Optimal Placement of Piezoelectric Actuated Trailing-edge Flaps for Helicopter Vibration Control

Transcription

1 Page 1 of 53 Optimal Placement of Piezoelectric Actuated Trailing-edge Flaps for Helicopter Vibration Control S R Viswamurthy and R Ganguli Department of Aerospace Engineering Indian Institute of Science, Bangalore, India 16th AIAA/ASME/AHS Adaptive Structures Conference Schaumburg, IL April 7, 2008 ganguli@aero.iisc.ernet.in

2 Overview Introduction A brief survey of active flap approach Page 2 of 53 Objectives of this study Actuator hysteresis model Aeroelastic analysis of helicopter Flap control algorithm Optimal placement of flaps Numerical results and discussions Concluding remarks

3 INTRODUCTION Page 3 of 53

4 Vibration issues in helicopters Very high degree of aeroelastic interaction in helicopters Rotor blades are long and slender; Highly flexible compared to aircraft wing structure Inherent unsteadiness in aerodynamic environment Strong coupling between elasticity, dynamics and aerodynamics Page 4 of 53

5 Vibration issues in helicopters (continued) Severe vibration and fatigue loads Passenger and crew discomfort Fatigue damage to structural components Frequent inspection: Increased maintenance costs Rotor is the main source of vibration Page 5 of 53

6 Methods of vibration control Passive structural changes Blade tip shape, blade mass and stiffness properties Page 6 of 53 Passive devices Vibration isolation devices Vibration absorbers Active approaches Higher harmonic control (HHC) Conventional individual blade control (IBC) Active twist rotor (ATR) Actively controlled trailing-edge flap (ACF) Active control of structural response (ACSR)

7 Active twist and active flap concepts Page 7 of 53

8 Active flap approach Generate new unsteady aerodynamic loads by moving one or more trailingedge flaps Low power consumption No detrimental effect on airworthiness Flaps are typically moved at (N-1)Ω, NΩ and (N+1)Ω frequencies; Ω = Rotor rotational speed; N = Number of rotor blades Page 8 of 53

9 Active flap approach (continued) Capable of targeting multiple goals Vibration control Blade-vortex interaction (BVI) noise suppression Dynamic stall alleviation Primary control of rotor, if necessary Possibility of retro-fit into existent helicopters Page 9 of 53

10 ACTIVE FLAP APPROACH A BRIEF SURVEY Page 10 of 53

11 Analytical studies Comprehensive study of rotor with trailing-edge flap (Millott & Friedmann, JGCD, 1995) Page 11 of 53 Parametric studies & comparison with experimental data (Milgram & Chopra, AHS Journal, 1998) Adaptive neurocontrol of simulated rotor vibrations (Spencer et al, JIMSS, 1999) Vibration suppression due to BVI at low forward speeds (Friedmann et al, Math. & Comp. Modelling, 2001) Primary control of swashplateless rotor (Shen & Chopra, AHS Journal, 2004) Simultaneous vibration and noise reduction (Patt et al, AHS Journal, 2005) Effect of piezoelectric actuator hysteresis (Viswamurthy & Ganguli, JGCD, 2006)

12 Experimental studies Piezoelectric bender actuation Wind-tunnel testing of 1/5th scale model (Spangler & Hall, SDM, 1990) Hinges replaced with flexural amplification mechanisms to improve performance (Hall & Prechtl, SMS, 1996) Multi-layer piezo-bimorph actuators (Samak & Chopra, SPIE Symposium, 1993; Walz & Chopra, SDM, 1994; Ben-zeev & Chopra, SMS, 1996) Testing of Froude and Mach scaled rotor with TEF s (Koratkar & Chopra, ) Page 12 of 53

13 Experimental studies (continued) Piezostack based actuation Wind-tunnel testing of piezostack actuated TEF (Chandra & Chopra, JIMSS, 1998) X-frame actuator (Hall & Prechtl, SPIE Conference, 1999) Double lever (L-L) amplification mechanism (Lee & Chopra, SMS, 2001) Bi-axial piezoelectric stack actuator (Straub et al, SMS, 2001) Page 13 of 53

14 Experimental studies (continued) Other actuator concepts C-block actuators (Clement et al, SDM, 1998) Magnetostrictive actuation of TEF s (Fenn et al, SMS, 1996; Fink et al, AHS Forum, 2000) Induced shear based piezoelectric actuation (Centolanza & Smith, SMS, 2002) Shape memory alloy wire actuated tab (Epps & Chopra, AHS Journal, 2004) Flight test conducted by Eurocopter, Germany in September 2005; Implementation in production helicopter by 2012 Page 14 of 53

15 Objectives of this study Maximize the advantage of dual trailing-edge flap configuration Obtain maximum possible reduction in hub vibrations Keep the flap power consumption to a minimum Adopt a systematic optimization procedure to meet the above objectives Include the effects of actuator dynamic hysteresis Page 15 of 53

16 ACTUATOR HYSTERESIS MODEL Page 16 of 53

17 Hysteresis multi-branch nonlinearity Page 17 of 53

18 Hysteresis model for ferroelectric materials Hysteresis model for ferromagnetic materials (Preisach, Z Physiks, 1935) Preisach model to study piezoceramic material hysteresis (Sreeram & Naganathan, ASME Winter Annual Meeting, 1993) Validation of Preisach model through experiments in stacked piezoceramic actuators (Ge & Jouaneh, Precision Engineering, 1995) Preisach modeling of hysteresis in piezoceramics & shape memory alloys (Hughes & Wen, SMS, 1997) Page 18 of 53

19 Hysteresis transducer system Page 19 of 53

20 Classical Preisach model (CPM) Elementary hysteresis operator (ˆγ αβ ) Page 20 of 53 δ(ψ) = µ(α, β) ˆγ αβ [u(ψ)] dα dβ α β µ(α, β) Characteristic of the hysteresis transducer

21 Extension of CPM for dynamic hysteresis Page 21 of 53 Relax the static property of CPM as suggested by Mayergoyz (IEEE Transactions on Magnetics, 1988) ( δ(ψ) = µ α, β, dδ ) ˆγ αβ [u(ψ)] dα dβ dψ α β Using Taylor series expansion for µ in terms of dδ dψ ( µ α, β, dδ ) = µ 0 (α, β) + dδ dψ dψ µ 1 (α, β) + d2 δ dψ 2 µ 2 (α, β) +... δ(ψ) = + dδ dψ + d2 δ dψ 2 α β µ 0 (α, β) ˆγ αβ [u(ψ)] dα dβ α β α β µ 1 (α, β) ˆγ αβ [u(ψ)] dα dβ µ 2 (α, β) ˆγ αβ [u(ψ)] dα dβ The unknown weighting functions µ 0, µ 1 and µ 2 are estimated from experiments conducted on a APA500L actuator from CEDRAT Technologies (Viswamurthy, Rao & Ganguli, SMS, 2007)

22 HELICOPTER AEROELASTIC ANALYSIS Page 22 of 53

23 Aeroelastic model Elastic rotor blades coupled with a rigid fuselage Moderate deflection theory is used (Hodges & Dowell, NASA Report, 1974) Page 23 of 53 Each blade undergoes flap bending, lag bending, elastic twist and axial deformation Formulation is based on Hamilton s principle ψ2 ψ 1 (δu δt δw )dψ = 0 Unsteady aerodynamic model to capture the effects of blade and trailingedge flap motion (Leishman & Beddoes, AHS Journal, 1989; Hariharan & Leishman, J. Aircraft, 1996) Free-wake model used to determine the induced inflow distribution over the rotor disk (Bagai & Leishman, AHS Journal, 1995)

24 Solution procedure Finite element in space Page 24 of 53 PDE s are converted to ODE s in time Each finite element has 15 DOF s Lag and flap bending deflections: Cubic Hermite polynomials Elastic twist: Quadratic Lagrange polynomials Axial deflection: Cubic Lagrange polynomials Normal mode transformation Significantly reduces the degrees of freedom Number of equations are greatly reduced Effcient solution procedure Finite element in time ODE s are converted to algebraic equations 5th order polynomials used as shape functions Algebraic equations are solved using Newton-Raphson procedure

25 Solution procedure (continued) Obtain the blade response and calculate blade loads Transform the blade loads to steady loads acting on the helicopter Page 25 of 53 Determine the pilot trim control angles at which the helicopter is at equilibrium Solve for blade response, helicopter orientation and pilot input simultaneously Coupled trim procedure Model has been validated using wind-tunnel tests and flight tests (Ganguli et al, AHS Journal, 1998) Total trailing-edge flap power can be written as P t = N b 2π N f i=1 2π 0 dδ i max( M hi, 0) dψ dψ M hi N b Number of rotor blades N f Number of flaps on each blade Instantaneous flap hinge moment for the i th flap

26 FLAP CONTROL ALGORITHM Page 26 of 53

27 Flap control algorithm Piezo actuators are excited at 2, 3, 4 & 5/rev harmonics of rotor frequency Total voltage applied to the piezostack driving the j th flap is given by Page 27 of 53 u j (ψ) = u j st + 5 [u j Nc cos(nψ) + uj Ns sin(nψ)], j = 1, 2 N=2 Steady component of voltage (u j st) adjusted to obtain zero steady flap deflection Minimize the quadratic cost functional (J) at the i th control step J(Z i, u 1 i, u 2 i ) = Z T i W Z Z i + Z i = [ F 4p x F 4p y 2 j=1 F 4p z β j u jt i u j i M 4p x M 4p y M 4p z u j i = [ u j 2c uj 2s uj 3c uj 3s uj 4c uj 4s uj 5c uj 5s ]T, j = 1, 2 ] T

28 Flap control algorithm (continued) W Z = (1 2 β j )I 6X6 j=1 (Hub load weighting matrix) 2 β j 1 (Flap control effort weighting factor) j=1 Feedback form of the global controller proposed by Millott & Friedmann (NASA Report, 1994) is implemented Page 28 of 53 Z i = Z i 1 + J u j i 2 j=1 T j 0 ( ) u j i uj i 1 = 0, for j = 1, 2 (Optimality criteria) The weighting parameters β 1 and β 2 are adjusted such that the voltage input to the piezo actuators are kept within allowable limits prescribed by the manufacturer (-20 to +150 V for APA500L from CEDRAT)

29 OPTIMAL PLACEMENT OF FLAPS Page 29 of 53

30 Optimization problem Where do we place the flaps? Design variables Position of the flaps Criteria for flap placement Objective 1: F v Vibration reduction achieved by a given flap configuration (normalized with respect to a chosen initial configuration) Objective 2: F p Flap control power required for achieving the above reduction (normalized with respect to the same initial configuration) Constraints Move limits on the location of the flaps to ensure that the flaps are not too inboard (to avoid very low dynamic pressure) or too near the tip (where tip losses dominate) Page 30 of 53

31 Optimization problem (continued) Minimize {F v, F p } subject to x 1 lower x 1 x 1 upper x 2 lower x 2 x 2 upper Page 31 of 53

32 Computational issues Each evaluation of F v and F p requires calling the helicopter aeroelastic anaylsis 17 times 16 times to evaluate the transfer matrix T Once to determine the reduced hub vibratory loads Each call to the aeroelastic code 170 seconds on a 256MB RAM computer One function evaluation of F v or F p 48 minutes Prohibits use of conventional optimization techniques Solution Surrogate models Page 32 of 53

33 Response surface methodology Allows decoupling optimization problem from aeroelastic analysis problem Construct an approximate model using polynomial response surfaces Optimum solution from polynomial expressions can be easily determined n n i f(x 1, x 2,..., x n ) = A 0 + A i x i + A ij x i x j Second order polynomial response surface: i=1 i=1 j=1 f(x 1, x 2 ) = A 0 + A 1 x 1 + A 2 x 2 + A 11 x A 12 x 1 x 2 + A 22 x 2 2 Page 33 of 53

34 Response surface methodology (continued) Evaluate the 6 unknown regression coefficients using Central Composite Design (CCD) (Myers & Montgomery, 1995) System response/output observed at 9 data points Regression coefficients determined using method of least square error Page 34 of 53

35 NUMERICAL RESULTS Page 35 of 53

36 Rotor properties and flight condition Advance ratio (µ) = 0.30 ; C T /σ = 0.07 Page 36 of 53 Blade properties N b 4 c/r Solidity, σ 0.07 Lock number, γ 5.20 Blade pretwist 0.0 EI y /m 0 Ω 2 R EI z /m 0 Ω 2 R GJ/m 0 Ω 2 R m 0 (kg/m) 6.46 Ω(rpm) 383 R(m) 4.94 Trailing edge flap properties c f /c 0.20 m f /m Xg f /c f 0.20

37 Initial configuration & move limits Physical variable Coded value x 1 lower 0.59R x 1 initial 0.65R 0 x 1 upper 0.71R x 2 lower 0.77R x 2 initial 0.83R 0 x 2 upper 0.89R Page 37 of 53

38 Response surface generation F v = x x x x 1 x x 2 2 F p = x x x x 1 x x 2 2 Outboard flap is more effective in vibration reduction than inboard flap Reason: Higher dynamic pressure near the blade tip Page 38 of 53

39 Error in F v response surface S.No. x 1 x 2 x 1 x 2 F v F v %Error Coded Coded Physical Physical RSM Analysis value value variable variable prediction prediction R 0.83 R R 0.89 R R 0.77 R R 0.83 R R 0.83 R R 0.79 R R 0.87 R R 0.79 R R 0.87 R Page 39 of 53

40 Error in F p response surface S.No. x 1 x 2 x 1 x 2 F p F p %Error Coded Coded Physical Physical RSM Analysis value value variable variable prediction prediction R 0.83 R R 0.89 R R 0.77 R R 0.83 R R 0.83 R R 0.79 R R 0.87 R R 0.79 R R 0.87 R Page 40 of 53

41 Best design point for minimum vibration Page 41 of 53 For minimum vibration Inboard flap: 65%R and Outboard flap: 89%R F vmin = % reduction in hub vibration Denoted as Configuration A ; F p = 1.723

42 Best design point for minimum flap power Page 42 of 53 For minimum flap power Inboard flap: 65.8%R and Outboard flap: 81.5%R F v = % reduction in hub vibration Denoted as Configuration B ; F pmin = 0.969

43 Distribution in criterion space Page 43 of 53

44 Pareto surface & Trade-off design Page 44 of 53 Configuration C is a trade-off between Configurations A & B Configuration C F v = and F p = Inboard flap: 63.6%R ; Outboard flap: 77%R 70% reduction in hub vibration

45 Initial and final design configurations Page 45 of 53

46 Final configuration: Actuator control input Page 46 of 53

47 Flap response to actuator input Page 47 of 53

48 Hub loads reduction Page 48 of 53

49 Performance at other speeds Page 49 of 53

50 CONCLUDING REMARKS Page 50 of 53

51 Important conclusions Page 51 of 53 Optimal position of dual trailing-edge flaps on a 4-bladed helicopter rotor in the presence of actuator dynamic hysteresis is sought. The performance criteria considered for the optimization study are the hub vibration level and the flap power. The hysteresis in the piezo actuators is modeled using a dynamic hysteresis model based on the CPM. A finite element approach is used to solve the coupled helicopter aeroelastic response and trim problem. The piezo actuators are excited at 2-5/rev harmonics and a frequency domain control algorithm is used to determine the optimal control inputs. Second order polynomial response surfaces are generated for the two objectives using the central composite design. This approach decouples the optimization problem from the helicopter aeroelastic problem and greatly reduces the computational effort. The response surfaces obtained using CCD offer valuable insight into the variation and sensitivity of the two objectives with respect to the location of the flaps. Results show that both objectives are more sensitive to the outboard flap location compared to the inboard flap location. The outboard flap is more effective in reducing hub vibration levels due its operation in a higher dynamic pressure region.

52 Conclusions (continued) Page 52 of 53 To achieve minimum vibration levels, the inboard and outboard flaps need to be placed at 65 and 89 percent radial locations, respectively. This configuration yields about 78% reduction in hub vibration from baseline conditions while using about 72% more flap power compared to the initial configuration. The dual-flap configuration with inboard and outboard flaps at 65.8% and 81.5% radial location requires least flap power. This configuration is quite close to the initial configuration and therefore consumes only marginally less power compared to the initial configuration. Vibration reduction in this case is about 62 percent from baseline level at µ = The Pareto curve between the two objectives is discontinuous but contains few useful trade-off design points which yield reasonable reduction in vibration while consuming only marginally more power than the initial configuration. A good trade-off configuration is selected based on careful examination of the Pareto front. In this configuration, the inboard and outboard flaps are located at 63.6%R and 77%R, respectively. This configuration yields 70 percent reduction in vibration and requires about 21 percent more flap power compared to initial configuration (at µ = 0.30). This design point appears to be a good trade-off design at all forward speeds.

53 THANK YOU QUESTIONS? Page 53 of 53