POLItecnico
di MIlano
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
Adaptive Lead-Lag Damping
• Approach and methods
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Introduction and Motivation
Lead-lag dampers are typically purely passive devices
Adaptive Lead-Lag Damping
The idea of using adaptive “smart” dampers has been around for a
long time:
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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
•
…
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Introduction and Motivation
Adaptive Lead-Lag Damping
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 Motivation
Adaptive Lead-Lag Damping
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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Outline
• Introduction and motivation
Adaptive Lead-Lag Damping
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Damper Model
Physics-based mathematical model of hydraulic damper:
Adaptive Lead-Lag Damping
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•
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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
By-pass valve
Coupled set of stiff non-linear ordinary differential equations
(solved with time-adaptive modified Rosenbrok 2nd order integrator)
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Damper Model
Characteristic load-speed curves for varying by-pass valve aperture
Adaptive Lead-Lag Damping
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
Low speed:
relief valves closed
Adaptive damper with by-pass:
Effect of by-pass aperture on
characteristic curve
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Knee moves to
higher speed for
increased by-pass
aperture
Δbyp = Abyp/Aor
Rotor-Vehicle Multibody Model
Detailed multibody model of rotor
coupled to rigid fuselage
(A109E helicopter):
Adaptive Lead-Lag Damping
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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)
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Control Laws
Adaptive Lead-Lag Damping
Valve
aperture
+
Speed-scheduled
aperture
Helicopter
speed
HHC
Damper
load
Damping criterion (provided by helicopter manufacturer):
For each flight condition, ensure ≥30% of damping of conventional
passive damper
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Adaptive Lead-Lag Damping
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
Criterion
Minimize peak loads without exceeding
allowed damping loss at each flight condition
Minimize 1-2-3P harmonic amplitudes
Pro’s
Pro’s
Maximum possible simplicity
Additional reduction of loads wrt SSA
Negligible effects on damping
Con’s
Con’s
Does not account for rotor-damper response Additional complexity (hardware & software)
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Estimation of Damping
Modified Prony’s method to account for periodic nature of problem
(Bottasso et al., EWEC 2010)
Adaptive Lead-Lag Damping
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 Damping
Given reformulated LTI system
.
x = A0x + Ub(ψ)
Adaptive Lead-Lag Damping
use standard Prony’s method (Hauer 1990; Trudnowski 1999)
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
Frequency domain verification
of correct identification
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Time domain verification
of correct identification
Outline
• Introduction and motivation
Adaptive Lead-Lag Damping
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Results
SSA control law:
Maximum loads
Δbyp = Abyp/Aor
Adaptive Lead-Lag Damping
Damping factors
30% damping constraint
Substantial reductions
in damper loads
(-37% ÷ -70%)
Significant valve
apertures
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Results
HHC control law:
Valve aperture
Adaptive Lead-Lag Damping
Damper loads
Further reductions in
damper loads peaks
Max SSA aperture: Δbyp = 38
Max HHC aperture: Δbyp = 68
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Adaptive Lead-Lag Damping
Results
Small maximum allowed by-pass
aperture:
- Valve opening is not enough to
prevent activation of pressure
relief valves
- Small load reduction
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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
Adaptive Lead-Lag Damping
Damping factors
Negligible effect of
HHC on lag damping
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Maximum loads
Outline
• Introduction and motivation
Adaptive Lead-Lag Damping
• Approach and method
- Damper model
- Rotor-vehicle multibody model
- Control laws
• Results
• Conclusions and outlook
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Conclusions
•
Adaptive Lead-Lag Damping
•
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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Adaptive Lead-Lag Damping
Outlook
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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
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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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Acknowledgements
Adaptive Lead-Lag Damping
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
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