Norton-Thevenin Receptance Coupling (NTRC) as a Payload Design Tool

Transcription

1 Norton-Thevenin Receptance Coupling (NTRC) as a Payload Design Tool Scott Gordon, NS/ Dan Kaufman, NS/ rya Majed, pplied Structural Dynamics, Inc. Spacecraft and Launch Vehicle Dynamic Environments Workshop June 20-22, 2017 This work performed for the NS Engineering and Safety Center (NESC) under NESC Request No: TI

2 genda Background Methodology NESC Study Results Summary 2

3 cknowledgement Curt Larsen, NS Technical Fellow for Loads and Dynamics 3

4 What is NTRC? NTRC combines Receptance Coupling methods with Norton- Thevenin theory Receptance Coupling = method of coupling dynamic structures based on frequency response functions (FRFs) [3] Norton-Thevenin Theory = n impedance-based method for simplifying the interaction between dynamic systems [1,2] llows for the behavior of the coupled system to be derived only from measurements at the boundary of the two systems to be coupled Does not explicitly require launch vehicle models or forcing functions. NTRC requires: Unloaded launch vehicle accelerations at interface (free acceleration response) Launch vehicle interface accelerance FRFs Payload interface accelerance FRFs 4

5 Why Was NTRC Developed? There is a need for a design tool that the LV payload community can use to estimate launch loads Very few methods for estimating launch loads for subsystems and components MC/MMC Base-drive Payload community has limited access to CL during life of a program (Typically 2 to 3 cycles) Difficult to define preliminary design loads Difficult to address design change that occur between load cycles Difficult to determine impact of as-built hardware llows the payload community to assess launch loads with minimal amount of information required from the launch vehicle provider Not intended to replace formal load cycles performed by the LV provider! 5

6 Benefits of NTRC Provides the payload community with ability to define/assess launch loads before and between official CL cycles Fast execution times Operates on minimum possible set of coordinates (equal to boundary DoFs) Solves in the frequency domain llows for parametric analysis and trade-studies to optimize structural design and limit surprises from official CL results [4] Cost effective for the payload community May provide benefit to the LV community Faster response times for evaluating multiple payload configurations than standard CL Improved assessment of CL models/forcing functions against measured flight data 6

7 NTRC Methodology r s B t Coupled System ccelerance [3] Cr Cs Ct Crr Csr Ctr Crs Css Cts Crt Cst Ctt F F F Receptance (ccelerance) Coupling for two substructures [3]: Crr Csr Ctr Crs Css Cts Crt Cst Ctt 0 rr sr 0 rs ss 0 0 Btt - Cr Cs Ct rs ss Bts ss (1) 1 Bss - rs ss Bts T C: coupled system (+B) : source with internal dofs r B: load with internal dofs t s: connecting dofs : accelerance [g/lb] F: [lb], : [g] Xyz = ccelerance for System X with response at y dofs due to forces applied at z dofs (2) 7

8 NTRC Methodology (Cont) From Receptance Coupling, we can relate the internal response of the payload ( Ct ) to the boundary acceleration ( Cs ) of the coupled system through payload accelerance matrices 1 Ct Bts Bss Cs (3) Cs ss From Norton-Thevenin [1,2], we can relate the LV free acceleration ( s ) to the coupled acceleration ( Cs ) at the boundary using payload and LV interface accelerance matrices [ Bss ] Combine (3) and (4) to get desired expression of coupled payload response ( Ct ) as a function of LV free acceleration ( s ): ss 1 s (4) Ct Bts Bss [ ss Bss ] ss 1 s (5) 8

9 NTRC Time Domain nalysis One implementation of Equation (5) NTRC is a frequency domain analysis technique FFT/IFFT processing is used to perform NTRC in the time domain Steps 1. Start with LV free-acceleration ( s ) at payload interface 2. Transform s to frequency domain via FFT. Extract positive frequency terms and remove the f=0 z term (save for later) 3. Calculate accelerance () for payload and launch vehicle at common interface (consistent frequency range and delta-f). 4. Derive NTRC transform and convert free acceleration ( as ) to the coupled system interface acceleration ( Cs ) in the frequency domain Cs [ ss 5. Use IFFT to transform Cs back to the time domain (w/ f=0 term from FFT of s ) 6. Basedrive PL with Cs to recover internal responses Bss ] ss 1 s 9

10 NESC Study Study approved December 2015, started January 2016 NESC approved the funding for a 1year study with effort broken into Quarters Quarter 1 = Frequency domain using in-house developed models eavy payload Determinate and indeterminate interfaces (24 DoFs) Multiple payloads Quarter 2 = Time domain (no steady-state) FFT/IFFT processing LV/Payload model truncation w/ residual vectors Quarter 3 = SLS/Europa + non-linear pad separation study SLS/Europa with in-house forcing functions (no steady). ighly indeterminate interface (144 DoFs) In-house pad separation models and non-linear liftoff simulations Quarter 4 = Liftoff CL Use in-house non-linear simulation developed in Q3 for benchmarking Liftoff pad sep with initial conditions and quasi-steady content Delta II/GLST [5] dditional Q5 Funding dded to benchmark against SLS liftoff and complete final report (Estimated Completion ugust 2017) 10

11 Launch Vehicle FEM St. Indeterminate Payload ttach 1 (4 points, 6 DoFs per point available) St. Indeterminate Payload ttach 2 (4 points, 6 DoFs per point available) Longeron/ring type structure made of Beam elements L = 60 m D = 5m m = 208,155 kg T = 3000 kn DMM: 54 Boundary DoFs modes Thrust location 11

12 eavy Payload FEM eavy payload FEM constructed to meet following requirements: Weight: 3717 kg (8177 lbs) Mass = 4618 kg Off-axis CoG 1 st lateral/rocking frequency z (FEM: kg z) added at each of 10 locations 1 st axial frequency z (FEM: 31.6 z) CoG ll Total frequencies mass increased wrt st. from det. constraints 840 kg to 4200 kg DMM: 24 physical DoFs modes cceleration and Stress Transformation Matrices (TM, STM) generated for internal response computations 12

13 NTRC Reminders Operates on LV free accelerations/accelerance at payload interface No mass loading of interface required Calculate LV free accelerations one time for multiple payload configurations Operates on the minimum possible set of coordinates to solve CL problem. For in-house LV + PL example: NTRC = 24 DoFs CL = = 1754 DoFs Solves in frequency domain Fast executions 13

14 Frequency Domain Results NTRC in the frequency domain is exact Results match within numerical accuracy of analysis ll urty/craig-bampton (CB) modes must be used or Free-free modes must be augmented with residual vectors I/F cceleration DOF (Thrust) 14

15 NTRC Time Domain Results NTRC results captures all relevant characteristics of a transient CL NTRC matches CL w/o steady-state to < 5% Time domain NTRC with steady-state matches CL < 5% for significant payload responses Source of differences Convergence of time domain analysis FFT/IFFT processing Will continue to refine time domain analysis for Q5 activities (SLS) I/F cceleration DOF (Thrust) Nonlinear CL Black NTRC - Blue 15

16 Summary NTRC is an alternate coupling approach that can be used to replicate a standard LV CL NTRC developed as a design tool for payload community with the minimum information required from LV providers NTRC is exact for frequency domain analysis NTRC shows excellent agreement with results from time domain CL Completion of SLS liftoff benchmarking and release of final NESC report expected ugust

17 References 1. Mechanical Impedance: Modelling/nalysis of Structures, Vernon. Neubert, Jostens Printing and Publishing Company, Random Vibrations in Spacecraft Structures Design: Theory and pplications, J. Jaap Wijker, Springer Science & Business Media, ug 19, Evaluation of the FRF Based Substructuring and Modal Synthesis Technique pplied to Vehicle FE Data, Cuppens, K., Sas, P., and ermans, L., Proceedings of the Twenty- Fifth International Seminar on Modal nalysis, Leuven Belgium, September, Variational Coupled Loads nalyses: Reducing Risk in Development of Space-Flight ardware, rya Majed, Kevin Partin, Ed enkel pplied Structural Dynamics, Inc., ouston, Texas and Thomas P. Sarafin, Instar Engineering and Consulting, Inc., Littleton, Colorado 5. Flight Force Measurements on a Spacecraft to Launch Vehicle Interface, Kaufman, Daniel S., Gordon, Scott., Proceedings of the 12th European Conference on Spacecraft Structures, Materials and Environmental Testing, held March, 2012 at ESTEC, the Netherlands. ES SP-691. ISBN , p