MULTIBODY MODEL OF FLYING WING WITH SIGNIFICANT DEFORMATION

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1 25 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES MULTIBODY MODEL OF FLYING WING WITH SIGNIFICANT DEFORMATION Balazs GATI, PhD* *Budapest Unversty of Technology and Economcs Department of Arcraft and Shps Keywords: elastc, multbody, vortex-lattce, flyng wng, UAV Abstract The mshap of the Helos has shown that the control of the hgh-wngspan flyng wng s not properly solved as of today. The reason s the sgnfcant deformaton that cannot be descrbed by the conventonal sngle body models. The model presented n ths paper treats wngs wth hgh aspect rato as a chan of flyng bodes. The lft dstrbuton over the wng s calculated usng a bult-n Vortex-Lattce method n every step of the smulaton. Prelude Fg.. Helos n flght and mmedately before mpact After a research perod of 20 years, the NASA and the AeroVronment, Inc. has constructed the ffth-generaton HALE (Hgh Alttude Long Endurace) UAV called the Helos. The wngspan of the arcraft was 247 ft, and t had an aspect rato of about 30. The hgh aspect rato, however, dd not result n a heavy structure by the flyng wngs, because the dstrbuted lft could counteract to the dstrbuted weght optmally, and thus the bendng moment n the wngspar s sgnfcantly less than n conventonal wng-and-fuselage structures. The Helos took off for the last flght on June 26, The reason of the mshap was an unexpectedly hgh degree of ptch nstablty by hgh wng dhedral, whch led to a hgh-speed dve and loss of wng skn due to the hgh dynamc pressure. The prmary structure of the wng was ntact up untl the mpact n the ocean. The nvestgaton report [] establshed that the prmary cause of the mshap was the nsuffcent knowledge about the behavor of the arcraft by hgh dhedral. 2 Modelng of Flyng Wngs wth Sgnfcant Deformaton On the vdeo footage showng the Helos prevous successful flghts, one can observe that the wng does not really behave as a classc elastc body. If some dsturbance deforms the wng, the structure has not enough elastcty to force t back nto the orgnal shape. Thus the behavor of the wng looks more lkely flexble than elastc, especally n the case of dhedral deformaton. Based on ths observaton, we create a model to smulate the moton and deformaton of the near-flexble or even fully flexble flyng wngs. In ths case, the multbody approach appeared the best choce, where the elastc forces have mnmal or neglgble role compared to the mass forces. A flexble flyng wng s unservceable wthout affordable flght and deformaton control. Constructng the above-mentoned model s the frst step to develop control that

2 BALAZS GATI can provde vrtual stffness for the wng, and supersedes the heavy wngspar. Thus, we can get a flyng object wth sgnfcantly mproved payload/take-off-weght rato, whch s a crtcal parameter wth HALE UAV-s because of the power consumpton. CM L CF L AC R M CF R CM R 2. The Multbody Model A multbody model conssts of bodes and the connectons between them. A very smple multbody system s a hang-glder [2], consstng of two bodes: the plot and the wng. In the case of Helos-lke flyng wngs, the frst step to create a multbody model s to partton the wng nto smaller bodes, whch requres more consderaton than hang-glders. Flyng wngs always have a hgh aspect rato, and thus the deformaton of the wng sectons s neglgble compared to the wng dhedral and wng twst. Therefore, we have splt the wng n spanwse drecton only (Fg. 2.). Fg. 3. Knetc scheme The equatons () and (2) descrbe the moton of a sngle body of the multbody system: m [ V Ω V ] = M G G CF R = G M A A G CG R M G M CF GL L L () I Ω Ω I Ω = r = r CR CL CM R M CF r G R AC M M GL L G ( M M A CF GL L A L CM L R ) M (2) M G [ V Ω V Ω rc Ω ( Ω rc) ] = = MG [ V Ω V Ω r C Ω ( Ω r C )] (3) Fg. 2. Splttng the wng nto bodes The second step s to defne the connectons. (Fg. 3.) We have chosen one ball jont between each body, whch enables the relatve rotaton but blocks the relatve dsplacement of the adjacent bodes. Each drecton of the rotaton can be affected by a cylndrcal sprng and a damper wth dfferent parameters as well, smlarly to the dfferent stffness and structural dampng of the wng n the three drectons. The left sde of the equaton (3) calculates the acceleraton of the connecton pont based on the moton of the left body, whle the rght sde calculates the same, but based on the rght body. The equaton reflects that the two acceleratons must be equal,.e. the bodes must reman connected at the connecton pont. The force emergng n the connecton pont s one of the varables of the equaton system, and wll be calculated durng the solvng procedure. Based on the above-mentoned three equatons, the moton of a flyng chan can be smulated. If we wsh to gve some elastc behavor to the model, we can use, for example, 2

3 MULTIBODY MODEL OF FLYING WING WITH SIGNIFICANT DEFORMATION equaton (4) to provde for moment and structural dampng n the connecton pont. The ψ ϑ ϕ are the Euler-angles between the,,,,, adjacent bodes. CM, k ψ, = k2 ϑ, k3 ϕ, k4 ψ, k5 ϑ, k6 ϕ, (4) In the next step, the equatons can be transposed n order to buld the followng type of equaton system: A x = b( x, u( t)) (5) Ths type of equaton system can be solved by means of numercal methods, namely the multplcaton of the numercally calculated A - (whch s equal to the nverse of the A matrx) and the rght sde results n the x vector. The numercal ntegraton provdes the values of the x vector n the functon of tme, whch, once evaluated, can predct the behavor of ths type of flyng object. 2.2 Aerodynamcs Based on the Vortex- Lattce Method The lft dstrbuton over the wng s calculated by means of the Vortex-Lattce method based on [3] and [5]. To keep the calculaton tme low, the vortces n the fxed wake do not change ther poston. The drag s calculated by means of the Blasus-equaton wth ncreasng Re number along the chord. 2.3 Trm calculaton The trm calculaton s based on the general assumpton that the dervatves of the varables are zero n statonary flght. Ths means that the left sde of equaton system (5) s zero. The Newton-Raphson method can fnd values for the x vector, whch causes the b vector to be equal to zero. It s not necessary to determne the value of every varable because some of them are naturally zero n trmmed flght. 2.4 The Software The smulaton software was wrtten n the MATLAB language. The preprocessor calculates the parameters of each body n the system, based on the pre-defned parameters of the entre wng. The ntegraton s performed by MATLAB s bult-n solver that s based on the explct Runge-Kutta (4,5) formula, namely, the Dormand-Prnce par. The A matrx n (5) s calculated automatcally for any number of bodes n the multbody model. The values of A T are recalculated by means of a Gaussan elmnaton wth partal pvotng n every tme step, n order to take nto account the nonlneartes n the model. The postprocessor frst checks f the bodes would notceably dsconnect as a result of the numercal ntegraton naccuracy, then calculates the tme functon of the parameters nvolved n the analyss. The vsualzaton module of the software plots fgures, dagrams and 3D graphs to support the analyss. 3 Analyss of the Model and the Smulaton The model and the smulaton has been avalable for less than a year, and consderable nvestgaton s necessary to evaluate such complex models and calculatons, therefore the work s stll n progress. The frst nvestgatons concentrated on the flght-mechancal and the numercal sde of the model. To keep the complexty of the smulaton low, these evaluatons omtted the Vortex-Lattce method and used smple aerodynamc parameters to calculate the lft, drag and momentum generated by the wng. In ths phase of the evaluaton, a low CG flyng wng confguraton was created, consstng of fve bodes, whch seems an affordable choce for the future nvestgaton of the Vortex-Lattce method as well. The advantage of ths confguraton s the natural longtudnal stablty, whch supersedes a bult-n control system and/or a specal S-chord profle whose specal behavor would ncrease the complexty of the evaluaton. On the other hand, the fve 3

4 BALAZS GATI bodes are enough to observe complex deformatons but keep the computatonal effort low. The results of the frst nvestgaton phase showed success, and subsequently, we ncorporated the Vortex-Lattce method nto our model. The new feature sgnfcantly extended the smulaton tme, so we had to work wth 72 grd ponts to keep the smulaton tme below one hour on a 2.6 GHz Pentum 4 computer. Ths was not a serous problem because at ths stage of the project, we tested the model only, thus the precson of the smulaton was not the most mportant aspect of the evaluaton. 3. Numercal Investgaton In the numercal methods used by the smulaton, we tested how the changng of four parameters affect the processor tme and the outcome of the smulaton. At frst, we had to fnd an affordable value for the dampng coeffcent n the Newton-Raphson method. As a result, we are usng the value k NR =2 2 f we can start t near the trm condton. However, f we are unable to predct t precsely, we have to use a value as bg as k NR =2 0, especally f the stffness of the wng s defned at a sgnfcantly lower value than that of a rgd one. Of course, ths value affected the computatonal demand only, not the precson of the trm condton. However, changng the tolerance of the Newton-Raphson method changed the outcome of the smulaton. Based on Fg. 4., we chose the value of 0-4 as a balance between processor tme and precson, because the value of 0-6 dd not sgnfcantly mprove the result of the smulaton. Senstvty of AoA on the tolerance of the Newton-Method 3 We looked for the affordable value of the tolerance of the Runge-Kutta solver, too. The effect of the tolerance was only remarkable n the dsconnect checkng between the bodes. We have chosen a value of 0-4 to keep the cumulated separaton lower than 0-5 m. The smulaton of statonary flghts always resulted n a dvergent lateral oscllaton started about by t=0s. We carred out the same 50s statonary flght smulaton, ths tme wth 264 grd ponts, n order to nvestgate how the number of grdponts affect the outcome of the smulaton. The calculaton ran for 2 hours. shows the dfference. [deg], [m] Alpha[deg] by 72 grdponts Beta[deg] by 72 grdponts Teta[deg] by 72 grdponts Pos y [m] by 72 grdponts Alpha[deg] by 264 grdponts Pos y [m] by 264 grdponts Beta[deg] by 264 grdponts Teta[deg] by 264 grdponts Tme [s] Fg. 5. Effect of No. of grdponts on the smulaton The red curves represent the lateral dsplacement of the mddle body; the dashed ones show the result of the mproved smulaton. The smulaton wth the hgher number of grd ponts shows three tmes less lateral dsplacement after 35s. 3.2 The Flght-mechancal Investgaton The Fg. 6 presents two smulatons, the left one wth lghter mddle body than the rght one. AoA [deg] 2 0 Tol=0-4 Tol= Tme [s] Fg. 4. Senstvty of AoA on the tolerance of the Newton Raphson method Fg. 6. Flght path and wng shape by dfferent weght dstrbutons The wng dhedral looks to gve approprate answer on the change n the weght dstrbuton. 4

5 MULTIBODY MODEL OF FLYING WING WITH SIGNIFICANT DEFORMATION The smulaton of wng twst caused by elevon deflecton was an other qualtatve test. The resulted shape can be observed n Fg. 7. The calculated deformaton suts the expectatons. for measurement and control systems. The frst tme we appled the ntal experence acqured from the multbody model was when we desgned [6] the thrd RC model. The specalty of ths plane s the actve aeroelastc control around the length axs (Fg. 9) Flght drecton Fg. 7. Effect of outer elevon deflecton on wng shape 3.3 Rado-controlled Test Model The next step s the valdaton of the model that means comparng the results of the smulaton to real test flghts. A year ago, we started the Open Arborne Test Platform project to fnd affordable technology to construct low-cost RC models n a lmted tme, for dfferent knds of test flghts. So far, we have bult three RC models. The frst one (Fg. 8) has a conventonal confguraton wth an unusual elastc wng n order to test elastc materals and technology. Fg. 9. RC model wth actve aeroelastc aleron control and onboard camera The fourth RC model (Fg. 0) s under constructon. It s desgned to valdate the multbody model of near flexble flyng wngs, descrbed above. Fg. 0. 3D vew of the RC model desgned to valdate the multbody model Fg. 8. RC model wth elastc wng The second one s a conventonal tranng plane, whch, at the same tme, serves as testbed 4 Future Work We expect to fnsh the valdaton of the model n the near future: then t wll be ready to apply 5

6 BALAZS GATI n the desgn of the next generaton HALE UAV or smlar flyng objects. The key pont of the development s an advanced control system, whch can be desgned and tested on the bass of our model. In the long run, our model s able to descrbe the behavor of a system of autonomous UAVs as well, where the unts are connected to each other and form a large wngspan flyng chan, n order to utlze the advantage of dstrbuted weght, dstrbuted lft, dstrbuted trust and mnmal nduced drag. References [] Noll T. E.,Brown J. M., Perez-Davs M. E., Ishmael S. D., Tffany G. C. and Gaer M. Investgaton of the Helos Prototype Arcraft Mshape [2] Gat B. Investgaton of Flght Dynamc of Hangglder Acta Polytechnka, Journal of Advanced Engneerng Desgn ISSN , Vol.40 No./2000 pp.3-6, Prague, January, [3] Shabana A. A., Dynamcs of Multbody Systems, A Wley-Interscence publcaton, 989, ISBN [4] Katz J. and Plotkn A. Low-speed aerodynamcs McGraw-Hll, Inc., 99 [5] Somos M. Repülgépszárnyak vselkedésének vzsgálata dben változó megfúvás esetén, deáls áramlásban Dploma thess, BUTE Dept. of Arcraft and Shps, 2005, Budapest [6] Szokol R. Aktv aeroelasztkus csrkormányzás lehetségének vzsgálata Dploma thess, BUTE Dept. of Arcraft and Shps, 2006, Budapest 6