1. 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

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

3. 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,
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 …

4. 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

5. 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)?

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

7. 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

8. 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

9. 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)

10. 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

11. 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)

12. 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

13. 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

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

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

16. 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

17. 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

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

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

20. 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: Aor; HHC: 70 Aor)
It appears that additional control loops aimed at selective increase in damping of lag mode are not necessary

21. 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?)

22. 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