POLI di MI tecnicolanotecnicolano LOAD REDUCTION IN LEAD-LAG DAMPERS BY SPEED-SCHEDULED APERTURE AND MODULATED CONTROL OF A BY-PASS VALVE C.L. Bottasso,

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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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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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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


• Approach and method

- Damper model


- Control laws

• Results


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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



- Damper model


- Control laws

• Results


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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



- Damper model


- Control laws

• Results


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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

Documents

POLI di MI tecnicolanotecnicolano LOAD REDUCTION IN LEAD-LAG DAMPERS BY SPEED-SCHEDULED APERTURE AND MODULATED CONTROL OF A BY-PASS VALVE C.L. Bottasso,