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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
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POLITECNICO di MILANO
OutlineOutline
• Introduction and motivation
• Approach and methods
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Introduction and MotivationIntroduction 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 1972Mechanical-hydraulic device for selective damping of lag frequency
• Bauchau et al., SBIR I & II, 2003-2004Active modulation of by-pass valve aperture for selective damping of lag frequency
• Gandhi at al., Aeronautical Journal 2003HHC modulation of by-pass valve for reduction of vibratory hub loads
• …
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Introduction and MotivationIntroduction 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
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Introduction and MotivationIntroduction and Motivation
By-pass valve: relatively straightforward way of changing damping (and hence loads) in a damper
Focus of present work:1. Can we significantly reduce loads if we allow for a
decrease in the damping to lower but still safe values?2. 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)?
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OutlineOutline
• Introduction and motivation
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Damper ModelDamper 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)
• 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 valveBy-pass valve
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Damper ModelDamper Model
Characteristic load-speed curves for varying by-pass valve aperture
Δbyp = Abyp/Aor
Low speed: relief valves closed
High speed: relief valves open
Knee: transition region
Knee moves to higher speed for increased by-pass aperture
Standard passive damper:Tuned to experimental data by identifying:- Orifice and relief valve discharge coefficients- Relief valve pre-load
Adaptive damper with by-pass:Effect of by-pass aperture on characteristic curve
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Rotor-Vehicle Multibody ModelRotor-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 conditionsValidation using experimental data (see paper)
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Control LawsControl Laws
Damping criterion (provided by helicopter manufacturer): For each flight condition, ensure ≥30% of damping of
conventional passive damper
Speed-scheduled aperture
HHC
+
Damper load
Helicopter speed
Valve aperture
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Control LawsControl 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 Criterion
Minimize peak loads without exceeding allowed damping loss at each flight
conditionMinimize 1-2-3P harmonic amplitudes
Pro’s Pro’s
Maximum possible simplicity Additional reduction of loads wrt SSANegligible effects on damping
Con’s Con’s
Does not account for rotor-damper response
Additional complexity (hardware & software)
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Estimation of DampingEstimation 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))
1. Approximate state matrix: A(ψ) ≈ A0
2. Transfer periodicity to inputs term
Obtain linear time invariant (LTI) system:x· = A0x + Ub(ψ)
where b(ψ) = exogenous periodic dummy inputs
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Estimation of DampingEstimation of Damping
Estimation process:
1. Trim helicopter and perturb with impulsive torque input at lag hinge
2. Identify discrete-time ARX model (using Least Squares or Output Error method) with harmonic inputs
3. Compute discrete poles, and transform to continuous time (Tustin transformation)
4. Obtain frequencies and damping factors
Given reformulated LTI system
x. = A0x + Ub(ψ)
use standard Prony’s method (Hauer 1990; Trudnowski 1999)
Frequency domain verification of correct identification
Time domain verification of correct identification
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OutlineOutline
• Introduction and motivation
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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ResultsResultsSSA control law:Δbyp = Abyp/Aor
Maximum loads
Damping factors
Substantial reductions in damper loads (-37% ÷ -70%)
30% damping constraint
Significant valve apertures
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ResultsResultsValve aperture
Damper loads
HHC control law:
Further reductions in damper loads peaks
Max SSA aperture: Δbyp = 38
Max HHC aperture: Δbyp = 68
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ResultsResults
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
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ResultsResultsSummary: SSA vs. HHC Maximum loads
Damping factors
Negligible effect of HHC on lag damping
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OutlineOutline
• Introduction and motivation
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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ConclusionsConclusions
• 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
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OutlookOutlook
• 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?)
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AcknowledgementsAcknowledgements
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