Tilt-Rotor Analysis and Design Using Finite Element Multibody Procedures

Transcription

1 Agusta Tilt-Rotor Analysis and Design Using Finite Element Multibody Procedures Carlo L. Bottasso, Lorenzo Trainelli, Italy Pierre Abdel-Nour Nour, Gianluca Labò Agusta S.p.A., Italy 28th European Rotorcraft Forum Bristol, September 17 20, 2002

2 Presentation Outline Finite element multibody procedures for rotorcraft modeling; Tilt-rotor virtual model; Three different constant speed joint realizations: universal joint, Agusta design, ideal joint. Structural and aerodynamic model validation; Whirl-flutter analysis; Results; Conclusions and future work.

3 Structural Dynamics Modeling A modern approach to rotorcraft modeling: Vehicle is viewed as a complex flexible mechanism. Model novel configurations of arbitrary topology by assembling basic components chosen from an extensive library of elements. This approach is that of the finite element method which has enjoyed, for this very reason, an explosive growth. This analysis concept leads to simulation software tools that are modular and expandable. Simulation tools are applicable to configurations with arbitrary topologies, including those not yet foreseen.

4 Structural Dynamics Modeling Definition of multibody: a finite element model, where the elements idealize rigid and deformable bodies (beams, shells, etc.) and mechanical constraints. Systems with complex topologies, where each body undergoes large displacements and finite rotations (but only small strains). Idealization process: Virtual prototype.

5 Structural Dynamics Modeling Body models Body models: geometrically exact, composite ready beams and shells; rigid bodies. Lower pairs: Other models: Flexible joints; Unilateral contacts; Sensors; Actuators, controls.

6 Numerical Challenges Highly non-linear equations. Differential-algebraicalgebraic nature (Lagrange multipliers), highly stiff. Dynamic invariants (energy, momenta). Solutions that satisfy the invariants Solutions that satisfy the constraints Classical approach: derive the equations and apply an off-the-shelf general-purpose DAE integrator. Pros: easy. Cons: the integrator knows nothing about the problem being solved. Invariants are not preserved, only linear notions of stability. Lack of robustness, failure for particularly difficult problems. Drifting solution System manifold Constraint manifold Manifold of the invariants

7 Geometric Integration Design (backward-engineer) integrators that incorporate specific knowledge of the equations being solved: Exact treatment of geometric non-linearities linearities. Exact satisfaction of the constraints (no drift). Non-linear unconditional stability and preservation of invariants: bound on the total energy of deformable bodies + vanishing of the work of the forces of constraint + conservation of momenta. The numerical procedure inherits qualitative features of the true solution greatly improved robustness, reliability. Energy methods: discrete energy conservation imply unconditional stability in the non-linear regime (Simo & Wong 1991: rigid bodies; Simo & Tarnow 1994: shells; Simo et al. 1995: beams). T f =T i (T=K+V)

8 Beyond Geometric Integration Energy decaying methods (Bottasso & Borri 1997: beams; Bottasso & Borri 1998: multibodies; Bottasso & Bauchau 1999: multibodies and shells): T f =T i -T D T D 0 dissipated total energy. Unconditional stability in the non-linear regime from the bound on the total energy. Mechanism for controlling the unresolved frequencies. Energy manifold Energy preserving solution T D Energy decaying solution

9 References on Structural Dynamics Modeling C.L. Bottasso, O.A. Bauchau, `Multibody Modeling of Engage and Disengage Operations of Helicopter Rotors', J. Amer. Helic. Soc., 46: , O.A. Bauchau, C.L. Bottasso, Y.G. Nikishkov, `Modeling Rotorcraft Dynamics with Finite Element Multibody Procedures', Math. Comput. Modeling, 33: , O.A. Bauchau, J. Rodriguez, C.L. Bottasso, `Modeling of Unilateral Contact Conditions with Application to Aerospace Systems Involving Backlash, Freeplay and Friction', Mech. Res. Comm., 28: , C.L. Bottasso, M. Borri, L. Trainelli, `Integration of Elastic Multibody Systems by Invariant Conserving/Dissipating Schemes. Part I Formulation', Comp. Methods Appl. Mech. Engrg., 190: , Part II Numerical Schemes and Applications', Comp. Methods Appl. Mech. Engrg., 190: , 2001.

10 Tilt-Rotor Whirl-Flutter Goal: investigate the effects of the design of the constant-speed speed joint on the flutter speed. Three possible solutions: W 3,hub = W 3,shaft 1) Universal joint. 2) The Agusta artichoke. 3) Ideal constantspeed joint.

11 Virtual Tilt-Rotor Model Detailed description of the control linkages; Equivalent mechanism models flexibility of controls; Aerodynamics based on 2D theory with unsteady correction and Peter s inflow model.

12 Constant-Speed Joint Models Agusta artichoke joint as implemented in the tilt-rotor model: Scissors Driving Driven AB hub shaft

13 Constant-Speed Joint Models Agusta artichoke joint as implemented for numerical characterization: Scissors Driving Hub Prescribed ACDEB shaft rotations at the universal joint

14 Constant-Speed Joint Models Oscillations in a plane: Oscillation amplitude: 20 deg. Oscillation speed: 4 times driver angular speed. Exact constant-speed transmission.

15 Constant-Speed Joint Models Cone motions: precession speed four times driver angular speed. Semi-aperture 20 deg. Hub frequency twice of precession frequency. Semi-aperture 5 deg. Nearly exact constant-speed transmission for small flapping motions.

16 Constant-Speed Joint Models Virtual model of the ideal joint:

17 Validation of: Model Validation Structural model; Aerodynamic model. Validation by comparison with alternative solution procedures: CAMRAD/JA; NASTRAN.

18 Structural validation: Wing eigenfreq. Model Validation Rotor eigenfreq. (airplane mode) Non-rotating. Rotating.

19 Model Validation Structural validation: comparison of tennis-racquet effects. Flexible controls, stiff blade. Stiff controls, flexible blade.

20 Model Validation Aerodynamic validation: airplane mode, axial flow. Thrust vs. power, CAMRAD/JA trim points.

21 Model Validation Aerodynamic validation: quasi-static conversion, off-axial flow. H-force vs. tilt angle.

22 Trim procedure: Whirl-Flutter Analysis 1. Static solution identifies equilibrated condition in axial flow at constant speed rotation. Loads: constant speed rotation, aerodynamic forces. Wing tip is clamped to prevent off-axial flow. 2. Transient dynamic solution uses static solution as initial condition, and leads to periodic trim condition. Wing tip clamp is removed, flow is off-axial. If unstable regime, structural damping added to the wing to artificially stabilize and reach periodic trim condition.

23 Whirl-Flutter Analysis Whirl-flutter solution procedures: 1. Implicit Floquet analysis. Evaluates dominant eigenvalues using the Arnoldi algorithm without explicitly computing the transition matrix. Ideal for systems denoted by many dofs. 2. Excitation followed by transient dynamic simulation. Time history shows stable or unstable behavior. a. Excitation by removing the wing tip clamp after static solution (note: this way the system is not perturbed about the periodic trim condition); b. Excitation by force (beam direction) triangular pulse at wing tip, starting from periodic trim.

24 Whirl-Flutter Analysis Implicit Floquet analysis results (stable: spectral radius < 1; unstable: spectral radius > 1): Spectral radius of transition matrix vs. flight speed.

25 Implicit Floquet analysis results: Whirl-Flutter Analysis Animation of the unstable eigenvector of the Floquet transition matrix.

26 Procedure 2.a Time history of wing tip displacements (350 kts): Ideal joint. Whirl-Flutter Analysis Artichoke joint. Universal joint.

27 Procedure 2.a Time history of wing tip forces (350 kts): Ideal joint. Whirl-Flutter Analysis Artichoke joint. Universal joint. Note: trends of Floquet solution are confirmed (ideal > artichoke > universal).

28 Procedure 2.b Whirl-Flutter Analysis Time history of wing tip beam forces (350 kts): All joints, max excitation 6000 N. Universal joint, excitations of 3000 N and 6000 N. Note: no apparent strong dependence on excitation level, trends similar to procedure 2.a.

29 Whirl-Flutter Analysis Transient simulation in the unstable regime.

30 Tested three joint models: Conclusions 1. Universal, representative of the level of detail allowed by nonmultibody procedures; 2. Artichoke, representative of possible actual hardware implementations; 3. Ideal, perfectly constant transmission but not realizable in practice. Basic (preliminary) conclusion: more accurate constant speed transmission of the angular velocity to the hub implies a progressive increase in flutter speed.

31 Conclusions Tested two basic solution procedures: 1. Implicit Floquet analysis; 2. System excitation. The basic conclusions found are similar (ideal better than artichoke, better than universal), but different procedures yield somewhat different results (e.g., damping levels). Issues: Linearized (Floquet) vs. non-linear (excitation) approaches; Effects of reference (trimmed) condition.

32 However, it is clear that : Conclusions 1. Modeling assumptions and simplifications might severely undermine the accuracy of the computed results; 2. The finite element multibody approach offers the potential for enhanced modeling, through a direct numerical simulation of the system components. Plans for future work: assess impact of constant speed joint design on a. Drive train loads and vibrations; b. Nacelle loads and vibrations.