segments are stored side by side as shown here

• Rotary actuators at the joints align the segments and lock them into place for lunar descent

Actuators• The landing struts will be stored folded into 3

sections during launch• Before lunar descent, the landing struts will deploy

using the space-rated rotary actuator shown below• This actuator was chosen because it can produce

high torque at low speeds. Lower speeds will reduce vibrational loads on the spacecraft

Supplemental Ladder

• The honeycomb piston is designed for worst-case scenario loading, so a best-case load would result in significantly less compression

• Because of this, a supplemental ladder is attached to the end of the second segment on the ladder strut

• The ladder will deploy in all scenarios, but will only be critical for light load cases where the astronauts would otherwise be unable to perform EVAs

Footpad Design• The footpad needs to be large enough to

remain stable across small variations in surface depth

• We chose a radius of 0.5 m because this covers a total area of 0.7854 m2, which should be sufficient to ameliorate the effects of an undesirable landing site

• The footpads are mounted with a ball joint to allow them to rotate as needed for various surface slopes

PROPULSION MODULE

Engine Mount Structure

• We are using a truss design to mount the engine to the module

• Needs to handle a maximum thrust load of 15568 N from engine

• The design is composed of 8 criss-crossing trusses which distribute the weight evenly amongst them Top View of Truss Engine

Mount

Engine

Side View of Truss Engine Mount

Engine

Truss Mount

Truss Analysis

In the analysis the truss was scaled by .2 and the force applied at each joint was (1/8)(Maximum Thrust)/10 or

195 N

Truss Design

• Each truss member is a hollow tube composed of aluminum and carries a maximum load of about 4070 N

• The radius of each member is 5 cm• The thickness of each member is chosen to be 1 cm

• Maximum Stress = 1.43 MPa– Well under the yield stress of aluminum, 386 MPa

Truss Member Stress vs. Thickness

0 0.01 0.02 0.03 0.04 0.050

2000000400000060000008000000

100000001200000014000000

Truss

Thickness (m)

Stre

ss (M

pa)

Propulsion Module Requirements• The full propulsion module is a two meter long

cylinder with a diameter of 3.57 m– Four 60x30 cm sections are cut from the overall

cylinder to store the landing struts• Required propellant volumes:

• This volume also holds the engine and engine mount, which occupy a total volume of 0.713 m3

Monomethyl Hydrazine (MMH) Nitrogen Tetroxide (N2O4):4.333 m3 4.208 m3

Tank Sizing• The tanks were cylindrical with ellipsoidal end

caps. The height of the ellipse was modeled as 0.25*radius of cylinder

• Using this equation and the volumes stated earlier produces the following radii, which fit well within our design limits:

Monomethyl Hydrazine (MMH) Nitrogen Tetroxide (N2O4):0.4227 m 0.4165 m

Mass TotalsComponent Mass (Kg)Crew Systems 1500Power, Propulsion, Thermal 4795Aluminum Shell 1687Propellant 9914Propulsion Inert Mass 2199Landing Struts 283.4Total Mass 20,378

Final Design

References• Cameron, John R.; James G. Skofronick & Roderick M. Grant.Physics of the Body. Second Edition. Madison, WI: Medical

Physics Publishing, 1999: 182.• http://www.gaudisite.nl/ElevatorPhysicalModelSlides.pdf• http://heroicrelics.org/info/lm/landing-gear-strut-honeycomb.html• http://www.plascore.com/pdf/Plascore_CrushLite.pdf• https://webspace.utexas.edu/jkm343/mikulak/compressive%20and%20lamination%20strenght%20of%20honeycomb%20%

20panels%20from%20ASTM.pdf• http://www.sciencedirect.com/science/article/pii/S0020768305003781• http://www.youtube.com/watch?v=q4GAomYWb2M• http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720018253_1972018253.pdf• http://www.wolframalpha.com/input/?i=volume+of+a+torus • http://airandspace.si.edu/collections/artifact.cfm?id=A19721346000• http://

www.lr.tudelft.nl/en/organisation/departments-and-chairs/space-engineering/space-systems-engineering/expertise-areas/space-propulsion/design-of-elements/rocket-propellants/liquids/

• http://dmseg5.cwru.edu/classes/emse201/overheads/Thermal.pdf• http://

www.faa.gov/other_visit/aviation_industry/designees_delegations/designee_types/ame/media/Section20III.4.1.7%20Returning%20from%20Space.pdf

• http://www.spaceaholic.com/apollo_cm_earth_entry.pdf• http://www.dummies.com/how-to/content/mechanics-of-materials-for-dummies-cheat-sheet.html• http://www.internationaldockingstandard.com/download/IDSS_IDD_RevA_Final_051311.pdf• standards.nasa.gov/documents/viewdoc/3315591/3315591• standards.nasa.gov/documents/viewdoc/3314903/3314903