UUnniivveerrssiittyy ooff CCeennttrraall FFlloorriiddaa SSTTAARRSS Electronic Theses and Dissertations, 2004-2019 2015 PPrreessssuurriizzeedd MMeettaall BBeelllloowwss SShhoocckk AAbbssoorrbbeerr ffoorr SSppaaccee AApppplliiccaattiioonnss.. John Trautwein University of Central Florida Part of the Mechanical Engineering Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. SSTTAARRSS CCiittaattiioonn Trautwein, John, "Pressurized Metal Bellows Shock Absorber for Space Applications." (2015). Electronic Theses and Dissertations, 2004-2019. 1412. https://stars.library.ucf.edu/etd/1412 PRESSURIZEDMETALBELLOWSSHOCKABSORBERFORSPACEAPPLICATIONS by JOHNTRAUTWEIN B.S.RutgersUniversity,1996 B.S.FloridaStateUniversity,2004 Athesissubmittedinpartialfulfilmentoftherequirements forthedegreeofMasterofScience intheDepartmentofMechanicalandAerospaceEngineering intheCollegeofEngineering&ComputerScience attheUniversityofCentralFlorida Orlando,Florida FallTerm 2015 MajorProfessor:JeffreyL.Kauffman ©2015JohnTrautwein ii ABSTRACT Numerous spacecraft designs exist for exploring the surfaces of planetary bodies and each have their own advantages and disadvantages. All successful landings have been made by stationary landers or wheeled rovers that rely on one-time use mechanisms, such as crushable aluminum honeycombshockabsorbersorinflatableairbags,toreduceshockloadingtothespacecraftduring landing. The stationary lander is the simplest type of lander, but can only take data from one location. Wheeled rovers add complexity in exchange for mobility to explore different locations. Roversarelimitedbytheterraintheycantraverse;roversbecomingstuckhaveendedmissions. In contrast to rovers and stationary landers, hoppers explore by making multiple launch and landing hops. They have the advantage of being able to avoid terrain that would cause a rover to become stuck. A hopper may require a landing shock absorber that can reliably operate multiple times in harshenvironments. Mostterrestrialshockabsorbersusehydraulicfluid,allowingforcompactandinexpensivedevices. Hydraulics have been used in space applications, but require thermal controls to maintain the proper fluid viscosity. They also require dynamic seals which, in the case of a leak, can degrade performance,shortenmissionlife,andcontaminatesensitivescienceequipment. Leakageisalsoa concerninpressurizedsystemsinspacebecausemissionscantakedecadesfromwhenasystemis installedtowhenitactuallyisused. To address these issues, a pressurized metal bellows shock absorber is proposed. This shock ab- sorber could operate at nearly any expected spacecraft environment. Metal bellows are designed to operate from cryogenic temperatures to several hundred degrees Celsius. Ahermetically sealed system eliminates the risks of a system with seals. Metal bellows are in common use for terres- trial harsh environments and vacuum applications. Small metal bellows are used as dampers for iii pressurecontrolsystemswithsmalldisplacements. Models for the dynamics of this device are developed and presented here. Starting from the ideal gas law, polytropic compression, and compressible flow through an orifice, differential equations of motion and pressure are derived. These equations are nonlinear for the displacements under considerationandarenondimensionalizedtohelpprovideinsight. Equationsforstaticequilibrium, maximuminitialdisplacementbounds,andestimatednaturalfrequencyarepresented. Metal bellows can operate as a passive damper with a simple orifice between the control volumes. Optimization is performed for the nondimensional model of a passive damper. Because the re- sponseishighlynonlinear,amethodisdevelopedtoestimateadampingcoefficientthatisusedas the objective function for this optimization. Feasibility of this concept is investigated through an exampledesignproblemusingdatafromametalbellowsmanufacturerasconstraints. Anoptimal massconfigurationisfoundthatmeetsthedesignconstraints. Performancecanbeimprovedoverthepassivesystembyaddingcontrol. Thefirstcontrolstrategy involves a check valve, such that the effective orifice size varies between compression and exten- sion. Thenextcontrolstrategyreplacestheorificewithacontrolvalve. Varyingthevalveopening and closing timing can achieve optimal performance. Finally, using the metal bellows as an ac- tuator to help launch the hopper is investigated. While the valve is closed, the gas in the second volumeiscompressed. Thenthevalveisopenedthehopperislaunched. The results of this research show that a metal bellows device holds promise as a landing shock absorberandlaunchactuatortoextendtherangeofhopperspacecraft. iv ACKNOWLEDGMENTS I would like to thank my graduate adviser Jefferey L. Kauffman for his guidance and patience during my journey through graduate school and this research. He always seems to provide just enough direction to keep me from getting hopelessly lost but the freedom to explore this topic. I would also like to thank Joette Feeney from Kennedy Space Center for selecting me for the KennedySpaceCenterGraduateFellowshipProgramwhichprovidedthefundingformyMaster’s Degree and my supervisors Todd Steinrock and Ned Voska for allowing the flexibility to juggle work and school responsibilities. I appreciate all of the help from my coworkers at the NASA PrototypeLaboratoryforputtingupwithwhatmustseemtobearandomscheduleforthepasttwo and a half years. Finally I could not have done this without the support of my loving wife Ileana and my children Robert, Victoria, and Thomas. We have spent many nights together around the kitchentableonourschoolworkandthisthesisistheculminationoftheseefforts. v TABLE OF CONTENTS LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv CHAPTER1: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 HopperSpacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ShockAbsorbersandDampingMechanisms . . . . . . . . . . . . . . . . . . . . . 2 1.3 MetalBellowsShockAbsorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 GoalsforCurrentResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 CHAPTER2: LITERATUREREVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 PlanetaryLandersandHoppers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Apollo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 PHOBOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.3 Hayabusa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 Rosetta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 vi 2.1.5 TalarisPlanetaryHopper . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 ShockAbsorbersandDampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 HydraulicShockAbsorbers . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 PneumaticCylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.3 LinearModelsforGasSpring . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.4 NonlinearModelsforGasSpring . . . . . . . . . . . . . . . . . . . . . . 15 2.2.5 NondimensionalizationofDampedPneumaticShockIsolators . . . . . . . 19 2.2.6 MetalBellows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.7 AdaptivePneumaticImpactAbsorber . . . . . . . . . . . . . . . . . . . . 20 CHAPTER3: METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 MetalBellowEffectiveArea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 MetalBellowsShockAbsorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 EquationofMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.3 IdealGasLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.4 AdiabaticCompression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.5 Conservationofmass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 vii 3.2.6 Massflowthroughanorifice . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.7 NondimensionalParameters . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.8 NondimensionalEquationofMotion . . . . . . . . . . . . . . . . . . . . 33 3.2.9 NondimensionalMassFlow . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.10 BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 InitialDesignEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.1 StaticEquilibriumSolution . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.2 MaximumInitialDisplacementBounds . . . . . . . . . . . . . . . . . . . 39 3.3.3 EstimatedNaturalFrequency . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 ControlConcepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4.1 CheckValveandOrificeConcept . . . . . . . . . . . . . . . . . . . . . . 43 3.4.2 On/OffValveControlConcept . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.3 AdaptiveControlConcept . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4.4 On/OffValveHopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.5 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5.1 NondimensionalOptimization . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5.2 DimensionalOptimizationUsingVendorsData . . . . . . . . . . . . . . . 50 viii CHAPTER4: FINDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1 InitialVerification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 InitialDesignEquationsVerification . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3 On/OffControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.4 AdaptiveControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.5 NondimensionalOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.6 OptimizationusingVendorData . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 CHAPTER5: CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.1 EffectiveArea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.2 EquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3 AnalyticalEstimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 ResponsetoParameterVariation . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.5 ControlConcepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.6 LinearEquivalentDampingCoefficientforNonlinearResponse . . . . . . . . . . 85 5.7 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.8 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 APPENDIXA: ANDERSONNONLINEARSPRING . . . . . . . . . . . . . . . . . . . . 87 ix