LOAD REDUCTION IN LEAD-LAG DAMPERS BY SPEED-SCHEDULED APERTURE AND MODULATED CONTROL OF A BY-PASS VALVE C.L. Bottasso, S. Cacciola, A. Croce, L. Dozio Politecnico di Milano, Italy American Helicopter Society 66th Annual Forum and Technology Display Phoenix, AZ, USA, May 11-13, 2010

Outline Introduction and motivation Approach and methods - Damper model - Rotor-vehicle multibody model Control laws Results Conclusions and outlook

Introduction and Motivation Lead-lag dampers are typically purely passive devices The idea of using adaptive “smart” dampers has been around for a long time: Reed, US Patent 1972 Mechanical-hydraulic device for selective damping of lag frequency Bauchau et al., SBIR I & II, 2003-2004 Active modulation of by-pass valve aperture for selective damping of lag frequency Gandhi at al., Aeronautical Journal 2003 HHC modulation of by-pass valve for reduction of vibratory hub loads …

Introduction and Motivation Motivation: high operating and maintenance costs of dampers and their interfaces to rotor system The main dilemma in damper design: Different damping levels are required for different flight conditions High damping required for very small range of the flight envelope (ground resonance, high-g turns, …) Much lower damping appropriate for all other flight regimes

Introduction and Motivation By-pass valve: relatively straightforward way of changing damping (and hence loads) in a damper Focus of present work: Can we significantly reduce loads if we allow for a decrease in the damping to lower but still safe values? Can load reductions be achieved with a simple speed-scheduled aperture of the by-pass valve or do we need a modulating control law (valve aperture as a function of blade motion)?

Outline Introduction and motivation Approach and method - Damper model - Rotor-vehicle multibody model Control laws Results Conclusions and outlook 6

Damper Model Physics-based mathematical model of hydraulic damper: Coupled set of stiff non-linear ordinary differential equations (solved with time-adaptive modified Rosenbrok 2nd order integrator) By-pass valve Compressible fluid state equations in the two chambers Fluid flow through orifice Flow through pressure relief valves Piston and relief valve dynamics: - Friction - Contact-impact Actuated by-pass valve

Damper Model Characteristic load-speed curves for varying by-pass valve aperture Standard passive damper: Tuned to experimental data by identifying: - Orifice and relief valve discharge coefficients - Relief valve pre-load High speed: relief valves open Knee: transition region Knee moves to higher speed for increased by-pass aperture Low speed: relief valves closed Δbyp = Abyp/Aor Adaptive damper with by-pass: Effect of by-pass aperture on characteristic curve

Rotor-Vehicle Multibody Model Detailed multibody model of rotor coupled to rigid fuselage (A109E helicopter): Elastic blades Kinematically accurate: - Control linkages - Damper and damper linkages Peters-He dynamic inflow Rotor-damper coupling: avoid direct coupling of models due to wildly different time scales Damper characteristic curves stored in a look-up table Used at run time during multibody simulation Vehicle model trimmed at various flight conditions Validation using experimental data (see paper)

Speed-scheduled aperture Control Laws Speed-scheduled aperture HHC + Damper load Helicopter speed Valve aperture Damping criterion (provided by helicopter manufacturer): For each flight condition, ensure ≥30% of damping of conventional passive damper

Control Laws Speed-Scheduled Aperture (SSA) Higher Harmonic Control (HHC) Bypass valve opens of given amount for each flight speed Additional (on top of SSA) azimuthal modulation of valve opening Criterion Minimize peak loads without exceeding allowed damping loss at each flight condition Minimize 1-2-3P harmonic amplitudes Pro’s Maximum possible simplicity Additional reduction of loads wrt SSA Negligible effects on damping Con’s Does not account for rotor-damper response Additional complexity (hardware & software)

Estimation of Damping Modified Prony’s method to account for periodic nature of problem (Bottasso et al., EWEC 2010) LTP system: x· = A(ψ)x + B(ψ)u where u = exogenous inputs (speed, collective and cyclic pitch), constant in steady trimmed conditions Fourier reformulation (Bittanti & Colaneri 2000): A(ψ) = A0+Σi(Aissin(i ψ)+Aiccos(i ψ)) B(ψ) = B0+Σi(Bissin(i ψ)+Biccos(i ψ)) Approximate state matrix: A(ψ) ≈ A0 Transfer periodicity to inputs term Obtain linear time invariant (LTI) system: x· = A0x + Ub(ψ) where b(ψ) = exogenous periodic dummy inputs

Estimation of Damping Estimation process: Given reformulated LTI system x. = A0x + Ub(ψ) use standard Prony’s method (Hauer 1990; Trudnowski 1999) Estimation process: Trim helicopter and perturb with impulsive torque input at lag hinge Identify discrete-time ARX model (using Least Squares or Output Error method) with harmonic inputs Compute discrete poles, and transform to continuous time (Tustin transformation) Obtain frequencies and damping factors Time domain verification of correct identification Frequency domain verification of correct identification

Outline Introduction and motivation Approach and method - Damper model - Rotor-vehicle multibody model Control laws Results Conclusions and outlook 14

Results SSA control law: Δbyp = Abyp/Aor Maximum loads Damping factors Substantial reductions in damper loads (-37% ÷ -70%) 30% damping constraint Significant valve apertures

Results HHC control law: Max SSA aperture: Δbyp = 38 Valve aperture Damper loads Further reductions in damper loads peaks Max SSA aperture: Δbyp = 38 Max HHC aperture: Δbyp = 68

Results Small maximum allowed by-pass aperture: Valve opening is not enough to prevent activation of pressure relief valves Small load reduction Larger maximum allowed by-pass aperture: Pressure relief valves remain closed Damper operates in the parabolic region Larger load reduction

Results Summary: SSA vs. HHC Maximum loads Damping factors Negligible effect of HHC on lag damping

Outline Introduction and motivation Approach and method - Damper model - Rotor-vehicle multibody model Control laws Results Conclusions and outlook 19

Conclusions Investigated reductions in damper loads achieved using a by-pass valve Two control laws: simple SSA and HHC modulation Results have shown that the 30% safe damping margin is achieved with: Significant reduction of loads wrt passive damper (SSA: 37-68%; HHC: 74-81%) Acceptable valve openings (SSA: 15-35 Aor; HHC: 70 Aor) It appears that additional control loops aimed at selective increase in damping of lag mode are not necessary

Outlook Perform more detailed investigation of the minimum damping requirement (air-resonance, high-g turns, damping-critical flight conditions) Translate load reductions computed here in extended life of damper and of its interfaces to the rotor system Develop an experimental facility comprising modified hydraulic damper with by-pass valve and damper test bench More fully understand trade-offs between improved performance of HHC wrt simple SSA and increased system complexity (is it worth it?)

Acknowledgements Research funded by MECAER Meccanica Aeronautica SpA and the Italian Ministry of Defense Thanks to AgustaWestland for modeling and validation data of the A109E helicopter, and for valuable feedback