MODELLING AND CHARACTERIZATION OF A NOVEL GIMBAL
TWO-BLADE HELICOPTER ROTOR
Alessandro Croce, Radek Possamai, Alessandro Savorani, Lorenzo Trainelli
Politecnico di Milano, Milano, Italy
Abstract
A novel rotor design specifically conceived for lightweight helicopters is described and analyzed with respect to its kinematic and basic performance characteristics. The design is based on an innovative gimbal mount which allows a quasi-constant-speed transmission from the mast to the hub in a wide variety of relative motions between these two elements. This is motivated by the need of alleviating substantial oscillating rotor loads transmitted to the mast as a result of cyclic flapping. The rotor design is illustrated in detail and the results of several studies are reported, which assess the validity of the proposed design and pave the way to further analysis concerned with the rotor dynamic behaviour.
This paper is dedicated to the memory of dr. Vladimiro Lidak (1944-2012), Italian helicopter designer and prolific inventor.
1. INTRODUCTION
Lightweight helicopters represent a widespread category of rotorcraft employed in a large variety of roles, ranging from pilot school to sports aviation, aerial work, scouting, and many more. Contrary to larger rotorcraft categories, with their complex design and manufacturing processes, economy considerations and simplicity of operations have led to a markedly lower degree of innovation in this field. As a result, the relatively simple two-blade teetering rotor architecture is still the prevailing design, with its known limitations and drawbacks.
These are especially to be found in the significant 2/rev (two periods per rotor revolution) loads transferred to the mast as a result of rotor cyclic flapping, such as in forward flight or while hovering under gust conditions, which impact considerably on component fatigue life and eventually in maintenance costs. Possible solutions include a radical change in configuration, such as with three-blade fully-articulated designs. However, this is done at the expense of the highly valued characteristics of the two-blade configuration with respect to ease of stowage and transportation, in addition to simplicity and economy.
Among the initiatives towards innovation in light helicopter rotor design, we address the gimballed main rotor head by Dr. Vladimiro Lidak (1944-2012), a missed Italian rotorcraft designer and innovator. Lidak’s concept preserves the two-blade configuration, while strongly innovates the rotor head design, introducing an original homokinetic joint below the rotor hub. This joint has been specifically designed to alleviate the 2/rev rotor loads, at a price of a higher mechanical complexity
compared to a teetering rotor head. This rotor design was chosen by the K4A S.p.A. Italian company, along with other patented innovative concepts from Dr. Lidak, to be implemented in a novel lightweight two-seat helicopter named KA-2HT which is currently in an advanced development state.
This paper presents a characterization of the kinematics and basic performance characteristics of this novel rotor design based on a high-fidelity modelling of the complete rotor assembly.
2. ROTOR MODEL 2.1. Overview
The main rotor designed for the KA-2HT light helicopter is a two-bladed gimballed, stiff-in-plane rotor. The gimbal joint is the main feature of this design, allowing the hub to rotate freely about the blade teetering and feathering axes. This is obtained through a complex hinge system located within the rotor head. The designer’s main goal for this peculiar architecture is the strive for a good approximation of a perfectly homokinetic mast-hub transmission, i.e. an ideal linkage providing the equality of the values of the mast and hub angular velocities, irrespective of the latter’s tilt with respect to the former.
This characteristic is particularly useful in rotary-wing systems such as helicopters and tilt-rotor aircrafts, because it allows to relief oscillating rotor loads exerted on the rotor shaft. Achieving perfect constant-speed transmission for general (spherical) motions is a complex task and some degree of approximation is usually entrained in rotorcraft gimbal mount designs. Typically, for a given
constant sp obtains a driven com that is lowe between th and the am the magnitu axes. Of co gimbal mo Cardan, join In-plane sti blade lag h the hub cen bar connec provided wit rotor stabil damping. T helicopters provides an Figure 1. C conside 2.2. Roto The rotor considered a specially coinciding require a c angles betw constant-sp provides th (teetering a arbitrary tilt shaft axis. A peculiar s this innovat constant-sp element in peed of the d time-varying mponent (hub r than the ma e average o mplitude of th ude of the m ourse, the sim
unt is repre nt. iffness is th hinges. The ntral body. It cted to two th typical ae lity and co This compon because o n overview of CATIA model of ered in this wo or head head is the in this work. y devised hinge cent centring elem ween the driv peed transm he two gim and featheri t rotation ex sequence of tive mount, w peed joint as this sequen riving compo g, oscillating b) around a ast value. Bo output and t he oscillation misalignment mplest and m esented by he result of flybar is rigi is composed o short blad rofoil section ontrol throug nent is well of its simp f this comple f the shaft-roto ork (courtesy o e very hear . Its gimbal m double Ca res. Double ment able to ven and drivi mission. Th mbal degre ing) that all xcept for mo mechanical which aims t s much as p nce the tran
onent (mast) g speed of n average v oth the differ the input sp ns are relate between the most approxi a universa the absenc dly connecte d by a transv des, or pad ns, contributi gh aerodyn suited for s plicity. Figur x rotor head or head assemb of K4A S.p.A.). rt of the de mount consis rdan joint e Cardan j o maintain e ng shafts for his arrange ees of free
low the hub tions around linkages rea to approxima ossible. The nsmission is , one f the value rence eeds ed to e two mate al, or ce of ed to verse ddles, ng to namic small re 1 . bly esign sts in with joints equal r true ment edom b an d the alizes ate a e first s the ‘carr conn conn ‘inte abou corr The to th allow perp corr The abou subj whe Fig inter In tu hub a pa inne addi exte devi the b Figu Eac arra cros the chai body The an a mas axis allow bise The but t two rier’ (Figure nected to th nections def ernal crossw ut an ax esponding to ‘external cr he internal wing a re pendicular esponding t refore, while ut a single jected to a c en referred to gure 2. Compon nal crosswhee (
urn, the exte central body air of holes e er part of the itionally pins ernal crossw ce for two s bisectors (Fi
ure 3. The bisec
h one of the nged on sswheel, is co upper and in provides a y to the bise first body c axis perpend st, and relati parallel to t wed to freely ector pin axi lower bisect this time from
correspondi 2, left). T he mast and ining a revo wheel’ (Figur is perpend o the feathe osswheel’ (F one through elative rota to the for o the teeter e the intern axis, the combination o the mast.
nents of the gim el (green), and e (courtesy of K4 ernal crosswh y by a revolu ngaging two hub central s protrude fro wheel. Thes scissor-shap gure 3). ctor arrangeme ese identica the two s omposed by lower chain a complex li ector pin thro an rotate rel dicular to th vely to the s the first. Fina y translate alo s, thus real tor chain pro m the carrier ng bodies co
This elemen d is provide lute joint tha re 2, centre dicular to ering degree Figure 2, righ h another re ation about rmer and ring degree rnal crosswh external cro of two relat mbal mount: c external cross 4A S.p.A.). heel is conn ute joint obta pins protrud l body. Furth om the oute se represen ped mechani ent (courtesy o l devices, sy sides of th y two subsyst ns. The up ink from the ough two sm
latively to th he bisector second abo ally, the sec ong and rota lizing a cylin ovides an ana r to the bisec coupled with nt is rigidly ed with two at allows the e) to rotate the mast, of freedom. ht), is joined evolute joint t an axis the mast, of freedom. heel rotates osswheel is ive rotations carrier (grey), wheel (yellow) ected to the ined through ding from the hermore, two r part of the nt a runner isms termed of K4A S.p.A.). ymmetrically he external tems termed per bisector hub central aller bodies. e hub about pin and the ut a second cond body is ate about the ndrical joint. alogous link, ctor pin. The the bisector y o e e , . d t s , . s s s ) e h e o e r d y l d r l . t e d s e . , e r
pin through to translate This comple is designed obtain the achieved b between re system com the effective correspondi two. Indee relative rot crosswheel hub to ass referred to external cro feathering a rotation abo of the extern Through the actually bis the hub a approximati 2.3. Cont The blade p of two ind primary and The primary mechanism control is respectively turn reflect commands. rotating sw motions to of linkages ‘mixers’, on example application. Figure 4. Ap seco The secon mechanical cylindrical j together. ex arrangem to constrain constant-sp by enforcing elative rotat mponents, th e degrees o ing to the s d, the bise tations betw and betwe sume the sa the mast, osswheel is h axis. On the out the teete
nal crosswhe e described sects the ang axis normal ing a homok trol system pitch control dependent c d secondary y command i in which generated y, of the non ts the pilot . A pair of co washplate, p the rotor he ending in tw ne for each of pure pplication of the ondary control ndary comm connection
joints are fur ent, patented n the hub mo peed transm g a nearly tions among hus reducing of freedom fr sequenced re ectors basic ween carrie en external ame values. the relative half that of th other hand, ering axis is t eel. setup, the gle formed b to the ro inetic transm is achieved control actio commands. is applied th collective a by trans n-rotating sw cyclic and ontrol rods, rovide the t ead through wo small bo blade. Figu primary cy e primary cycl (courtesy of K mand is th n between rther constra d by Dr. Lida otions in ord mission. Th y constant g some of g the numbe rom three (t evolute joint ally impose er and exte crosswheel In other wo e rotation of he hub abou , the hub rel the same as bisector pin by the mast otor plane, mission. by a combin ons termed rough a stan and cyclic lation and washplate. Th collective connected to transfer of a suitable s odies termed ure 4 shows yclic comm ic control with K4A S.p.A.). he result o the hub ained ak [1] der to is is ratio f the er of those ts) to e the ernal and ords, f the ut the lative s that axis t and thus ation the ndard pitch tilt, his in input o the input eries d the ws an mand null of a (and ther moti com invo rece is th and an appl tran to bo Figur 2.4. In th achi a fu of th idea the C art f with struc capa can mod appr enfo code proc stab com asse rigid appr 2.4.1 The elem This As i a nu carr bran cros
efore the flyb ion about th mponent of olves only c eives mecha he end-effec from the co example lication. The sferred to th oth mixer an re 5. Applicatio primary c Multibody he present w ieve a high m ully represen he hub and b alized as a m Cp-Lambda finite-elemen a large libr ctural eleme able beams be equipped dels and a ropriate holo orced by me e implemen cedures tha ble [4]. The mplex system embly of thre d bodies a ropriate. 1. Rotor h rotor-hea ments that r s assembly is t can be see umber of rig ier to the h nches. One sswheel, i.e.
bar) and the he featherin the pitch im cyclic effects nical input fr ctor of the p nnection to t of pure e resulting he blade by d blade throu on of the secon control (courte y model ork, an effort modelling fid ntative, nonli blade motion multibody mo tool [2,3]. Th nt aero-servo rary of eleme nts such as and shells, d with backla re modelled onomic or no eans of Lag ts special i at are non-multibody re is presente ee subsystem and diverse ead sub-sys d subsyste realise the s symbolicall en, the subsy gid bodies co hub by mea goes throug the lower bo mixer, reflec ng axis. Thi mposed to s. The mixe rom the pitch primary comm
the hub. Fig secondary mixer mot a pitch horn ugh spherica ndary cyclic co esy of K4A S.p rt has been c delity in orde near kinema ns. The rotor
odel and imp he latter is a o-elastic mu ents includin rigid bodies and joint mo ash, free-play d through on-holonomic grange mult implicit time -linearly un epresentatio ed in the follo ms comprisin e holonomic stem em include mast-hub tr y depicted in ystem mode onnecting th ans of two gh a joint to ody at point A
cting the hub is additional the blades er therefore h link, which mand chain, ure 5 shows command ion is then n, connected al joints.
ontrol with null .A.). carried out to er to perform atic analysis system was plemented in state-of-the-ltibody code ng the basic s, composite odels. Joints y and friction the use of c constraints tipliers. The e integration conditionally n of such a owing as the ng numerous c joints as es several ransmission. n Figure 6. el consists of he mast and mechanical the internal A, the upper b l s e h , s d n d l o m s s n -e c e s n f s e n y a e s s l . f d l l r
being the e rotate relat hinge centr design. The system. Als representing upper and l level, the re since one o motion. Figure 6. To 2.4.2. Con The contro mechanism the sake of into two sm transfer and Figure 7. Top The primary Figure 7, rotating sw body terme external cro tively to one e, as a nece e other branc so this is mod g all the actu ower chains edundancy of of them is su opological sket ntrol chain s ol chain s providing p f clarity, it i maller mech d pitch applic pological sketc su y control tra represents washplate to ed ‘rocker’ i osswheel. Th e another a essary featu ch goes thro delled in a v ual constrain s. Of course, f the bisecto ufficient to de tch of the rotor sub-system subsystem itch input to s presented hanisms: the cation subsys ch of the prima bsystem. nsfer subsys the linkage the rotor h is located. T hese two bo bout a com re of the pre ough the bise
ery detailed nts included at the mode ors is not nee etermine the r-head subsyst is a com rotor blades d here separ e primary co stems.
ary control tran
stem, depicte from the head, where This mecha odies mmon esent ector way, in its elling eded, e hub tem. mplex s. For rated ontrol nsfer ed in non-e thnon-e anism inclu the nece prim swa arra syst degr colle tran joint Cyc swa rock The repr appl mec linki subc linka tran horn arou actio moti flyba The pitch flyba Fig As s hub coni allow 2.4.3 Eve geom capa stiffn stati
udes the non control rods essary joints mary control shplate up ngement gu tem with n rees of free ective pilot slations of t t, and eventu lic inputs shplates an ker. pitch co resents the lication from chanism incl ng the rocke chain linking age from th
sfers the mix n and the pit und its axis on is transfe ion, the sec ar tilting, as
prevailing h h is that co ar, cited abov
ure 8. Topolog seen in Figur is not limi ing, through ws the relief 3. Blades ntually, the metrically ex able of ac ness cross-c and dynam n-rotating an s, the rocke s allowing t actions impa p to the uarantees a no redunda dom. By wa inputs are he swashpla ually into a t translate i nd correspon ommand a double mec the rotor h udes the pr er to the mixe the flybar to he mixer to xed pitch com
ch hinge to s. While the rred to the m condary cont a result of hub motion orresponding ve also as hu gical sketch of subsyste re 8, the blad ted to pitch h a dedicate of lifting blad blades ha xact, nonline ccommodatin sectional m mic analysis nd rotating s er, the mast
the transmis arted to the rocker. T a statically ant nor u ay of this a represented ates through translation o into a tilti ndingly a ti application chanism of p head to the rimary contr er, the secon o the mixer, o the blade mmand throu provide blad e primary p mixer by way trol action d the hub gim component g to the flap ub feathering the complete c tem. de motion re hing, but in ed hinge. T de loads in o ave been m ear finite elem
ng a fully matrix. This
of laminate
swashplates, and all the ssion of the non-rotating The overall determined ndetermined arrangement, by vertical a prismatic f the rocker. ng of the ilting of the sub-system pitch control blades. This rol subchain ndary control and the final . The latter ugh the pitch de feathering pitch control y of a rocker derives from mbal motion. upon blade pping of the g. control chain elative to the ncludes also This feature peration. modelled as ment beams y populated allows the d composite , e e g l d d , l c . e e m l s n l l r h g l r m . e e e o e s s d e e
blades with couplings. N full finite ele In addition, are endowe the calcul modelling a on classica airfoil ch aerodynami unsteady co 3-D correc model with The subsys together in Cp-Lambda control tran subsystems control cha Figure 8. Fi subsystem assembly. bodies, 21 number of 1 Figure 9. 3. KINEMA The rotor m and analyse studies. In p pitch contro system. Sec constant-sp present gim 3.1. Cont A prelimina multibody kinematics with the CA provided by were impos range of c both put in Figures 9 a h their tailo No modal red ement equati the blades, ed with aerod ations of adopted in th l two dimens haracteristics ic center orrections. T ction implem a variable nu stems descri the multibod a code. In f nsfer and s via the ro ain subsyste inally, this is via the ma The resultin beam eleme 1756 degrees Blade pitch as translation (co ATIC STUDI model describ ed by mean particular, we ol and flappi cond, we ch peed approx mbal mount. trol mixing ary verificatio model with was perfor ATIA model y K4A. Diffe sed on the ro collective an nto effect by nd 10 show ored cross duction is pe ons are used as well as th dynamic pro aerodynam he Cp-Lambd sional strip th s, account offset, twis The model is menting the umber of stat ibed above dy framework fact, connec pitch comm ocker elemen em is obtain s connected ast, obtainin ng model in ents, and 44 s of freedom s a function of ollective comm IES bed above h ns of a num e considered ng actions o aracterised ximation ob on of the co respect to med throug of the KA-2 erent relativ otor system d primary c y actuating the results o sectional el erformed, and d at all times he flybar pad perties that a mic loads. da code is b heory using ting for st, sweep, s completed dynamic in tes [2,3]. are easily li k provided by cting the pri mand applic nt, the com ned, as see to the rotor-ng the full ncludes 59 joints, for a m. the swashplat mand). has been ve mber of kinem
d first the effe on the statio the quality o tained with orrectness o o geometry h a compa 2HT rotor sy ve motion in spanning the cyclic comm the swashp of the compa lastic d the s. ddles, allow The ased local the and by a nflow nked y the mary cation plete en in head rotor rigid total te rified matic ect of onary of the the of the and rison ystem nputs e full mand, plate. rison in te Ana com Figu insta two blad Fig 3.2. The cons simi roto The hub mas spee diffe In o mod with show erms of the re logously, th mmand was ure 11 illustra ances show different mo de pitch angle gure 10. Blade (p Figure 11. Bla (se Homokin constant-sp sidered in th lar approach r-head subs numerical e through pre st at constant ed compone erent motions A. banking referred B. oscillatin that con C. enforcin about th order to pe difications we respect to ws this mo esulting blad he full span imposed b ates the com an excellent odels, with a e barely reac pitch as a func primary cyclic c de pitch as a f econdary cyclic etic behavio peed capabil his work has h to that pre ystem was c experiment w scribed rotat t speed, and nt along the s were impos the hub t to rotating m ng the hub tains the ma g a conical m e mast axis. erform thes ere required a fixed refe odified mod e pitch. n of secon by flapping mparison in t t agreement a maximum ching 1.2%. ction of the sw command). function of the c command). our lity of the gi s been analy esented in [ considered i was conducte tions, while d measuring e hub normal sed to the hu through a mast-fixed ax normal in a ast axis; motion of the se tests, s to impose h erence frame del where ndary cyclic the flybar. this case. All between the mismatch in washplate tilt flybar tilt imbal mount ysed using a 4]. Only the in this case. ed tilting the spinning the the resulting l axis. Three ub: fixed angle xes; fixed plane e hub normal ome model hub motions e. Figure 12 the hub is c . l e n t a e . e e g e e e l l s 2 s
connected t joints whose By imposin joints, the d enforced. Figure 12. To modified Type A tes relative tilt This was ob ϕ1 = 0° and this case, observed, contrary to Cardan join Figure 13. speeds (a Type B te oscillation a Oscillations frequency v the constan ϕ2 with amp and with th to the groun e relative rot g suitable p esired plana opological ske to perform the a sts were ca of 20° betw btained by e ϕ2 = 20° as a perfectly demonstrate o what wou t (Figure 14) Time histories bove) and rela oscilla ests were c amplitude to s were cons values. This nt value ϕ1 = plitude equal he same fre nd by means tations are de prescribed ro ar and conica
etch of the roto e constant-spee nalysis. rried out se ween the hu enforcing the seen in Figu homokinetic ed in Figu ld be deliv ). s of the mast an ative rotation (b ating motion. carried out o 20°, with n sidered at s was obtain 0° and a co to the desir equency. An s of two rev enoted ϕ1 an otations to t al motions ca or-head subsys ed transmissio etting a con b and the m e constant va ure 13 (below c behaviour re 13 (abo ered if usin nd hub rotation below) for plan
setting the null mean v 2/rev and 4 ned by enfo osine functio ed semi-ape example of volute nd ϕ2. these an be stem on stant mast. alues w). In was ove), ng a nal nar hub value. 4/rev rcing on for erture f the inpu Figu hom Figu Figu pre Fi spee Type diffe 15°, prec enfo equa sam this achi osci than aper moti cons This in th vary 16, for t 7% 20° osci aper ut functions ure 15 (belo mokinetic beh ure 15 (above
ure 14. Time his esent design (r
igure 15. Time eds (above) and
p e C tests w erent motion and 20° cession freq orcing a cos al to the d me frequency case, the ho ieved. In fa llating behav n the mast rture and/or ion induces stant-speed t s phenomeno he case of 2 ying semi-ape a loss of 3% the 10° semi for 15° sem semi-apertu llations are rture, growin for the 20°, ow). In this haviour was e). stories of the h ed dash-dotted (black lin histories of the d relative rotat planar oscillatin were carried s describing semi-apertur quencies. T sine function esired semi y, and ϕ2 = omokinetic b act, the hu viour and its speed. Incr r the freque a progress transmission on is depicte 2ev and 4/re erture values % in average
-aperture co i-aperture an re. Also, the contained be ng to less tha 4/rev case case also, observed, a hub rotational s d line) and the ne).
e mast and hu tion (below) for ng motion. d out enforc g cones of θ re, at 2/rev This was o n for ϕ1 wit i-aperture a acos(cos(θ behaviour is ub speed p s average va reasing the ency of the sive degrada n performanc ed in Figures ev conical m s, respective e hub speed onical motion nd to 12% fo amplitude o elow 0.2% a an 2% at 20 e is given in a perfectly as shown in
speeds for the Cardan joint b rotational r the 20°, 4/rev cing several θ = 5°, 10°, v and 4/rev obtained by h amplitude nd with the )cos(ϕ1)). In not perfectly presents an alue is lower cone semi-precession ation on the ce. s 16 and 17 motions with ely. In Figure is observed n, growing to or a sizeable of hub speed at 10° semi-°. It is worth n y n v l , v y e e n y n r -n e 7 h e d o e d -h
noting that present roto a 2/rev wo amplitude approximati transmissio range of in angular spe periodic var behavior is characterist where an blade load other rotor h Figure 16. speeds for Figure 17. speeds for Figure 18 transmission the Agusta the foresee or when cyc obbling resp values wi ion of a n appears fa nterest, both eed value a riations withi s at the ro tics discusse improvemen transfer to head architec Time histories the 5°, 10°, 15° Time histories the 5°, 10°, 15° 8. Comparison n performance aWestland ‘arti conic en dynamic lic control is ponse with thin 10°. an ideal airly good in h in the pre and in the n a revolutio ot of the p ed in anothe nt is observ the airfram ctures. s of the mast an ° and 20°, 2/rev s of the mast an ° and 20°, 4/rev n between the c e between the p ichoke’ in the c cal motions. behaviour o applied invo typical hub Therefore, constant-s n the operat eservation of ability to re on. This favo positive dyn er study, see ed in oscill me compare nd hub rotation v conical motio nd hub rotation v conical motio constant-speed present design case of 20°, 4/r of the olves b tilt the peed tional f the estrict rable namic e [6], ating ed to nal ons. nal ons. d n and rev Furt gimb tilt-ro resp are Lida seen 4. To c perf fund mer the t 4.1. The inde cond ratio expe idea mom from We mini weig coe Figu agai show pred for t [7]. certa the pres As a we c thermore, a bal design ad otor project d pect to 20°, 4 very close, w ak’s design n in Figure 1 ROTOR PER complete the ormance an damental qu it, the powe torque coeffi Figure of rotor figure ex related t dition. The f o of the id ended to ho al power is mentum theo m the multibo explored th mum weight ght values co Figure 19. Figu efficient for the
flight me
ure 19 illustra inst the roto ws a secon dicted using the same rot Although sim ain mismatc finely deta sent multibod a further ele calculated al compariso dopted in the described in 4/rev cone m with a slight a at lower se 8. RFORMANC e considered alysis was c antities such r loading, th cient. merit and p of merit is an to the effic figure of mer eal power over at a g computed b ory, while th ody model in e range fro t to 170% o onsidered for ure of merit as e Cp-Lambda m echanics simul
ates the roto or thrust co d curve rep a flight mec tor based on milar, it is p h between t iled modelli dy framework ement for pe so the powe on with the e AgustaWes [5] was carr motions, the advantage o emi-aperture CE rotor charac carried out t h as the rot he thrust coe power loadin n important p ciency of th rit FM is de and the ac iven weight by means of he actual po steady-state om 70% of of the nomin r the KA-2HT s a function of t model (blue), co lation model (r or figure of m oefficient CT. presenting t chanics simu n a formulati possible to a the curves a ng reached k. erformance a er loading PL e ‘artichoke’ stland ‘Erica’ ied out. With two models n the side of values, as cterisation, a to determine tor figure of efficient and ng performance he hovering fined as the ctual power , where the f the simple ower results e conditions. the nominal al maximum T helicopter. the thrust ompared to a red). merit plotted . The figure he behavior lation model ion following appreciate a s a result of d within the assessment, L, defined as ’ ’ h s f s a e f d e g e r e e s . l m d e r l g a f e , s
the ratio o behavior wi merit FM. T that, altho maximum a the operativ peak in vicin Figure 20. Po 4.2. Thru Another imp ‘polar’ curve the torque coefficient C of the collec the polar c comparison those predi model alrea Figure 21. T model (blue Again, a ve slight mism levels of de computation of thrust to th weight va This is reporte ugh the fi at very high ve range, the nity to the hig
ower loading (b functions of th st/torque cu portant perfo e, i.e. the cu coefficient CT in hover c ctive pitch. F curve const n between t icted by the ady considere Thrust/torque e) , compared t mo ery good ag atch that ca etails in mode nal tools. power, an ariation to tha ed in Figure gure of m weight valu e power load gher operativ
blue) and figure he helicopter w
urve ormance indi
rve that rela CQ to thos conditions, a Figure 21 sho ruction. We the Cp-Lam e flight mech
ed for the fig
relationship fo to a flight mech odel (red).
reement is o n be justified elling the rot
nd compared at of the figu 20, which sh merit reache ues, well be ding attains ve weight va e of merit (blac weight. icator is the ates the value
se of the t at different va
ows the resu considered bda results hanics simul ure of merit. or the Cp-Lamb hanics simulat observed, w d by the diffe tor within the
d its ure of hows es a yond at its alues. ck) as rotor es of hrust alues lts of d the and ation bda tion with a erent e two 5. The desi at v arch by com com elem Lam dyna anal verif testi asse Bas stab in t pres the gimb perf inclu with varia oper resu head alter 6. [1] [2] [3] [4] [5] [6] CONCLUDIN present wo ign for two-b
ariance with hitecture. The Lidak’s con mplex mecha mponents, ha ment aero-s mbda in view amic and st lysis was li fication of th ng in compa ess the val
ed on these bility studies the compan sent framewo constant-spe bal mount. I orms very w uding preces respect to ations betwe rative range ults confirm L d arrangem rnative to the REFERENC Lidak V., “C rotors”, pate Bauchau O “Modeling ro multibody Computer M Bottasso C. Trainelli L., “ Wind Turbin Multibody Dynamics, 1 O.A. Bauch Robust Int Multibody Applied Mec 420 (2003). Bottasso, C Labò, G., T Finite-Eleme European R UK, Septem Croce A., P Properties o Blade Helico NG REMAR ork focused blade lightwe the well-es e core of th nstant-speed anism, as as been ide servo-elastic w of a thorou tability chara mited to ge he model, an arison with o idity of the e preparator have been c nion paper ork allowed eed transmis t was verifie well in severa ssional conic the mast, een the mast e of the hu
Lidak’s conc ment for lig
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