Flight Loads Analysis of a Maneuvering Transport Aircraft

Transcription

1 Flight Loads Analysis of a Maneuveing Tanspot Aiaft Hui hang, a, Jie Li, b, Qiong Liu, Shool of Aeonautis, Nothesten Polytehnial Univesity, China Univesidad Politénia de Madid, Spain a hanghui_@6.o, b lijieuihao@63.o, iong@tooja.dt.up.es Keyods: flight load; dynai deivative; dynai aneuves; doublet lattie ethod; ontol sufae Abstat: The pape povides a ethod appliable fo the deteination of flight loads fo aneuveing aiaft, in hih aeodynai loads ae alulated based on doublet lattie ethod, hih ontains thee piay steps. Fistly, non-diensional stability and ontol deivative oeffiients ae obtained though solving unsteady aeodynais in subsoni flo based on a doublet lattie tehnial. These stability and ontol deivative oeffiients ae used in seond step. Seondly, the siulation of aiaft dynai aneuves is opleted utiliing fouth ode Runge-Kutta ethod to solve otion euations in diffeent aneuves to gain esponse paaetes of aiaft due to the otion of ontol sufaes. Finally, the esponse esults alulated in the seond step ae intodued to the alulation of aeodynai loads. Thus, total loads and loads distibution on diffeent oponents of aiaft ae obtained. Aoding to the above ethod, abupt pithing aneuves, olling aneuves and yaing aneuves ae investigated espetively. Intodution Flight loads inluding aeodynai loads and inetia loads ae the oiginal data of aiaft stutue design. Only unde the athe auate stutue loads the designed aiaft an satisfy the given aiaft iteia suh as flight uality iteia, stength iteia. Theefoe the auate pedition of stutue loads is a key fato fo aiaft stutue design hih ipats dietly on the eight of a aiaft, the apaity of aneuveability and the safety of flight. When a pilot anipulates the ontol sufae to ake it otate aoding to an expeting ule, the esponse of aiaft suh as pith, oll o ya ill stat. To deteine loads duing aneuves, the flight ehanis euations of otion need to be solved to obtain the esponse haateistis of the aiaft. On the othe hand, it is neessay to onside the flexible effets on aneuve loads alulation, espeially fo oe highly flexible aiaft [,, 3]. Thus stutual ehanis euations have to be taken into aount siultaneously. Theefoe the auate pedition of aneuve flight loads need to siulate aneuveing aiaft by aeodynai, flight ehanis, and stutual ehanis oupling [, 5]. Hoeve these advaned siulation ethod ay be oplex and involve the use of lage digital oputes, and a ass of alulation tie has to be ost fo a aneuveing flight siulation on the uent opute ondition. Moeove, the agnitude of the nube of load points and onditions ay be investigated fo the aiaft stutue stength design, leading to the teendous diffiulty in deteining the loads fo aneuveing aiaft by opletely using the oupled ethod. In fat, it is the ost ost tie to solve Eule/Navie-Stokes to obtain the unsteady aeodynai loads in the oupled ethod. If this potion of alulation tie an be edued, the above diffiulty ill be oveoe. The alulation tie of solving unsteady aeodynai loads an be geatly edued based on doublet lattie ethod [6, 7]. Of ouse, the auay of solution based on doublet lattie ethod ill dop opae ith Eule/ Navie-Stokes. Wheeas the auay of

2 solution an satisfy the engineeing euieent in initial aiaft design stages. In addition, even fo the detailed design stage the aneuve loads an be deteined though doublet lattie ethod fistly then validating the esults fo Eule/ Navie-Stokes euations. The ethod disussed in the pape is appliable fo the deteination of flight loads fo aneuveing aiaft, in hih aeodynai loads ae alulated based on doublet lattie ethod. Dynai Deivative Coputations The definitions of longitudinal stability deivatives ae given in the euations fo the lift oeffiient and oent oeffiient C = C + C + C + C V V C = C + C + C + C V V h i t Haoni plunging ith aplitude h is onsideed, then i e ω = ω, and E. and E. beoe V h i ω C = ikc k C e t (3) h C = ikc k C e () i ω t In addition, based on a doublet lattie tehnial one an obtain C ( ) i t = Ce ω and C i t = Ce ω, Thus h C = ikc k C (5) h C = ikc k C (6) ( ) Siilaly, if haoni pithing ith aplitude is next onsideed, one an obtain C = C + ik C + C () () (7) C = C + ik C + C (8) Obviously, obining E.5 though E.8 and the esults fo a doublet lattie tehnial, longitudinal stability deivatives ill be obtained. The alulation of lateal-dietional deivatives is siila to that fo the longitudinal deivatives illustated above, in hih haoni sideslip oll and ya otions ae espetively onsideed. In the sae ay, ontol sufaes stability deivatives ith thei angle veloity ill be deteined though haoni otions of ontol sufaes. Dynai Maneuves The euations of otion fo both pithing aneuves and olling aneuves ae deived fo the ok of Jan R. Wight and Jonathan E. Coope in Ref., hih ae epeated espetively as follo. Ue δ δ I + y = M M Mδ (9)

3 Whee, Mδ ρv SC M δ = ρvsc, =. = ρvsc, δ = ρv SC δ, I p L p = L δ δ x p a a M = ρvscm, M = ρvs CM, () Whee, L ρ p = VSb CLp, Lδ = ρv SbC a L δ. a E.9 ay be solved to deteine the esponse oesponding to a patiula elevato input, and E. ay be used to deteine the esponse to any aileon input. The euations of otion fo yaing aneuves ae deived fo Ref.. dβ dt Y Y Y β β δ = δ d Nβ N + Nδ dt [ ( β ) +Δ ] gs gs W β W Lv xcg β S Wb Lv β +ΔxCG AW β Whee, Yβ = CY, Y = C Y +, N = Cn + SW CY, v, WV WV IV V I gsw δ S ( Wb δ S ) W Lv δ +ΔxCG δ Yδ = C Y, Nδ = C n + CY. WV I I E. ay be used to deteine the esponse to any udde input. E.9 to E. ae solved by using fouth ode Runge-Kutta ethod to deteine the tie histoy of aiaft load fato and elated paaetes suh as pith veloity, oll veloity, ya veloity, angle of attak, oll angle and side angle. () The Deteination of Flight Loads fo Maneuveing Aiaft Aoding to the ethod disussed in the pape, the alulation of flight loads fo a aneuveing aiaft is deonstated as follos. Desiption of the Calulation Model. The aeodynai odel is given in Fig., hih inludes the efeene hod of.9, span of.5, Wing, hoiontal tail and vetial tail idealied as lifting sufaes, hile fuselage idealied as slende body and intefeene body. Non-diensional stability and ontol deivative oeffiients ae alulated at Mah nube of.3, the dynai pessue of 637Pa, and listed in Table. The total eight of the aiaft is kg, the ente of gavity is. foad of the intesetion of the fuselage and ing elasti axis, and the entoidal oent of inetia in pith, oll and ya ae 9 kg, 536 kg and 533 kg espetively. Fig. Aeodynai odel Abupt Pith Maneuve. Fo abupt pith aneuve, the initial ondition is Steady level flight, in hih load fato is. Afte aiplane is tied, elevato is defleted ith the axiu available ate, and the deflet angle is deteinate hen load fato beoes the design value in the hole aneuve. The input of elevato angle depited in Fig. (a) is applied to the aiplane, and the

4 esponse esults of pith ate, angle of attak, and load fato ae also desibed in Fig. (a). The oesponding aeodynai loads on diffeent oponents of aiaft vaiation ith tie ae given in Fig.3 (a). The sevee load states of oponents of aiplane on the above ondition an be obtained. Beause abupt pith aneuve is often the itial load ondition of hoiontal tail, elevato and aft fuselage, thei axiu load values have to be onsideed hee. Hoiontal tail load gets a negative axiu value, -67N, at. seond, and a plus axiu value, 7565N, at.89 seond. The esults indiate that hoiontal tail load hange extensively in abupt pith aneuve, even ith ontay dietions. In addition, elevato and fuselage load eah the axiu value, -583N and 59N, at. and.87 seond espetively. Table Non-diensional stability and ontol deivative oeffiients C CM C C M M C C N -. L β C.69 N β C Yp C Lp C Np C Y Y -.3 L.363 N Y a -.8 C -.36 C L.7 Y β C -.9 N δ a Roll Maneuve. Fo oll aneuve, the aileons ae defleted ith the axiu available ate in oll aneuve. When the pesibed angle of oll is eahed, the aileons etun to stop the aneuve. The input of aileon angle depited in Fig. (b) is applied to the aiplane, the esponse esults of oll ate, angle of oll ae desibed in Fig. (b). The oesponding aeodynai loads on ing and aileon of aiaft vaiation ith tie ae given in Fig.3 (b). Tie histoy of aeodynai loads on ing and aileon sho that ight ing load beoe iniu hen left ing load eah the axiu value, and that aileon behave the sae poess as ing. Right ing load is 69799N hen left ing load eah 5N, and ight ing load is 5967N hen left ing beoe 67N. Maxiu left aileon load is N hen ight one is -55N. Ya Maneuve. Fo ya aneuve the udde is defleted ith the axiu available ate in ya aneuve. When the steady angle of side is eahed, the udde etuns to stop the aneuve. The input of udde angle depited in Fig. () is applied to the aiplane, the esponse esults of angle of side and lateal aeleation ae desibed in Fig. (). The oesponding aeodynai loads on vetial tail and udde of aiaft vaiation ith tie ae given in Fig.3 (). The axiu loads of vetial tail and udde ae espetively 95N and 7N. L a. 3 n(g) Delt(deg) Alpha(deg) pith ate(deg/s) 8 oll ate(deg/s) Delta(deg) oll angle(deg) Bny(g) Delty(deg) Beta(deg).8 6. deg g (a) Abupt pith aneuve (b) Roll aneuve () Ya aneuve Fig. Response paaetes vaiation ith tie

5 F_tail(N) F_WFP(N) F_Elevato(N) F_Fuselage(N) 6 F_Ring(N) F_Ling(N) F_LAileon(N) F_RAileon(N) Fy_Vtail(N) Fy_Rudde(N) (a) Abupt pith aneuve (b) Roll aneuve () Ya aneuve Fig.3 Aeodynai loads on diffeent oponents of aiaft vaiation ith tie Suay Flight loads on diffeent oponents of aiplane in diffeent aneuve an be obtained uikly and effetively using the ethod intodued in the pape. Subseuently the sevee load states of oponents of aiplane ae found, hih should be onsideed in stutue design. And the distibution of flight loads on oponents of aiplane auied an be dietly applied to the finite odel in intensity hek of aiaft. In addition, the uent eseahes only onen the alulation of flight loads fo igid odel. Atually, aiaft elastiity has an ipotant ipat on analysis esults and the distibution of flight loads. Aodingly, the alulation of flight loads fo flexible odel ill be aied out subseuently. Aknoledgents This ok as suppoted by the National Siene Foundation of China (Gant No. 9867, 778, 7,). The authos ould like to thank Pofesso LI Fengei fo any insightful tehnial disussions. Refeenes [] Jan R. Wight, and Jonathan E. Coope, Intodution to Aiaft Aeoelastiity and Loads, John Wiley & Sons, Ltd, 7, 66-69, [] Aiaft Design Manual, the 9th Volue: Loads Stength and Stiffness, Bei Jing: Aviation Industy Publishing House,, 8-3. [3] Loax, T.L. Stutue Loads Analysis fo Coeial Tanspot Aiaft: Theoy and patie, AIAA Eduation Seies, 996. [] Andeas Shutte, Gunna Einasson. Nueial Siulation of Maneuveing Aiaft by Aeodynai, Flight Mehanis, and Stutue Mehanis Coupling, Jounal of Aiaft, Vol.6, No., 9. [5] Li Xile, Yang Yong, Nueial Siulation of the Fee Rolling Motion of a Delta Wing Configuation ith Aileon Defletion, Ata Aeonautia et Astonautia Sinia, Vol.33, No.3,. [6] Gay, W.L, and Shenk, K.M., A ethod fo Calulating the Subsoni Steady-State Loading on an Aiplane Wing of Abitay Plan Fo and Stiffness, NACA TN 33,De [7] Albino, E. and Rodden, W.P. A doublet-lattie Method fo Calulating lift distibution on osillating sufaes in subsoni flos. AIAA Jounal, 7().