Flutter analysis of a composite light trainer aircraft

Transcription

1 Journal of Scientific & Industrial VITTALA Research et al: FLUTTER ANALYSIS OF A COMPOSITE LIGHT TRAINER AIRCRAFT Vol. 69, February 2010, pp Flutter analysis of a composite light trainer aircraft N G Vijaya Vittala, A C Pankaj* and D V Venkatasubramanayam National Aerospace Laboratories (NAL), Bangalore , India Received 17 March 2009; revised 10 December 2009; accepted 14 December 2009 This paper presents dynamic and aero elastic characteristics simulation of a composite light trainer aircraft using Msc/ Nastran code and typical section method. Correlation of dynamic characteristics of aircraft with results obtained from ground vibration test of aircraft was studied. Critical flutter, divergence and control reversal velocities of complete aircraft were computed. Close agreement was observed between computational and experimental frequencies. Aircraft had a flutter margin (23%) against required (20%) as per FAR 23. Keywords: Aircraft, Finite element, Flutter, Ground vibration test, Typical section Introduction Dynamic and aeroelastic analysis of an aircraft with main reference to its lifting and control surfaces is essential in finalization of design cycle for obtaining flight clearance and certification of aircraft 1. FAR 23 1 requires flutter critical velocity (Vcr) to be 1.2 times that of dive speed (Vd, 68 m/s). Flutter velocities should be more than critical Vcr (81.6 m/s) to satisfy FAR 23 requirements. This study presents dynamic and flutter characteristics of aircraft at component level and at integrated level, using NASTRAN code and typical section method. Experimental Aircraft under consideration is an all composite two seater light aircraft fitted with a turbo-supercharged Rotax-914 F3 engine (maximum power, rpm) coupled to a constant speed 2-bladed Hoffmann propeller (diam, 1730 m). Entire air frame is of moulded composite sandwich construction and materials used are glass and carbon fibres, epoxy resin and PVC foam cores. It has a cantilever low wing, tractor engine and side by side seating with dual controls. Landing gear is of tricycle with nose wheel configuration. Aircraft, designed for ab-initio training, sport and hobby flying, has following optimum values: cruise speed, 58.3 m/s; endurance, 4 h; short take off distance, 415 m; and landing distance, 540 m. *Author for correspondence Fax: ; acpankaj@nal.res.in Material Properties Material properties ( A or B basis) used in aircraft design, obtained from hot-wet tests on conditioned specimens, have been derived in a statistical manner (Table 1). A is a value, above which at least 99% of population of values is expected to fall with a confidence of 95%, whereas B is a value, above which at least 90% of population of values is expected to fall with a confidence of 95%. Bi-directional glass cloth and unidirectional carbon tapes have been used either for sandwich or solid laminate construction. Carbon has been employed for high load transfer members like main spar of wing, longerons of fuselage with predominant bending loads. A basis allowables are used for primary structures (single load path) like spars, attachments, critically loaded bulkheads etc. and B basis for redundant structures (multiple load paths). Carbon has been covered with glass cloth in most of the applications to maintain continuity with rest of the structure made of glass/foam/glass sandwich. Plywood is used in all mechanical joints to build up thickness and serve as a spacer between aluminum and composite parts. Geometry and Finite Element Model (FEM) Fuselage is of sandwich construction with foam core and glass fibre facings. Cowling and fairings are glass epoxy laminates. Wing is detachable with 3 spar construction attached to fuselage through leading and rear edge spars. It has a trailing edge outboard aileron attached on its either side to rear spar cap of wing through

2 114 J SCI IND RES VOL 69 FEBERUARY 2010 Table 1(a) Material properties Material type Stiffness properties, kg/mm 2 Thickness Density mm kg/m 3 E11 E22 G12 V12 Bi directional glass cloth interglass mil Bi directional glass cloth interglass mil Carbon tape ANCAREF C160 PVC-Foam HEREX T PVC-Foam HEREX T Plywood Al 2024-T E11, longitudinal Youngs modulus; E22, transverse Youngs modulus; G12, inplane shear modulus; V12, Poissons ratio Table 1(b) Material properties Material type Strength properties, kg/mm 2 txt cxc σ tzt yt yc σ tzt s σ yt σ yc τ s A B A B A B A B A B Bidirectional glass cloth interglass mil Bi directional glass cloth interglass mil Carbon tape ANCAREF C160 PVC-Foam HEREX T PVC-Foam HEREX T Ply-Wood Al 2024-T σ txt, longitudinal tension; σ cxc,, longitudinal compression; G12, σ yt,, transverse tension ; σ yc, transverse compression; τ s, inplane shear three piano hinges and a flap. Horizontal tail (HT) has two spars attached to two fuselage bulkheads. Elevator consists of a spar attached to stabilizer at four hinge points. Fin portion of vertical tail (VT) is integrally bonded to fuselage during assembly, with a leading edge spar, rear spar and equally distributed four ribs. Hinge brackets (3) have been provided on web of fin rear spar to support rudder, which consists of a single spar four ribs and a leading edge cover. FEM of aircraft components have been modeled using Hyper-Mesh software. Stress-cleared models of fuselage, control surfaces, and wing have been used for dynamic analysis. FEM was generated using Quad4 and Tria3 shell elements of MSC/ NASTRAN 2. Bolts at attachment points are modeled by bar and rigid elements. Appropriate multipoint constraints have been applied to simulate motion of control surfaces. FEMs have been updated by adding nonstructural masses including balance masses and stiffness of actuating mechanisms for control surfaces. Individual FEM component models were checked for mass, centre of gravity details and then integrated together to realize

3 VITTALA et al: FLUTTER ANALYSIS OF A COMPOSITE LIGHT TRAINER AIRCRAFT 115 Fig. 1 Finite Element Model of complete aircraft Fig. 2 Aerodynamic model of aircraft (case 1) full aircraft FEM (Fig. 1). Convergence analysis for size and number of elements has been carried out on component models and integrated aircraft model. Final integrated aircraft model consisted of 46,300 degrees of freedom. Aerodynamic Model Aerodynamic mesh model of complete aircraft consists of flat panels for lifting surfaces only in first case (Fig. 2) and a combination of slender and interference bodies for fuselage in second case. Mesh

4 116 J SCI IND RES VOL 69 FEBERUARY 2010 for all lifting surfaces has been idealized by means of trapezoidal boxes lying parallel to flow direction, without overlapping at attachment points and hinge lines. Finer mesh at leading edge has been generated to ensure alignment of boxes along hinge line and to include wing tips as well. Surface spline functions have been used to generate necessary interpolation matrix to estimate displacement of aerodynamic grids based upon displacement of structural grids. Slender body elements account for forces arising from motion of the body, whereas interference elements account for interference effects among all bodies and panels in the same group. Right and left wing surfaces have been divided into three main zones (tip region, root chord region and flap region) modeled integrally with wing and ailerons. These zones have been subdivided depending on chord and span. One half of the wing has 242 boxes, making a total of 484 boxes for total wing. HT (328 boxes) has been divided into two main surfaces (horizontal stabilizer and elevator). Two surfaces (fin and rudder) of VT (455 boxes) have been suitably subdivided into trapezoidal boxes. Fuselage of aircraft has been modeled as a slender body consisting of a series of elements having half-widths equal to cross-sectional radii at each bulkhead station to realize fuselage contour. Interference tube has been defined with its half-width equal to maximum cross-sectional radius of fuselage. Beam spline interpolates between aerodynamic and structural displacements of fuselage. Aerodynamic meshes of individual components are integrated to realize aerodynamic model of full aircraft. Interference between various components has been taken into consideration by declaring interference groups. Analysis Dynamic Analysis Under free vibration 3 analysis of aircraft, initial analysis is carried out using associated control circuit stiffness supplied from design office. Linear actuation stiffness (41.9, and 4.1 kg/mm) have been applied at aileron, rudder and elevator control points. Subsequent to ground vibration tests, rotational modes of control surfaces obtained from FEM analysis were fine tuned to realize rotational mode frequencies obtained from ground vibration test (GVT) of aircraft. Dynamic frequency spectrum of complete aircraft has been obtained by invoking Lanczos method in NASTRAN with unit mass criteria for normalizing mode shapes. Ground Vibration Test (GVT) GVT system consists of 3 electrodynamic modal shakers (force rating, 220 N; maximum frequency rating, 2000 Hz), acquiring excitation force signals from 3 force transducers and structural response from 113 accelerometers. Data acquisition is done by a 120 channel LMS SCADAS III system with a signal conditioning unit. Modal test and analysis software resident on Intel Pentium IV PC communicates with SCADAS system by a SCSI connection card. Aircraft tires have been deflated to 50% pressure to simulate freefree condition. Vibrator exciter locations have been selected to excite entire aircraft to capture all modes of interest. One shaker has been placed on right and left wing tips respectively, and one on a fuselage rear bulkhead. Burst random (50%) has been used as excitation signal (frequency bandwidth, 100 Hz; and resolution, 0.2 Hz). Time domain signals of force transducers and response accelerometers have been monitored online. Amplitude weighting of time signal used with gated continuous signals to give them a slow onset and cut-off in order to reduce generation of side lobes in their frequency spectrum (uniform window) has been applied to both excitation and response signals. Frequency response function and coherence have been monitored and checked before acquiring final data. Flutter Analysis In flutter solutions, full aircraft FEM has been used. Structural frequencies and modal vectors obtained from Eigen value solution have been used for subsequent flutter analysis in NASTRAN 2. Structure is assumed to undergo harmonic oscillations and generalized equation of motion for flutter in frequency domain is as ( ω [ M ] + iω[ B ] + [ K ]){ ξ( iω) } { F ( iω) } 2 S S S = S (1) where, M S, generalized mass matrix; B S, modal damping matrix; K S, generalized stiffness matrix; ξ, generalized displacements vector; ω, frequency of oscillations; and F S (iω), generalized unsteady force, which is expressed as { F ( iω) } q[ Q ( ik) ]{ ξ( iω) } S = hh (2) Generalized unsteady aerodynamic force matrix is complex and calculated for user-defined values of

5 VITTALA et al: FLUTTER ANALYSIS OF A COMPOSITE LIGHT TRAINER AIRCRAFT 117 Fig. 3 Sketch of aero elastic typical section reduced frequency k = ωb/u, where b is reference chord, Q hh is modal aerodynamic damping matrix, q= (1/2) ÁU 2, where U is true air velocity and ρ is air density. Flutter analysis of aircraft has been carried out by taking first 30 modes into consideration, up to Hz of spectrum. Cut off frequency includes rotational modes of control surfaces, and bending and torsion modes of lifting surfaces, which are susceptible for flutter. Velocity range, considered for analysis, starts from 50 m/s to 110 m/s in steps of 10 m/s. Approximate determination of true damping in terms of complex variable (p), assuming harmonic motion for aerodynamic forces at discrete values of reduced frequency (k), is known as PK method, whereas structural damping type of solution to maintain harmonic motion is known as KE method 3. Both methods have been used for flutter solutions. PK-method produces results directly for given values of velocity, whereas KE-method requires iteration to determine reduced frequency of flutter. Damping obtained by PK method is a more realistic estimate of physical damping than artificial damping used in KE method. Typical Section Aero elastic Analysis Sectional properties vary along span in case of tapered wings. Position of 75% of semi-span of cantilever lifting surface is often approx. at 50% of control surface position and gives mean sectional properties of structure. Therefore, control surface unsteady aerodynamic terms can be expressed as functions of reduced frequency k = ωb/u, where b is semi-chord at 75% semi-span. This facilitates aeroelastic results for a non-uniform lifting structure. Finite aspect ratio is to be obtained conservatively by considering motion of unit span of structure at a representative position of 75% of semi-span 4. Typical wing section with three modes of motion (plunging, pitching and aileron rotation) is shown in Fig. 3. Airfoil is restrained in bending, torsional motion and control surface rotation by springs having stiffness K h, K α and K β respectively. Unsteady aerodynamic forces acting on typical section airfoil for pure sinusoidal motion has been calculated using Theodorsen s approach. Flutter stability equation has been solved by velocity-structural damping (U-g) method. In addition to 3 degree of freedom flutter, binary flutter due to bending-torsion, bending-rotation and torsion-rotation have also been studied. Typical section computations have been carried out for FEM and GVT obtained frequencies. In order to account for fuselage flexibility, vertical and side bending of fuselage have also been included as a combination in flutter computations of HTand VT respectively. Results and Discussion Free vibration analysis of aircraft results in clear six rigid body modes (< 0.1 Hz), followed by elastic modes (Table 2). Pure rotational mode of elevator occurs

6 118 J SCI IND RES VOL 69 FEBERUARY 2010 Damping, g Frequency, Hz Vilocity, m/s Vilocity, m/s Fig.4 Flutter plots at 7.2 Hz. HT first asymmetric bending (7.746 Hz), and wing first symmetric bending (8.815 Hz) are obtained, followed by VT lateral bending, aileron symmetric and asymmetric rotation modes. Rudder rotational mode takes place at Hz. Wing asymmetric and symmetric torsion modes occur at Hz and Hz respectively. Wing bending and torsion modes are well separated. Coupling of symmetric modes of lifting surfaces with longitudinal movement of fuselage, as also that of anti-symmetric modes with lateral movement has been observed. Fuselage torsion occurs well before fuselage longitudinal and lateral bending modes. Fuselage lateral bending mode is quite high at Hz. Flap modes lay between Hz and further flaps of port and starboard side have separate symmetric and anti-symmetric modes. HT asymmetric torsion mode (65.84 Hz) and symmetric torsion mode (75.86 Hz) are well separated. VT has high torsional rigidity with its torsion mode occurring at Hz. Dynamic frequencies obtained through FEM of aircraft are compared with ground GVT results (Table 3). Wing torsion mode (26) couples with aileron

7 VITTALA et al: FLUTTER ANALYSIS OF A COMPOSITE LIGHT TRAINER AIRCRAFT 119 Table 2 Free vibration analysis Mode No. Frequency, Hz Remarks 'Y' Translation 'X' Translation 'Z' Translation Pitching Rolling Yawing Fuselage torsion (FT) Tail plane rigid movement FT + HT asymm +VT lateral Elevator rotation Elevator rotation (predominant) HT asymmetric. bending + VT lateral Wing 1st symmetric bending VT lateral + HT asymmetric + Fuselage lateral Aileron rotation asymmetric Aileron rotation symmetric Aileron rotation asymmetric + rudder rotation Rudder rotation HT 1st symmetric bending Fuselage longitudinal bending HT inplane + (VT+rudder) lateral Wing inplane bending Fuselage lateral + Elevator 3rd asymmetric bending Elevator 2nd bending asymmetric Wing torsion asymmetric Wing torsion symmetric Wing 2nd symmetric bending Elevator 3rd symm. bending + HT symm. out of phase HT elevator inplane HT torsion asymmetric HT torsion symmetric VT torsion Table 3 Ground vibration test results Mode Remarks FEM GVT Damping% Frequency, Hz Frequency, Hz Pitching Rolling Fuselage torsion HT asymm. bending + VT Lateral Wing 1 st symmetric bending VT Lat. + HT asymm. + Fus.Lateral Aileron horns rotation symmetric Rudder rotation Ht 1 st Symm Bend Fus. Longitudinal bending Fus Lat + Elevator3 rd asymm. bending Wing torsion asymmetric Wing torsion symmetric Wing 2 nd symmetric bending

8 120 J SCI IND RES VOL 69 FEBERUARY 2010 Table 5 Summary of critical flutter speeds and flutter margins Mode Method Critical flutter speed Flutter margin wrt m/s Vd, % Wing Torsion (Symm) & Typical section Aileron Rotation (Symm) (FEM) Wing Torsion (Symm) & Typical section Aileron Rotation (Symm) (GVT) Wing Torsion (ASym) & Typical section Aileron Rotation (Asym) (FEM) Wing Torsion (Asym) Nastran (PK) & Aileron rotation Table 4 Flutter analysis using NASTRAN for Mode 26 Aero-Mesh case Method Flutter velocity Flutterfrequency m/s Hz 1 PK KE PK KE rotation and leading to flutter (velocity, 83.8 m/s; frequency, Hz) for aero-mesh case 1 by PK method (Table 4), where only lifting surfaces are considered. However, inclusion of slender bodies in aero-mesh (case 2) does not change behavior of flutter trends but flutter velocity increases marginally (86.9 m/s) with a flutter frequency of Hz. Fig. 4 shows flutter plots for some critical modes. No flutter corresponds to flutter velocity more than 600 m/s is observed. Lowest flutter velocity computed by typical section approach is obtained at m/s for combination of wing asymmetric torsion and aileron asymmetric rotation (Table 5). Divergence and reversal velocities are far higher than computed flutter velocities. Conclusions Good correlation between analytical and experimental frequencies is observed. Flutter velocities obtained by PK and KE methods are consistent. Inclusion of slender bodies and interference elements in aero mesh increases flutter velocity marginally. Thus, aerodynamic model excluding slender bodies is conservative from design point of view. Typical section approach provides quite good results for binary and three degrees of freedom flutter. Critical divergence and reversal velocities of wing, horizontal tail and vertical tail are higher than computed flutter velocity. Aircraft had a flutter margin of 23% against a requirement of 20% as per FAR 23. Acknowledgements Authors thank colleagues of different groups in NAL, Bangalore, for support. Authors also thank Director, NAL for kind permission to publish this paper. References 1 FAR 23 Regulations, MSC/NASTRAN Documentation (Msc Software Corporation, USA) Vijaya Vittala N G, Swarnalatha R & Pankaj A C, Dynamic and aeroelastic analysis of a transport aircraft, in Int Conf on Aerospace Technologies (Indian Institute of Science, Bangalore) June Theodersen T & Garrick I E, Mechanism of flutter, A theoretical and experimental investigation of the flutter problem, NACA TR 685, Scanlan R H & Rosenbaum R, Introduction to the Study of Aircraft Vibration and Flutter (The Macmillan Company) 1996, Abramson H N, An Introduction to the Dynamics of Airplanes (The Reynold Press Company) 1958,