Modal MAC Analysis vs. Sine Vibe A Case Study

Transcription

1 Modal MAC Analysis vs. Sine Vibe A Case Study Bing C. Chen, Walte S. Tsuha and Chia-Yen Peng Jet Populsion Laboatoy Califonia Institute of Technology Mechanical Systems Engineeing, Fabication and Test Division Spacecaft Stuctues and Dynamics Goup June 21-23, 2016 bing-chung.chen@jpl.nasa.gov 2016 Califonia Institute of Technology The Aeospace Copoation 2010 Govenment sponsoship acknowledged

2 Oveview Sine Vibe vs. Modal Mass Acceleation Analysis Descibe Modal Mass Acceleation Cuve (MMA Cuve): the coe concept of MMA Load Analysis methodology, widely adopted at JPL Intoduce the notion of mapping modal acceleation esponses to the space of acceleation vs. effective mass and compae with MMA Cuve Evaluate the esponses of diffeent enfoced acceleation sine vibation notching stategies with MMA Cuve Povide connection between sine vibe analysis with MMA Load analysis methodology 2

3 Modal MAC Loads Analysis - Backgound (1/3) Bounding Loads Methodology geneates bounding loads fo the low fequency launch dynamic envionments (< 100 Hz) fo stuctual design Not a simulation, but bound loads fom a CLA Quick Tunaound Loads analysis fo a payload (e.g. spacecaft) accomplished in 1 2 weeks, as opposed to the typical 2-3 month tunaound time fo a coupled loads cycle Modal MAC Analysis 1 2 Weeks Coupled Loads Analysis 2 3 Months Accommodates Lage Output Requests Possible to output loads fo an entie payload model Modal MAC Analysis > 500,000 Output Items Coupled Loads Analysis < 10,000 Output Items 3

4 Modal MAC Loads Analysis - Backgound (2/3) Modal Mass Acceleation Cuve (MMA Cuve) MMA-Cuve based on widely accepted pinciple: acceleation esponse of a base diven system is invesely popotional to the squae oot of its mass. Each mode chaacteized by its effective mass of a sping-mass system cantileveed fom the payload to launch vehicle inteface The cuve is intended to bound the CLA Paametes tuned to bound CLA events MMAC( m) = Tan m M 1 Go sc m M sc lv lv 2 e tan( ) m 1 m 2 m n k 1 c 1 k 2 c 2 k n c n Launch vehicle inteface a(w) 4

5 Analysis Input - Backgound (3/3) Modal MAC Loads Analysis vs. Sine Vibe Analysis Modal MAC Analysis Inputs FEM of Payload modes, fequencies, effective masses, etc. Modal Mass Acceleation Cuve Payload to Launch Vehicle Inteface Acceleations Sine Vibe Analysis Inputs FEM of Payload Base dive fequency esponse Quasi-sinusoidal vibation level Quasi-static load factos Sinusoidal vibe level fo Atlas V 400 & 500 Seies* 5 * Atlas launch system mission plane s guide

6 Modal MAC Bound Absolute acceleation x( t) i i 1 cm cm x nm mean x qs N cm dyn 2 nm eff MMAC x s ms q s 1 s1 i 1 cm x ( t) 2 N s1 nm s q s ( t) x x q mean dyn m eff s MMAC s P/L to L/V inteface accel, mean component P/L to L/V inteface accel, dynamic component Effective mass, squae-ooted Modal Mass Acceleation Root-Squae-Sum scale eigenvectos with x dyn Scale facto detemined by MMA Cuve and squae-oot effective mass 6

7 Concept of Effective Mass Effective mass fo mode s eff ms nm T RB φ M φ s NASTRAN case contol command MEFFMASS tun on calculation Equivalent physical mass of the coesponding modal DOF summation ove all modal effective masses will esult in igid-body mass measue sufficiency of mode numbes a measue to gauge significance of a vibation mode Modes with low effective mass yield low esponses by enfoced acceleation Modes with high effective mass can be eadily excited by base excitation Popotional to the eactions foce acting on the base of the base dive enfoced acceleation φ M φ nm s RB nomal mode s Mass matix Rigid body mode, diection 7

8 Suface Wate Ocean Topogaphy (SWOT) Mission Mission Objective: povide global suvey of Eath s oceans and teestial suface wates combine the concepts of WaTER (Wate and Teestial Elevation Recovey) and the Hydosphee Mappe Collaboation between NASA and Fench CNES Candidate Launch Vehicles ATLAS V FALCON 9 8

9 SWOT Oveall Sine Notching Stategy SWOT Payload mass compaable to S/C bus mass: P/L and S/C bus modal behavios coupled Pefom extensive Obsevatoy Model sensitivity studies on stiffness/mass vaiation of S/C and P/L Identify seveal acceleation outputs as epesentative global P/L esponses Envelope acceleation of all sensitivity esults fo each acceleation output Foce Limiting Sine inputs notched so that P/L to S/C inteface load, not exceeding quasi-static load Response Limiting Sine inputs notched so that stategically selected P/L esponses do not exceed Obsevatoy-level sine esponses. PL sine base dive Obsevatoy Sine input 9

10 Notched Modes in Modal Acceleation Cuves Foce Limited Sine Vibe Analysis Notched input sine vibe level bing down the majo bending modes (#1, #2) Modes of lage effective mass (10 1 ~ 10 2 kg) still well above MMA Cuve 10

11 Notched Modes in Modal Acceleation Cuves (2) Foce and Response Limited Sine Vibe Analysis As a esult of notched sine input level due to foce and esponse limiting modal acceleation esponses move lowe and close to MMA Cuve Most Sine-X modes esponse in the vicinity of MMA Cuve Sine-Y Modes of lage effective mass (10 1 ~ 10 2 kg) still well above MMA Cuve 11

12 Payload Sine Result vs. Physical Mass Acceleation Cuve Mass Acceleation Cuve exceedances of maximum sine esponses ae mainly diven by z-axis sine. Activating esponse limiting fo the z-axis sine educe Mass Acceleation Cuve exceedances 12

13 SWOT Sine Vibe Analysis Results Acceleation Ratio: Payload / Obsevatoy Acceleation fom notched P/L sine-x and sine-y analysis bound those fom Obsevatoy Sine-Y acceleations show moe consevatism ove Sine-X due to moe modal esponses exceedance ove MMA Cuve 13

14 SWOT Sine Vibe & Modal MAC Analysis Results Acceleation Ratio Sine Vibe & Modal MAC ove Couple Load Analysis 14

15 Summay MMAC vs. Base Dive Sine Vibe Mapping the modal acceleation esponses fom base dive sine vibation analysis to the acceleation vs. effective mass space intoduces anothe pespective on the sine vibation analysis Compae the sine vibe modal acceleations esponses against Modal Mass Acceleation Cuve to assess the input sine level In geneal, notching sine vibe input level based on foce-limiting of quasi-static load inteface load can bing down modal acceleations of the fist bending modes close to Mass Acceleation Cuve It is an indication fo additional notching on the input sine level when modal (o physical) acceleations of lage effective mass egiste significant exceedance ove Mass Acceleation Cuve 15

16 Thank you 2016 Califonia Institute of Technology The Aeospace Copoation 2010 Govenment sponsoship acknowledged