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N76-29268 (NASA-TM-X-73153) ANALYTICAL 30D%LS POP ROTOR TEST MODULE, STRUT, AND BALkNCB FRAtlt DYNAMICS IN Tit", IV- 13Y 9- FT WTND TUNN%'L uilcld3 CSCL 14B (NASA) 18 p tic ,$ 3, G3/. i 9 46387 NASA TECHNICAL NASA TM X. 73,153 MEMORANDUM Ln M 17l x ANALYTICAL MODELS FOR ROTOR TEST MODULE, STRUT, AND BALANCE FRAME DYNAMICS IN THE 40- BY 80-FT WIND TUNNEL Wayne Johnson Ames Research Center Moffett Field, California 94035 June 1976 /` v 2. Gowrnmsnt Aztaasion No, , 1, Report No, 3, Recipient's Catalog No.
NASA TM X-73,153 4. Title and Subtitle 5, Report Date ANALYTICAL MODELS FOR ROTOR TEST MODULE, STRUT, AND g 6, Performin Organization Code WIND BALANCE FMIE DYNAMICS IN TnE 40- BY 80-FT TUNNEL 7, Authorial — 8, Performing Organitation Report No.
A-6692 Wayne Johnson 10, Work' Unit No, 9, PorformIng Organization Name and Address 0 -22 505- 1 and Ames Research Center, NASA 11. Contract or Grant No.
Antes Directorates USAAMRDL Moffett Field, California 94035 13, Type of Report and Period Covered and Address Iz Sponsoring Agency Norm Tech nical Mem orandum NASA, Washington, D. C. 20546 and Sponsoring Agency code 14, U.S. Army Air Mobility R&D Laboratory, Moffett Field, 15, Supplementary Notes 18; Abstract A mathematical model is developed for the dynamics of a wind tunnel support system consisting of a balance frame, struts, and an aircraft or test module. Ames 'Data are given for several rotor test modules in the 4.0- by 80-Ft Wind Tunnel.- A model for ground resonance calculations is also described.
17, Key Words (Suggaated, by Authorial) 18. Distribution' Statement' Wind tunnel module-balance dynamics Unlimited Rotor testing` STAR Category -<09 19. Securitq Claself, (of this report) Security`Claaif, iof this peel Price' 20, 21. No, of Pages 22, Unclassified Unclassified - 16 $3625 IBC,1TOLA' U 1, i ;Z rotor bl.rarie tWo-r` rvienr;1ona,'l 1,3 :'t-curve , lone r1'R a ^ :r otor' °force d oeff lolent lt C;; x rotor roll moment coePficion* rlrly rotor T)Itch moment Coe!"' i.cient vo lox toroue_ m.Mciern G,l r roto thrws.t coo f f l cient rotor sid e force coefficient 'y TY vector of rotor forces anO moments acting, ort huh, vec , 6or of aeroOynami,o gust velocity comnonent:s 111 , 11t vector"; or s shaft a xls sy. tern , Mk ra r tor ra i inn rotatlon na,trix betweun shaft axis an(I tunnel axe.:,: s ysto ms, long,iturl Inal, Fru,,t velocity Ur i lateral gust; velocity v(; vecto,,' of ^sup'no'rtsyw^tem input vari;a,bler vS W vertical gust velocity x h r,yh,7 ' shaft axis component,., of' rotor hub linear OASplacement x r vector of support System degrees of freee'om vector of of rotor hub :11nea,r and! angular motion ocx, oe y , a^ shaft; axis components of rotor hub a.ng i),lar r1isplacement rotor lock nun'he Penfi air i ty Q- rotor e..oli.riity :ratio .f2 i:o•t:or rot.at•i.ona,l sfeeO ORIG OP POD I$ QUAGE ALITyI ANALYTICAL 1` CDOLS V(;l RQT0 , R TEST 140,11LB o STRPT, AND BALANtrE 1 0 AME DYNA! , 11115 3 XN T111 0 , 40- BY SO-VT n TUNNEL e7TN Wayne Johnson 1i.S. Army Air nobility 1 , ?eh Laboratory Moffett 1i ield , California SUMMARY A mathematical model is developed for the dynamics wind tunnel of a support system consisting of a balance frame, struts;, and an aircraft or test module. Data are given for several rotor test modules in the Ames 40- by 90-ft wind tunnel. A morlel for ground resonance calculations is also described..
, INTRODUCTIC h; The wind tunnel tenting; of helicopter rotor.', requires a consideration of the dynamic characteristics of the cou- p ler y rotor and wand. tunnel support system. An aeroelastic analysis of a rotor in a mind tunnel is described in reference 1. Such an analysis requires to mathematical description of the wind tunnel balance, strut, and. test module. This report documents a model developed for the dynamics of a wand tunnel support system, Including data for particular rotor test modules in the Ames 40- by 80-ft wind tunnel..
SUPPORT EQUATIONS OF MCTION The required. description of the rotor support system takes the form of a set of linear, constant coefficient differential equations, exciter by forces and, moments at the rotor hub (and also possibly by fixed system control inputs), plus the rotor 'hub motion produced by the sup port degrees of freedom ( see reference 1). Let xs be the vector of support degrees of freedom., and. v s the vector of control inputs for the support system. Let *research Scientist, Large Scale Aerodynamics Branch, NASA-Ames Research Center ORIGINAL' PAGE Iu OF POOR QUALITY] oc be the linear, and angular shaft motion at the rotor hub, F the rotor forces and moments actin; on the hub, ant] g the vector of aerodynamic gust components. Following the definitions of reference 1, cK , P', an d are; the components of g O ;—r X, UU TO J c!.
2 %Ao. o dx ZW wG rw De y d Co rd9 ^ 2CMy f ZCM11 V-4 The gust components are in a tunnel axis system (x aft, y right, and z up), while of and V axe in the .shaft axis system (see reference 1) . These quantities are timennionles . -- based on the rotor tip speed A-1R, the g and the hub forces linear: hub cjisnlacements based on the rotor radius R, coefficient form. The general form considered for and moments in rotor, the rotor support equations of motion and the hub motion is thus x S + a 0 x s bv G g + IF 1 s + b a?XS + a oc exs For use in the aeroel,astic analysis of reference 1, these equations are made dimensionless, based on ^ , S^L , and R. With F in rotor coefficient form it is also convenient to normalize the equations by dividing by (NJZ)xb the characteristic inertia of the (where N is the number of blames, and I obtainer.? from the rotor blade). Note that the natrix a may always be matrix c (reciprocity theore',a) IJormal Mode Description Consider a general normal mo=le description of the elastic wind tunnel G(x,t) at an System. The (?isplacement u(r,t) and rotation support -2- ORIGIRAD PAGE 19 , F POOR QUALM arbitrary point r are expanded in :series of orthogonal vibration moAes, with the generalized coordinates qk(t); 11(r', t) qj,(t) T R A O , t) `' q k t) ^K(r)
k
equation: for the r1egrees of Freedom q are then The differential `^tikg t1k(9 k + Clr, k + 'lt qk)
is
frequency; Fr,, the macs and L-^ the natural,
I$ , -, the modal
where r+'k is the generalized structural stam ping coefficient for the moAe; and Q
"A-4 and a at
force. The hub motion is obtained from the mode shapes the rotor hub: 0^ Z.
c Z qk1 where ^ ^•lk dS` k K5T ^ k f G .:: ... _ ...
• ..
RST ^6k LS k jS , 2Sk V.
Ics Here '^ and fi are in the tunnel, axis system, so R ST is the rotation matrix to the shaft axes. The generalized forces clue to the rotor hub forcer" and moments are: ak' where I •laking these equations dimensionless as appropriate produces the required support equations of motion.
Ground lenona.nce "lo{lel A oimple model for ground is resonance calculations obtained by describing the nupaort by lateral and longitudinal inplane flexibility with an arbitrary number of modes, vertical, yaw, pitch, and roll motions of the hub are neglected. It in ansumed that the measured hub impedance in available from shake testa. Then the equations of motion for the generalized coordinates q k axe; C1kgk fk Ckgk + ; `I.
qk where f - H or Y for longitudinal and lateral, mode: respectively. The hub motion i xh long.modes k y h l.atmodes k The natural frequency sJ generalized mass rtk , and modal damping coefficient k , "k may be obtained from the hub impedance. The matxlces in the support equations of motion are thus [ F^k a ji k a2 _ C 1 a 1 ^' [ C * it -.]
where
t1k = rlk^(2 b/ 2)I ck = Gk/(?NIb n^132) , and lfk r1 k ( w k ln) 2 ; and the
hub motion matrices are zero except for the elements = 1 c w longitudinal modes ak2 1k AO aka - c lateral. modes ?k Cantilever wing A model for a wing attached to the wind tunnel with cantilever root restraint (no balance motions) is developed in reference 2 for proprotor dynamics calculations. The rotor is located on a pylon at the wind; tip, with the rotor hub a distance h forward of the wing tip elastic axis. An arbitrary angle of the pylon with respect to the tunnel velocity I,% considered.
The wing motion in described by three degrees of freedom: vertical bending, chordwise bending, and torsion. For further details of the model, r ee ref, 2.
.1p.
3ALAVOO '' a'i':t11`.I`, AND HC OULE V(.:JEL We shall now Develop a generalized coordinate description of a wind tunnel au..Ppoz:t consisting of _a balance frame, strut~ ♦, and an aircraft body or rotor tent module.
The analyni.s will use the Free vibration mo faes of the aircraft or module, coupled with a simple model for the balance frame and strut system. The resulting equations in normal mode form are ••N T + I'!c(e4 + w I: `I^k) n'Ici.cLi,k a'k F akcfk °t Here g , are the generalized coordinates for the complete system.
The matrix a (with rowF . a,,^) may be obtained ro f m the matrix o (with columns c k ) n.lway .
Balance r-'rame ='ones lder a balance frame nupportee by a scale system.
The balance has a turntable; the turntable yaw angle W is defined; positive to the W rig ht, 0 with -the Main struts forward and the tail` strut aft.
The balance frame motion is described by the ` six linear and angular rigid cCLs.
body degrees of freedom --XD• Y ^ ^ y , and The elastic c ^ I3' ^ deflections of the balance frame are neglected.
Thus the motion of an arbitrary point (x,Y,$) red: ttve 'to the balance frame CG is given by x g + 049 a a k The balance scale system is represented by springs to fixed ,grounds four lift scales (I.TJ ), two side scales (I".), anal. one crag , scale (Y. The balance system optionally has viscous dampers between the frame and ground -- eight Mampers at the corners of the balance frame working verticall y, 4 lo n gitudinally; an d laterally).
PAGE ORIGINAL TYI OF POOR QUALITY
struts
and `here are two m4In atrutn a tall strut. It is assumed that are cantilevered at the root (the balance frame), and the main struts the taps. The tall strut is pinned at the tips pinned at the pinned, at root longitud .nallyr and cantilevered at the root l,a.teral.l.y. The inertia is included In reaction of the strats Is not consiAered (the, strut mass ame Inertia). Only the npri.ng restraint between the balance the balance g for the and module in considered lateral, longitudin4l, and vertical for the tail strut. The strut lateral and vertical main ntruts, ands on the modes of a uniform cantilever team.
c1efl.ection mod-el is based The vertical stiffness of the strut is very high; It is only included motion constraint*, It a: the simplest mean* of handling the vertical be noted that the assumption of pinned ,joints at the strut tips should even _cantilever at the roots, i,, , probably not very ;oovi (based on and experimental -results) . ' `Vhe the stiffneaseo required to match various more complex, perhaps so complex that even a physical system is of course moclel such as PiASTRAN will not improve sophisti.cateO structural dynamics correlation much.
also considered., for which only the two main A prop test rig 16 pitch at the s trut tips are used. The mc+lule is constrained. in Rtruts In that case.
The strut tip displacement is given by the >sum of the bending .movies du e of a cantilever, beam. Thus for the left main strut, the tip motion bending is: to elastic ,dX^, 9n^sx longitudinal py = GMs ,^ lateral tA s vertical 4^c, cj "'sL^ M pitch C ¢M ^^ 4a ^G =- Mss where R is the strut length. These components are defined with respect to
p
axon, yawed with the balance turntable. The ti deflection for the ri ht
g
cR)
mlin strut (; and the tail c trut (T^) are deftnoc Y ntmilarly
^cln^ay lateral and vortioal defloctionG tor the t ail ; trut, the mai n ntrut
an d
pitch motion io only r equired for the Trop test rig). The potential onexr.ion of ben n ding anO extonslo of the ntrut are qn bending bon(' ^extenri.on ,. -ext qn The modes of. la uniform cantilever 'beam b.i.ve s n , 0 ,lL
1 YY ..3 1 ' / ^
' . ^: ' y any qq}} > 81.g ^M 10-996 3 656.
Nominally theoZnink; conrkte ntz axebex13 fix/ R 3 s nr^oxt » , LA/3^; i n practice these parameters are evaluated by metchinp to the xnt?as uxer? frequenoips.
Module The module motion is describer) by the normal modes of free vibration; the first six mores are the linear and angular rigiO body degreea of Preedort.
'The motion in defined with respect to the yawed axis system, with origin at the module GG. The linear anO anVIa<r motion of the point x # (x, ,z) is thus given by the module eeneralizen coordinates 4!I 1, at follows: 4(+q^{^t^M^^x,, module k
J
e moeu le `l^^k^t)^MK^r)
For the six ri.AV boozy modes ^N^ ° x In particular, the rotor hub notion is given by o< M Y to are in so it is n000ssary and the yaW axis oyatems Here jnatri x rromulti.pl,y by the rotation VA w ' TU to obtain the hub motion in the tunnel, axis oyntem.
irtodule/strut Connection The o otem has constrainto i,mpon d by the connections 1)etween the module and strut tips. Specifical ly, it is r equi re , ! that the striA tip l or balance motion plue strut bent Ing terms)' equal the motion (composec r i module motion; xa.t the connectio n raoi.nts, This constraint is appl.ie to the three linear deflection it the main strut tips and to ,the lateral o Q the tail st r the prod test rig,
and vertical defl,eoti,on at rut ti
p.
the pitch deflection constraints at the main strut tipa replace the tai rait constraints.
De ees of Freedom The degrees of freedom of the system consist of the six balance rnodtrl.e riai.d body motions, the six module xigVl body motions, anO N e freedom eince elastic modes. The strut aeflectie. ► s rho not aft degrees of The constraint equations the strut bending inertia Is not considered.
thus must be used to eliminate the strut deflections from the set of coupled normal equations to be solved for the equations, leaving _12+H mod e s of the balance/strut/mooule system.
Energy and Constraints The kinetic energy of the model describers above is .
Z t M^^'^Q 1- MgtR T MBx Yg r '} otgx +;^32 Ogg + ^`3x e uati onu inoInd ing ennst ai ntn o The nn. a can.Ftraint f^qua ti ro of tho for n
r. sq) r 0 for k i ... h
nt.n (As horn), o ve eqtatillo ma y .iith I^nwar oonrtrai, th K3S:.` wA'tten qn ,'hon the f;igr^ingo equ!"lono with tho i.nto are c constra U1 uY' k ^a # x f or a ! e .!^ v1 ^ A Si CJ9M „ 4l `Phur*: there are NO oquationc for the n of froe#nor nO the Agr anon ► OnE r e e qn
0411 .tirltorn No°to that th o mass W Hi ffneng mattloen am rymmc ixingl
with linear constraint .
proce0ure the olvationn Oercribly the balance, ntrgt, `4y thin g an! too ale )ynami a r y s ten may be` constructed.
Sol"tion 111nIna.ting the LAGranac multipliers anO cone trai,nt equati onr f~r, the system given a o p t of 12+21e Line ctMerential equations, of ar the fori: C APii, + .1^^ + A .fs 0x aaeroOynamic damping), .there ,^^ Ir,, a Aamping matrix (balance dampers or > and 4 is the generalized force vector (due to hub d nonentni a,W Forces an contvibu^ti.ons So; a.e oOynamie gusts or support € e ten control. 1peryhnp, p ^ a The homogeneous, War pad equations are V + A ox 0 -10- PAGE OF,pW^ OOR QU^.^ where A and A are real oymmetric matrices.
It follows that the eigenvalues 2 0 are real and positive, and the elgenvectors real.
Lot Wk be the eigenvalues of A2 Ao, ant i . T the modal matrix (columns are the eigenvectors).
Thsn the modal coordinates for the coupled system axe defined 'by q = T - 1x; the natural .frequencies of the_mod.es are , 0 1 a nti the (diagonal) generalized mass matrix is `gA 2'i" P1
I ki
The damping matrix Is then G— 'X`r A T J (only the diagonal terms are usually important,), Finally, the hub motion in terms of the modal coordinates of the coupled system is: Tg M j s0 ... ...
k o tl{ TMM' -J a where is the appropriate column of the modalmatrix To This completes c the description of the rotor support equations of motion and the hub motion in the required, form.
DATA FOR THE AMES 40- BY 80-FT WIND TUNNEL The following sections give the geometric, mass, and. stiffness data for several rotor test modules and strut combinations in the Ames 40- by 80-ft wind. tunnel. The geometry was measured directly.
The inertia data were obtained from direct measurements and from NAS TPRAN calculations. The stiffnesses were obtained by matching the calculations with shake test results for the principal natural frequencies of the system.
Experiment is the only reliable source for mod.a.l damping values, because even for the balance dampers the 'modal damping is very sensitive to the details of the motion. The shake test data used was from references 3 to 5.
Balance M k 53500
^ z A
x 32.5000 kg— m I ly 340000 kfr, -m2 '1 810000 %a-m^ relative to center turntable, drag x 0G = -,49 m fnr vaw ' elevat{ on ^ 0.
link s x .03 zPC' tm KE 9000000 Nlm K^ 9000000 KIm XL 36000000 IT/m ' .^ 15000 N / m/sec Cr3emper P ositiono m drag link elevation) (relative center turntable, y ^.
x scale springs A 3.08E a 0 IBS ?.553 FS -3 0 0 M 99 ; 1.8 IIL 4.877 —5.153 1.8 -4.877 -6.153 UL 1.8 LIIL 4.877 5 -153 1.8 1,L - 4.877 5.153 ria;mpers 3.05 1.4 Long ,5E - 4.8R - 88 3.05 Sw -4.
-3.05 1.4 2 4.88 ; 4.88 3.05 1.4 +I 1.4 lat SE -? . 1 - :.15 Sw -3.51 t.4 5.15 3.20 -5.15 1.4 NE 1.4 raa 20' 5. 15 3.
Rotor 'Test Apparatus M 13800 kg 2600 kg-m xx 1 X4500 kg-m2
1z 0500 kg-r 2
M 2900 %g-m?
IT 71x tail length = 4-521 'm tread 2.438 m long long struts, short short struts, struts bal.'locked bal. locked struts w strut height 4.72 4;72 3.96 m 3.96 1120000 .5500 00 45 0000 NIm 830000 riS x ,500000 tI/m K , 17 30000 920000 $30000 ll. i y 56 0000 ' 410000 270000 N /m ?30000
X 6 x N/m
Vert Position, m (relative module CC) x y z left main strut - 1.503, - 1.219 -.15 ,right main strut -1'. 03 1,219 tail strut 3:018 hub 0 1.679 -13- A Rig;
Propellor T est
M 8600 kg Ix 14600 kg-m2 C 0 for turntable yaw Yy kg-m2 95 0 22 = 14600 k-m e tread - 2.438 m strut height"- 6.07 m t balance free balance locked K 310000 ;310000 N/m ri MS 580000 450000 N/m Kh1S Y 6 x 10^ N/m Vert j Position, m (relative module CG, 0) x ?
Y left main strut 0 - 3.39 0 right main strut 0 0 -.95 hub 0 3.20 0 -14- REPERENCES Johnson, Wayne, "Aeroelastic Analysi.e for Rotorcraft in Flight or 1.
In a Wind Tunnel," NASA TN-A, in preparation 2. Johnson, Wayne, "Analyti.cal, Model for Tilting Proprotor Aircraft Dynamics, 'including Blade Torsion and Coupled Bendina Modes, and Conversion Mode NASA TM X-6?,369, August 1 Operation," 9 7^6 Johnson, Wayne, and B goers, James C;,, "Shake Test of Rotor Test 3- 2418, Apparatus In the 40- by 80-ft Wind Tunnel," NASA TM X- 6 February 1975 Johnson, Wayne, and. Blgaers, James C., "Shake Test of Rotor Test 4.
-ft Wind 'runnel," Ang^,ratus with Balance Dampers In the 140- by 830 .
NA 5A T" X 4 ('11 1,70, July 1,,.75 the 160- by Johnson., Wayne, "Shake 'Pest of a Propeller 'Pest Rig i n 5.
80-ft Wind. Tunnel," NASA TI'i X-730$0, November i5