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,t ' STATIC AND DYNAMIC HELICOPTER " AIRFRAME ANALYSIS WITH NASTR A N By H. E. Wilson and J, D. Cronkhite . Bell Helicopter Company SUMMARY The use of NASTRAN at Bell H e licopter Company for structural static and dynamic analysis of a helicopter airframe is described. Analysis of air- frame internal loads, main rotor isolation systems, and airframe vibration is discussed. The use of each rigid format for these types of analysis is summarized. Suggested improvements to NASTRAN to increase its effectiveness in performing helicopter airframe analysis ace given.
INTRODUCT ION Before the availability of large finit e elem e nt programs, internal loads were calculated from two-dlmenslonal shear and moment diagrams and the r d y namic b eha vior was ap pr oxim a t e d with a Myklestad-typ e b e am an a l y sis. After / th e d e v e lopm e nt of NASTRAN, and oth e r sim i lar progr a ms, mor e e x ac t analys e s c ould b e p er form e d. How e v e r, b e for e NASTRAN ca n b e e x ec ut e d, th e h e li c opt e r a irfr a m e must b e r e pr e s e nt e d a s a thr ee -dlm e nslon a l finit e e l e m e nt mod e l w hi c h involv e s g e n e rat i on o f a l a rg e a mount of input d a ta to d e fin e th e st r u c tur e . A t y p ica l a i rfr a m e st r u c tu r al m od e l is s h own in figure i. In 4 addition to d e v e loping a stru c t u r a l mod e l, t h e problem of d i stributing structural a nd nonstru c tu r al w e ight to th e appropriat e areas of the finite elem e nt mod e l proved to b e a time c onsuming and tedious task requiring many j ud gm en tal d e ci s io ns . An a ut o m ated proc edu r e fo r d i stribut i on o f w ei ght - _ i te ms to t he st ru ctu ra l mod e l wa s dev is e d so t h a t NASTRAN c o u ld b e u s e d : ef fi c i e nt l y for both s t at i c a nd d y nami c stru c tur a l a n al ysis.
_ = _ AIRFR A ME S T ATI C A NA L Y S I S _ . , . A s t a tl c ana l ysis of a helicop t er airf r a m e involves t h e de t er ml n _tlon ,) _ - o f internal loads and stre s ses usi ng NAS TRA N1. To faci l i t a t e t h e u s e o f NAS T R A N vario us preprocessor and po st proce s s or co m pu t e r p ro g ra m s w e r e !' w rit t en . The prepr o ces s or p r o g ra m s i nc l udc auto m at i c da t a g enerat i on of .
, , _ ' finite e l e m en t m ode l s of cer t ain t ypes of s t ruc t ure such a s the t a i l boo m, " eleva t or , an d ver t ical t a i l a s s ho w n in f i g ure 2 . Th e r e pre s entati o n o f t he ,, " ._. . _ - _ ' _ inertia l oads is provided w ith an in t erface p r o g ram to N A S TRA N. , ) _ -- ":i PR I _CF DI NG PAG E BLAN K NO T FILMF D " . - 4 + ' The interface program calculates six load vectors which represent the inertia reactions for independently applied unit translati o n and angular accelerations at the helicopter center of gravity. By scaling the inertia reactions to balance the applied loads and applying a set of determinant constraints, a NASTRAN static analysis can be done.
I Postprocessors are used to calculate shear flows and adjusted rod loads for rod-shear panel type structure, to scan the output from several subcases and determine the critical loading condition for each element, and to pre- sent the output data in a report format, t Alternate output from the inertia distribution program is concentrated weights punched on data cards in NASTR A N format. These weights may be used directly in a st a tic analysis with inertia relief, natural frequency analysis, o r dynamic response a n a l y sis.
AIRFRAME DYNAMIC A NALYSIS Main Rotor Isolation ' Dynami c anal y sis of the h elicopter involv e s e val u ating different methods , + , of isol a ting the e x cit a tion of th e main r otor from the a i r fr a me. These methods include a focused pylon 2 for isolation of horizontal main rotor e x c it a tion a nd nod a l b ea m 3 for isolation of v e rti c al ex c itation. A sk e t c h .. an d b rief e x p lanation o f th e s e s yste ms is shown in figure 3. NASTRAN mod e ls o f th e s e s y st e ms are d eve lo pe d u sin g ba rs, li n k a ges (rod s ), s ca lar springs, multipolnt con s traint s , and con ce ntrat e d mas se s.
V i b ra tion r e spons e ch a r ac ter i st ics o f the isol a t i on system c an be ev a l- u a ted by a tt ac hi n g it to a r i g id body fus e l a ge. N a tur a l f req q en c les, mod e sh apes , a n d f req u e n cy re s p on se c h aracteri st ics o f t h e m ai n r otor i sol a t i o n syst e m ca n t he n b e d et e rmin e d w i tho u t h a v i ng to c on side r th e a dd e d c om- pl e x i ty o f ela sti c a nd dyn a mi c e f fec ts o f th e f us ela g e . A f t er h a v i ng • d e v e lop ed a n d t une d thi s t y p e of mod e l, t he i s ol a tion sys t e m is i n c o r po r at e d i n t o a s truc tu ral dy n a m ic a i rframe m od e) t o d o a v ib ra ti on a n a l y s i s of th e + .
;++ e nt ire c ou p l e d s ys t e m.
_ '' A ir fr a m e V ib ra t io n - _ ' + The a ir f r a m e dy n a mi c resp on se analysi s i s per fo r m ed b y co m b ini n g th e +_ o m a in ro t or pylon and i s o la ti o n sys t e m w i t h t he e l as t ic a i rframe m ode l. Th e : , :" a i rfra m e m o de l w i ll be ei t her an e l as t ic a x is repres ent a t i on m ade u p o f b ar el e m en t s with f usela g e sec t ion p r op er t ies or a b ui lt - up t h r e e - d lm e n sio n al repres en t a t i on u si ng bars , rods , shear panels , and m e m brane e l emen t s to mo de l \_ t he s t ruc t ure . Th e el a s ti c axis models have f com 3 00 t o 4 0 0 degrees o f freedo m and the t hree-dl me ns lon al m odels usual l y have 1 2 00 Lo 1 400 de g rees i_:_ o f freedo m m axi m u m.
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A modal •pproach is most often used for a vibration analys i s of the air- l fr•me where the system degrees of freedom are reduced below 200 and the i n•tur•l frequencies and mode sh•pes are computed using the GIVENS eigenvalue extraction n_thod. This method is used primarily bec•use of the number of modes required for low frequency (0 to 50 hertz) vibr•tlon response analysis, usually at le•st 30 modes.
The princlp•l types of dyn•mlc •n•lysls done wlth the •irframe model •re the following: (I) Tuning the airframe n•tur•l frequencies with respect to main rotor exclt•tlon h•rmonlcs by m•king structur•l and weight ch•nges.
(2) Determining the ste•dy state frequency response ch•r•cteristics of the airframe where forces and moments are applied separ•tely a t de gr ee s of fr ee dmn h a ving e xclt•tion sources and the forcing fr eque nc y is swept ov er the r•nge of interest (usually 0 to 50 h e rtz).
(3) Determining the steady state respons e to in-fligh t rotor harmoni c e x c itation.
(4) Determining the tr•nsient response of the •irframe to we•pon firing using NASTRAN and a h ybrid computer. The NASTRAN norm•l mode d • t• f or t h e airframe mo d el is input t o a hybrid computer p ro g ra m w h l ch c o mp u t es t h e • ir fra m e re sp o ns e . A s implified f low d i a g ram of t he hybrid ana l ys is is sh own in f igure 4.
SU MMARY OF T H E US E OF NASTKAN RIGI D FORMA TS FO R AI RF R A ME ANALYSIS R igi d Fo rm a t I - S t a ti c An • l y sls { R igid for mat I i s u s ed t o ca lcul • te t he i n t er n a l l oad s of the h e li c o p t e r ,._ . f or t he d i f f ere nt des ign l oadi ng co n di ti o n s . The s t a t i c s t ru ctu ra l m ode l @ I . wit h rods , b a r, a n d s hear pa n el s. The i n iti a l r un, when th e s ti ff nes s _ : _o% ""_, typ i ca ll y con t a i ns 2 5 00 t o 3 0 0 0 de gr ees o f freedo m and i s m ode l ed pr im ar il y _I _ mat r i x i s d e c om posed , t a k e s about 6 0 cpu mi nu t es on a n IBM 360-65 co m pu t er .
v : Each s ucc e ed i n g l oad ing condi ti on t akes approx imat ely 20 cpu min u t es .
, Ri g i d For m a t 2 - S t a t ic Anal ys i s W i t h Ine r_ . _ al R e li ef i for m a t . I t perfor m s a sta t ic an • lys l s o f • f ree hel i cop t er i n fl ig ht w ith s t e a dy l oads app l ied . The resu lt s f r om r i g i d f orma t 2 can be comp a red wit h Th e w e ig h t distribution of t h e h e l i cop t e r i s checked wit h t h is ri g id _ - t hose ob t ained using forma t I t o en s ure a correc t in e r ti al repr e s en t a t ion _ - is ach i eved .
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I Rigi d Forma t 3 - N or m a l M ode A n aly sis This rigid f orma t is us e d fo r t un ing of t he a i r fr ame na t u r al f requen cie s wit h resp e ct t o p redo m i n an t e xcitation frequencies. The na t ural f requ e nc i e s and n or m al mode data ou t pu t f rom N A S TRAN are al s o us e d in o th e r p ro g ra m s such a s t he hybrid co m puter pro gr am p r ev i ously discussed or co m b in e d with main rotor a n alys i s pro g ram s t o de t e rmin e t he r e sponse o f t h e co up l e d ro L or a n d a i rf ram e.
T h e fl e x i bil it y ma t r i x ( [K] "l) and m a s s matrix are ou tp u t a n d us e d in a flu tt e r pro gr a m . The n a t u r al fr equenc i es a n d m ode shapes f o r t he zero v e loc it y case a r e co m par e d t o t h e NA STRA N results as a check on t h e fl u t t e r p r o gr a m .
Rigi d For m a t 4 - S t a ti c Ana l ys i s Wit h D i ffe r e nti al S tif f n e ss Rigi d fo rm a t 4 has been used for d e s ig n i n g t he s t a t ic s t ops fo r t he ma i n r o t or pylon suppo rt sys t e m . The us e of d iff ere nti al s ti ffnes s r e duced t he loads caus e d by crash c o n d iti o n s , t hu s sav i ng w e ight i n t he d e sign . The in c lu sio n of second order d i ff er e ntia l s ti ffness eff e ct s w ould • I lo w NASTRAN t o b e us e d t o s olve severa l o t her s t r u c t ura l prob l e m s s uc h • s t e n s i o n stresses d e v e loped i n m e m b r ane pla t e s due t o t ra n sve r se p r essu r e s .
Rigid For m at 5 - Buc kl i n g The s t abil it y a n a l ysis in N A S T R A N i s u sed o n a l i m ited basis. M a n y d e grees of fr eed om•r e required t o ob tai n an accurat e s olu ti on to a buil t - up t hr ee -di m ens l onal m odel. A buckling •n • ly sls w a s perfor m ed on a heli- copter t ai l boo m . Fo r • m od e l co n t ai n i n g 1 800 d eg ree s of fr ee do m, NA S TRA N predicted an e lg e n value o f 6 w hen u s in g t he l im i t de s i g n load s . Th e an a ly s i s too k ov e r 4 cpu hours. It w as fe l t this eig e n valu e wa s too high , bu t to r e m od e l finer an d prob a bly reduc e th e e lg envalue w ould ta k e e xcessive cpu time.
R igid Forma t 6 - Piec ew i s e Linear The pi e c ew l se li ne ar s olu t ion in N ASTRA N has never been used s uccess- fully. I t cou l d be a very he l pful a n al y t ica l too l i f it func ti on e_ properly, i Rigid F o rma t 7 - Direct Complex E i g env a lue A n •lys l s 4 1 This rig id fo r nu mt i s t i me consumin g . An i m proved complex elgenvalue routine is desired, a preferred met h o d w ould be • Q R a l g ori t hm such as the available ALIJ 4 AT ro u tl n e 4 .
i I . ¢ ' " 4 Rigid Fo_" . :' 8 - Dir e ct Fr e qu e ncy R e spons e Analysis Internal osci:_-_.ory loads and stresses for the response to _otor har- monic excitat{on , ' , ,_ ,alculated with rigid format 8. This rigid f_rmat . _ : would s e ldom _ ..... _ 'f the mod e a c c e l e ration t e chniqu e in rigid format II _* wo r ked _ t,_', : , ,. ' i5.1 v e rsion of NAS T RAN
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Rigid Form a t 9 - Dire c t Transient Respons e Rigid _.ormat 9 is us e d t o c al c ulate transient int e rnal loads an d " str e ss e s for su c h probl e ms as p a nel r e sponse to blast overpressur e s, air- f rame r e sp o ns e to gun r ec oil, an d landing lo a ds. As with rigid format B, this rigid format would seldom be used if the mode a cc eleration te c hnique worked in rigid format 12.
R igi d Forma t I 0 - M oda l Co m p l ex Eig en v a lu e A n a l ys is A s in rigi d f o r m a t 7, ru n t ime s hav e b ee n e x ces si v e• A n improved co m- p lex e ig e n value m e t hod i s needed t o m ake u se of t h i s ri gi d for mat p rac ti ca l .
Rig id For ma t II - M oda l Frequency R esponse An a l y si s R igi d for m a t 11 i s used t o a n alyz e s teady s t a t e resp onse of t he a i rfra me t o har m o ni c e x c it a ti o n wit h vary i n g f requenc i e s to s im ula t e sha k e t e st re su l t s . I t i s a lso used to ana l yze s t eady st ate _ e s p ons e to in- f light ro t or h a r m o n i c exci t a ti on. M ode accel e ra t ion i s requ i red t o ob ta in in t e rn a l lo ads, I n o u r cu r ren t l e vel , 1 5. 1 , it doe s n ot w or k. T heref o r e, to g e t t he i n te rnal l oa ds , r igi d f or mat 8 m us t be e xe c ut ed .
R i gi d F o r mat 12 - Mo dal Trans i e nt R e s pon s e An aly s i s Thi s r i g i d f or mat i s used to L n a lyze tran si e nt resp o nse pr o ble ms a _ described in ri g id for mat 9 .
Approac h . _ p r ogran n i ng h a s bee n f ound diffic u lt t o u s e . Ho w ever , s om e [ M AP alt e r s a r e ma de . _ a lt ers a r e used to obt ai n s p e cial o u tput to b e used in other ana ly se s. M od e p ri ntout and n orm a l mod e plottin g are a lt e r e d into ri g id form a t 11. _ is used to add dl ffe ren tlal s t i ffn es s to r ea l ei s en- v a l ue analys ls to d e t erm i n e c e ntrifugal s ti f f e nin g ef f e ct s on rotor bl a de s .
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CONCLUSIONS NASTRAN has been found tc be very useful in performing aircraft struc- tural analysis. When coupled with preprocessor and postproces_or programs, it h a s been used very efficiently and effectively in th design environment.
It is felt, though, that NASTRAN's effectiveness can be greatly enhanced t for our use with the following incorporations: i • (I) Fix the mode acceleration technique in rigid formats Ii and 12.
(2) An improved complex elgenv a lue solution is needed in rigid _ormats 7 and IG.
(3) Add r o tating b e a ,. dynamic effects such as the addition of Coriolis a cce l e r a tion t e r m s.
(4) Add rot a ry tr a nsfo rma t i on from rotor bl a de rot a ting system to the f i xed a irf ra m e syst e m.
(5) Rotor bl a d e ae rodyn a mics should b e in c lud e d a lo v g wi+h (3) and (4) f or a nalysis o f th e c oupled rotor a nd a i rf ram e .
(6 ) S ec ond ord e r di ffe r e nti a l sti f fn e ss t e rms ne ed to be a dd e d in rigid f orm a t 4 (7) Pi ece wise lin ea r a n a lysis sh o uld b e improv e d.
R EFEREN C ES I. Galli a n, D. A ., a nd Wi l so n , H. E.: The Int e gr a tion of N A STRAN I nt o He li c opt er A irf r a m e D es ig n / A n alysis. 29 th A nn u a l N a tio na l Fo r um o f t h e A n m r _ c a n He l ic o p t er S o cie t y , W ashin gton, D . C. , M ay 1 9 73.
" 2. B_ I k e , P W.. D e ve l op m en t of t he K ine mat ic F o ca l Iso l atio n ° y s t e m f or Hel icop t er R o to rs . 3 8 t h S hock and Vibra ti on S y m pos i u m, S t. L o ui s, M ay 1968 .
3. Shl p at a n, D. P . , W hi t e , J. A., a n _ C ron k h lt e , J.D. : Fuse l a g e - _' * Noda liz at i on. 28 t h An nu a l Nati o na l F or um o f th e Am er i ca n Helic o p t er Societ y , W ash l n z ton , D . C ., l_ y 1972.
# 4. W ilkinscn , J . N . : The A l ge bra i c Ei s env a lu e P r o ble m. O x f o rd Un iver s_. y Press , 1 9 65.
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i Figure i.- Finite Element Model of Helicopter Airframe i ",_ r.
_2 Fig ure 2 . - C om pu t er Gene r a t ed M o del ._ - '_"_ i VERTI C A L MAIN ROTOR I_ HORIZONT A L PYLON _ J R / " /
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f F sin _ f t i Note : A fo c used pylon ba l an c e s i __ . t he a p plied in p lane she a r, I p y lon inertia lo ad s, and _ r e st o ring spring l o ad to , .
_ OCAL POINT g iv e no r e su l tant pit c h- I , _ ! FO CUSED_PYLON _ / ing moment about the t I _ f us e l a g e c .g. !
-. .... . , ,- - _ --..- LINKS - Kin e m a ti ca lly RE ST ORING S PRING j c onstr a i n the py l on to rot a te a b o ut th e fo c al p o i n t . l & F s i n . _ft_ I N OD A L BF. A _ _._ _ : Nod al point s f r om wh i c h fus e l a g e , , , ; i s suspe nd e d t o gi ve no e x c itat i on i ,/ :,._'_ I to t he f u s e lagc a t t he fo rci ng •' . ' ' f r e q u ency, ®f ." "","I V I BRA T ING B .,r,
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Fig ure 3. - F ocused P y l on and N odal Bea m - U s ed f or _,'_,_, I so lati on of the Ai rfra m e F ro m M a i n R o t or Z xc i t ation '1 F US ELAGE S TIFFNES S AN I MASS D ISTRIBUTION P ARAMETERS f | OU TPUT DEV I C ES i NASTRAN DIGIT A L STRUCTL m __AL DYNAMI C S PROGRAM i NAT I_ AL F R E Q U LN C I _ - _S [ MOO E SHA P ES J HYBRID : P L O TTE R DIGITAL PROGRAM , " :. T R A N_F OI _IS N O _.L..X L • M_)DE RES,ONS ES TO G _N KRALIZE D COORD I NA T E S