The Pennsylvania State University The Graduate School STRUCTURAL AND AERODYNAMIC CONSIDERATIONS OF AN ACTIVE PIEZOELECTRIC TRAILING-EDGE TAB ON A

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1 The Pennsylvania State University The Graduate School STRUCTURAL AND AERODYNAMIC CONSIDERATIONS OF AN ACTIVE PIEZOELECTRIC TRAILING-EDGE TAB ON A HELICOPTER ROTOR A Dissertation in Aerospace Engineering by Gabriel Jon Murray c 2013 Gabriel Jon Murray Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2013

2 The dissertation of Gabriel Jon Murray was reviewed and approved by the following: Farhan Gandhi Professor of Aerospace Engineering Dissertation Advisor, Chair of Committee Edward Smith Professor of Aerospace Engineering Joseph Horn Professor of Aerospace Engineering Timothy Miller Senior Research Associate George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering Signatures are on file in the Graduate School.

3 Abstract Rotorcraft have a unique ability not typically shared with their fixed-wing brethren, namely the ability to hover, maintaining position over a fixed point on the Earth in a zero-wind environment. The rotation of the rotorcraft s wings (rotor blades) allows them to experience apparent wind, even if the rotorcraft is not moving relative to the surrounding air. However, this ability comes at a cost, namely a more complex operating condition for the rotor. One of the consequences of this complex environment is increased noise and vibrations compared to airplanes. Research has been focused on this issue for some time, considering myriad methods of achieving noise and vibration reduction. Thisdissertationisconcernedwithanactivetabforuseonarotorcraftfornoise and vibration reduction. The tab is located at the trailing edge of the airfoil. The tab consists of a shim sandwiched by layers of the piezoelectric actuators, macro fiber composites, of varying length. This configuration is similar to a bimorph. The modus operandi is similar to that of a trailing edge flap. The actuators deform the tab, bending it to achieve a tip displacement. This provides a change in the lift, moment, and drag coefficients of the airfoil. By actuating the system at 3/rev to 5/rev, reductions in noise and vibration can be realized. The system was examined and designed around using the UH-60 Blackhawk as the model rotorcraft. The tab is envisioned to operate between 65% to 85% of the main rotor span. The tab s chordwise dimensions considered were 20% and 15% of the blade chord. In order to assess the potential of the tab to change the lift and moment coefficients of the airfoil-tab system, a steady computational fluid dynamics study was conducted. The results were generated via the University of Maryland s Transonic Unsteady Navier-Stokes code. Various tab deflection angles, Mach numbers, and angle-of-attack values were computed. These results were compared to a trailing edge flap of similar size. The comparison shows that the tab produces lift and moment increments similar to that of the trailing edge flap. The moment increment iii

4 of the tab is consistently larger than the moment increment of the trailing edge flap. The 15% chord tab produces a smaller increment in lift and moment for a given tip deflection than the 20% chord tab. The longer tab has a lift coefficient on average 1.18 times the shorter tab and a moment increment 1.15 times that of the shorter tab. The design of the tab composed of both active piezoelectric actuators and passive materials was conducted using finite element analysis. The objectives were to maximize the tip deflection due to the actuators, while minimizing the deformation due to inertial and aerodynamic forces and loads. The inertial loads (acceleration terms) come from both blade motion, such as flapping and pitch, as well as the rotation of the rotor (centrifugal force). All of these previously mentioned terms cause the tab to undergo undesirable deflections. The original concept consisted of a bimorph configuration with a single layer of macro fiber composite the entire length of the 20% chord tab. The final design has three, tapered actuator layers on either side of a shim. Also, the length of the tab was reduced to 15% of the chord. A multitude of designs were compared via their performance objectives as well as how the design variables changed performances relative to the objectives. The result of this detailed analysis was the selection of several configurations that were investigated in detail. With several designs selected, they formed the basis to build a prototype tab. This prototype was based on a 15% chord tab. Due to the available commercial actuator lengths, a two layer system was ultimately built. The tab tip displacement was measured with both static and harmonic inputs. Various input voltages, both with and without a DC offset, were tested, up to -500 V to 1500 V. The input frequency was varied between 0 Hz to 17.2 Hz. Also, a frequency response of the tab was generated. High voltage static tip displacement compares well with the expected result. The first bending natural frequency was measured at 138 Hz and compares well with the computed range of 135 Hz to 142 Hz, depending on bond layer thickness. The results of dynamic inputs uncovered an unexpected reduction in tip displacement of 60% to 65% of the static result, for high voltages. It is suspected that the actuator suffers from a time-dependent response, with quick initial displacement followed by a slow creeping to the final displacement value. This phenomena has also been observed in the literature, although it is not prevalent. Using the experiment as a guide to quantify the time-dependent behavior, the overall viability of the system is discussed. The maximum dynamic tip deflection (accounting for time-dependent behavior) of a 15% chord tab is 4. The tab is able to generate lift coefficient increments up to and moment increments of for positive tab deflections. Deflections due to aerodynamic loads range from 0.3 to 2. Deflections due to blade motions are less than 0.5 and due to the centrifugal iv

5 force, This system can be stiffened, reducing the dynamic tip deflection to 3.25 and limitingtheaerodynamic responseto1. Overall, bydesigningthetab to modest deflections, moderate reductions in vibration are possible, but are limited by actuator authority. v

6 Table of Contents List of Figures List of Tables List of Symbols Acknowledgments xi xix xxiii xxvi Chapter 1 Introduction Background and Motivation Actuators and Smart Materials Individual Blade Control US/German MOU on helicopter aeromechanics Deutsches Zentrum für Luft- und Raumfahrt (DLR) ZF Luftfarhrttechnik University of Maryland Trailing Edge Flap University of Maryland Massachusetts Institute of Technology McDonnell-Douglas and Boeing companies US Army Aviation RD&E Center University of Michigan Advanced Technology Institute of Commuter-helicopter Eurocopter The Pennsylvania State University vi

7 1.4.9 Office National d Études et de Recherches Aérospatiales (ONERA) Royal Institute of Technology (Sweden) and Technion Japan Aerospace Exploration Agency (JAXA) Seoul National University US Army Research, Development, and Engineering Command (ARMDEC) Non-piezoelectric driven flaps Variable Camber Blade Twist Active Gurney Flap Trailing Edge Tab and Variable Chord National Aerospace Laboratory of Japan/JAXA Western Michigan University EADS/Eurocopter Technical University of Denmark The Pennsylvania State University Multiple Morphing Device Helicopter Performance Analysis Concept and research objectives Organization structure of dissertation Chapter 2 Steady Aerodynamic Study of Tab Analysis Method Aerodynamic Coefficient Results and Discussion: 0.20c tab Lift coefficient and increment for Mach number= Moment coefficient and increment for Mach number= Drag coefficient and increment for Mach number= Lift coefficient increment per unit drag for Mach number= Moment coefficient increment per unit drag for Mach number= Lift coefficient and increment for Mach number= Moment coefficient and increment for Mach number= Drag coefficient and increment for Mach Number= Lift coefficient increment per unit drag for Mach number= Moment coefficient increment per unit drag for Mach number= Lift coefficient and increment for Mach number= Moment coefficient and increment for Mach number= Drag coefficient and increment for Mach Number= vii

8 Lift coefficient increment per unit drag for Mach number= Moment coefficient increment per unit drag for Mach number= Comparison of Aerodynamic Coefficients: 0.20c & 0.15c tabs Comparison of 0.20c & 0.15c for boundary rotor conditions Comparison of SC-1094R8 With and Without Tab Extension Chapter 3 Design and Analysis of Tab Basic Analysis Simple analysis Analysis using Euler-Bernoulli beam theory Layered-Actuation Tab c tab c tab Nondominated set: flapping, aerodynamics, and active displacement Spanwise Actuator Variation Tab Design Selected Configuration Mode shapes and natural frequencies Active, aerodynamic, and flapping deflections: 0.15c and 0.2c tab Rotating environment and blade pitching and flapping angles: 0.15c tab Assessment of Design Achieving Objectives Chapter 4 Benchtop Tab Demonstrator Design of Experimental Tab Experimental Setup Testing equipment Requirements Equipment specifications Test specimen Experimental Results and Discussion Testing objectives Finite element model of experimental tab Testing results and discussion DC input Tab frequency response viii

9 Example time trace of output subjected to harmonic loading Harmonic input with DC offset Harmonic input without DC offset Amplifier voltage and current output Low frequency response High-speed camera results Exploration of frequency response Tab robustness Chapter 5 Assessment of Reduced Performance Impact on Inertial and Aerodynamic Response Impact on Optimal Designs Impact on Active Performance and Viability of Concept Chapter 6 Conclusion Steady Aerodynamics Tab and Actuator Design Benchtop Prototype Assessment of Reduced Performance Future Work Appendix A Aerodynamic Coefficient Tables, 0.20c 186 A.1 Lift Coefficient A.2 Moment Coefficient A.3 Drag Coefficient A.4 Increment in Lift Coefficient A.5 Increment in Moment Coefficient A.6 Increment in Drag Coefficient Appendix B Aerodynamic Coefficient Tables, 0.15c 213 B.1 Lift Coefficient B.2 Moment Coefficient B.3 Drag Coefficient B.4 Increment Lift, Moment, and Drag Coefficients ix

10 Appendix C CFD Code Used to Generate Tab Pressure Differences 222 C.1 Steady Comparison Appendix D Macro Fiber Composite Properties 226 Appendix E Effect of Damping on the Tab Response 227 Bibliography 233 x

11 List of Figures 1.1 The rotor velocities at (a) hover and (b) forward flight Some of the difficulties a rotor encounters in forward flight [2, 3] The active systems for reducing vibrations, rotor noise, or improving performance A four bladed rotor with 2/rev swashplate higher harmonic control [4] Various piezoelectric actuator configurations: (a) stack actuation, an (b) active fiber composite Actuator, and a (c) macro fiber composite actuator [6] A piezoelectric element with an electric field in the 3 axis direction [5] A piezoelectric bimorph, resulting in beam bending (exaggerated) An (a) external flap and a (b) plain flap A piezoelectric bimorph actuated trailing edge flap by the University of Maryland [12] A (a) two-layer and (b) four-layer bimorph [13] A piezoelectric bimoprh actuated trailing edge flap by the University of Maryland [14] A tapered piezoelectric bimorph actuated trailing edge flap by the University of Maryland [16] Schematic of piezoelectric stack driving a flap by the University of Maryland [18] An integrated mechanical amplifier for a stack actuator by the University of Maryland [19] A double lever mechanical amplifier for a stack actuator by the University of Maryland [22] Actual double lever stack actuator by the University of Maryland [22] Parallel stacks, double lever actuator by the University of Maryland [21] Composite layup configuration for bending-twist coupling [24] Undulating beam deflection using bending-twist coupling [24] xi

12 1.20 A (a) hinged plain-flap mechanism and (b) an integral beam-flap mechanism for the bending-twist coupled actuator [24] An active blade tip using a bending-twist coupled piezoelectric actuated beam by the University of Maryland [26] A tapered piezoeletric bender driving a TEF by MIT [28] The X-frame powered by a dual piezoelectric stack by MIT [30] The X-frame actuator installed in a rotor blade driving a flap by MIT [30] A hybrid actuator developed by McDonnell-Douglas [34] Biaxial piezoelectric flap actuator developed by Boeing [38] MITs X-frame actuator as used in the SMART rotor by Boeing [37] The SMART rotor blade with flap by Boeing [39] The SMART rotor system in the 40 ft by 80 ft NASA wind tunnel [39] The piezoelectric bimoprh powered flap used in US Army tests [41] The University of Michigan s (a) piezoelectric C-block actuator and (b) its implementation in a rotor blade for driving a TEF [43] (a) Piezoelectric shear-twist plate and (b) the X-sectioned composite piezoelectric shear-twist plate by the Advance Technology Institute of Commuter-helicopter [45] A piezoelectric actuated trailing edge flap by Eurocopter [47] Penn State s induced-shear piezoelectric actuator, (a) the shearing piezoelectric elements resulting in torsion and (b) its implementation to drive a TEF [50] (a) The concept for using a buckling beam to amplify piezoelectric input for driving a TEF and (b) the final design iteration [51] The piezoelectric stack driven flap actuator with elliptical amplifier by ONERA [52] A tab controlled floating flap by Heinze and Karpel [54] The piezoelectric based active flap system used by JAXA [55] The piezoelectric based active elevon (flap) by the US Army [59] The push-pull actuator configuration used to rotate an elevon by the US Army [59] A static Gurney flap, as first introduced to the aeronautical world by Robert Liebeck [112] Example tab configurations: (a) flat tab, (b) tip bent tab with full retraction, and (c) tip bent tab with partial retraction by the National Aerospace Laboratory of Japan [123] Active tab concept used on a rotating test by the National Aerospace Laboratory of Japan [124] xii

13 1.44 A NACA 0012 airfoil with a trailing edge tab by the Western Michigan University [126] (a) Piezoelectric driven smart tab, (b) active trailing edge, and (c) blend by EADS/Eurocopter [127] An active tab with piezoelectric low profile stacks by EADS/ Eurocopter [127] The creation of a low profile multilayer piezoelectric stack: (a) the stack, (b) electrode, (c) flexible electrode, (d) dicing, (e) multilayer plate, (f) final processing, by EADS/Eurocopter [128] The segmented composite piezoelectric bender plates by EADS/ Eurocopter [129] A variable chord device using a deployable trailing edge tab [131] A bistable deployable trailing edge tab by Penn State [132] A continuous variable chord device, by Penn State [135] The dimensions for a trailing edge flap, Gurney flap, and a trailing edge plate, by Penn State [136] The concept of the active piezoelectric tab Long range goal is to incorporate active tab into a variable chord system consisting of a deployable plate: (a) retracted and (b) deployed and actuating The C-grid used by CFD for two tab deflections: (a) 0 and (b) The active trailing edge tab concept and dimensions Lift coefficient of tab at Ma= Increment in lift coefficient of tab at Ma= Increment in lift coefficient of trailing edge flap at Ma= Moment coefficient about the 1/4-chord of the tab at Ma= Increment in moment coefficient about the 1/4-chord of the tab at Ma= Increment in moment coefficient about the 1/4-chord of the TEF at Ma= Drag coefficient of the tab at Ma= Increment in drag coefficient of the tab at Ma= Increment in drag coefficient of the tab at Ma= Increment in lift coefficient per unit drag of tab at Ma= Increment in lift coefficient per unit drag of trailing edge flap at Ma= Increment in moment coefficient about the 1/4-chord per unit drag of tab at Ma= xiii

14 2.15 Increment in moment coefficient about the 1/4-chord per unit drag of trailing edge flap at Ma= Lift coefficient of tab at Ma= Increment in lift coefficient of tab at Ma= Increment in lift coefficient of TEF at Ma= Moment coefficient about the 1/4-chord of tab at Ma= Increment in moment coefficient about the 1/4-chord of tab at Ma= Increment in moment coefficient about the 1/4-chord of TEF at Ma= Drag coefficient of tab at Ma= Increment in drag coefficient of tab at Ma= Increment in drag coefficient of TEF at Ma= Increment in lift coefficient per unit drag of tab at Ma= Increment in lift coefficient per unit drag of trailing edge flap at Ma= Increment in moment coefficient about the 1/4-chord per unit drag of tab at Ma= Increment in moment coefficient about the 1/4-chord per unit drag of trailing edge flap at Ma= Lift coefficient of tab at Ma= Increment in lift coefficient of tab at Ma= Increment in lift coefficient of TEF at Ma= Moment coefficient of tab at Ma= Increment in moment coefficient of tab at Ma= Increment in moment coefficient of TEF at Ma= Drag coefficient of tab at Ma= Increment in drag coefficient of tab at Ma= Increment in drag coefficient of TEF at Ma= Increment in lift coefficient per unit drag of tab at Ma= Increment in lift coefficient per unit drag of trailing edge flap at Ma= Increment in moment coefficient per unit drag of tab at Ma= Increment in moment coefficient per unit drag of trailing edge flap at Ma= Rotor boundary AOA values and Mach numbers, red stars denote values considered in this section [145] Comparison of tab aerodynamic effectiveness between 0.20c and 0.15c Comparison of aerodynamic coefficients for standard SC-1094R8 and with 0.2c tab (SC-1094R8 results from [145]) xiv

15 2.45 Comparison of aerodynamic coefficients for standard SC-1094R8 (both numerical and experimental), 0.2c tab (SC-1094R8 computational results from [145] and experimental results from [148]) Basic actuation concept, using two MFC actuators sandwiching a thin shim plate The force-strain relationship for a piezoelectric material (eg MFC) Illustration of aerodynamic loading, dynamic(inertial) loading, and active actuation forces experienced by the tab ThepressurecoefficientontherearoftheairfoilandtabatMach=0.6 and an angle of attack of 8 as predicted by TURNS Design charts based on Euler-Bernoulli beam theory Both active deflection (a) and shim thickness (b) versus passive deflection of the tab with two MFCs sandwiching a shim, at 1/rev flapping and actuation, ǫ = 0.2, span location 0.75R The multilayered MFC tab Active and passive 1/rev tab displacements with various MFC layering for ǫ = 0.2, span location 0.75R, ±500 V The best 0.2C design with an active deflection of 3 and a passive deflection of A comparison of the 0.2c tab with an aluminum shim with the 0.15c tab with a composite shim, span location 0.75R, ±1000 V Active (4/rev) and flapping (1/rev) tab displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000 V The pressure coefficient on the rear of the airfoil and tab (blunt tip see Section 3.4.2) at Mach=0.6 and an angle of attack of Active (4/rev), flapping (1/rev), and aerodynamic (static) tab displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000 V Length of the active layers and number of shim plies corresponding to figure 3.13a Schematic for the spanwise variation concept Comparison between designs with spanwise variation and designs uniform spanwise Span variation tab: active (4/rev) and flapping (1/rev) displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000V First three mode shapes for tab, looking from blade root towards the blade tip (left) and from the trailing edge towards the leading edge (right) xv

16 3.19 Isometric views of the first three mode shapes for tab Tip deflection due to actuation, blade flapping, and various aerodynamic loading Tab s 2D chordwise pressure distribution, pointed tip Outline of the bluntly tipped (TURNS) tab versus sharply tipped (Fluent) airfoil Tab s 2D chordwise, centerline displacement distribution, pointed tip Tab s 2D chordwise pressure distribution, positive pressure results in a lifting force, blunt tip Tab s 2D chordwise, centerline displacement distribution, blunt tip The centrifugal force acting on an airfoil selection on the rotor Smart Materials macro fiber composites: (a) 56 mm by 28 mm active and (b) 28 mm by 14 mm active Aluminum shim with doubler bonded at one end Schematic of tab prototype, units in millimeters The maximum voltage input to the MFCs actuators Trek 609c/b-6 series high voltage amplifiers: (a) front view with control input and voltage monitor output and (b) back view with high voltage output and ground The Tektronix AFG3022D signal generator The Polytec vibrometer controller (bottom) and laser unit (top) The terminal block with input leads and output leads Testing Fixture: (a) front view of clamp and (b) rearview of clamp Testing fixture with tab: (a) view from trailing edge and (b) side view Layout of the tab used for finite element analysis Static deflection of the tab Static deflection of the tab The output power spectrum over the input power spectrum for -50 V to 50 V input via a 1 Hz to 250 Hz Sine sweep The displacement response versus frequency from the finite element model Fundamental mode of the finite element model Plots of laser vibrometer output and amplifier voltage monitor versus time, 1=[0 V : 250 V & 27 rad/s], 2=[0 V : 250 V & 162 rad/s, and 3=[-500 V : 1500 V & 27 rad/s]] Experimental results with DC offset: a) ratio of experimental over estimated and b) experimental displacement xvi

17 4.18 Experimental results without DC offset: a) ratio of experimental over estimated and b) experimental displacement The displacement versus voltage of the experimental results at 0 Hz, 4.3 Hz, and Hz Laser vibrometer output, amplifier voltage monitor, and amplifier current monitor versus time for -500 V : 1500 V & 27 rad/s Displacement via the high speed camera at -500 V : 1500 V & 108 rad/s Displacement resulting from a square wave(-500 V to 1500 V) going from deflected down to deflected up: a) the entire 1.25 s half period and b) temporal zoom from 0 s to 0.1 s Tip twist frequency response of NASA s active-twist rotor at ±75 V, ±200 V, ±350 V, and ±500 V, [160] Experimental dynamic results over static results with DC offset Experimental dynamic results over static results without DC offset Estimated and measured tip twist frequency response of NASA s active-twist rotor at ±75 V, ±200 V, ±350 V, and ±500 V, [160] Measured tip displacement of a cantilevered beam for a) quasi-static and b) dynamic voltage [161] Beamtipresponsetoa500Vstepinputa)entiretimeandb)initial step response [162] Original Pareto front(black) compared to Pareto front with reduced active authority C.1 Outline of the Fluent airfoil vs TURNS airfoil C.2 The grid used for the Fluent based CFD simulations C.3 Comparison of pressure coefficient at Ma=0.6 and AOA=0 (a) entire airfoil and (b) trailing edge C.4 Comparison of pressure coefficient at Ma=0.6 and AOA=4 (a) entire airfoil, (b) rear portion, and (c) trailing edge E.1 Magnitude of tip response for various bond layer stiffness values E.2 Magnitude of the tip response with structural damping applied to the bond layer, t epoxy = 0.05 mm and E epoxy = 3.85 GPa E.3 Magnitude of the tip response with viscous damping applied to the bond layer, t epoxy = 0.14 mm and E epoxy = 100 MPa E.4 Magnitude and phase of the tip response with both (a) structural and (b) viscous damping applied to the entire system xvii

18 E.5 Magnitude (a) and phase (b) of a single-degree-of-freedom system with structural and viscous damping xviii

19 List of Tables 1.1 The performance improvement predicted for a medium lift helicopter by Advanced Rotorcraft Technology [138] Important parameters used by the CFD codes and values varied dc m /Cd for both the tab and TEF for various AOA values and tab/tef deflections, Mach= dc m /Cd for both the tab and TEF for various AOA values and tab/tef deflections, Mach= dc l /Cd for both the Tab and TEF for various AOA values and Tab/TEF deflections, Mach= dc m /Cd for both the tab and TEF for various AOA values and tab/tef deflections, Mach= Mach number and AOA values forming the rotor blade boundary Lift and moment increments for both 0.20c and 0.15c tabs for various Mach number and AOA values UH-60 and tab properties MFC material properties ([150]) Plain weave carbon fiber composite material properties Design variables, actuated tip deflections, and flapping tip deflections for several configurations Active tip displacement in the rotating environment at various pitching or flapping angles (single-shim ply, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1) Active tip displacement in the rotating environment at various pitchingor flappingangles(two-shimply, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1) Dimensions and capacitance for MFC actuators [150] Shim materials Test frequencies xix

20 4.4 The voltage ramping steps used during testing Percent error between the experimentally measured displacement and the finite element predicted displacement Experimentally measured (peak amplitude) of the benchtop tab ( denotes data acquired via high speed camera) (peak amplitude) calculation from finite element model of the benchtop tab Experimentally measured (peak amplitude) of the benchtop tab without any DC offset (peak amplitude) calculation from finite element of the benchtop tab without any DC offset Experimentally measured (peak amplitude) of the benchtop tab Design variables and performance of tab accounting for reduced displacement, with the active values reduced 60% to 65% of the originally predicted value Increments in lift and moment comparison for of tip displacement with and without the reduced deflection (see table 5.1 for configuration details) Increments in lift and moment comparison for of tip displacement with and without the reduced deflection for stiffer tab configurations (see table 5.1 for configuration details A.1 C l for 0.20c tab, = A.2 C l for 0.20c tab, = A.3 C l for 0.20c tab, = A.4 C l for 0.20c tab, = A.5 C l for 0.20c tab, = A.6 C l for 0.20c tab, = A.7 C l for 0.20c tab, = A.8 C m for 0.20c tab, = A.9 C m for 0.20c tab, = A.10 C m for 0.20c tab, = A.11 C m for 0.20c tab, = A.12 C m for 0.20c tab, = A.13 C m for 0.20c tab, = A.14 C m for 0.20c tab, = A.15 C d for 0.20c tab, = A.16 C d for 0.20c tab, = A.17 C d for 0.20c tab, = xx

21 A.18 C d for 0.20c tab, = A.19 C d for 0.20c tab, = A.20 C d for 0.20c tab, = A.21 C d for 0.20c tab, = A.22 dc l for 0.20c tab, Ma= A.23 dc l for 0.20c tab, Ma= A.24 dc l for 0.20c tab, Ma= A.25 dc l for 0.20c tab, Ma= A.26 dc l for 0.20c tab, Ma= A.27 dc l for 0.20c tab, Ma= A.28 dc l for 0.20c tab, Ma= A.29 dc l for 0.20c tab, Ma= A.30 dc l for 0.20c tab, Ma= A.31 dc m for 0.20c tab, Ma= A.32 dc m for 0.20c tab, Ma= A.33 dc m for 0.20c tab, Ma= A.34 dc m for 0.20c tab, Ma= A.35 dc m for 0.20c tab, Ma= A.36 dc m for 0.20c tab, Ma= A.37 dc m for 0.20c tab, Ma= A.38 dc m for 0.20c tab, Ma= A.39 dc m for 0.20c tab, Ma= A.40 dc d for 0.20c tab, Ma= A.41 dc d for 0.20c tab, Ma= A.42 dc d for 0.20c tab, Ma= A.43 dc d for 0.20c tab, Ma= A.44 dc d for 0.20c tab, Ma= A.45 dc d for 0.20c tab, Ma= A.46 dc d for 0.20c tab, Ma= A.47 dc d for 0.20c tab, Ma= A.48 dc d for 0.20c tab, Ma= B.1 C l for the 0.15c tab, = B.2 C l for the 0.15c tab, = B.3 C l for the 0.15c tab, = B.4 C l for the 0.15c tab, = B.5 C l for the 0.15c tab, = B.6 C l for the 0.15c tab, = B.7 C l for the 0.15c tab, = B.8 C m for the 0.15c tab, = xxi

22 B.9 C m for the 0.15c tab, = B.10 C m for the 0.15c tab, = B.11 C m for the 0.15c tab, = B.12 C m for the 0.15c tab, = B.13 C m for the 0.15c tab, = B.14 C m for the 0.15c tab, = B.15 C d for the 0.15c tab, = B.16 C d for the 0.15c tab, = B.17 C d for the 0.15c tab, = B.18 C d for the 0.15c tab, = B.19 C d for the 0.15c tab, = B.20 C d for the 0.15c tab, = B.21 C d for the 0.15c tab, = B.22 dc l for 0.15c tab B.23 dc m for 0.15c tab B.24 dc d for 0.15c tab D.1 Material roperties for MFC actuators [150], where 1 is rod direction and 2 is electrode direction D.2 Properties for MFC actuators [150], where 1 is rod direction and 2 is electrode direction D.3 Dimensions and capacitance for MFC actuators [150] xxii

23 List of Symbols ǫ η act κ Λ ν Ω ψ ψ bc ρ τ C d C l C m E E b Angle tab tip makes with undeformed tab Tab length in chord direction, in terms of chord Ratio of tab width with active layers Curvature Free strain per voltage Poisson s ratio Rotor angular frequency Blade azimuth angle measured from helicopter rear, positive counter-clockwise E b t b E ct c Mass density A nondimensional number representing bimoprh performance based on beam composition, see equation 3.3 Airfoil section drag coefficient Airfoil section lift coefficient Airfoil section moment coefficient Young s modulus Young s modulus of shim xxiii

24 E c G Young s modulus of piezoelectric layers Shear modulus R space Spanwise width of the actuator unit cell t b t c Thickness of the shim, between the MFCs Thickness of piezoelectric layers /rev Per revolution of the main rotor AFC Active Fiber Composite AOA Angle of Attack AOA Angle-of-Attack BVI Blade Vortex Interaction c CF Rotor blade chord length Centrifugal Force CFD Computational Fluid Dynamics FEA Finite Element Analysis HHC Higher Harmonic Control IAL Inner Active Length IBC Individual Blade Control Ma Mach Number Ma Mach number MAL Middle Active Length MFC Macro Fiber Composite N Number of blades OAL Outer Active Length PZT Lead zirconate titanate, a common piezoelectric material xxiv

25 R Rotor radius SMA Shape Memory Alloy T t b t c TEF Trailing Edge Flap TEF Trailing Edge Flap TEP Trailing Edge Plate TET Trailing Edge Tab TURNS Transonic Unsteady Navier-Stokes WENO Weighted Essentially Non-Oscillatory xxv

26 Acknowledgments I would first like to thank my advisor, Professor Farhan Gandhi. My association with him was serendipitous. As an undergraduate, I went to visit him in order to get paper work signed for my minor. When I left, I had been given an opportunity to spend the summer conducting research. This was the beginning of the path that has lead me here, for that I am eternally grateful. I would also like to thank him for guiding me in academic life. Showing me the ropes of conferences, journal papers, and fellowship applications among many others will prove invaluable to my future. I would also like to acknowledge the Science, Mathematics, and Research for Transformation Scholar for the financial support they provided. Also, I would like to thank all the kind people I met at Patuxent River I met during my two summer internship and I look forward to working full time with them. I would like to acknowledge Rick Auhl and Mark Catalano for that help they provided during my experimental testing. I rarely visited them with out laughing at least once. Also, a special thanks to all the ladies of the Aerospace Office. We all know where the real decisions of the department are made. I would like to thank Jeff Long of the Materials Research Institute for providing the high voltage amplifiers used for the experiment. I would like to thank my friend and roommate Mihir Mistry. Your support and suggestions have been most useful. I would also like to thank Eric Hayden, who not only sat next to me at the Vertical Lift Center of Excellence during most of this research. I reminder to Dave, we have yet to watch any of the Star Wars movies. Also, thanks to Sam, who upon Eric leaving, had to suffer my random comments. A special note to the two I leave behind to be the last of the group, Julia and Sean. Best wishes for a quick graduation! Thanks to Mike Wozniak for answering my laser vibrometer questions. Thanks to all my friends and colleagues I met along the way. Lastly, I would like to say thanks to my family. Pop-pop and Ga who have attended more of my banquets, graduations, concerts, and sporting events than xxvi

27 many parents. I will never forget how freshmen year you came up to visit, on your wedding anniversary. To my Granddad and Connie, who follow my achievements closely and are always proud of me. All of you have expressed your support in my academicpursuitsandforthatiamgrateful. IwouldliketothankmybrotherKyle for being everything a great brother should be. I look forward to many adventures together. Lastly, I would like to thank my loving parents. Your guidance and opinions are important to me. I am eternally grateful for the financial support you provided for my undergraduate education. But the greatest gift you gave me was the values, beliefs, and opportunities that you provided as you raised both Kyle and me. All of my achievements are rooted in your parenting. You played no small part in the creation of this dissertation. xxvii

28 Dedication A straight line may be the shortest distance between two points, but it is by no means the most interesting. The Doctor I would like the dedicate this dissertation to my parents. It is only fitting that the final achievement of my education be dedicated to the two who were present when it all started so many years ago. xxviii

29 Chapter 1 Introduction 1.1 Background and Motivation Compared to the wing of an airplane 1, the rotor blade of a helicopter 2 experiences a more diverse environment. Even in hover, the blade tips are traveling at 207 m/s (402 knots) [2], while the root sees almost no in-plane airflow.this tip speed vastly exceeds many small airplane s never exceed speed (V NE ). As result of the blade s rotation, there is a linear variation in the velocity the blades see, shown in figure 1.1. In forward flight, the aircraft s velocity adds to the blade velocity on the advancing side and subtracts from the blade velocity on the retreating side. This means the tip on the advancing side of a helicopter flying at 150 knots sees a flow around 550 knots, while the retreating side sees 250 knots. Near the root of the retreating side is an area that sees reverse flow, shown in figure 1.2. The tip on the advancing side experiences high Mach numbers. Compressible effects are important and Mach-divergence drag can be encountered. While the retreating tip can experience stall, again another source of drag. Both of these phenomena create vibrations. As with any finite wing, the rotor blades produce tip vortices. With each blade generating these tip vorticies and rotating, the rotor flowfield becomes very 1 Airplane means an engine-driven fixed-wing aircraft heavier than air, that is supported in flight by the dynamic reaction of the air against its wings. [1] 2 Helicopter means a rotorcraft that, for its horizontal motion, depends principally on its engine-driven rotors. [1]

30 2 (a) (b) Figure 1.1: The rotor velocities at (a) hover and (b) forward flight complex. Unlike an airplane, the rotor blades operate amongst these vortices; only the blades at the front of the rotor have a chance of seeing clean air. These tip vortices can shed around ψ = 120 and interact with blades at around ψ = 60 [3], where ψ is measured from the rear of the helicopter increasing counterclockwise(figure 1.1). These blade vortex interactions (BVI) create both vibrations and noise, particularly in descending flight. All of these phenomena generate vibrations, causing varying loading on the rotor blades. These vibrations are transmitted through the blades to the hub. These vibrations result in periodic loading on the pitch links and blade-root connection. However, the N/rev load experienced in the fixed frame, that is the helicopter body itself, has contributions from the rotating frame of (N-1)/rev, N/rev, (N+1)/rev, where N is the number of blades. In order to reduce these vibrations, rotor noise, and improve rotor performance

31 3 Figure 1.2: Some of the difficulties a rotor encounters in forward flight [2, 3] researchers have looked towards active methods of changing the rotor. Rotorcraft 3 control systems provide a 1/rev change in blade pitch when flying in trimmed flight. The goal of active systems are to provide additional ways to change blade properties. The methods can be broken down into two major categories. Those that change the blade pitch (typically measured at the root), leaving the blade the same and those that try to morph the blade in some manner. The various active systems considered for rotorcraft are presented in figure 1.3. Higher Harmonic Control (HHC), uses inputs to the swashplate to achieve blade pitch inputs above 1/rev in steady flight. While the idea of using HHC, that is introducing aerodynamic loading at higher frequencies can be accomplished using various methods, it will refer to swashplate inputs. However, there is a limitation when using swashplate based HHC, for each rotor blade to experience the same phase, a N/rev input is required [4]. For example, using a 2/rev input on a four-bladed rotor results in 3 Rotorcraftmeansaheavier-than-air aircraftthatdependsprincipally foritssupportinflight on the lift generated by one or more rotors. [1]

32 4 Figure 1.3: The active systems for reducing vibrations, rotor noise, or improving performance blades 1 and 3 being 180 out-of-phase from blades 2 and 4, shown in figure 1.4. To overcome this deficiency, one can use Individual Blade Control (IBC). IBC shall refer to using active pitch links to change the pitch of the blade, but some generalize it to mean any on-blade control system. This system typically uses the standard swashplate for control (1/rev inputs). The pitch links are actuators that have limited authority in comparison to the swashplate, but can achieve higher frequencies. As IBC is in the rotating system, it can give 2/rev inputs so that all blades follow the same schedule, such that the desired pitch occurs at the same azimuth angle. As both of these systems pitch the entire blade, they require large actuation forces and therefore energy. On-blade morphing or effectors (ie flaps) are investigated primarily with the promise of lower actuation requirements than either HHC or IBC. Several concepts exist for on-blade control such as: flaps, variable camber, variable chord, variable twist, variable span, and variable droop. These systems can be broken down into two major groups: quasi-static and dynamic actuation. Variable span and chord

33 5 Figure 1.4: A four bladed rotor with 2/rev swashplate higher harmonic control [4] are typically used for quasi-static performance benefits. These systems would operate for a particular condition, such as high speed or large gross weight. Flaps, variable camber, variable twist, and variable droop would typically operate at 1/rev and higher frequencies, depending on application. These systems reduce vibration, noise, or improve performance. 1.2 Actuators and Smart Materials All of these active systems require an actuator. Various actuator technologies are used and selection depends on requirements such as force, stroke, and frequency. The use of smart materials has become widespread and refer to using a material property to provide actuation. For large helicopters, hydraulics are used to control the swashplate. Hydraulic actuators have been used for systems beyond swashplate control. Hydraulic actuators benefit from having large stroke capability, large forces, or even frequencies of 5/rev or higher. A drawback of hydraulics in the rotating system is the need to transfer hydraulic fluid through a slip ring. Another non-smart actuator seeing use is the electric motor. They benefit from

34 6 being powered via low voltage electricity, which uses simpler slip rings than hydraulic fluid. While motors typically run steady-state, rotating one direction, they can be driven cyclically. In most some the rotary motion needs to be transformed to linear motion. The most common smart materials are piezoelectric materials. These are materials that strain when placed under an electric field this is known as the reversepiezoelectric effect. The piezoelectric effect is a strained material producing a voltage across the material. A high electric field is applied along one direction, causing the material to become poled in that direction [5], aligning internal domains. Figure 1.5 shows a piezoelectric element that has been poled in the 3- direction. Applying a smaller electric field in the same direction (3-direction), will result in in-plane deformations in the 1- and 2-directions, as well as out-of-plane deformations in the 3-direction. The coefficients relating the applied electric field to free strain are d 31 and d 33, for in-plane and out-of-plane respectively. A material s d 33 coefficient is typically larger than the d 31 coefficient [5]. A common piezoelectric material is lead zirconate titanate (PZT). A common PZT free strain is 1,000 µ-strain. Piezoelectric materials exhibit small displacements, but have a large block force (force applied while constrained from displacing) and can operate at high frequencies. Piezoelectric materials used as actuators have various configurations. All of the following three actuators take advance of the d 33 coefficient s higher values. Stack actuators are simply thin piezoelectric elements stacked in the 3-direction as shown in figure 1.6a. The elements have electrode layers in between the active layers. Stack actuators are able to produce large axial forces. The next type of actuator is the Active Fiber Composite (AFC). This is a thin, patch like actuator, that can be bonded to the surface of skins or beams. Round PZT fibers are bound on the top and bottom by alternating electrodes as shown in figure 1.6b. Electrodes vertically aligned are of the same voltage, with the nearby electrodes being a different voltage(one is typically ground and the other is the applied voltage). This creates an electric field through the fibers (which is the poled direction), resulting in the desired in-plane (with respect to the AFC patch) axial deformation. The fibers are embedded in a matrix. An improvement called a Macro Fiber Composite (MFC), uses rectangular fibers, which are more effective (figure 1.6). MFCs benefit

35 7 (a) (b) (c) Figure 1.6: Various piezoelectric actuator configurations: (a) stack actuation, an (b) active fiber composite Actuator, and a (c) macro fiber composite actuator [6] from improved manufacturing and represent an improvement over the AFC [6]. The above methods produce axial deformation, but piezoelectric elements can also produce bending. By sandwiching a shim with piezoelectric elements, a bimorph or bender beam is created. Driving the beams at opposite voltages results in bending of the beam, deflecting the tip. An example is shown in figure 1.7. In the figure, the upper pieoelectric element is expanding, while the lower one is contracting, resulting in a tip down bending. Shim thickness strongly influences tip deflection, with thin shims resulting in more deflection and thicker ones providing more tip force. Improvements using multiple layers and taper have all been considered by researchers and is detailed throughout. Figure 1.5: A piezoelectric element with an electric field in the 3 axis direction [5] Shape Memory Alloy (SMA) materials exhibit the shape memory effect. This means the material can be given a shape, deformed, and then heated resulting in it changing back to the original shape [5]. This ability is related to temperature induced phase changes. SMA materials can recover up to 8% strain [5]. These materials have larger stroke potential compared to piezoelectric materials, but

36 8 operate at low frequencies (quasi-steady to 1 Hz) limited by cooling. Other less commonly used smart materials are magnetostrictive and electrostrictive materials. These materials strain when a magnetic or electric field is applied, respectively. Unlike piezoelectric materials, electrostrictive materials don t need poling [5]. In addition, electrostrictive materials do not have the reverse effect, deforming them creates no voltage. These materials have similar limitations in stroke as piezoelectric materials, but can operate at higher frequencies than SMAs. Figure 1.7: A piezoelectric bimorph, resulting in beam bending (exaggerated). Hydraulic actuation is used mostly for pitch link IBC, where large forces and moderate stroke are required. Piezoelectric materials are frequently used for applications requiring 1/rev or higher frequencies. They are used for axial, bending, and torsion deformations. In many cases, stroke amplification is required. SMAs are best suited for quasi-static actuation, but their larger stroke capability is attractive. 1.3 Individual Blade Control Due to the limitations of swashplate HHC, researchers looked at IBC, using hydraulic actuators to change the blade pitch at frequencies of 2/rev and higher. The following results are used to highlight the potential improvements achievable using active controls. All subsequent sections are organized by the school or organizations involved and then either chronologically or by design concept amongst each group US/German MOU on helicopter aeromechanics Jacklin et al.(1993) [4] and Jacklin et al.(1995) [7] described the preparations for a BO 105 rotor test in NASA s 40 ft by 80 ft wind tunnel. The program was a joint

37 9 US/German test of IBC. Goals of the program included hub vibration reductions, fuselage vibration reduction, changing blade airloads, BVI noise reduction, and improvements in rotor performance. The tests were conducted on a full scale BO- 105 rotor. Harmonic inputs from 2/rev through 6/rev were inputted using the IBC actuators. 2/rev IBC was able to reduce both advancing and retreating side BVI noise. Maximum noise reduction was 10 db. Combined noise and vibration reductions were accomplished using 2/rev inputs, with reductions in vibrations up to 85% observed. At an advanced ratio of 0.1, 2/rev, 3/rev, or 4/rev inputs were able to reduce vibration by a greater amount than 2/rev inputs (near 99% reduction). At an advanced ratio of 0.3, 3/rev or 4/rev was better suited for vibration reduction. Power reductions up to 7% were observed with 2/rev inputs at advance ratios above 0.3. Jacklin et al.(2002) [8] presented experimental results of IBC on a UH-60. This program was again a joint US/Germany operation among NASA, Sikorsky, the US Army, and ZF Luftfahrttechnik GmbH. Results at 46 knots showed a reduction in 4/rev vibration being reduced by 70% with 1 of input. Most of the reduction was in the shear forces and moments. BVI noise at 75 knots with a 7 rearward shaft tilt was reduced by up to 12 db. This was with 3 of actuator input at 2/rev. These results are comparable to those for the BO Deutsches Zentrum für Luft- und Raumfahrt (DLR) Kube et al.(1999) [3] provided an overview of experimental and numerical results regarding IBC of a BO 105. The experimental results predate the joint US/Germany tests, but were restricted to lower IBC deflection. 2/rev IBC actuation reduced both BVI noise by 4 db and vibrations by 50%. The 2/rev input was able to reduce BVI noise by 6 db, but the vibration level increased. BVI noise reduction was accomplished by displaceing the vortices via the downwash ZF Luftfarhrttechnik Kessler et al.(2003) [9], on the behalf of the Germany Federal Armed Forces, considered IBC on a CH-53G. The tests show the importance of (N-2)/rev in reducing vibration (the CH-53G has a six-bladed rotor). The required authority was found

38 10 to be 1, with reductions in vibrations of 63% in the cargo compartment using nonoptimized 5/rev inputs. Using 2/rev inputs, noise reductions of 3 db were recorded. In high speed flight, a reduction in rotor power of 6% was measured using 2/rev inputs University of Maryland Chengetal.(2003)[10]lookedattheroleofa2/revinputtobladepitchonreducing rotor power. The blades were modeled using rigid flap and lag modes, coupled, with a three state dynamic inflow model was used. The authors found that 2/rev affects the profile drag distribution therefore the rotor power via torque. The nonlinear nature of drag with AOA values and Mach number resulted in large changes with small 2/rev inputs. Small power reductions were predicted, up to 3.8% for a 22,000 lbs gross weight vehicle at an adavanced ratio of 0.3. The advancing tip played a prominate role in whether HHC reduces rotor power. Cheng et al.(2005) [11] considered the effect of a free-wake model and elastic blade deformations on their previous work. The authors also optimize the 2/rev blade pitch inputs to minimize rotor power. At a gross weight of 22,000 lbs, the power reduction was estimated around 11% with a ±1, 2/rev input. The authors compared the linear inflow reslts with a nonlinear inflow, free wake model. Comparing the two inflow models, they trim to different rotor powers, however the optimum 2/rev phase remains similar. The inclusion of elastic blades lead to the same conclusion, that is the phase for minimum power remains the same. 1.4 Trailing Edge Flap The use of a flap on the rotor blade was pioneered by Charles Kaman. These flaps are still used on Kaman Helicopters. This type of flap, which the company calls a servo-flap is external to the blade as shown in figure 1.8a. Most active flaps use a plain flap the flap forms a portion of the airfoil and is flush with the surrounding trailing edge when in the neutral position (figure 1.8b). Both of these flaps are being considered trailing edge flaps (TEF).

39 11 (a) (b) Figure 1.8: An (a) external flap and a (b) plain flap Figure 1.9: A piezoelectric bimorph actuated trailing edge flap by the University of Maryland [12] University of Maryland Samak and Chopra(1993) [12] developed and tested a piezoelectric bimorph actuated TEF. The flap is powered by 3 bimorphs, 1.5 in (38 mm) long, 1.0 in (25.4 mm) wide and in (0.53 mm) thick. The flap the bimorph drives is 4.38 in (111 mm) in span and 0.6 in (15.2 mm) in chord (20%). The bimorphs drive a hinge as shown in figure 1.9, for strain amplification. The TEF was tested in an open-jet at speeds up to 65 knots and frequencies of 5 Hz, 10 Hz, and 15 Hz. The response did not greatly change with wing angle-of-attack or frequency. Rather, the displacement was most sensitive to airspeed. With flap deflection of about ±7 at 65 knots. The system was also tested on a hover test stand, reaching speeds of 152 knots at the flap s midspan. At the highest RPM (corresponds to 152 knots), the amplitude of flap deflection decreased to about ±2. Lastly, the authors tried using a dual bimorph configuration, but only achieved a 15% increase in perfomrance. Ben-Zeev and Chopra(1996) [13] expanded upon the previous bimorph. In order to better understand the limitations of the previous design, the actuator s

40 12 (a) (b) Figure 1.10: A (a) two-layer and (b) four-layer bimorph [13] performance was analyzed using analytical theories (constant strain and Euler- Bernoulli). In addition, dynamic effects were accounted for in the analysis. The authors considered both a two-layer and four-layer bimorph (figure 1.10). Both systems were tested in the rotating environment, via a vacuum whirl stand. At high rotor RPM, the flap deflection greatly decreased. The addition of a thrust bearing at the hinge point greatly reduced friction and improved performance at the higher RPM. At 600 RPM, the four-layer bimorph peak-to-peak deflection increased from about 3.5 to 11. The test was rerun on the hover stand and the deflection decreased to 5 at 600 RPM. Walz and Chopra(1994) [14] discuss the design of the four-layer bimorph used by Ben-Zeev and Chopra. The four-layer bimorph provided greater tip force, for a given length, but less tip displacement. To analyze the various bimorph configurations, the aerodynamic hinge moments were predicted using a quasi-steady, incompressible aerodynamic model. The result of the aerodynamic analysis was that a four-layer bimorph should provide sufficient authority (10% change in lift), whereas the two-layer bimorph was unable to do so. The authors also improved upon the original mechanical design (figure 1.9). The bimoprh is offset from the center to acocunt for the vertical linkage. This linkage accomadates the bimorph s vertical as well as horizontal motion. Unfortunitaly, this design lead to the bimorph requiring a small cutout in the airfoil skin. An improved, centered bimorph using

41 13 Figure 1.11: A piezoelectric bimoprh actuated trailing edge flap by the University of Maryland [14] a cusp was developed and is shown in figure A rounded tip was added to the end of the bimorph and designed to fit inside the cusp. Low fequency delfections of ±7, as well as ±17 at high frequencies were achieved in a static test. The design of the bimorph actuator with the cusp was further refined by Koratkar and Chopra(1999) [15, 16]. The piezoelectric bimorph was tampered amongst the various layers, as in figure The performance of the flap was estimated from an analysis broken up into four parts. First, a time-domain, unsteady aerodynamic model was developed, including compressible flow. A finite element model was used for the bimorph, including effects due to the rotating environment. The rotor blades were modeled as elastic beams with flapping and elastic torsion deformations. The flap and rotor systems were coupled aerodynamically and inertially. The analysis compared favorably to hover stand test results. This analysis showed, that although the flap is integrated into the rotor, it produces a significant pitching moment, twisting the beam elastically. So although such a flap arrangement is commonly considered a lift flap (ie the flap directly changes the lift), it also has the potential to operate as a moment flap. A moment flap is used in conjunction with a torsionally soft blade, twisting the blade, causing a change in lift. A Mach scale test showed flap deflections of ±7.7 at 2000 RPM in a vacuum chamber. The authors, Koratkar and Chopra(2001) [17], also conducted a wind tunnel test of the above actuator. The tested rotor used a NACA 0012 airfoil with a 3 in (76.2 mm) chord and a flap chord 20% of that value. The flap was 2.4 in (61 mm, 8%R) wide and located at a spanwise location of 75%R. The operating RPM was 1800 leading to a tip speed of 280 knots (472 ft/s), giving a Mach number of The wind tunnel itself had a top speed of 191 knots (322 ft/s). The blades were

42 14 Figure 1.12: A tapered piezoelectric bimorph actuated trailing edge flap by the University of Maryland [16] mounted to a 1/7th scale Bell 412 hingless rotor hub. First open-loop testing was conducted, testing flap deflection at 3/rev, 4/rev, and 5/rev. At an advance ratio of 0.3, deflections ranging from ±4.1 to ±4.4 were achieved. The authors also encountered an uncommanded 1/rev flap response of ±1.5 due to blade flapping. Peak actuator power use was measured at 59 W, or 1.12% of steady rotor power. The authority of the actuator on the bending moment due to flapping was best for a 3/rev flap frequency. This was because the first elastic twist frequency of the blade is 3.13/rev, providing amplification. Using a neural network based controller, initial closed-loop testing indicated reduction in vibrations on the order of 40%. The system was designed for a deflection of 5.5. Spencer and Chopra(1996) [18] considered actuating a TEF using a piezoelectric stack. The stack configurations have larger block forces at the expense of smaller displacements compared to the bimorphs previously considered. To drive the flap, two stacks were arranged in series. The stacks drove a L-shaped hinge, converting spanwise motion to chordwise motion (figure 1.13). This chordwise motion was transferred via a pushrod to the flap, where the pushrod was offset vertically from the flap s pitch axis. This allowed the pushrod to rotate the flap. A spring was used to precompressed the stack and ensure the L-hinge remained attached to the stack when it retracts. Using a basic aerodynamic model, based on thin-airfoil theory, flap deflection versus air velocity was estimated. The model has an 8 in (203 mm) chord with a 4 in (102 mm) wide flap, with a chord of 1.6 in (41

43 15 Figure 1.13: Schematic of piezoelectric stack driving a flap by the University of Maryland [18] mm, 20%c). A static test showed experimental results were about 20% lower than analytical results. Again, when comparing static flap deflection with a non-zero velocity, the latter showed reduced deflection. Chandra and Chopra(1997)[19] worked on improving the mechanical amplification of the stack actuator. An integrated mechanical amplifier was developed and is shown in figure The amplifier is a compliant mechanism with the L-arm attached via an elastic hinge. The L-arm was then attached to a pushrod, similar to Spencer and Chopra [18]. The actuator was tested both with and without aerodynamic forces, with the experimental values 12% and 30% lower than predicted, respectively. Without aerodynamic forces, deflections were about 8 peak-to-peak. Lee and Chopra(1999) [20, 21, 22, 23] in a series of papers considered using piezoelectric stacks to drive a double lever amplification system. Stacks in series and parallel configuration were considered. The concept for the stack in series is presented in figure The actual actuator is in figure The double lever was chosen to provide larger mechanical advantage, while minimizing elastic deformation of the levers themselves. The goal was to obtain a flap deflection of ±5 for a TEF on an MD Explorer helicopter. While the actuator was not connected to any flap, it was tested both statically and in a rotating frame. The

44 16 Figure 1.14: An integrated mechanical amplifier for a stack actuator by the University of Maryland [19] Figure 1.15: A double lever mechanical amplifier for a stack actuator by the University of Maryland [22] rotating frame results indicated the actuator would perform properly at full-scale CF loading. Lee and Chopra(2000) also considered using the piezoelectric stacks in parallel [21]. The piezoelectric stacks were placed either side of a lever s fulcrum, as shown in figure This was done as the single stack design experienced a loss of symmetry in deflection at high frequencies. A spring had been used to provide a returning force, but at high frequencies was unable to fulfill this task. This was the source of the asymmetry. The dual acting nature of the parallel stacks eliminated this issue. Testing in the rotating environment indicated that the actuator will work under centripetal acceleration. However, the actuator was not used to drive an actual flap. Bernhard and Chopra(1996) [24, 25] developed an actuator that used the

45 17 Figure 1.16: Actual double lever stack actuator by the University of Maryland [22] Figure 1.17: Parallel stacks, double lever actuator by the University of Maryland [21] bending-twist coupling of composites together with piezoelectric benders. A beam with an inner core of composite material was sandwiched between piezoelectric elements. Figure 1.20 details how the beam is split into segments with alternating layups, with bending-twist coupling of opposite sign. Every other layup was required to be bent in the opposite direction to produce rotation in the same direction. By using the opposite coupling and alternating the bending of the piezoelectric elements, the authors created an undulating beam, that overall undergoes limited out-of-plane deformation. This undulating shape is shown in figure The authors had two concepts for transmitting the rotation of the beam to the flap. These concepts are shown in figure The first concept (figure 1.20a) took the rotation of the beam tip via a link to a control horn connect to the flap. The

46 18 Figure 1.18: Composite layup configuration for bending-twist coupling [24] Figure 1.19: Undulating beam deflection using bending-twist coupling [24] second method (figure 1.20b) connected the flap directly to the tip of the beam, meaning the flap undergoes both rotation and vertical deflection. Analysis showed that the plain flap can achieve ±16 deflection with a simulated aerodynamic load of a 20% chord and 10% span flap with a 546 mm long actuator beam. The integral flap was estimated to achieve ±2.1, for a similar flap with a 20% span. A demonstrator was built and produced a deflection with 12.5% of predicted values. A hover test produced deflections on the order of ±4. Bernhard and Chopra(2001) [26, 27] took the bending-twist coupled beam and applied the twist at the end to an active blade tip. As seen in figure 1.21, the active blade tip is simply the tip being turned into a large all-moving flap. Results of testing showed tip deflections of ±2 at 2/rev, 3/rev, 4/rev, and 5/rev. This corresponded to vertical blade root shear forcing 10% to 20% of the nominal blade thrust (8 collective) Massachusetts Institute of Technology Hall and Prechtl(1996) [28] developed a TEF driven by a tapered piezoelectric bender. This design has the bender beam fixed to the spar and running aft to the flap. Figure 1.22 has illustrated the concept. The junction of the flap and bender was a connection of flexures. An analytical model was developed and benchtop tests

47 19 (a) (b) Figure 1.20: A (a) hinged plain-flap mechanism and (b) an integral beam-flap mechanism for the bending-twist coupled actuator [24] Figure 1.21: An active blade tip using a bending-twist coupled piezoelectric actuated beam by the University of Maryland [26]

48 20 Figure 1.22: A tapered piezoeletric bender driving a TEF by MIT [28] Figure 1.23: The X-frame powered by a dual piezoelectric stack by MIT [30] conducted. The benchtop testing achieved a half-peak deflection of 11.5 at 10 Hz. The authors expect deflection (half-peak) for a full scale helicopter to be greater than 5. The researchers Prechtl and Hall(1999) wrote several papers regarding an X-frame actuator [29, 30]. The X-frame actuator is depicted in figure The actuator consisted of dual piezoelectric stacks on top of each other. The pivot end served as the hinge for the two frames. Actuating the stacks caused the two frames on the output end to move with respect to each other. For implementation in a rotor blade, the output end connected to a control rod to drive the flap, as in figure The actuator was tested for sensitivity to blade accelerations and only under the highest acceleration cases were there any effects noticed. Whirl stand tests showed that spinning the actuator caused no major degradation of the actuator performance [31]. Results of a hover test [29] showed peak-to-peak flap deflections of 5 to 7.

49 21 Figure 1.24: The X-frame actuator installed in a rotor blade driving a flap by MIT [30] McDonnell-Douglas and Boeing companies Dawnson and Straub(1994) [32] looked at how a flap can be used to reduce rotor loads and noise. This study considered both predicted results and compares them with tests. The test flap used a cam follower actuation system. The authors found good correlation between there predictions and the test results. Friedrich Straub has written several papers regarding the use of trailing edge flaps using smart materials, first for McDonnell-Douglas and later for Boeing. Straub(1993) [33] first considered the various smart materials available as well as different actuation methods. The goal was to drive a flap that can replace the swashplate control system of the standard helicopter. The various methods considered included: pitch control, twist control, camber control, and control surfaces. The servo-flap was considered the most feasible. Straub also considered the different smart materials available: piezoelectric materials, electrostrictive materials, magnetostrictive materials, shape memory alloys, and electrorheological fluids. Lastly, various actuator designs were considered including: bender elements, stack actuators, actuation tubes, and ultrasonic motors. Straub and Merkley(1995) [34] considered a servo-flap (one where the flap extends beyond the airfoil) for a AH-64 sized helicopter. This builds on the previous paper. A hybrid actuator was developed and is shown in figure The actuation was two-part. First a piezoelectric or magnetostrictive actuator is used for cyclic and active control. A composite tube connected this actuator to a hydraulic

50 22 Figure 1.25: A hybrid actuator developed by McDonnell-Douglas [34] amplification system. The composite tub had shape memory alloys for collective control. Each blade has 4 servo-flaps, located between 62% and 82% radius. Estimatedflapdeflectionrequiredtocontrolthehelicopterwere±7.3 collective, ±3.8 cyclic, and ±0.4 for active vibration reduction, based on flap and rotor design. Straub and Merkley(1997) presented a paper discussing a magnetostrictive based hybrid actuator [35]. In trying to design a magnetostrictive actuator to provide cyclic and active control authority, it was found that the best the materials could manage was limited maneuvering. An initial study looked at SMAs for collective controls showed capability. Straub et al.(1999) [36, 37, 38, 39] participated in the DARPA SMART (Smart Material-actuated Rotor Technology) program. The goal was to use smart materials to augment the traditional swashplate control system. In particular the hope was to reduce vibration and noise. A piezoelectric actuator was chosen to drive a flap to reduce noise and vibration. A SMA actuator was chosen for blade tracking. The MD900 helicopter was chosen and testing in the NASA Ames 40 ft x 80 ft wind tunnel. Goals for the program included an 80% reduction in vibrations and a 10 db reduction in blade vortex interaction (BVI) noise. The SMA actuator would provide in-flight blade tracking, reducing vibrations. The first actuator considered was a biaxial piezoelectric driven actuator [36, 38] shown in figure The design consisted of four stack actuators rotating an

51 23 Figure 1.26: Biaxial piezoelectric flap actuator developed by Boeing [38] outer housing. The initial design had a second amplification stage, whereas the final design did not. The final design was expected to meet design requirements. In phase II of the program, the actuator was switch to MITs X-frame actuator, where two were used [37] and depicted in figure The actuator was successfully tested for 66 million cycles (560 hours at 5/rev). The actuator drove a flap 36 in (914 mm) long and with a chord of 3.5 in (89 mm). The flap integrated into the rotor blade as shown in figure The SMART rotor weighs 113% of the MD900 rotor blade. A whirl tower test was conducted with both static and dynamic deflections (up to 6/rev). Static flap deflection of 3 peak-to-peak was observed. Similar deflections were achieved with dynamic deflection of the flap. This level of deflection resulted in a 10% variation in thrust compared to steady state. Results from a wind tunnel test of the rotor showed BVI noise reductions on the order of 3-6 db, with increased hub vibratory loads. Using the flaps for vibration reduction, the 1/rev-5/rev normal hub vibrations were reduced by 95% for level and decending flight. The rotor system used for these tests is depicted in figure US Army Aviation RD&E Center Fulton and Ormiston(1997)[40, 41] considered trailing edge flaps powered by piezoelectric bimorphs. The authors call the flap an elevon and used a piezoelectric bimorph driving a flap via a cusp similar to the University of Maryland, figure The test rotor s radius was 45 in (1.1 m) and chord length was 3.4 in (86 mm). The flap dimensions in chord were 10%c with 12%R in span. Flap deflections of ±5 at 4/rev in hover were observed. Forward flight tests in a wind tunnel indicate the

52 24 Figure 1.27: MITs X-frame actuator as used in the SMART rotor by Boeing [37] Figure 1.28: The SMART rotor blade with flap by Boeing [39]

53 25 Figure 1.29: The SMART rotor system in the 40 ft by 80 ft NASA wind tunnel [39] Figure 1.30: The piezoelectric bimoprh powered flap used in US Army tests [41] bending moments generated by the flaps was not sufficient for vibration reduction University of Michigan Clement et al.(1998) [42, 43] considered the TEF using what they called a C-block, a piezoelectric based actuator shown in figure 1.31a. By coupling the C-blocks such that an undulating actuator results, the actuator provides axial motion. Static benchtop tests revealed maximum peak-to-peak deflections of 8. Dynamic tests up to 40 Hz showed similar performance. A slightly different flap configuration (in figure 1.31b) was used in a wind tunnel test. With the tunnel running at 100 ft/s (59 knots), static peak-to-peak deflections of 9 were achieved driving the 10%

54 26 (a) (b) Figure 1.31: The University of Michigan s (a) piezoelectric C-block actuator and (b) its implementation in a rotor blade for driving a TEF [43] chord flap that was mass and aerodynamically balanced. Again, dynamic tests showed similar results. The system was not tested in the rotating frame. Liu et al.(2008)[44] looked at rotor performance and vibration reduction achievable with TEFs. The helicopter rotor was modeled as a hingeless blade with flapping, lead-lag, and torsion degrees all accounted for and coupled. Seven modes are used, 3 for flapping and 2 each for lead-lag and torsion. Attached flow uses a rational function approximation, which is a 2D, unsteady time-domain theory with compressible flow. The blade aerodynamics are coupled to a free wake model. With separated flow, ONERA s dynamic stall model is used. Two controllers were used, the first is the HHC algorithm, which seeks to reduce both vibration and noise. Flap inputs are 2/rev to 5/rev. A nonlinear least-squares optimizer found

55 27 in Matlab was also used. The rotor was based on the BO 105. Two flap configurations were used, each with a chord of 0.25c. The single flap had a span of 0.12R and is centered at 0.75R. The two flap configurations were each of span 0.06R and were centered at 0.72R and 0.92R. At advance ratios of 0.35 and 0.40 the power reductions were 4% and 6.37% respectively. However, these power reductions result in an increase in vibrations. Targeting both power reduction and vibration reduction, rotor power was reduce by 1% to 4% and vibration was reduced 47% to 70%. The nonlinear matlab solver provided greater power reductions, indicating the nonlinear nature of the problem Advanced Technology Institute of Commuter-helicopter Hongu et al.(1999) [45] considered several actuators to drive a TEF. The first concept involved twisting an aluminum plate by inducing shear with piezoelectric elements as in figure 1.32a. An improvement used an X-section composite plate (figure 1.32b), giving twice the active material. The x configuration also reduced bending deflection of the plate. The authors do not mention the use of shear-twist coupling in the composite material. The last concept used magnetostrictive materials with either a mechanical or hydraulic amplification. The aluminum and composite plate achieved free deflections of ±7.6 and ±7.1, respectively. The hydraulic and mechanical stroke amplifications of the magnetostrictive material achieved ±3.4 and ±4.6, respective. A piezoelectric stack with mechanical amplification was testing in a wind tunnel. The actuator drove a 20% chord flap with a span of 500 mm. At Ma=0.3 the deflection was ±2.3 and at Ma=0.7 deflections were only ±1.1. Hasegawa et al.(2001) [46] of Kawasaki Heavy Industries and in partnership with Advanced Technology Institute of Commuter-helicopter conducted a whirl test considering amongst other things, a TEF. Dual piezoelectric stacks were used to drive a stoke amplification system. The actuators drove 3 different flaps, each 10% of the blade radius. Three different flap chords were considered: 10%c, 15%c, and 20%c. During a whirl tower test, the flap with 10%c chord had measured deflections of ±2.8 to ±3.9 for 1/rev and 5/rev actuation frequency respectively. The 20%c chord flap acheived deflections around ±1, changing little with fre-

56 28 (a) (b) Figure 1.32: (a) Piezoelectric shear-twist plate and (b) the X-sectioned composite piezoelectric shear-twist plate by the Advance Technology Institute of Commuterhelicopter [45] quency Eurocopter Enenkl et al.(2002) [47] described the piezoelectric actuators used in a series of Eurocopter whirl tower and flight tests. Being located inside a whirling rotor

57 29 Figure 1.33: A piezoelectric actuated trailing edge flap by Eurocopter [47] blade places stringent requirements on the actuation, including accepting high loading and fitting in a constrained space. Both piezoelectric and electromechanical actuators were considered, but piezoelectric was selected based on the centripetal acceleration experienced by the actuator and the zero-power stiffness. Important flap design characteristics included a frequency range of 0-40 Hz, no mechanical play, and an aerodynamically sealed flap. A monolithic co-fired multilayer stack actuator was used, with a 1000 µm stroke, amplification was required. Compliant hinges were used to provide a stroke amplification of around 10. The flap can be seen in figure In 2005, Dietrich et al. [48], successfully flew a BK117 (EC145) with piezoelectric actuated TEFs. The TEF had a chord of 50 mm and a span of 300 mm each blade consisted of up to 3 flap units. The span locations of the units was 71.8%R to 82.7%R. A whirl tower test was conducted in 2002 and The goal was to measure blade characteristics with both static and dynamic flap actuation. The latter test was used to ensure the rotor was ready for the flight test. The flight test showed reduction of vibration for level flight at 60 knots and 100 knots, with TEFs deflecting ±3. Roth et al.(2006) [49] described the same test. The flap unit deflection angle limits were ±10. The authors detail the control system used in actuating the TEFs as well as data acquisition. The control system targeted the 4/rev hub force

58 30 and moments. In particular the roll moment, pitch moment, and vertical force were targeted. Dynamic feedback compensators were implemented to achieve this. In level flight vibration reduction between 50% and 90% were observed, the system was also effective in climb and decent at 65 knots The Pennsylvania State University Centolanza et al.(2002) [50] used the shear present in piezoelectric materials to create twist. The concept is illustrated in figure 1.34a. By arranging the elements in a circle, this shearing results in a twisting of the actuator. The torsion of the actuator is connected to an arm that connects to the flap via a cusp, as in figure 1.34b. A benchtop test was conducted and flap deflections from ±2.75 with no hinge moment to 1.5 for a 400 RPM equivalent hinge moment (based on the MD900) were observed. The authors expected a future improved induced shear tube to provide similar performance to the double X actuator of MIT, with less than half the weight. In 2006, research by Penn State and local company Invercon considered a piezoelectric driven actuator utilizing a buckling beam [51]. Szefi et al. envisioned using a piezoelectric stack to buckle a pinned-pinned beam, with the beam s tip rotation driving the flap. The concept is depicted in figure 1.35a. In order to control the direction of buckling, dual stacks were used, vertically offset from the beam. Issues experienced including controlling the beam buckling direction and ease of which loading at the output could reverse the commanded buckled direction. The final design iteration in figure 1.35b was designed to address these issues. Benchtop testing using both free displacement and simulated aerodynamic loading resulted in deflections of 8.4 and 4, respectively Office National d Études et de Recherches Aérospatiales (ONERA) ONERA conducted a study involving an Active Blade Concept (ABC) in cooperation with Eurocopter and the Deutsches Zentrum für Luft- und Raumfahrt (DLR). Leconte and Des Rochettes(2002) [52] considered the design and initial testing of the actuation system. The goal actuation was a minimum of ±5 at 78 Hz, ideally

59 31 (a) (b) Figure 1.34: Penn State s induced-shear piezoelectric actuator, (a) the shearing piezoelectric elements resulting in torsion and (b) its implementation to drive a TEF [50] ±15 at 262 Hz. This was all in an acceleration of 2300 g. After looking at several designs, a piezoelectric stack circumscribed by an ellipse, seen in figure 1.36, was selected. This amplification is achieved via a compliant mechanism, providing a 2.6 amplification factor. The flap itself was connected via a compliant hinge. The actuator was tested at rest and under a 2000 g acceleration with flap peak-topeak deflections of 6 and 5, respectively. Low-speed wind tunnel tests showed good flap deflection values. At higher Mach numbers, it was found that the flap lacked sufficient stiffness. Using an updated actuator, wind tunnel tests were conducted [53]. The results showed the flap behaving as both a direct-lift flap and servo-flap, that is changing the local loft coefficient as well as twisting the blade.

60 32 (a) (b) Figure 1.35: (a) The concept for using a buckling beam to amplify piezoelectric input for driving a TEF and (b) the final design iteration [51] Figure 1.36: The piezoelectric stack driven flap actuator with elliptical amplifier by ONERA [52]

61 33 Figure 1.37: A tab controlled floating flap by Heinze and Karpel [54] Royal Institute of Technology (Sweden) and Technion Heinze and Karpel(2006) [54] considered the use of a piezoelectric actuator for aeroelastic application. The tab is connected to a floating flap, with tab deflections less than ±3. The tab and floating flap are shown in figure The authors achieved a flap deflection of 4.6 with a tab deflection of Japan Aerospace Exploration Agency (JAXA) Noboru et al.(2007) [55] used an active flap for reduction in BVI noise. The authors first worked on sizing the flap to achieve the objectives while not exceeding limitations of the actuator. The active flap dimensions are 10%c for chord, 10%R for span, and located between span locations of 70% to 80%. The requirements for the actuator were an operating frequency of 2/rev and an amplitude of ±6. Two stack actuators were used in a push-pull arrangement, thus rotating an arm. This arm drove a linkage connected to the flap s control horn. Static deflection tests indicated sufficient flap deflection. Dynamic tests revealed deflections of ±6. Estimateddeflectionathighspeedis±4.8. NoboruandSaito[56]performedwind tunnel tests (nonrotating) of the flap. At Mach numbers of 0.47, 0.55, and 0.7, flap displaced of ±6, ±6, and ±3.8 were recorded at a 2/rev actuation frequency. Saito et al. [57] reported on a joint project between JAXA and NASA. The active rotor of JAXA is to be tested in the 40 ft by 80 ft wind tunnel at NASA Ames.

62 34 Figure 1.38: The piezoelectric based active flap system used by JAXA [55] The goal is conduct the test in Seoul National University Lee et al.(2010) [58] considered a Piezoelectric stack actuation system similar to that used by ONERA (it being a commercial actuator) for driving a flap. The flap actuator system is capable of producing ±5.49 of deflection US Army Research, Development, and Engineering Command (ARMDEC) Fulton et al. [59] developed and hover tested an active elevon rotor. The active is simply the last 15% of the chord able to deflect ±5. The elevons are loactaed on a 27% scaled AH-64 Apache blade, with two flaps per blade, centered at 0.64R and 0.9R, each with having a span 5%R. Figure 1.39 shows the piezoelectric material forming the lower surface of the blade, the conformal actuators are PZT based actuators, utilizing the d 13 coupling. The actution system consists of an upper and lower actuators, operating in opposite directions, as illustrated in figure This results in a rotation of the elevon, which is not connected to the upper surface. Elevon deflections of ±2 was measured experimentally at an RPM of 1025 at 7

63 35 Figure 1.39: The piezoelectric based active elevon (flap) by the US Army [59] Figure 1.40: The push-pull actuator configuration used to rotate an elevon by the US Army [59] Hz (0.41/rev). The authors also tested two seperate controllers, one a classical approach the other used Model Predictive Control Non-piezoelectric driven flaps Others have considered driving flaps, though using actuators not using piezoelectric materials. Electromagnetic actuators are another common method. Researchers using motors include: Saxena and Chopra(2011) [60] of the University of Maryland, Lee and Pereira(2008) [61] of McGill University, Sikorsky [62, 63, 64], Duvernier et al.(2000) [65] of Aerospatiale, and Fink et al.(2000) [66] of Diversified Technologies in conjunction with the Aeroflightdynamics Directorate (AMRDEC). Other researchers have looked at using other smart materials, such as Bothwell and Chopra(1995) [67] of the University of Maryland using a magnetostrictive actuator, Fenn et al.(1996) [68] of MIT also looked at magnetostrictive materials, Sirohi and Chopra(2003)[69] of the University of Maryland investigate piezoelectric pump to drive flaps. The University of Maryland considered pneumatic artificial muscles [70, 71, 72, 73]. Daynes et al.(2009) [74] from the University of Bristol looked at using bistable composite materials driven by electric motor. Bernhard et al.(2001) [26] with Sikorsky Aircraft used hydraulic actuators.

64 Variable Camber Variable camber is similar to using a TEF. The major difference being a flap is a discrete system, whereas with variable camber, typically the aft portion of the airfoil is being deformed continuously. Without having the discrete change in the airfoil shape, variable camber is more a more aerodynamically clean design. A downside is that the rear portion of the airfoil needs to be elastically deformed, requiring more energy than deflecting a flap, which typically only needs to overcome aerodynamic forces. Büter et al.(2000) [75] of DLR considered variable camber for a rotor blade. The basic idea was that the blade has a three-cell cross section, with the outer cells having opposite extension-twist coupling. The concept called for a piezoelectric stack providing the actuation. Initial finite element analysis and CFD studies were conducted. Results indicated a maximum change in camber of 0.547%. The Pennsylvania State University looked at variable camber in terms of topology optimization [76], shape optimization [77], and focusing on the skin [78] At Virginia Polytechnic Institute and State University, the use of variable camber for a micro air vehicle has been, tested, and flight demonstrated [79, 80, 81]. The researchers used MFCs mounted to a thin plate. The researchers also looked at using a 2D airfoil [82, 83], instead of the simple thin plate. Quackenbush et al.(2010) [84] of Continuum Dynamics looked at SMA-based active camber change for use on tiltrotor and tiltwing vehicles. Both of these systems would benefit from being able to change the blade twist distribution in cruise verses hover. Deflection of ±6 were measured, with the deflection occurring in less than 10 seconds. McKillip and Quackenbush(2012) [85] considered the design and aerodynamic analysis of bistable SMA actuated tabs. These tabs displace out-of-plane and into the airstream and would be mounted near the trailing edge. These tabs can produce an effect similar to a flap and were focused on high frequency(3/rev-5/rev) actuation.

65 Blade Twist Blade twist refers to changing the twist distribution of the blade, rather than the blade root pitch. Most helicopters have at least a linear twist distribution, with the tip nose down [2]. Quasi-static variable twist looks to change the twist distribution between hover or high speed flight. In hover, a large blade twist is more efficient, but at high speeds it is undesirable. High frequency blade twist has small twist amplitude and operates more like a TEF or IBC, that is reducing noise and vibration. Any performance improvements comes from 2/rev actuations, rather than large blade twist modification. One of the biggest programs in active-twist was a joint NASA/ARMY/MIT Active Twist Rotor (ATR) [86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]. The blade uses Active Fiber Composites to induce a twist in the blades. In [92], results measuring the reduction in vibratory loads were presented. At a low advanced ratio µ = 0.14, the loads in the fixed-frame were reduce by 60% to 90% with 3/rev 1000 V input. At a high advance ratio of µ = and 3/rev 1000 V input an 80% reduction in 4/rev fixed-frame normal loads was observed. Active twist amplitudes of 1.1 to 1.4 were reached for 3/rev to 5/rev actuation at ± 1000 V. 3/rev actutation was better than 4/rev, as the latter caused large increases in pitch link loads. Additional studies were conducted on the ATR, testing closed loop controllers, matching simulations to experimental data, and optimizing the blade topology. Boeing considered an active-twist rotor using AFC [100, 101] as well as a large displacement SMA based torsion actuator [102, 103, 104]. The SMA was only able to achieve a few degrees of blade twist. The German Aerospace Center has also looked at the active-twist rotor concept using MFC [105, 106, 107, 108, 109, 6, 110]. Static twist values up to ±2.9 /m were obtained. Riemenschneider et al.(2009) [110] also described a unique concept, where the trailing edge is slit. An actuator is placed along the span, closing the section. Displacing the upper and lower edges in opposite spanwise directions induces wrapping, resulting in blade torsion. Chen and Chopra(1997) [111] of the university of Maryland also looked at active-twist. The most successful active-twist programs have looked at small

66 38 Figure 1.41: A static Gurney flap, as first introduced to the aeronautical world by Robert Liebeck [112] displacement, but high frequencies (2/rev to 5/rev). Attempts to obtain large amounts of torsion have been unsuccessful, given the typical torsional rigidity of rotor blades. 1.7 Active Gurney Flap TheGurneyflapwasfirstusedbyracecardriveDanGurneytogenerateadditional down force for the cars. Figure 1.41 shows an example of a static Gurney flap. The height of a Gurney flap is typically described in terms of chord length (eg 2%c). The Gurney flap increases the lift generate by the airfoil. An Active Gurney flap is able to deploy and retract, allowing the benefits of high lift when desired, but avoiding the increased drag when the extra lift is not needed. At the North Carolina State University, Price et al.(2002) [113] numerically considered an oscillating airfoil with a fixed Gurney flap. Researchers Tang and Dowell(2006) [114, 115] at Duke University also looked at oscillating airfoils with Gurney flaps. The authors tested airfoils in a wind tunnel, including tests with an oscillating Gurney flap [115]. Bieniawski and Kroo(2003) [116] at Stanford University considered using active Gurney flaps to suppress flutter in high aspect ratio wings, both experimentally and analytically. Researchers at The Pennsylvania State University have considered methods to actively deploy a Gurney flap [117, 118, 119] and determining optimal deployment schedules and their benefits [120, 121]. Padthe et al.(2011) [122] of the University of Michigan numerically considered BVI noise reduction.

67 Trailing Edge Tab and Variable Chord A trailing edge tab or variable chord are very similar systems. Both work to increase the chord of the airfoil. Static tabs are used on rotor blades, including the AH-64. Some researchers have considered using MFC patches to bend the tabs, while others consider the tab more of a plate to be deployed. Work has been conducted on both quasi-static deploying tabs/plates up to deployment frequencies of 2/rev. Variable chord in rotorcraft closely parallels the use in aircraft, meaning quasi-static deployment is used. The main goal with such systems is to increase the lift for a given portion of the flight, rather than with blade rotations National Aerospace Laboratory of Japan/JAXA Kobiki et al.(2003) [123] experimentally investigated an active deployable tab for noise reduction. The goal was a lift section coefficient change of more than 0.3 with an active tab of length 0.08c to 0.15c. A static wind tunnel test was conducted with tabs of various chords, spans, and deflections. Dynamic wind tunnel tests were conducted using various tab geometries. Figure 1.42a shows a simple flat tab. A tab with a deflective tip is shown in figures 1.42b and c. The difference between the two, is that in the latter when fully retracted, a portion of the undeflected tab is still exposed. Tip deflections of both 5 and 10 are tested. Static test results showed a 15% increase in lift with a 15% increase in chord. The increase in drag is minimal up to lift coefficients of 1. The dynamic wind tunnel test showed that a tab of length 0.11c with a 10 deflection will satisfy the authority requirements Kobiki et al.(2004) [124] conducted a rotating test with the active tab concept. The goal was to reduce BVI noise by deploying the tab at 2/rev. The concept pivots from the inboard corner as shown in figure Both on-blade pressure and microphone measurements were collected during the test. The wind tunnel speed was 18 m/s (35 knots), with a rotor speed of 600 RPM, with the shaft tilted back2. Resultsofthetestshowthatrotornoisereducesby3dB.Also, areduction in both the maximum pressure on the blade and noise reduction occurred at the same active tab phase angle, 90. Aoyama et al.(2004) [125] considered the reduction in BVI noise possible with use of an active tab, similar to the previous system. The authors were interested

68 40 (a) (b) (c) Figure 1.42: Example tab configurations: (a) flat tab, (b) tip bent tab with full retraction, and (c) tip bent tab with partial retraction by the National Aerospace Laboratory of Japan [123] Figure 1.43: Active tab concept used on a rotating test by the National Aerospace Laboratory of Japan [124] in using CFD to analyze the performance of the active tab system. The authors used a 3D unsteady Euler CFD code with an acoustic code for analysis. Tabs with no deflection angle had little effect on rotor thrust statically and dynamically. Including a tab angle resulted in sufficient variation in rotor thrust allowing the rotor to be slowed to reduce noise. Dynamically, these tabs controlled the miss

69 41 distance for a BVI event. The tab was able to affect the vertical position of the tip-vortex center, to a similar degree as HHC. Also, the tab moves the tip-vortex center horizontally. BVI noise was predicted to be reduced by 5 db. Saito et al.(2010) [57], with JAXA, reported on the above system, with the inclusion of a control law. The controller used blade surface pressures for the quadratic performance function. The authors used a T-Matrix approach with both off-line identification for initial values and on-line identification with a Kalman filter. Experimental results showed the control law taking 8 cycles to converge Western Michigan University Liu et al.(2007)[126] experimentally considered the lift increment of a static trailing edge tab on a NACA 0012 airfoil. The authors were considering this for use on a fixed-wing aircraft. The wind tunnel speed ranged from 6 m/s (12 knots) to 73 m/s (142 knots). The airfoil model had a chord of 10 in (254 mm) and a span of 12 in (305 mm). An test specimen is shown in figure The tabs were made of both aluminum (0.216 mm thickness) and Mylar (0.254 mm thickness) with lengths of 5% and 10% of the chord. Static deflection angles of 0, 5, 7, and 10, all downwards, were tested. The addition of the tab shifted the C L curve upwards, but stall occured at lower AOA values, particularly for larger tab deflections. Without tab deflection, the C L was not noticablly larger than the baselineuntilaoavalueslargerthan10. Theauthorsconcludedthetabincreases C L, while not having much effct on L/D. In comparison, a GF with heights 0.5%c to 3%c, had much lower L/D. As a result, the authors do not recommend the GF for cruise flight. A 1.2%c GF had compariable lift to a 10%c tab with a 5 tip down EADS/Eurocopter EADS and Eurocopter has produced a series of papers starting in 2007 [127, 128, 129] about smart trailing edge tabs of various configurations. Maucher et al. [127] considered three different concepts for trailing edge aerodynamic effectors. The first concept was the Smart tab and is shown in figure 1.45a. The idea was to use piezoelectric patches on the surface of a plate for deflection. The second concept

70 42 Figure1.44: ANACA0012airfoilwithatrailingedgetabbytheWesternMichigan University [126] was the Active Trailing Edge (ATE) and is in figure 1.45b. The difference from the Smart tab, is that the plate is faired and behaves like a continuous TEF. The last concept in figure 1.45c is a combination of the previous two concepts. Essentially the fairing only exist partway down the plate. The plate is made up of a three-layer (trimorph) bender. The authors conclude that the ATE offered more aerodynamics benefits over the Smart Tab and focus there efforts on that configuration. The authors conduct sizing optimization for the active plate configuration. Low profile stack actuators are used and an active plate for testing is shown in figure Tip deflections are ±2.2mm for 180 VDC input. Results of an aerodynamic study by Grohmann et al.(2008) [128] indicated an increment in moment coefficient of C m = ±0.05 was achieved with a tab deflection of ±5 and a flap chord around 0.2c. Working with DLR, a multilayer piezoelectric actuator similar to MFC was created. The basic concept created a piezoelectric stack with electrodes and slice off thin layers. These thin layers were then processed. The process is illustrated in figure Steps b and c are the application of an electrode and placing an elastic electrode on top. This was done to prevent cracking in the electrode layer. The benefit of this process was MFC like strains at lower voltages, (-50 VDC to 200 VDC versus -500 VDC to 1500 VDC). Grohmann et al.(2011) [129] discussed the issue with using a piezoelectric bender concept. First, bender stiffness is proportional to t 3. A stiffer system responds less to aerodynamic loads and flapping of the blade. However, the curvature achiev-

71 43 (a) (b) (c) Figure 1.45: (a) Piezoelectric driven smart tab, (b) active trailing edge, and (c) blend by EADS/Eurocopter [127] Figure 1.46: An active tab with piezoelectric low profile stacks by EADS/ Eurocopter [127] able by piezoelectric systems is proportional to ǫ/t, where ǫ is the active strain of the piezoelectric element. Therefore, the thicker system undergoes less curvature and therefore deflection. So a balance between stiffness and deflection must be obtained. The authors conducted analysis and estimated that hub vibratory loads could be reduced by 70% to 80%. In order to reduce strains in the piezoelectric bender, the elements were broken into segments, as seen in figure These modules had slots between them and the next module, with the goal that this reduces

72 44 Figure 1.47: The creation of a low profile multilayer piezoelectric stack: (a) the stack, (b) electrode, (c) flexible electrode, (d) dicing, (e) multilayer plate, (f) final processing, by EADS/Eurocopter [128] Figure 1.48: The segmented composite piezoelectric bender plates by EADS/ Eurocopter [129] spanwise stresses due to CF. Experimental testing showed that the existance of the slot did reduce the spanwise strain experienced by the ATE actuator modules Technical University of Denmark The Risø National Laboratory of Sustainable Energy has looked at using trailing edge flaps for active load reduction. Bak et al.(2010) [130] present an overview of a wind tunnel test. The test is conducted on a 2D airfoil, the Risø-B1-18 airfoil, with a chord of 600 mm and a span of 1900 mm. A tab like extension

73 45 was bonded to the trailing edge of the airfoil. Unimorph piezoelectric benders, called Thunder elements by Face International Corporation. These elements have a length of 75.8 mm, making the tab 8.4%c. The unimorphs have a steel substrate, thepiezoelectriclayer, andanaluminumlayer. Appliedvoltagesof-450Vto900V result in deflections of 3.5 mm to the aluminum side and 1.5 mm to the steel side. This results in an effective flap deflection of 3 to 1.8. The authors conduct steady and unsteady aerodynamic experiments. The authors also look at how effective the system is an accommodating chages in wind speed The Pennsylvania State University In 2009, Léon et al. [131] conducted both an aerodynamic study and developed a benchtop prototype of a variable chord device. The concept was to have a deployable plate or tab come out of the trailing edge to increase the maximum lift coefficient. The aerodynamic study used a rotor code for trimming. A rigid prescribed wake was used with a rigid blade approximation. The Theodorsen-Garrick model was used to account for quasi-steady airloads associated with pitching and flapping. The authors looked at TETs lengths of 10%, 20%, and 30% of the chord. The TET was compared with Gurney flaps (of 0.5%, 1%, and 2% deflections), and a TEF with a chord 20% of the airfoil deflected at 4, 8, and 12. The authors compared the three methods of increasing the lift coefficient near stall and found that a 10% chord TET provides an increment in lift similar to a 0.5% GF. A 20% chord TET was similar to a 2% GF. The TET s increase in drag was more gradual than the GF. The TEF had a lover C 1,max than the GF or TET. The TET had the more favorable lift-to-drag ratios compared to the GF. Above C L coefficients of 1.2, the TET was the most efficient means of increasing lift. Based on the aerodynamic study using the rotor code, the TET showed potential to increase the absolute ceiling of a UH-60A. Examples of this improved altitude were: at 131 knots with a gross weight of 18,000 lbs a 30% chord TET provides a 1,500 ft (10%) increase in absolute ceiling and at 112 knots with a gross weight of 24,000 lbs, the same TET provides a 2,000 ft (25%) increase in ceiling. The TET allowed for increases in gross weight as well. For a 24,000 lbs helicopter at 112 knots, a 30% chord TET increased the gross weight by 6.7%.

74 46 Figure 1.49: A variable chord device using a deployable trailing edge tab [131] Figure 1.50: A bistable deployable trailing edge tab by Penn State [132] The benchtop prototype was based on a symmetric airfoil, NACA The prototype s chord was in. with a plate length 30% of that value. The protopyte is shown in figure The plate was support on each side with sliding rails and deployed using a x-frame actuation deivce, driven by an electric motor. Johnson(2010) [132] considered a plate that was restrained by a bistable arch. The concept, drawn in figure 1.50 shows a deployable tab connected to a bistable arch. The two stable states corresponded to fully retracted and fully deployed. The system deployed using a SMA actuator. Khoshlahjeh et al.(2010) [133] considered using chord extension to prolong the onset of blade stall. The chord extension would be deployed quasi-statically, depending on the flight regime. The author used the Uh-60A as the basis of the

75 47 model. The chord extension was located between 0.63R and 0.83R. The aerodynamic airfoil section coefficients were generated using 2D CFD. The chord extension was 0.2c long and deploys 2 downwards. The aerodynamic model used a lifting line vortex wake model with prescribed geometry. The blades were modeled rigid. Various flight conditions were examined: 120 knots cruise and 140 knots high speed, density altitudes from sea level to 12,000 ft, and gross weights of 16,000 lbs to 28,000 lbs. Chord extension significantly increased high lift capacity at high density altitude, at 12,000 ft the gross weight increased from 20,500 lbs to 22,700 lbs with the chord deployed. The chord extension increased lift over the annulus they span. The chord extension allowed for a lower collective, reducing the AOA and drag on the retreating side. This reduced power by 12% at maximum speed (2,355 hp to 2,068 hp). The authors cooncluded that at cruise at sea level, the chord extension is of little value, but at higher altitudes it allowed for increased gross weight. At high speeds gross weight increases were smaller than in cruise. The chord extension did little to increase maximum speed of the vehicle. Khoshlahjeh et al.(2011) [134] considered the use of chord extension in conjunction with the Rotorcraft Comprehensive Analysis System (RCAS). This allowed for the blades to be modeled elastically. In addition the aerodynamic model accounted for dynamic stall and unsteady aerodynamics. The chord extension span was the same range and was the same chord length of the previous consideration. The speeds considered were high speed at 130 knots and cruise at 90 knots. The density altitudes considered were sea level, 4,000 ft, 8,000 ft, and 12,000 ft. Using the baseline gross weight (the weight at which the baseline vehicle was stalling), power reductions of 12% to 15% with use of chord extension were predicted across the considered altitudes. The chord extension could instead provide gross weight increases up to 1,400 lbs. At cruise, power reductions in the range of 10.5% to 16% were predicted. Or, a gross weight increase of 1,200 lbs to 1,400 lbs could be obtained at high altitudes. Chord extension increased maximum speed from 90 knots to 110 knots when flying at 8,000 ft and 24,000 lbs gross weight. Alternatively, a reduction for power by 12% at 90 knots was predicted. The chord extension increased the lift in the area it was deployed, alleviating stall on the retreating side. The chord extension also increased the nose down pitching. An interesting observation was that this twists the blade nose down, off loading the out board

76 48 Figure 1.51: A continuous variable chord device, by Penn State [135] lift. This reduced drag, rotor torque, and power. This reduced the collective trim reduction that would otherwise be expected using rigid blade analysis. Barbarino et al.(2010) [135] considered the design of a variable chord mechanism, with the goal of creating a continuous structure, rather than discrete (ie a plate). The retracted and expanded configurations are shown in figure The authors used minispars connected with cellular structures in the chord direction. The spars provided an attachment point for an elastic skin. Finite elements were used to design a structure such that the strains remained elastic. Bae and Gandhi(2011) [136] used two-dimensional CFD to analyze the aerodynamic coefficients of a TEF, a GF, and a TEP. The three configurations are shown in figure The authors conducted the CFD study, using compressible and viscous flow over the SC-1094R8 airfoil of the UH-60. The authors used the University of Maryland s TURNS code. The 20% chord TEF was deflected ±2, ±4, and±6. Gurneyflap heightsof0.5 %c, 1%c, 1.5%c, and2%cweresimulated. The TEP had chord lengths of 0.1c and 0.2c with static deflection angles of 2 and 4. A TEF with a deflection of 6 generated a maximum C l of 1.5, but the TEP with 0.2C generated larger lift coefficients. But the flap and the plate generated lower drag until approaching stall. At high AOA values the TEP had a larger increment in lift over the TEF for a given C d value. At low lift values, the TEP had much lower drag values comapred to the Gurney flap. The maximum C l value was higher for the GF compared to the TEP. However, the TEP produced a larger lift coefficient for a given drag coefficient. The TEP increased the maximum C l by 19% at Ma=0.4 and 23% at Ma=0.6. Comparing the TEF and TEP, both devices had a compariable drag increase, but the plate had a large nose down pitching moment. The GF was associated with higher drag increases at lower AOA values.

77 49 Figure 1.52: The dimensions for a trailing edge flap, Gurney flap, and a trailing edge plate, by Penn State [136] 1.9 Multiple Morphing Device Helicopter Performance Analysis Yeo(2008) [137],US Army Research, Development, and Engineering Command, conducted a rotor performance study of various morphing/active systems. The rotor system was based on the AH-64 Apache and used the comprehensive analysis method CAMRAD II. The active technologies considered are: leading edge slat, variable droop, oscillatory jets, Gurney flap, blade root IBC, active twist, and trailing edge flap. For all but IBC and active twist, airfoil tables were required as the concepts change the airfoil characteristics. The slat and variable droop both affect the nose of the airfoil, with the slat being physically separated from the airfoil, whereas the droop changes the nose shape. The oscillatory jet was a zero net mass synthetic jet. The slat, droop, oscillatory jet, and Gurney flap all increased maximum lift on the retreating side of the rotor. IBC, active twist, and the TEF increased the lift to drag ratio of the rotor with a 2/rev input. These methods were not considered ideal for increasing blade maximum loading. Kang et al.(2010) [138], containing authors from Advanced Rotorcraft Technology and Penn State, looked at various blade morphing methodologies and investigated the benefits. The study used a medium lift helicopter of generic properties. The rotor was modeled using finite elements. An unsteady airloads model includ-

78 50 Table 1.1: The performance improvement predicted for a medium lift helicopter by Advanced Rotorcraft Technology [138] Figure 1.53: The concept of the active piezoelectric tab ing rotor wake, yawed flow, and elastic blade motion effects was implemented. The blades had a linear twist distribution. The authors considered a variety of morphing concepts including variable rotor speed, variable chord, variable twist, variable span, and LE slat. All of these were investigated quasi-statically. The dynamic chord and LE was also considered at 1/rev. The table 1.1 summarizes the results of the study. The performance increase by variable chord deployed statically is one of the top 3 and was predicted to give a 6% decrease in cruise power Concept and research objectives This dissertation focuses on an active trailing edge tab to change the lift or moment coefficient of an airfoil for rotorcraft noise and vibration reduction. The concept is illustratedinfigure1.53. Theideatakesarotorcraftbladeandaddsanactivetabto the trailing edge. This tab is able to undergo bending, as illustrated. The method of actuation uses piezoelectric materials, particularly the micro fiber composite

79 51 Figure 1.54: Long range goal is to incorporate active tab into a variable chord system consisting of a deployable plate: (a) retracted and (b) deployed and actuating actuator. The concept is similar to the bimorph, with actuators on both sides of a thin shim. The application of voltages with opposite signs results in a bending of the system. In practice, both the shim and the actuators make up a plate, extending along a span of the rotor blade. One long range goal of the concept is to integrate with a form of chord morphing, the trailing edge tab. This concept is illustrated in figure In this concept, the shim and piezoelectric actuators are able to be retracted into the airfoil. This combines the current concept with the TET concept. Of course, one limitation is that the active tab is limited to operating only when deployed. The overall goal is to consider the active tab concept just described and evaluate its feasibility in reducing noise and vibration of rotorcraft. This study can be broken down into two main objectives. The first objective is quantifying the aerodynamic properties of an airfoil with a deformable trailing edge tab. The second objective is developing an actuation system to achieve the bending of the tab. To satisfy the first goal, the aerodynamic coefficients of the airfoil for both the undeflected and deflected positions are calculated. Computational Fluid Dynamics (CFD) is used to determine the sectional aerodynamic properties. The CFD analysis uses an assumed displacement of the tab, unaffected by the aerodynamic load on the tab. The CFD analysis focuses on the steady-state flow with static tab deflection at various flow Mach numbers and Angle-of-Attack values. The active tab is compared with a TEF. This provides a baseline for establishing aerodynamic efficiency. The second goal of designing the actuation system includes design of both the tab as well as the actuators needed to deform the tab. The tab is deployed using

80 52 piezoelectric actuators on the tab. Various actuator placements and designs are analyzed. This analysis is conducted using Finite Element Analysis (FEA). This allows for both static and dynamic deflections to be analyzed, including blade motions. The rotation of the blade about the hub is also be accounted for, as this imposes large loads on the blades. Results showed that blade motions result in undesirable tab deflections in designs without sufficient stiffness. Such uncommanded deflections result in undesired changes in the airfoil properties. The final design needs to be able to provide the deflections that aerodynamic analysis predicts are necessary, while undergoing minimal deformations with blade motions and aerodynamics loading. This design was tested experimentally as a benchtop prototype Organization structure of dissertation This chapter, chapter 1, considers background information and motivation for research. It also discusses relevant research related or of importance to the topic. This chapter also introduces the concept and the goals of the research. Chapter 2 is concerned with the steady aerodynamic performance of the airfoil with the tab. The computational fluid dynamics code and grid used are discussed in detail. The results of the study are presented for certain Mach numbers and compared against a trailing edge flap of similar dimensions. Chapter 3 chronicles the development and design of the tab, from initial concept to final designs. Both analytical and finite element methods are used to understand the relation between design variables and objectives. Lastly, a few designs are examined in detail to understand how both the dynamic and aerodynamic environment the tab will operate in affects the tab. Chapter 4 discusses the benchtop prototype design, fabrication, testing, and the results from testing. The first three subjects deal essentially with the overall setup of the experiment. This includes the equipment used to power the actuators and record important parameters. The results of the experiment are compared with expected results generated using FEA. Chapter 5 takes the implications of the testing and looks at the viability of the concept. It combines the results of several chapters to answer the question: does

81 53 that tab have potential for reducing noise and vibration on rotorcraft? Chapter 6 is the conclusion and provides a summary of the entire dissertation. A short overview of all methods of analysis and the most important results from each chapter. Lastly, suggestions for future work are presented.

82 Chapter 2 Steady Aerodynamic Study of Tab In order to estimate the aerodynamic coefficients of the tab, CFD is utilized. Such an analysis will provide estimates of the important aerodynamic properties. This analysis is compared with similar results for the trailing edge flap. This allows benchmarking of the tab s aerodynamic performance with a well known method, the trailing edge flap. 2.1 Analysis Method The University of Maryland s Transonic Unsteady Navier-Stokes (TURNS) CFD code [139, 140, 141] solves the Reynolds-Averaged Navier-Stokes equations. A third and fifth order Weighted Essentially Non-Oscillatory (WENO) scheme [142] computes the inviscid terms. The WENO scheme uses Roe s upwind flux difference splitting to estimate the derivatives. The WENO scheme provides total variation diminishing (TVD), ensuring a stable solution despite the discontinuities associated with shocks. A second order central differencing scheme calculates the viscous terms. The Spallart Allaras model [143] is used for turbulence modeling. Several studies have used this code to estimate the aerodynamic properties of airfoil sections for rotorcraft applications [139, 141, 144, 136]. Chris Duling [144] compares experimental results with zero flap deflection experimental data. Considering the lift coefficient, the lift-curve slope, the maximum lift coefficient, and the zero-lift angle are all compared to experimental data. Comparisons relating to drag include the zero-lift drag coefficient and the maximum lift-to-drag ratio. Ex-

83 Y X (a) 0.2 Y X (b) Figure 2.1: The C-grid used by CFD for two tab deflections: (a) 0 and (b) 6 perimental moment-curve slope and the zero-lift moment coefficient are compared to TURNS results. The overall conclusion is that lift compares well across all Mach numbers [144]. The drag results compare well in the lower transonic region, but the CFD exhibits an early drag divergence [144]. The moment comparison is fair, but the TURNS results trend towards the larger nose down bounds of the experimental results [144]. The basic C-type grid used has 329 grid elements around the airfoil and 97 grid elements from the surface outwards into the airflow. The first grid element height was set to with the chord being a unit of length. The grid was concentrated at both the leading edge and the trailing edge. Figure 2.1 contains examples of the grid used. Convergence was based on the residual of the solver. In few cases convergence was not obtained and no results are presented for these cases.

84 56 Figure 2.2: The active trailing edge tab concept and dimensions Table 2.1: Important parameters used by the CFD codes and values varied Parameter Value or Range Re AOA [ ] Ma [ ] The SC-1094R8 airfoil, used on the UH-60, was chosen for the baseline airfoil. A tab 20% of the orignal chord was added to the airfoil. For the calculations in this chapter the main airfoil is rigid and only the tab deforms. The deflection of the tab was based on the first chordwise bending mode shape of a cantilevered beam. The tab thickness is 0.42% of the chord (2.2 mm for full size blade). Figure 2.2 shows the tab in a deflected position. The angle,, formed between a line from the tip to the base of the tab and the x-axis of the airfoil coordinates (figure 2.2) is used as a measure of tab deflection. Deflection is defined as positive tip down, so that lift is increased with the tab deflection. In order to obtain a comprehensive database, different angle-of-attack(aoa) values and Mach numbers are evaluated. Table 2.1 contains the ranges of these parameters to be considered in in the simulations. 2.2 Aerodynamic Coefficient Results and Discussion: 0.20c tab Although results for 9 different Mach numbers have been generated (Table 2.1), only results for Mach numbers 0.4, 0.6, and 0.8 will be presented to give an idea of tab effectiveness. For simplicity, these Mach numbers will be described as low, moderate, and high, respectively, referring only to the relative difference amongst the Mach numbers selected. A complete tabulation of the CFD results are found

85 =6 =4 C l =2 δ =0 θ δ = 2 θ δ = 4 θ = AOA Figure 2.3: Lift coefficient of tab at Ma=0.4 in Appendix A. The tab aerodynamic coefficients are compared with a those of a trailing edge flap. This flap is also 20% of the chord. The data for the TEF comes from Duling [145]. This data was also generated using the TURNS CFD code Lift coefficient and increment for Mach number=0.4 Figure 2.3 presents the lift coefficient results for Ma=0.4 with tab deflections ranging from = ±6. The deflection of the tab has two major effects on the lift curve. First, the lift curve is shifted vertically, positive for downward deflections and negative for upward deflections (positive and negative deflections, respectively). The vertical shifting affects the maximum lift coefficients. The second effect is to shift the C l,max to lower AOA values for positive tab deflections and higher AOA values for negative tab deflections. The maximum lift coefficients vary from AOA values of 10 for the maximum positive deflection angle to 14 for the maximum negative tab deflection value. The undeflected tab s C l,max AOA value is 12. The increment in lift coefficient as a result of tab deflection (with respect to the undeflected tab) is presented in figure 2.4. From this figure, an area of near constant lift increment exists for all 6 flap deflection values with inclusive AOA values of 4 to 8. The maximum lift increments is attained over a larger range of airfoil AOA for smaller tab deflections and a shorter range for larger tab deflections. For example, the upper AOA value for the maximum lift increment of = 6 is 6

86 =6 =4 =2 dc l = 2 = 4 = AOA Figure 2.4: Increment in lift coefficient of tab at Ma=0.4 whereas for = 2 the upper AOA value is 10. The maximum increments in lift are: 0.4 and -0.4 for = ±6, 0.27 and for = ±4, and 0.14 and for = ±2, respectively. With a negative tab deflection, observable in figure 2.4, the region of maximum lift increment does have a slight to moderate positive slope and so the above values are averages. Even post stall, tab deflection effects an increment in lift, for example an increment of for = 6 at α = 16. Figure 2.5 contains the increment in lift for a 20% chord trailing edge flap (TEF). The TEF deflection angle is measured in the same manner as the plate. For the TEF, the AOA range where the maximum increment in C l is reached is similar to the tab. The increments in lift for the TEF range from 5% to 11% lower than the tab for the same deflection angle. In otherwords, to achieve the same C l increase, the tab requires a slightly smaller deflection, when compared to the TEF Moment coefficient and increment for Mach number=0.4 The moment coefficient for the tab is plotted in Fig Between AOA values of 5 and 10 the moment coefficient value increases slightly with AOA. High AOA values have increasingly stronger nose-down pitching moments, with C m values also depending on. The effect of tab deflection is increased nose-down pitching moment for a downward tab deflection and a nose-up pitching moment for an

87 59 dc l =6 δ =4 θ =2 = 2 δ = 4 θ δ = 6 θ AOA Figure 2.5: Increment in lift coefficient of trailing edge flap at Ma=0.4 upward tab deflection. The increment in C m for tab deflection retains effectiveness over the AOA range considered. This is easily confirmed in figure 2.7. The tab retains effectiveness at extreme AOA values (both high and low values), which both figures 2.6 and 2.7 confirm. The increment in moment coefficient for the TEF can be compared to the tab, via figures 2.8 and 2.7, respectively. Qualitatively, the two figures are similar. The tab has a larger increment in moment coefficient, for the same deflection amplitude, than the TEF. Considering an AOA value of 4, the tab has dc m values of: ( = 6 ), ( = 4 ), ( 2 ), ( = 2 ), ( = 4 ), and ( = 6 ). The TEF dc m are, respectively: 0.066, 0.044, 0.022, , , and The peak tab incremental moment coefficients are just under 20% larger than the TEF. So the tab requires a smaller deflection for a given increment in moment coefficient. This is similar to the increment in lift coefficient Drag coefficient and increment for Mach number=0.4 The drag coefficient is presented in figure 2.9. Over the AOA range of 2 to 4 the change in C d is modest, with differences in minimum and maximum drag being 33% to 52%, respectively and based on the smaller drag value. Also, for positive AOA values an increase in drag occurs for positive tab deflection and a decrease in

88 = 6 = 4 = 2 =0 C m =2 =4 = AOA Figure 2.6: Moment coefficient about the 1/4-chord of the tab at Ma= = 6 = 4 = 2 dc m =2 =4 = AOA Figure 2.7: Increment in moment coefficient about the 1/4-chord of the tab at Ma=0.4 drag for negatve tab deflections with respect to basline drag. The opposite is true at negative AOA values. For larger positve or negative airfoil AOA values, the change in C d with tab deflection is much greater. At both AOA value limits, the drag coefficient increases of an order-of-magnitude with respect to minimum drag. The increased change in drag increment for the various tab deflections is seen in figure Deflecting the tab upwards at above an AOA value of 10 decreases drag up to 24% (below baseline and for α = 14 and = 6 ) and deflecting the

89 61 dc m = 6 δ = 4 θ = 2 =2 δ =4 θ = AOA Figure 2.8: Increment in moment coefficient about the 1/4-chord of the TEF at Ma=0.4 tab downwards above an AOA value of 6 likewise increases the drag coefficient up to 28% (for α = 16 and = 6 ). In comparing the tab (figure 2.10) to the TEF (figure 2.11), there is not a large difference qualitatively for the increment in drag coefficient. For example, the TEF also shows a decrease in drag coefficient over the baseline at positive AOA values and negative flap deflection values. Compared to the tab, the TEF shows a smaller increase in C d at the endpoint AOA values, for positive values of. For example, dc d for α = 16 and = 6 is and 0.044, tab and TEF, respectively Lift coefficient increment per unit drag for Mach number=0.4 A comparison of lift increment per unit drag is presented in figures 2.12 and 2.13, for the tab and TEF respectively. This ratio represents a metric indicating the cost (in drag) for a given increment in lift. Figures 2.12 and 2.13 maintain the qualitative similarity that has been observed between the tab and TEF. However, that tab does appear to be slightly more aerodynamically efficient. For example, looking at an AOA value of 6 and = 6 the tab has a dcl/c d value of 25 whereas the TEF has a value of 20. Likewise, at the same AOA value, but with = 6, the tab s metric value is -40, whereas the TEF metric value is -36. This

90 = 6 δ = 4 θ δ = 2 θ δ =0 θ =6 =4 =2 C d AOA Figure 2.9: Drag coefficient of the tab at Ma= dc d δ =6 θ =4 =2 = 2 δ = 4 θ = AOA Figure 2.10: Increment in drag coefficient of the tab at Ma=0.4 AOA represents a realistic value for a rotor blade at this Mach number. These trends also hold for the lower deflection angles at α = Moment coefficient increment per unit drag for Mach number=0.4 The increment in moment coefficient per unit drag is presented in figure As with the previous section, this metric provides a measure of efficiency, the increase

91 63 dc d δ =6 θ =4 =2 = 2 δ = 4 θ = AOA Figure 2.11: Increment in drag coefficient of the tab at Ma=0.4 dc l /C d = 2 = 4 = 6 =6 =4 = AOA Figure 2.12: Increment in lift coefficient per unit drag of tab at Ma=0.4 in moment over the drag. Qualitatively, the increment in moment per unit drag compares well (see figures 2.14 and 2.15). As with the lift metric, the tab is slightly more aerodynamically efficient than the TEF. Looking at an AOA value of 6 illustrates this point. The tab s moment metric with = 6 is -4.5, whereas the TEF for the same deflection amplitude is With a deflection of 6 the tab s dc m /C d is 7.7 and the TEF s is 6.3. Table 2.2 further illustrates the greater aerodynamic efficiency in producing a lift increment of the tab over the TEF. This holds true for the range of AOA values and deflection amplitudes.

92 64 dc l /C d =6 =4 =2 = 2 = 4 = AOA Figure 2.13: Increment in lift coefficient per unit drag of trailing edge flap at Ma= = 6 = 4 = 2 dc m /C d 0 5 =2 =4 = AOA Figure 2.14: Increment in moment coefficient about the 1/4-chord per unit drag of tab at Ma= Lift coefficient and increment for Mach number=0.6 The lift coefficient for the tab at Ma=0.6 is qualitatively different from the lower Mach number (figures 2.16 and 2.3). At high AOA values, stall is not as defined as with the lower Mach number. Stall occurs at a lower AOA value, 4 rather than 10 for = 6, but the lift resumes increasing by α = 8. For the other deflection amplitudes, no decrease in lift occurs for increasing AOA values, but the slope

93 = 6 = 4 = 2 dc m /C d 0 5 =2 =4 = AOA Figure 2.15: Increment in moment coefficient about the 1/4-chord per unit drag of trailing edge flap at Ma=0.4 Table2.2: dc m /CdforboththetabandTEFforvariousAOAvaluesandtab/TEF deflections, Mach=0.4 Tab TEF AOA does decrease. Comparing the increment in the lift coefficient at Mach=0.6 (figure 2.17) with Mach=0.4 (figure 2.4) the higher Mach number lacks the region of constant lift increment predicted at the lower Mach number. The peak increments in lift are: for = 6 at α = 0 and for = 6 at α = 2. At AOA values greater then 6 to 8, the lift increment flattens for all tab deflections. These high AOA value lift increments are larger than for Ma=0.4 (peak values of 0.2 (figure 2.17) versus 0.12 (figure 2.4). Comparing the lift increment for the tab and the TEF, figures 2.17 and 2.18, reveals qualitative similarities. Both the tab and TEF exhibit a sharp decline in their increment in lift values, ending at around the same AOA values, α =

94 66 C l =6 =4 =2 =0 = 2 = 4 δ = 6 θ AOA Figure 2.16: Lift coefficient of tab at Ma= dc l δ =6 θ =4 δ =2 θ = 2 δ = 4 θ = AOA Figure 2.17: Increment in lift coefficient of tab at Ma= The TEF s peak lift increment values are slightly lower than the tab s, with percent differences ranging between 5-8%. Likewise, at higher AOA values, the tab has slightly larger lift increment values over the TEF(0.2 compared to 0.16, respectively). At a Mach number of 0.6 the AOA value a rotor might encounter is around 2 to 4 (see figure 2.42). For a positive deflection amplitude of 6 and an AOA value of 4 the tab has an increment in lift of 0.36 and TEF s increment is At an AOA value of 2 the increment for the tab, 0.45, beats the TEF, With = 6 the tab performs better than the TEF at both α = 2 and

95 =6 =4 =2 dc l = 2 = 4 = AOA Figure 2.18: Increment in lift coefficient of TEF at Ma=0.6 4, & for the tab at α = 2 & 4 compared to & for the TEF at α = 2 & 4. Overall, at Ma=0.6, for a given deflection, the tab continues to have the same or slightly larger lift increment values than the TEF Moment coefficient and increment for Mach number=0.6 The moment coefficient in figure 2.19 compares well to the lower Mach number results (figure 2.6). The slightly larger moment coefficient values for Ma=0.6 result in a larger range of coefficient values compared to Ma=0.4. At Ma=0.6 the C m rangesfrom-0.2to0.2, whereasatma=0.4c, rangesfrom-0.16to0.17. Thehigher Mach number can be distinguished from the lower Mach number by a smaller internal region of positive slope, found around α = 0. The increment in the moment coefficient in figure 2.20 corresponds qualitatively to Ma=0.4 (figure 2.7). The increment in moment maintains effectiveness over the entire angle-of-attack range, a desirable feature. There are slight increment value increases associated with the flattening of the lift coefficient, particularly associated with positive tab deflection at α = 6. The increase in Mach number does not change the increment magnitudes; they are comparable between Ma=0.4 and Ma=0.6. Comparing the tab (figure 2.20) to the TEF (figure 2.21) reveals that the TEF has much more variation in moment increment with AOA than the

96 = 6 = 4 = 2 =0 C m =2 =4 = AOA Figure 2.19: Moment coefficient about the 1/4-chord of tab at Ma=0.6 dc m = 6 δ = 4 θ = 2 δ =2 θ =4 = AOA Figure 2.20: Increment in moment coefficient about the 1/4-chord of tab at Ma=0.6 tab. The results for the TEF have several gaps. A lack of converged results is the source of these gaps. The TEF moment increment exhibits greater oscillation than the tab results. The cause of these oscillations could be related to the convergence issues of the surrounding conditions. Considered an AOA value of 2 the moment coefficient increments for the tab are and for = ±6, respectively. At the same AOA value the TEF s moment increments are and for = ±6, respectively. With an AOA value of 4 the Tab s moment increments are and ( = ±6 ), compared to the TEF s increments of and

97 = 6 = 4 = 2 dc m =2 =4 = AOA Figure 2.21: Increment in moment coefficient about the 1/4-chord of TEF at Ma= ( = ±6 ). These observations can be generalized, the tab generates larger increment in moment coefficient than the TEF Drag coefficient and increment for Mach Number=0.6 At the higher Mach number, the drag coefficient has a distinct v shape, as depicted in figure Deflection of the tab moves the AOA value of minimum drag and the entire curve, with a positive deflection moving the values to lower AOA values and vice versa. This compares well with the lower Mach number in figure 2.9. The drag coefficients at α = 0 compare well between Ma=0.6 and Ma=0.4. However, this is not true for high AOA values, where the higher Mach number has greater drag than the lower Mach number. The increment in drag for the higher Mach number demonstrates that although the drag coefficient is larger than at the lower Mach number, the increment in drag is similar (figure 2.23 and 2.10). Comparing the tab and TEF at α = 2 and 4 revels a greater drag penalty for the tab. With a deflection amplitude of 6, the tab s drag increases by and for AOA values of 2 and 4, respectively. With the same deflection, the TEF s drag increases by only and for AOA values of 2 and 4, respectively. Likewise, for = 6 the tab s drag decreases by and 0.01 for α = 2 & 4, whereas the TEF s drag decreases

98 70 C d δ = 6 θ δ = 4 θ = 2 =0 =6 =4 = AOA Figure 2.22: Drag coefficient of tab at Ma= =6 =4 =2 dc d = 2 = 4 = AOA Figure 2.23: Increment in drag coefficient of tab at Ma=0.6 by and 0.011, respectively Lift coefficient increment per unit drag for Mach number=0.6 Figure 2.25 of the lift coefficient increment per unit drag, dc l /C d, depicts a narrower region of large metric values compared to the lower Mach number (figure 2.12). However, the figure 2.25 of the tab compares qualitatively to that

99 =6 =4 =2 dc d = 2 = 4 = AOA Figure 2.24: Increment in drag coefficient of TEF at Ma=0.6 dc l /C d δ =6 θ =4 =2 δ = 2 θ = 4 = AOA Figure 2.25: Increment in lift coefficient per unit drag of tab at Ma=0.6 of the TEF, figure At an AOA value of 2, the tab s lift coefficient per unit drag is 25 and -55 for = 6 and 6, respectively. These values are larger than the TEF, which are 22 and -52, respectively. Likewise, at α = 4 the tab s metric values are 8.2 and -46 for = 6 and 6 and for the TEF, 7.4 and -37. These results maintain the conclusion of better aerodynamic performance of the tab over the TEF for a given tip displacement.

100 72 dc l /C d δ =6 θ =4 δ =2 θ = 2 δ = 4 θ = AOA Figure 2.26: Increment in lift coefficient per unit drag of trailing edge flap at Ma= Moment coefficient increment per unit drag for Mach number=0.6 Figure 2.27 depicts similar trends to the lower Mach number, figure More important is the comparison to the TEF, which shows a broader region of large moment coefficient increment per unit drag metric values. In particular, the TEF s deflection amplitude of 6 is smaller, -3.3 at α = 2, than that of the Tab, -4.4 at α = 2. The same holds true for = 6 at the same AOA values: 10 for the tab and 8.8 for the TEF at α = 2. Table 2.3 compares both the tab and the TEF for higher angles of attack. This includes an AOA value of 4 for which the tab outperforms the TEF, particularly with negative deflection values. Generally, the tab outperforms the TEF in generating increments in moment coefficient per unit drag Lift coefficient and increment for Mach number=0.8 The lift coefficient for a Mach number of 0.8 is presented in figure As stated in the beginning of this section, the is the highest Mach number considered in the text. The complete data is found in appendix A. At the lowest AOA values, up to 6 for = 6 and 2 for = 6, the lift coefficients are the least sensitive

101 73 15 dc m /C d = 6 δ = 4 θ = 2 =2 δ =4 θ δ =6 θ AOA Figure 2.27: Increment in moment coefficient about the 1/4-chord per unit drag of tab at Ma=0.6 dc m /C d δ = 6 θ = 4 = 2 =2 =4 δ =6 θ AOA Figure 2.28: Increment in moment coefficient about the 1/4-chord per unit drag of trailing edge flap at Ma=0.6 to AOA. Above this region, the lift curve slope is quite steep at and below a zero AOA. In this region, the various lines representing the different tab deflections show a uniform separation with AOA. Above this steep region, above to 0 for = 6 and 4 for = 6, is another region of moderate slope. In this region the different tab deflection lift coefficients begin to converge. The lift curve at this high AOA compares qualitatively to the moderate Mach number lift curve, figure 2.16.

102 74 Table2.3: dc m /CdforboththetabandTEFforvariousAOAvaluesandtab/TEF deflections, Mach=0.6 Tab TEF AOA =6 =4 =2 C l =0 = 2 = 4 δ = 6 θ AOA Figure 2.29: Lift coefficient of tab at Ma=0.8 The increment in lift coefficient for Ma=0.8, found in figure 2.30, contains a narrow region of large lift increment centered around 2 to 0. This region is not found with the TEF, figure This region differentiates the tab s and TEF s increment in lift coefficient from each other, unlike at the Mach numbers of 0.4 and 0.6. At this high Mach number of 0.8, and AOA value of 2 is a realistic for comparison between the tab and TEF. At the maximum positive deflection amplitude, the lift increment of the tab is 0.71, whereas the TEF is For the maximum negative deflection amplitude the tab increment in lift coefficient is and the TEF s is Figures 2.30 and 2.31 maintain the expectation of greater aerodynamic effectives of the tab over the TEF for increasing lift. At this Mach number, the TEF results have many AOA and flap deflection values where convergence was not obtained and therefore no results are plotted.

103 =6 =4 =2 dc l = 2 = 4 = AOA Figure 2.30: Increment in lift coefficient of tab at Ma= =6 =4 =2 dc l = 2 = 4 = AOA Figure 2.31: Increment in lift coefficient of TEF at Ma= Moment coefficient and increment for Mach number=0.8 Figure 2.32 contains the moment coefficient results for Ma=0.8. In contrast to the lower Mach numbers considered, the slope of the C m curves remain negative across the range of AOA values considered. Above an AOA value of 0, the various tab deflection curves begin to converge. Compared to the moderate Mach number, figure 2.19, extreme C m values are larger in magnitude at the higher Mach number, although mainly at α = 16. The increment in moment coefficient exhibits a

104 76 C m = 6 = 4 = 2 = =2 =4 = AOA Figure 2.32: Moment coefficient of tab at Ma= = 6 = 4 = 2 dc m =2 =4 = AOA Figure 2.33: Increment in moment coefficient of tab at Ma=0.8 sensitivity to AOA, depicted in figure 2.33, that the dc m figures of Ma=0.4 and 0.6 did not exhibit. The TEF and tab exhibit similarity, however the TEF produces no double peak, comparing figure 2.33 and This double peak feature illustrates a penalty the tab for positive tab deflections at α = 2, with the tab producing a moment increment of compared to the TEF s at = 6. However, with a tab deflection of 6, the tab produces a moment increment of 0.19 compared to the TEF s of only 0.14.

105 77 dc m =2 =4 =6 = 6 = 4 = AOA Figure 2.34: Increment in moment coefficient of TEF at Ma= Drag coefficient and increment for Mach Number=0.8 The drag coefficient, in figure 2.35 has a distinct V shape, with the bottom shifted rearward for positive tab deflections and forward for negative tab deflections relative to zero tab deflection. Compared to the moderate Mach number drag, figure 2.22, several differences exist. First, the trough of the higher Mach number is rather sharp and steep. Second, the lower Mach numbers have regions of insensitivity to AOA. At Mach 0.8, the tab does not have this region and has a higher minimum drag. Third, the higher Mach number tab has higher maximum drag, located at the AOA value endpoints. The increment in drag coefficient shows the crossing of the drag coefficient lines for various tab deflection as a sign change in drag increment. As the lines cross the zero tab deflection line, the sign of the drag increment changes, as found in figure For positive tab deflections and negative AOA values, drag is reduced. Whereas for negative tab deflection, a drag reduction occurs at positive AOA values. In both both cases, the increments in drag diverge from the point of sign change, with increase in AOA. Peak drag increment is 0.06 and peak drag decrement is Which compares closely to the results for Ma=0.6, figure The major difference between the figures, is the moderate Mach number has a small region of low drag increment, compared to the high Mach number which does not. Above an AOA value of 5, the drag increments of the two Mach numbers are comparable in magnitude.

106 78 C d δ = 6 θ = 4 = 2 =0 =6 =4 = AOA Figure 2.35: Drag coefficient of tab at Ma=0.8 Comparing figure 2.36 and 2.37, the tab and TED share some similarities, but also have some differences. Both figures show the increment in drag switching signs with AOA. However, the increment in drag coefficient for the TEF is scattered for positive AOA values and positive deflection amplitudes. But, at negative AOA values, the same deflection amplitudes are qualitatively similar. At an AOA value of 2, the tab and TEF have drag increment values of and , respectively, for = 6. For a deflection amplitude of 6, the tab and TEF values of drag increment are and 0.03, respectively. The deflection of the tab or flap determines whether the tab or TEF generates more drag Lift coefficient increment per unit drag for Mach number=0.8 The incremental lift coefficient over the drag coefficient in figures 2.38 and 2.39 compare well qualitatively. The tab produces a larger dc l /C d value for positive deflectionamplitudesthanthetef.inparticular, atanaoavalueof 2 thetabs performance yields a metric value of 34, compared to the TEF s 24 for maximum deflection. However, at a value of 6, the TEF has a metric value of -12 compared to the tab s -10. Table 2.4 contains the metric values for three additional AOA values: 0, 4, and 8. For α = 0, the tab s metric values are larger than the TEF. At α = 4, the TEF has better metric values for positive deflections,

107 dc d δ =6 θ =4 =2 = 2 δ = 4 θ = AOA Figure 2.36: Increment in drag coefficient of tab at Ma= =6 =4 =2 dc d = 2 = 4 = AOA Figure 2.37: Increment in drag coefficient of TEF at Ma=0.8 but worse for the negative deflections. In the AOA range of interest, the tab performance is about equal or slightly better than that of the TEF Moment coefficient increment per unit drag for Mach number=0.8 The increment in moment per unit drag for the tab and the TEF compare well, figures 2.40 and At an AOA of 2 the tab shows a higher moment increment

108 80 dc l /C d =6 δ =4 θ δ =2 θ = 2 δ = 4 θ = AOA Figure 2.38: Increment in lift coefficient per unit drag of tab at Ma=0.8 Table2.4: dc l /CdforboththeTabandTEFforvariousAOAvaluesandTab/TEF deflections, Mach=0.8 Tab TEF AOA dc l /C d δ =6 θ =4 δ =2 θ = 2 = 4 δ = 6 θ AOA Figure 2.39: Increment in lift coefficient per unit drag of trailing edge flap at Ma=0.8

109 81 dc m /C d =2 δ =4 θ δ =6 θ δ = 6 θ = 4 = AOA Figure 2.40: Increment in moment coefficient per unit drag of tab at Ma=0.8 Table2.5: dc m /CdforboththetabandTEFforvariousAOAvaluesandtab/TEF deflections, Mach=0.8 Tab TEF AOA per unit drag than the TEF. For = 6 the tab is predicted to have a metric value of -5.2 versus the TEF s With equal to 6, the tab has a metric value of 2.8, nearly the same as the TEF s 2.7. Table 2.5 contains the metric values for three additional AOA values: 0, 4, and 8. Comparing the results between the tab and TEF in table 2.5, the tab generally has larger or comparable moment metric values compared to the TEF. At zero AOA, the tab is superior, except at = 6. At α = 4, the tab is better except for a deflection of 4. At this value, the TEF has a metric value larger than the either the tab or TEF with a deflection of 6.

110 82 8 dc m /C d δ = 6 θ = 4 = 2 δ =2 θ =4 = AOA Figure 2.41: Increment in moment coefficient per unit drag of trailing edge flap at Ma= Comparison of Aerodynamic Coefficients: 0.20c & 0.15c tabs While studying the response of the tab under inertial and aerodynamic loads it became apparent that a 20% chord tab may not be viable and a shorter (15% chord) tab may have to be considered. Several AOA values and Mach numbers were analyzed for a tab length of 0.15c. These results are compared to the longer tab length of 0.2c. Only a small subset of the previously considered configurations are examined, to develop an understanding of the differences Comparison of 0.20c & 0.15c for boundary rotor conditions During a single revolution of the rotor, a blade section typically experiences a variation in AOA value and Mach number. Specifically, high AOA values couple with low Mach numbers and vice-versa. Figure 2.42a shows Mach number and AOA value combinations selected for CFD analysis, based on the result presented in Figure 2.42b. Both of these figures were created by Chris Duling for his Master of Science thesis [145]. The red stars denote the combinations considered in this section. The combinations are also found in table 2.6.

111 83 (a) AOA values and Mach numbers selected for a CFD study by [145] (b) AOA values and Mach numbers experienced by UH-60 rotor at an advanced ratio of 0.33 by [145] Figure 2.42: Rotor boundary AOA values and Mach numbers, red stars denote values considered in this section [145] The rotor blade experiences the highest Mach number on the advancing side, accompanied with low AOA values. From figure 2.42b, the AOA values at the tip are negative, due to blade twist. At both the front and rear of the rotor disk the blades experience a mix of moderate AOA values and Mach numbers. On the retreating side, the Mach number is low and the AOA value is correspondingly high. Figure 2.42b helps to explain why rotor stall occurs on the retreating side. The selected points Table 2.6: Mach number and AOA values forming the rotor blade boundary AOA Mach Number of operation are good choices for comparing between the 0.2c and 0.15c tabs. Figures 2.43a and b simply present the change in lift and moment coefficient with tab deflection, respectively, for both tab lengths. In general, the magnitude of the slope of the line for the 0.15c case is slightly lower than that for the 0.2c case. Which implies that a slightly larger would be required with the 0.15c tab to generate the same lift and moment increment. When comparing 0.15c and 0.2c aerodynamic coefficients, they are non-dimensionalized to the same baseline chord length. Table 2.7 presents the incremental aerodynamic coefficients for = ±6. The incremental moment coefficient reduces by a smaller amount with tab

112 84 Table 2.7: Lift and moment increments for both 0.20c and 0.15c tabs for various Mach number and AOA values dc l dc m Ma AOA = 6 = 6 = 6 = c 0.15c 0.20c 0.15c 0.20c 0.15c 0.20c 0.15c length than the incremental lift coefficient, as can be observed in figure 2.43b. As with the lift increment, the moment increment of both tab lengths follow similar trends, looking at table 2.7. Also apparent is the degree of effectiveness loss about 10% to 20% in increment in the moment coefficient of the smaller tab. Figures 2.43c and d present the ratio of the aerodynamic coefficients for the 0.2c tab s over the 0.15 tab. In figure 2.43c the ratio of the longer tab over the short tab for increment in lift is presented. Although both systems are nondimensionalized by the total chord both airfoil and tab extension the longer tab makes up a great portion of the overall airfoil, 1 (0.1 6) versus 3 (0.1304). Therefore, if the 6 23 change was only due to the change in the amount of the airfoil that is active tab, the lift ratio expected would be 23 (1.2778). The average ratio falls below this 18 number, but as can be seen from the figure individual configurations differ widely. For a Mach number of 0.8 (θ = 2 ), the ratio of lift coefficients remains close to constant as the tab deforms. The average is 1.16 with a low standard deviation of This average is below the expected ratio based on the tab ratio to entire airfoil length. At a lower Mach number of 0.7 (θ = 4 ), a large variance with tab deflection exists. For negative tab deflections, a large difference between the two tab is predicted. But, at positive tab deflections, the ratio is much smaller. On average, the ratio is The standard deviation is over an order of magnitude higher than at Mach The results for the Mach number 0.6 (θ = 6 ) are as widely spread as the previous Mach number. In this case the negative tab deflections have smaller ratios, with the positive deflections being larger upwards of 1.5. The average value of the ratio is 1.27 with a standard deviation of The lowest Mach number, 0.3 (θ = 8 ), shows a similar pattern to the previous.

113 85 Namely, the ratio being smaller for the negative tab deflections and reverse for the positive tab deflections. The major difference is a lower average of 1.18 and standard deviation of The increment in moment coefficient for both the 0.2c tab and 0.15c tab is in figure 2.43d. As can be seen from the figure, the ratio of the two moment coefficients is smaller, that is, the shorter tab loses less moment increment than lift increment. The Mach number 0.8 has a higher average ratio of 1.17 when compared to the incremental lift coefficient ratio and a higher standard deviation of Considering both charts, it seems that the moment results show the same trends as lift. At a Mach number of 0.7, this trend is also apparent. The average value is 1.41 with a standard deviation of Unlike the higher Mach number, the mean for the moment increment is lower than the lift at The standard deviation is also lower at At a Mach number of 6, both the lift and moment increments show large variation amongst the different tab deflections. For the moment increments, the average ratio value is, 1.19, indicating this condition experiences the largest average reduction in moment increment amongst the four conditions. The standard deviation is also a high 0.1 (compared to the other moment increments). The lowest Mach number Ma=0.3 is similar in spread to the lift increment, but with a lower average The standard deviation is In general the moment increment has a similar or lower average reduction value with tab deflection. The ultimate conclusion is that with a reduction in tab length, the moment increment shows similar or lower reduction compared to the lift increment. On average, the 0.2c tab has a lift increment of the 0.15c tab, with a standard deviation of The increment in moment of the 0.2c tab is of the 0.15c tab, with a standard deviation of Not only is the average moment coefficient reduction slightly smaller, the variation is also smaller (ie when comparing coefficients of variation).

114 86 dc l α= 2 o, Ma=0.8 α=4 o, Ma=0.7 α=6 o, Ma=0.6 α=8 o, Ma=0.3 dc m α= 2 o, Ma=0.8 α=4 o, Ma=0.7 α=6 o, Ma=0.6 α=8 o, Ma= (a) dc l,0.20c (black line) and dc l,0.15c (grey line) versus (b) dc m,0.20c (black line) and dc m,0.15c (grey line) versus dc l,0.20 /dc l, α= 2 o, Ma=0.8 α=4 o, Ma=0.7 α=6 o, Ma=0.6 α=8 o, Ma=0.3 dc m,0.20 /dc m, α= 2 o, Ma=0.8 α=4 o, Ma=0.7 α=6 o, Ma=0.6 α=8 o, Ma= (c) dc l,0.20c /dc l,0.15c versus (d) dc m,0.20c /dc m,0.15c versus Figure 2.43: Comparison of tab aerodynamic effectiveness between 0.20c and 0.15c 2.4 Comparison of SC-1094R8 With and Without Tab Extension For the results in this chapter, a tab is added onto an existing airfoil, providing an area for the actuators to attach. An important question is what does the addition of the tab due to the airfoil s characteristics compared to the standard airfoil? Since most airfoils do not have a tab extension at the trailing edge, the natural expectation is a decrease in overall performance. According to the US Army Helicopter Design DATCOM [146] there are two reasons a trailing edge tab is added. First, this addition of material is required for rotor blade structural

115 87 integrity. Second, the tabs are often deflected or reflexed to adjust the airfoil section s pitching moment. According to the US Army DATCOM [146], a trailing edge tab is 5% to 10% of the chord and spans the entire rotor blade. This is in contrast to trim tabs, which are applied only over a short span. Trim tabs are bendable and used to adjust blade tracking. The Sikorsky S-76 is the example of a helicopter with airfoils SC1095 and SC1094 R8 with tabs added, whereas the UH-60 Blackhawk uses the same tabs, but without the tabs [147]. In the case of the S-76, the tab is 0.03c in chord length and is reflexed 3, to reduce pitching moment [147]. The US Army DATCOM [146] provides the following guidelines regarding trailing edge tabs: A deflected trailing edge tab will change the zero-lift pitching moments An upward deflected trailing edge tab decreases airfoil camber and reduces maximum lift The zero-lift angle of attack is changed with the addition of a tab A upward deflected trailing edge tab shifts the aerodynamic center aft A deflected trailing edge tab changes the location of the center of pressure For tab deflections of 3, the drag increase is negligible In this section, the performance of both a tabbed and untabbed SC1094 R8 is compared via the aerodynamic coefficients, using the total chord as the normalizing length. That is both airfoils are assumed to have the same total length. The airfoil with tab is scaled in both width and height as has been used in all aerodynamic coefficients regarding the airfoil with tab. The lift coefficients for both airfoils are plotted in figure 2.44a. Several AOA values and Mach numbers are plotted. The AOA values range from 2 to 8 and the Mach numbers are 0.4, 0.6, and 0.8. The amended airfoil is plotted in black, dashed lines whereas the standard airfoil is plotted in grey, solid lines. At the low Mach number, the regular airfoil has a slightly larger lift coefficient throughout the AOA range. At α = 16 this difference is less than 10%. The way the tab emanates from the trailing edge, parallel to the chord line, results in a reduction in camber

116 88 at the rear, accounting for the decrease in lift. At the moderate Mach number, the tab decreases the lift for AOA values below 8, at and above which the two have the same lift coefficient. At the highest Mach number, just the airfoil has greater lift for AOA values below 4. Above this value the airfoil-tab combination has a larger lift coefficient by 12%. In general, the amended airfoil exhibits a reduction in lift compared to just the airfoil. However, at higher Mach numbers and AOA values, the tab and airfoil combination provides a little more lift. Figure 2.45a-c presents the drag polars for Mach numbers 0.4, 0.6, and 0.8. This figure adds experimental data from Noonan and Bingham [148]. This data was acquired at NASA Langley s 6 in by 28 in Transonic Wind Tunnel [148]. The SC1094 R8 airfoil airfoil used in this experiment has a 0.03c tab added, with 3 of reflex. Testing was conducted on two length scales (model and full-scale) and at Mach numbers up to 0.88 [148]. Considering the results at Mach 0.4, figure 2.45a, the drag polar shows that the airfoil without the tab has a greater lift capability than the tabbed airfoil. The difference becomes apparent at C l values of 0.9 and greater. The experimental data show a departure from both of the CFD results at a lift coefficient of 0.4. The experimental data experience the drag increases at high lift coefficients compared to the CFD Results. At low lift coefficients, all three lines converge. At Mach 0.6, figure 2.45b, all three lines are closer overall. At lift coefficients of 0.4 and lower, the three lines are overlapping. The CFD standard airfoil results are located just inside the experimental results. The tabbed airfoil is located further inside of the standard CFD airfoil results. Again, the tabbed airfoil has lower lift capability than the standard airfoil. Likewise, the tabbed airfoil has a drag penalty compared to the standard airfoil at high lift coefficients. At Mach 0.8, figure 2.45c, the experimental data is only available for a small range of C l values. In this C l range, 0 to 0.6, the CFD results are similar or exhibit greater drag for a given lift. At high lift coefficients (which are unlikely from a practical standpoint) the tabbed airfoil is predicted to have greater lift capability, or lower drag for a given lift. Overall, thedragpolardatashowsthattheadditionofthetabreducesthemaximum lift capability, one of the consequences outlined by the US Army DATCOM. Also, the experimental data show that the CFD results are typically conservative

117 89 (a) C l (b) C m (c) C d Figure 2.44: Comparison of aerodynamic coefficients for standard SC-1094R8 and with 0.2c tab (SC-1094R8 results from [145])

118 90 (a) Ma=0.4, Re= (b) Ma=0.6, Re= (c) Ma=0.8, Re= Figure 2.45: Comparison of aerodynamic coefficients for standard SC-1094R8 (both numerical and experimental), 0.2c tab (SC-1094R8 computational results from [145] and experimental results from [148])

119 91 and are not predicting unreasonable values. At low lift coefficients, the data and the CFD results compare particularly well. At these low lift values, the difference between tabbed and untabbed is small. Comparing the moment coefficients Figure 2.44b great differences between theairfoilwithandwithouttabareevident. AtthelowMachnumber,thestandard airfoil has low moment coefficients, nearly constant with AOA. There is a slight trend to increase, approaching zero at α = 10. The addition of the tab changes these trends. At the low end of the AOA range, the moment coefficient is just below zero The coefficient increases with increasing AOA, becoming larger in magnitude than the plain airfoil, reaching At the middle Mach number, the regular airfoil shows greater variation than the lower Mach number. Below an AOA value of 6 the middle Mach number is above or equal to the lower. Above this AOA value, the moment coefficient decreases to at α = 10. The modified airfoil at Mach 0.6 matches its lower Mach number coefficient of moment at low AOA values up to 4. Above that AOA value, the coefficient of moment decreases at a steeper slope, dropping to at α = 10. At the highest Mach number, the airfoil only mostly decreases in moment coefficient, remaining below zero regardless of AOA value. Also, the moment now decreases with AOA, from to This is a change in moment less than that values seen for the airfoil-tab combination. At the high Mach number, the modified airfoil starts at a similar moment of coefficient as the lower Mach numbers (-0.014), but decreases at a greater rate. At α = 10 the moment coefficient is At low Mach numbers and AOA values, the addition of the tab increases the moment coefficient. This is expected as the tab comes out of the trailing edge with the slope of the chord line, not the camber line. This decreases the camber of the airfoil, resulting in a more positive pitching moment. At high Mach numbers and AOA values, the addition of the tab is associated with nose down pitching moments larger than the standard airfoil. These larger moment coefficients are not an improvement in airfoil performance. The reason being that higher moments result in larger control loads, increased blade torsion, and increased vibrations [2]. However, it should be noted that changing the angle of incidence of the tab with respect to the chord line would also change the moment coefficient. It might be possible to select an incidence angle with reduced moment coefficient.

120 92 The drag coefficients for the configurations with and without the tab are best compared together at a particular Mach number, figure 2.44c, as they are very similar. Mach 0.4 has the lowest drag, with a noticeable drag increase between α = 4 and 6. The drag of both configurations are about the same. At Mach 0.6, the two configurations show an increase in drag with AOA above α = 2. At this Mach number, the drag coefficient increases to a larger value than at the lower Mach number. Again, there is little difference between the two configurations, with the tab configuration having a little larger drag coefficient. At the highest Mach number, the drag is shifted upwards at the low AOA values and increases with AOA at α = 0. Both configurations increase at a rate similar to that of the middle Mach number. At α = 0, the airfoil-tab combination has lower drag than the airfoil alone. However, at the higher Mach numbers above α = 4 the airfoil-tab combination has slightly higher drag. Overall, the difference in drag is small and both airfoil configurations behave the same. The addition of the tab changes the lift by small amounts, either decreasing or sometimes increasing, depending on the flow conditions. The moment coefficient is impacted the most, with the addition of the tab decreasing the moment coefficient to around 0, to greater than Compared to just the airfoil, the tab results in a larger magnitude of moment. The difference in drag with or without the tab is small. In general, the addition of the tab does not enhance the airfoil s properties, but with a different tab incidence, the increase in moment loads might be reduced.

121 Chapter 3 Design and Analysis of Tab The structural design and layout of the tab is critical. The aerodynamic analysis indicates that deflecting the tab provides an effective means to change the lift and moment coefficients. The aerodynamic authority of the tab is comparable to a similarly sized trailing edge flap. The tab needs to meet several requirements, leading to a challenging structural design. The requirements stem from various aspects of the operating environment as well spatial constraints. Active tab deflections of ±6 Passive tab deflections due to aerodynamic and inertial loads < 1 Operate in a rotating environment Minimize driving voltage Likewise, the tab deflection due to applied aerodynamic loads or inertial loads due to blade motion (flapping or pitching) should be minimized. These passive deflections (in that the actuator is not active) result in uncommanded changes to the airfoil section aerodynamic coefficients. Conversely, the tab deflection due to actuation should be sufficient to provide useful changes in section lift and moment coefficients and this should be realized at acceptable actuator weight and actuation powerrequirements. Atabdeflectionof±6 isthetargetdeflectionwithactuation, whereaspassivedeflectionsshouldremainbelow1. Thesegoalsprovidethesystem with authority at least 6 times any uncommanded motions. The actuation of the

122 94 Table 3.1: UH-60 and tab properties Property Value R m (26.83 ft) c m (1.73 ft) Ω 27 rad/s (4.3 Hz) ǫ 0.2c R tab 0.2R Span Location 0.65R 0.85R tab is anticipated to be in the 3/rev to 5/rev frequency range, as this is the typical frequency range for reducing noise and vibration. Also, the system must operate subjected to the rotating environment of the rotor blade. Just like the aerodynamic study, the UH-60 provides the basis for the tab s dimensions and operating environment. The properties of the UH-60 and the tab are in table 3.1. The commercial finite element analysis software ANSYS R provides the means to analyze the tab motions. The element type used is SHELL281. This shell element has 8 nodes, one in each corner and one at each wall midpoint [149]. Each node has 6 degrees-of-freedom: 3 translational and 3 rotational. The element uses the first-order shear deformation theory, Mindlin-Reissner shell theory [149]. The MFC s piezoelectric property is modeled as a thermal strain. These shell elements allow for the creation of a composite layering, allowing for sandwich layer construction. The various components making up the tab shim and MFC actuators are all modeled as a single layer of a shell element. For example, a simple bimorph would consist of three layers: the bottom MFC actuator, the shim, and the upper MFC actuator. The shell elements have the capability of modeling elastic coupling resulting from the use of orthotropic materials (such as the MFC). The tab is analyzed using linear harmonic analysis. When analyzing the actuation authority, the actuator voltage is the sinusoidal input and the output is the tab response. For passive loads, associated with blade motion, a base excitation is in the sinusoidal input and again the output is the tab response. For aerodynamic loading a static analysis is used with the input being a pressure force across the surface.

123 95 Figure 3.1: Basic actuation concept, using two MFC actuators sandwiching a thin shim plate 3.1 Basic Analysis The initial concept, shown in figure 3.1, consists of a thin shim plate sandwiched by MFC actuators. The actuators are driven at opposite voltages, extending on one side and contracting on the other. This results in a bending of the tab. The combined stiffness of the shim and the MFCs resists deflection under aerodynamic and inertial loads, and needs to be overcome during actuation Simple analysis Using simple analysis, certain fundamental trends associated with the system can be determined. First to be considered is the active tip deflection of the tab. The analysis assumes that the plate behaves independently of span location and a beam approximation is appropriate. Also, the MFC is assumed to be of infinitesimal thickness and able to obtain a given strain, regardless of the inner layers. This assumption relates the actuator induced curvature of the tab to the axial straining of the actuator, which is assumed independent of the flexural stiffness of the tab. As a result of this assumptions, this analysis will over predict tab tip deflection, serving as an upper limit. This is because the inner layer will resist bending and reduce the achievable strain of the MFC compared to the free strain. The curvature of the beam κ can be related to the strain on the top or bottom of the beam, as in equation 3.1. Λ is the free strain of the MFC and t b is the distance between the two MFCs (that is, thickness of the shim). κ = d2 w dx 2 = 2Λ/t b (3.1) ( ) Λǫ = tan 1 t b (3.2)

124 96 Assuming a cantilever boundary condition, the tab deflection can be determined. Equation 3.2 shows that the tip displacement is proportional to 1/t b (for small values of ), the closer the two MFCs, the greater deflection. This conclusion has also been presented by Grohmann et al. [129]. This result indicates the greatest deflection can be achieved by bringing the MFCs together. However, the flapping of the blade and applied aerodynamic loads require a certain level of stiffness. The bending stiffness of a beam (per unit width) is Et 3 b /12, meaning the stiffness is proportional to t 3 b. The flapping inertial force is proportional β 2 t b ρ, where ρ is the mass per unit length and width, and β is the flapping angle. Since stiffness is proportional to thickness cubed, it is possible to drive the passive deflection due to flapping to zero, as the stiffness increases with thickness at a rate greater than inertial loading. There is a trade-off between maximum active tab deflection and minimum passive tab deflection. For a given deflection, there is a maximum actuator separation distance, above which inadequate deflection is obtained. If a given tab has its thickness double, the actuator is now required to strain twice as much to maintain the same tip deflection. It is similar to a beam having its thickness doubled will also have twice the strain on the surface if deflected to the same degree. This maximum separation distance is related to the strain capability of the MFC. Piezoelectric materials have an approximately linear force-strain diagram (for a given applied voltage), shown in figure 3.2. At a given voltage, the actuator is defined by two parameters: free strain and block force. These two parameters define the strain and force the actuator is able to produce. Point a represents a case of large strain, but the force the actuator is able to produce is low. Likewise, to generate a large force, strain is limited. Therefore, in order to obtain the free strain, for deflecting a tab, the resistance to this bending must be low (technically zero). This is in contrast to hydraulic or screw-based linear actuators, which generate a force for a given stroke. If drawn, the force-stroke (strain) line is horizontal. These actuators can also be thought of as being very stiff compared to the block force.

125 97 Figure 3.2: The force-strain relationship for a piezoelectric material (eg MFC) Analysis using Euler-Bernoulli beam theory In order to get a conceptual grasp on how the various design variables impact tab performance, a simple constant thickness cantilevered beam is considered. This system has a shim forming the inner beam layer. All properties associated with this base beam are denoted with the subscript b. Sandwiching the inner layer are the active elements, in this case generic piezoelectric crystals of unspecified properties. The active layer (crystal) properties are denoted with the subscript c. This notation follows from early work in bimorph benders [5]. The tab experiences three different types of loading: aerodynamic, dynamic, and active actuation (Figure 3.3). The aerodynamic loading is resisted by the structural stiffness of the tab and other tab properties such as material densities, slight variation in thickness, and actuator performance do not change the loading, assuming no deformation. Of the dynamic motions of the blade, flapping primarily causes the tab to deform. This current analysis does not consider the centrifugal force, but it is considered in subsequent analysis. Both the tab s stiffness and mass density distribution influence the amount of displacement. Lastly, the effectiveness of the actuators to actively deform the tab depends both on the overall tab stiffness and density, but also the cross sectional geometry, shim material properties relative to the actuators, and the capability of the actuators themselves. When considering the three loadings together, a natural order presents itself. This order allows the designer to satisfy performance requirements one at a time, rather then simultaneously. The aerodynamic loading defines a minimum stiffness for a given displacement resulting from the pressure distribution. Dynamic flapping prescribes

126 98 Figure 3.3: Illustration of aerodynamic loading, dynamic (inertial) loading, and active actuation forces experienced by the tab a maximum density, based on the minimum required stiffness. As previously mentioned, the density of the tab does not affect the tab s response to aerodynamic loading. Lastly the desired active displacement provides the material properties and the thicknesses of the actuators and shim, based on the prescribed stiffness and density. These properties include material stiffnesses, layer thicknesses, and required actuator free strain. The number of decision variables exceed the objectives, so it is possible multiple solutions exist. A representative aerodynamic loading at a Mach number of 0.6 and an AoA valueof8 isapplied thetabisassumedtohavenodisplacement. Thisloadcomes fromtheturnsresultsruninthepreviouschapterandisshowninfigure3.4. The load is applied statically and is assumed to be constant in the span direction. The tip displacement and the flexural stiffness per unit length is plotted in figure 3.5a. The log-log plot transforms the relation between tip displacement and flexural stiffness to a linear one. This figure provides the designer with the flexural stiffness required to limit the aerodynamic deflection to an acceptable level. The material properties and thickness of the tab are not prescribed (within the major constraint of constant chordwise properties). Once the maximum permissible aerodynamic deflection is established, the flexural stiffness is likewise defined for this particular aerodynamic distribution. Considering the next loading condition, dynamic flapping of the blade, figure 3.5b provides similar information as the previous figure. The flapping amplitude is assumed to be ±4. This is based on the blade flapping motion at 0.7R for a UH-60 at an advanced ratio of 0.3. A flapping of ±4 at 0.74R is converted into a vertical motion of ±43 cm. For comparison, the vertical motion due to blade

127 99 Figure 3.4: The pressure coefficient on the rear of the airfoil and tab at Mach=0.6 and an angle of attack of 8 as predicted by TURNS pitching is only ±6.9 cm for blade pitching of ±10. For this reason, the focus will be on blade flapping motion. This motion is applied to the base of the beam and the motion of the tip is calculated and presented in figure 3.5b. Again, a log-log plot is used. Now tip displacement due to blade flapping is plotted versus the flexural stiffness per unit width over the mass per unit length. The mass per unit length was chosen, so that the tab thickness variable could remain unprescribed, that is depth is required to obtain volumetric mass density. As expected, increasing the density, or decreasing the flexural stiffness results in a system with a larger flapping response. As the flexural stiffness is adjusted to meet aerodynamic deflection requirements, use of this figure provides the designer with the maximum density of the system to ensure that tab motions due to blade flapping remain within constraints. The above paragraphs considered the passive response of the system. The performance of the actuator depends on both the relative material properties of the active materials and passive materials, as well as their thickness ratios. Equation 3.3 [5] defines τ, a variable that combines both of the above ratios, the thickness ratio (shim/crystal) and the axial stiffness ratio (shim/crystal). τ = 6(1+T) T 2 ψ bc +2(4+6T +3T 2 ),where T = t b t c and ψ bc = E bt b E c t c (3.3) τ ranges from no actuator (0) to all actuator (0.75). Figure 3.5c plots the relationship between a measure of tip displacement and τ. From the figure, maximum tip

128 δ θaero δ θflapping EI (Pa*m) unit width EI unit width /m unit length (a) Aerodynamic displacement versus flexural stiffness (b) Displacement due to flapping versus flexural stiffness to density ratio t c /Λ τ (c) Active displacement versus actuator composition Λ (µ Strain) t c (mm) 0.29 mm 0.34 mm (d) Required free strain to achieve static displacement of 8 (e) Actuator Young s modulus and density Figure 3.5: Design charts based on Euler-Bernoulli beam theory

129 101 displacement is achieved with having only the actuator (τ = 0.75) no shim, for a given actuator free strain and thickness. The figure also provides a constant relating free strain, actuator thickness, and tip displacement. Thickness and free strain are directly proportional, increasing the actuator thickness requires an increase in free strain to maintain the same tip displacement. This is also found in figure 3.5d, which plots the relationship between free strain and thickness for an actuator only (τ = 0.75) configuration for a static tip displacement of 8. As a guide, Smart Material Corporation s MFC patches have free strain values of 675 to 810 µ-strain [150]. This limits the maximum thickness to 0.29 mm to 0.34 mm (shown in figure 3.5d) for obtaining a static tip displacement of ±8. Although this value is larger that the goal of ±6, it was selected to provide a performance surplus. Figure 3.5e shows both the actuator material s Young s modulus and density (no shim), for a given thickness, required to limit aerodynamic and flapping displacements to 0.5 each. From this figure, using the MFC material properties in table 3.2, aerodynamic loading (limited by the 30 GPa Young s modulus of the actuator) requires a thickness of at least 0.55 mm. Using figure 3.5e, 30 GPa is first located on the y-axis, a line is drawn horizontal until the Young s modulus plot line is reached, upon which a vertical line is drawn to the x-axis and the required thickness is read. This thickness is the minimum thickness required to provide sufficient flexural stiffness with a 30 GPa actuator. The flapping motion requires a thickness no more than 0.28 mm. This value is determined in a similar fashion as with the Young s modulus, using a density of 5440 kg/m 3. This thickness value represents the maximum thickness to satisfy the mass per unit length requirement. From figure 3.5d, it is clear that the tab can be no thicker than 0.34 mm, otherwise the actuators lack the free strain to deflect the tab. If the thickness is set at 0.28 mm to satisfy density (also under 34 mm), the system is too soft to resist the aerodynamic loads (recall that thickness is 55 mm), but the larger thickness required to satisfy the flexural stiffness would resultinatabthathastoomuchmassandinsufficientactuatorauthoritytodeflect ±8. Another way to look at it, is to use figure 3.5d to drive the thickness. That is insist on the thickness that results in a ±8 deflection due to actuation. For a thickness of 0.34 mm, the stiffness and density of the hypothetical actuator are E c 128 GPa and ρ c 4492 kg/m 3, respectively. These values are obtained by

130 102 Table 3.2: MFC material properties ([150]) E 1 = GPa E 2 = GPa ν 12 = 0.31 ν 21 = 0.16 G 12 = GPa Λ = 0.9 µ-strain/v ρ MFC = 5440 kg/m 3 t = 0.3 mm finding 0.34 mm on the x-axis of figure 3.5e and drawing a vertical line to both the Young s modulus and density lines, where a vertical line is drawn to the y-axis where the stiffness and density can be read. This provides the designer with the material properties required, ultimately showing that a uniform thickness actuator design exceeds the MFC s material properties by a large margin. An initial analysis of a single layer tab was briefly examined, confirming the above conclusion. This analysis uses the finite element model to calculate the tab s 1/rev response due to blade flapping and actuation. This finite element analysis uses ANASYS R and the SHELL281 element. The tab spans 20% of the blade span and has a chord 20% of the basline value. The element size was selected to ensure at least ten elements in the chordwise direction. The flapping amplitude is also ±4. The input voltage is ±500V. The system is considered non-rotating initially, no centrifugal force considered. Tab deflection values for the 75% span location are in figure 3.6. The properties of the MFCs used are shown in table 3.2 and are commerically available products from the Smart Material Corporation. Three different shim materials are examined: aluminum, steel, and brass. The minimum thickness is governed by commercial material availability. The figure shows how the two objectives are in direct opposition. A beneficial change in one objective results in a negative change in the other objective, as predicted. Aluminum represents the best material selection, likely due to having the highest stiffness to density ratio. Having this ratio high reduces the passive deflection due to flapping. Regardless of material selection, none of the configurations are able to approach the desired objectives. It is evident that another configuration is required the next configuration considered is one with tapered actuators and a shim.

131 103 (a) (b) Figure 3.6: Both active deflection (a) and shim thickness (b) versus passive deflection of the tab with two MFCs sandwiching a shim, at 1/rev flapping and actuation, ǫ = 0.2, span location 0.75R 3.2 Layered-Actuation Tab The use of one pair of MFCs was unable to meet the design requirements. Considering multiple MFC layers and allowing their lengths to vary (tapering) was explored. The concentration of MFCs near the root and tapering towards the tip provides the greater stiffness where the moment is larger, while reducing it at other locations, improving both active performance and resistance to inertial and aerodynamic loads. Figure 3.8 shows the results of the analysis. The tapered tab has one to up to three active layers an inner, middle, and outer active layers (IAL, MAL, and OAL) sandwiching a shim. Regardless of the number of layers, the layer next to the shim is always referred to the inner layer and the second layer is always referred to the middle layer. The length of any layer is constrained to be less than or equal to that of the layer beneath. Both the middle and outer layers can have zero length; if the middle layer has zero length so does the upper layer. Zero length meaning that the layer does not exist. The lengths of the inner, middle, and outer layer are L 1, L 2, and L 3, respectively. This is shown schematically in figure 3.7.

132 104 L 3 L2 L 1 L Figure 3.7: The multilayered MFC tab c tab These results were generated using finite element analysis. A shell element SHELL281 was used in this model with the various actuator layers and shim being modeled as separate layers in a single shell element. The mesh was generated using a edge length one-fortieth the tab chord length. The applied voltage is ±500 V at a frequencyof1/revandtheshimisassumedtobealuminumwithathicknessof mm. Each FMC sheet has a thickness of 0.3 mm, so adding a layer (essentially two sheets, one top and one bottom) increases the overall thickness by 0.6 mm. The flapping motion is based on the vertical motion of a blade flapping ±4 at radius value 0.75R. This vertical motion is applied to the base of the tab. The analysis considers only a small spanwise section, one-tenth the tab chord length, rather than full span. The inner MFC in figure 3.8 spans 25%, 50%, 75%, and 100% of the entire tab chord length. The middle actuator is evalutated for lengths 0%, 25%, 50%, 75%, and 100% of the IAL. The outer actuator is evaluated with lengths 0%, 25%, 50%, 75%, and 100% of the MAL. o A total of 100 designs were evaluated. Considering the inner layer, very short IAL would have low active deflection, since only a small portion of the tab has induced curavture (that is actuation). Likewise, the short IAL adds little flexural stiffness, so passive deflections would also be high. The results plotted in figure 3.8a support the intutive statements. The blue markers all have an IAL length 0.25L and have both the lowest active deflections and some of the highest passive deflections. A longer IAL (light blue) improves the design in terms of both objectives. A further increase in length, represented by the green makers, again improves performance. The improvement is by a smaller degree than for the previous increase in the IAL length. Recall that the x-axis parameter is to be minimzed, the smaller passive deflection is desierable.

133 105 Whereas the y-axis parameter is to be maximized, the greatest active deflection is the goal. With this in mind, the nondominated set is close to the y-axis and far from the x-axis. In this figure, to be a member of the nondominated set, the marker must have no other markers above or to the left of it. For example, all of the blue markers fail this, whereas many of the orange markers pass this test and are members of the nondominated set. The turquise markers are associated with the longest IAL. Most of these configurations have inferior performance, compared to the 0.75L IAL length. This occurs for two reasons. First, the active layer is near the tip, while adding curvature, produces less of a displacement increase than curvature at the root. Second, the MFC is denser than the shim and adding it to the tip exacerbates the tab s response to blade flapping motion. Also, considering loading due to flapping motion, the tip does not require the flexural stiffness near the root end, as the bending moment goes to zero at the tip. RecallthatthemiddleMFCislimitedbythelengthoftheinnerMFC.Also, the expectation is that this layer will be shorter than the inner layer. By considering figure 3.8b, one observes the general trend that a longer MAL reduces both passive and active displacement. Longer MAL are associated with both low active and passive deflections, with shorter MALs having larger active and passive deflections. A long MAL prevents the system from actively deforming stiffening the system. As the MAL approaches the tip, the decrease in flapping response reduces. In a few cases the orange markers near a passive deflection of 2 increase in passive response while continuing to decrease in active response. This is the degradation of both objectives! However, with the middle layer too short, the response to flapping is large. The OAL length is presented in figures 3.8c & d. The first figure plots L 3 /L and the second figure plots L 3 /L 2. The latter plot more clearly shows how the relative length of the OAL changes. Each IAL length forms a line of markers in figure 3.8a. In the discussion of the MAL, it was noted that these lines have the longer MAL near the x-axis, decreasing in length as the active deflection increases. However, the MAL had several markers with the same length in a row, with a row being defined as the set of markers wit the same IAL. In each row (identical IAL length), the OAL length varies from longest (lowest active deflection) to shortest (highest active deflection). Considering just the actual length of L 3, this pattern

134 Active Deflection (deg.) L 1 /L Active Deflection (deg.) L 2 /L Passive Deflection (deg.) (a) Inner MFC, IAL Passive Deflection (deg.) (b) Middle MFC, MAL 0 Active Deflection (deg.) Passive Deflection (deg.) (c) Outer MFC, OAL L 3 /L Active Deflection (deg.) Passive Deflection (deg.) (d) Outer MFC, OAL L 3 /L 2 Figure 3.8: Active and passive 1/rev tab displacements with various MFC layering for ǫ = 0.2, span location 0.75R, ±500 V is obscured due to the length of the outer layer being dependent on the middle layer s length. The best design with an active deflection of 3 has a passive deflection of 1.9. The design for this configuration is: IAL=0.75/L, MAL=0.375/L, and OAL=0.187/L, where L is the tab chord length (10.5 cm). This configuration is drawn to scale in length (not thickness) in figure 3.9. The design has a thick root, containing all three actuator layers. At a distance just over a third of the length of the tab, the system tapers to only a single active layer. The last quarter of the tab is shim material only.

135 107 OAL MAL IAL Shim 0.187/L 0.375/L 0.75/L L Figure 3.9: The best 0.2C design with an active deflection of 3 and a passive deflection of 1.7 Given the active and passive deflection combinations, further improvements will be required. The MFC material itself is able to achieve a greater strain with positive voltage, up to 1500V, whereas the negative voltage maximum is -500V. Although high voltage going through the slip ring is undesirable, it may be unavoidable. Changing the length of the tab has an effect on tab deflection, both passive and active. Considering equation 3.2, the active deflection is proportional to the length. So a reduction in length will reduce the tab deflection for a given MFC strain. In all cases, the first natural frequency of the tab is above the actuation frequency. The inertial load is similar to a uniformly applied load, whose effect on tip displacement proportional to L 4. Converting to, the inertial effect on the tab is practically proportional to L 3, which has been numerically verified. Considering a tab length of 0.15c, is expected to reduce the active displacement by about 75% relative to the 0.2c tab, and reduce the passive deflection by 42%. The reduced tab length will affect a change in aerodynamic performance which is reported in section Several important AOA values and Mach numbers will be evalutated to get an estimate on the aerodynamic impact of the tab length change. Greater tab deflections are required for the shorter tab as reduction in aerodynamic performance is around 85% and is discussed in Section 3.10.

136 108 Table 3.3: Plain weave carbon fiber composite material properties E 1 = 64.1 GPa ν 12 = 0.04 ρ ply = 1445 kg/m 3 E 2 = 64.1 GPa G 12 = 4.83 GPa t ply = mm c tab The use of a shorter tab will reduce the tip deflection due to blade flapping motion. In addition to using a shorter tab, the use of a composite shim (rather than an aluminum shim) is also considered. The material properties for the plain weave carbon fiber material are given in table 3.3. This shim has a greater stiffness to density ratio and is thinner. For design purposes, a vast number of designs were analyzed. This allowed for an enumeration of the design space. The IAL varied in chordwise length from 10% to 100% of the tab chordwise length by 10% incremenets. The MAL varied in chordwise length from 0% to 100% of the IAL chordwise length by 10% incremenets. Lastly, the OAL varied in chordwise length from 0% to 100% of the MAL chordwise length by 10% incremenets. Also, the number of composite plies in the shim varied amongst one to three plies. The total number of design evaluated was 3,630. In order to visualize the data and because the 0.2c tab was considered in greater detail, only the non-dominate or Pareto front solutions are presented and considered. The objectives were active displacement and flapping displacement, which results in a non-dominated set that is a planar curve. The design variables are the length of the inner, middle, and outer active layers (IAL, MAL, and OAL) respectively and the number of shim plies. These layers are shown schematically in figure 3.7. Before considering the shorter tab in detail, the two tab sizes are compared. Both tab lengths are being actuated with the same voltage, ±1000 V (which produces the same response as 500 V and V). The only other difference besides length, is the 0.2c tab has an aluminum shim and the 0.15c tab has a composite shim. Figure 3.10 illustrates the superior performance of the short tab in achieving small flapping displacement. The longer tab has no designs with flapping displacements less than 1.5. However, the longer tab is able to achieve larger

137 109 Active Displacement (deg.) c 0.2c Flapping Displacement (deg.) Figure 3.10: A comparison of the 0.2c tab with an aluminum shim with the 0.15c tab with a composite shim, span location 0.75R, ±1000 V active displacement values, if displacement due to blade flapping is not a concern. Figure 3.11 contains four plots. In each graph, flapping displacement is on the x-axis and active displacement is on the y-axis. The colors represent the values of the four design variables. Therefore, considering all four plots allows one to select a configuration knowing both the design and performance. Considering the shape of the curve, recall the goal is for the flapping displacement to be minimized while the active displacement is maximized. Due to the stiffness required to minimize flapping displacement, active displacement tends to be small as well. However a small increase in passive displacement is accompanied by a substantially larger increase in active displacement. From 4 to 5 active displacement, the curve begins to flatten out, slowly at first. The slope decreases more between an active displacement of 5 to 6. Just above 6 of active displacement, the passive displacement exceeds 1. Four different designs, all located on the Pareto front will examine, in increasing active and passive displacements. The first design has a passive deflection of 0.25 and an active displacement of 4.2. This design has active lengths of L 1 /L = 0.8, L 2 /L = 0.48, and L 3 /L = This design has a single ply shim, in fact looking at figure 3.11, all designs with an active displacement 3.6 or more have only a single-ply shim. From the figures 3.11a-b, several designs exist around the above design on the Pareto front how do these design differ? Figure 3.11a indicates the designs all have the same IAL, 0.8/L. The length of the MAL is also the same,

138 which is denoted with red in figure 3.11b. Only the OAL differs for nearby designs. The OAL length varies from 0.43/L for an active displacement of 4 to 0.24/L for an active displacement of 4.3. Shortening the OAL allows for greater active displacement, reducing in length by almost one-half for a small performance gain. If a larger passive displacement of 0.49 is permissible, an active displacement of 5.23 can be obtained. This design has active lengths of L 1 /L = 0.7, L 2 /L = 0.28, and L 3 /L = 0. Although difficult to see in figure 3.11a, the nearby designs have IAL lengths of both 0.7/L and 0.8/L. The length of the middle actuator measures 0.33/L for the configurations with the longer inner actuator. Designs with shorter inner actuator lengths also have shorter middle actuator lengths, 0.21/L or 0.28/L. The outer actuator varies between 0 (no actuator) up to 0.11/L in length. The results reveal that nearby designs offer similar performance, but have slightly different configurations. This fact allows a designer some flexibility in selecting the configuration, while maintaining a similar level of performance and remaining on the Pareto front. If a 1 passive displacement is tolerable, than an active displacement around 6.3 is achievable. The designs clustered in this region all have the same inner and middle actuator lengths, which can be observed in figures 3.11a and b. The IAL length is 0.7/L and the MAL length is 0.07/L. The OAL is small, under 5% of the total tab length, varying from 0 to 0.035/L. The shorter the OAL length, the greater active and passive displacement of that design. The last range considered are configurations with active displacements approaching to 6.9. These designs have passive displacements around 1.6. Figure 3.11a shows the designs clustered in this range all have long IAL lengths 90% of the tab chord length. Likewise, the MAL lengths are also all the same, 0.09/L. These designs are nearly all inner actuator, for greater displacemnts the design is approaching a simple bimorph. In fact, the design with the greatest active (and passive) tip displacement is a simple bimorph (figures 3.11a-c. For the designs approaching an active displacement of 7, the outer most layer is negligable, measuring at most 3.6% of the tab chord length.

139 111 Active Displacement (deg.) Flapping Displacement (deg.) (a) Inner MFC, IAL L 1 /L Active Displacement (deg.) Flapping Displacement (deg.) (b) Middle MFC, MAL L 2 /L Active Displacement (deg.) L 3 /L Active Displacement (deg.) Number of Shim plies Flapping Displacement (deg.) (c) Outer MFC, OAL Flapping Displacement (deg.) (d) Number of Shim Plies Figure 3.11: Active (4/rev) and flapping (1/rev) tab displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000 V Nondominated set: flapping, aerodynamics, and active displacement The previous section considered only two objectives: active displacement and displacement due to blade flapping. In this section, a third objective is added, displacement due to aerodynamic loading. The aerodynamic loading takes the pressure distribution for the airfoil at Mach 0.6 and an AOA value of 8 shown in figure 3.12 (see Section for details). Any change in pressure distribution due totabdeflectionisnottakenintoaccount, thisisnotacoupledapproach. Allthree objectives are calculated individually, no combination of loading is considered. The

140 112 Figure 3.12: The pressure coefficient on the rear of the airfoil and tab(blunt tip see Section 3.4.2) at Mach=0.6 and an angle of attack of 8 addition of a third objective transforms the nondominated set from a line to a surface. Instead of trying to plot in three-dimensions, three two-dimensional plots are used. Figures 3.13a-c collectively plot the nondominated set. Figure 3.13a has the same x- and y-axes as figure 3.11 and looks similar. The Pareto front of figure 3.11 is contained within the plot, with addition configurations with lower aerodynamic deflections. In the region between 5 to 6 of active displacement, the designs behind the original Pareto front, that is design with greater flapping displacement, clearly have lower aerodynamic displacements. Figure 3.13b has flapping displacement on the x-axis and aerodynamic displacement on the y-axis, with the active displacement denoting the marker color. This figure shows that a penalty is paid when trying to reduce the aerodynamic response. The figure illustrates that the chordwise pressure distribution at Mach 0.6 and an AOA value of 8 deforms the beam to a greater extent than the flapping. Figure 3.13c has aerodynamic displacement on the x-axis and active displacement on the y-axis, with flapping displacement denoting the flapping displacement. This figure directly shows how the stiffness required to resist aerodynamic deformation hampers active displacement. Figure 3.14a-d contain the design variables for the nondominated set, in the form of figure To understand how the designs relate to performance, three aerodynamic displacements are examined: 0.5, 1, and 1.5. If a displacement due to aerodynamic loading of 0.5 is the maximum tolerable value, than the

141 Active Displacement (deg.) Aero Displacement (deg.) Aero Displacement (deg.) Active Displacement (deg.) Flapping Displacement (deg.) (a) Flapping Displacement (deg.) (b) 8 Active Displacement (deg.) Aero Displacement (deg.) (c) Flapping Displacement (deg.) Figure 3.13: Active (4/rev), flapping (1/rev), and aerodynamic (static) tab displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000 V maximum active displacement is 2.5, of all the designs considered. The flapping induced motion is This design has a three-ply shim, L 1 /1 = 1, L 2 /L = 0.8, and L 3 /L = This is a rather stiff design, with long active layers. If the tolerable aerodynamic displacements are around 1 to 1.1, larger active displacement, exceeding 3.5 are practical. For a design with a single-ply shim, L 1 /1 = 1, L 2 /L = 0.8, and L 3 /L = 0.48 active and passive displacements of 3.56 and 0.35 are possible. With a slightly softer design having a single-ply shim, L 1 /1 = 1, L 2 /L = 0.7, and L 3 /L = 0.49, a slightly greater active displacement of 3.69 can be achieved. If 1.5 of deflection due to aerodynamic loading is acceptable, than

142 114 Active Displacement (deg.) Flapping Displacement (deg.) (a) L 1 /L Active Displacement (deg.) Flapping Displacement (deg.) (b) L 2 /L 8 8 Active Displacement (deg.) L 3 /L Active Displacement (deg.) Shim Plies Flapping Displacement (deg.) (c) Flapping Displacement (deg.) (d) Figure 3.14: Length of the active layers and number of shim plies corresponding to figure 3.13a an active displacement over 4.19 can be obtained. This design configuration has a single shim, L 1 /1 = 1, L 2 /L = 0.6, and L 3 /L = Spanwise Actuator Variation Tab Design All of the previous analysis assumed a uniform system in the spanwise direction, that is full-span actuation. A configuration with a spanwise variation creates additional design variables and the possibility of improved performance. The rational behind the design was that full spanwise actuators might be unnecessary. They add significant mass (recall they are lead based), increasing the system s

143 115 Actuator No actuator Figure 3.15: Schematic for the spanwise variation concept 8 Active Displacement (deg.) Spanwise Variation Constant Spanwise Flapping Displacement (deg.) Figure 3.16: Comparison between designs with spanwise variation and designs uniform spanwise response to blade flapping. The interspacing of actuator and nonactuator regions was proposed as in figure This figure shows the unit cell of the configuration. The variable R space represents the distance between the actuator region s midpoints or the spanwise dimension of the unit cell. The variable is presented in terms of percent of the blade radius. The variable η act is the ratio of actuator region to the unit cell width, R space. Likewise 1 η act represents the portion of the unit cell without actuation. All previous configurations had an η act values of one. Figure 3.16 compares the designs with and without spanwise variation. The result clearly show that there is no benefit to the proposed spanwise variation design. Many of the configurations on the Pareto front of the spanwise variation are dominated by the Pareto front without spanwise variation. Figures 3.17a-f are very similar to figures 3.11a-d, that is the tab without spanwise variation. Considering the inner active layer, figure 3.17a, the area of

144 116 interest spans from an active displacement of 4 to a flapping displacement of about 1. For almost this entire range, the IAL has a length 0.8 of the total tab length. There is a small region of 0.6 tab length ratio. Overall, this represents an increase in the IAL length compared to the full-span actuator. The middle layer shows the same general trend as the IAL, being slightly longer for the tab with span variation (figure 3.17b) than the full-span tab (figure 3.11b). The difference is small and not always consistent, but still forms a general trend. The outer layers of both configurations are similar with the longer OAL reducing both the active and flapping displacements. Likewise, the configurations with more plies in the shim layer also have low active and flapping displacements (figure 3.17d). One of the new design variables, R space, is plotted in figure 3.15e. R space represents the spanwise width of the unit cell, in terms of percent of blade radius. Small unit cell widths require more spanwise repetition for a given span length. From the figure, only two R space values 1% R and 0.5% R, spanwise lengths of 8.2 cm and 4.1 cm respectively, are found in the nondominated set. However a 5% R spanwise length was also enumurated, but does not show up in the Pareto front. The figure shows that the shortest span configurations make up the lower quarter of the nondominated set. Between an active displacement of 4 and 6, the region of most interest, a mixture of both spanwise lengths is found, with the longer width slightly more prevalent. The other new design variable is η act, the portion of the tab width with active layers. Configurations with no spanwise variation have an η act equal to one. Two η act values are found in the nondominated set, shown in Figure 3.15f. This design variable was varied from 0.1 to 0.8, in steps of 0.1. Clearly the wider actuator regions result in a better design, with only η act values of 0.6 and 0.8 showing up on the Pareto front. The highest η act dominates the lower region of the Pareto front. The middle section is an even split, particularly in the region of interest. In fact, comparing figures 3.15e & f, shows that a shorter unit width is often associated with a greater proportion of actuator. The overall conclusion is that the spanwise variation provides little improvement over the full-span actuator configuration. The additional complexity of having a spanwise variation provides no appreciable benefits.

145 117 Active Displacement Flapping Displacement (a) Inner MFC, IAL L 1 /L Active Displacement Flapping Displacement (b) Middle MFC, MAL L 2 /L Active Displacement L 3 /L Active Displacement Ply Numbers Flapping Displacement (c) Outer MFC, OAL Flapping Displacement (d) Number of Shim Plies 8 8 Active Displacement R space Active Displacement η act Flapping Displacement (e) Unit Cell Span Flapping Displacement (f) Actuator Span Fraction Figure 3.17: Span variation tab: active (4/rev) and flapping (1/rev) displacements with various MFC layering for ǫ = 0.15, span location 0.75R, ±1000V

146 Selected Configuration From plots of the non-dominated set, a few configurations have been selected for additional analysis. These configurations design variables are found in table 3.4. These configurations are based on the MFC data in table 3.2 and the shim is composite with the properties in table 3.3. The selection of the configurations was based on flapping motion deflection. For the 0.15c tab configurations, two,flap values were selected, 0.5 and 1. Table 3.4 also contains actuated tip deflections, assuming an applied voltage of ±1000 V. As expected, the configuration with greater flapping deflection has a larger actuated deflection, but by only 21%. The 0.5 of deflection due to flapping was considered a comprimise between large active deflection and large active to flapping deflection ratio. In both configurations the outer most layer length is 10% or less than the tab chord length. What impact would simplifying the system removing this layer have? For the three layer tab, the removal of the OAL increases the active tip deflection to 5.43 and the flapping tip deflection to This is a minor trade-off and the simpflication of the design is worthwhile. Taking the two layer tab and removing the MAL increases the active tip deflection to 6.74 and the flapping tip deflection to 1.3. With this case, the increase in tip deflections increases more than the previous case. The suitability of the simplfication depends on the amount of passive tip deflection tolerable. The two configurations with a chord length of 0.15c have an active to flapping ratio of 10.8 and 6.4 for the 0.5 and 1 passive deflection, respectively. The peak active to flapping ratio is just over 22 and occurs with a configuration (L 1 /L = 0.7, L 2 /L = 0.5, L 3 /L = 0.35, and a three ply shim) with only of flapping induced motion. Another consideration is a certain level of active delfection is required. The maximum active to flapping ratio has an active displacement of only With all of these factors in consideration, a half degree of flapping deflection seems a suitable selection. Overall, the tab with a chord length of 0.15c, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1 is the configuration of choice Mode shapes and natural frequencies One way of increasing actuator authority is to operate near resonance. Although this can introduce additional challenges, it can also provide greater deflections

147 119 Table 3.4: Design variables, actuated tip deflections, and flapping tip deflections for several configurations L/c L 1 /L L 2 /L L 3 /L Shim Plies,act,flap than operating off resonance. The first 3 mode shapes are plotted in figure 3.18 and figure The mode shapes were generated using the finite element method and were conducted on a 10% span tab. The tab configuration is a chord length of 0.15c, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1. The boundary conditions are clamped at the tab root and free on the other three edges. The fundamental mode occurs at Hz, well above the 4/rev frequency of 17 Hz. The system will operate off-resonance. The high natural frequency is a logical consequence of wanting a high stiffness to density ratio to reduce flapping induced motion. The first plate mode is similar to the first chordwise bending mode of a cantilevered beam, with a symmetric spanwise tip deflection, as in figure 3.18a and figure 3.19a. The second and third modes of tab are all very close in frequency, Hz and Hz, respectively. The tab s long spanwise dimension to chordwise dimension is the reason the first three natural frequencies are so close. Analytically, the natural frequencies are spaced closer as the difference between the two dimensions increases [151]. The second mode has asymmetric tip deflections and the third mode consisting of the edge midpoint moving opposite of the end ends. A natural frequency of a thin tab, one similar to a simply cantilevered beam was also considered. The span of the rotor having the active tab would likely be broken up into smaller units. By considering such a short spanwise segment a limit to the frequency could be established. The first model frequency is Hz, close to that of the full sized plate. Therefore spanwise width has little impact on the first natural frequency, as expected based on the tab s cantilevered beam like mode shape. Without drastically reducting the stiffness or increasing the mass, both of which would exacerbate the response to blade flapping and aerodynamic loading, the system will operate well below the resonance frequency.

148 120 (a) Mode 1, Hz (b) Mode 2, Hz (c) Mode 3, Hz Figure 3.18: First three mode shapes for tab, looking from blade root towards the blade tip (left) and from the trailing edge towards the leading edge (right) Active, aerodynamic, and flapping deflections: 0.15c and 0.2c tab Figure 3.20 contains data for comparing a 0.15c tab to a 0.2c tab in terms of active, aerodynamic, and flapping displacement. The design variables used are for configurations with passive deflections of 0.5. For the tab with a chord length of 0.15c, the design variables are: L 1 /L = 0.8, L 2 /L = 0.32, L 3 /L = 0.1, with both one- and two-ply shims (0.203 mm and 0.41 mm). For the tab with a chord length of 0.2c, the design variables are: L 1 /L = 0.7, L 2 /L = 0.35, L 3 /L = 0.14, with both two- and four-ply shims (0.41 mm and 0.82 mm). The differences in active and flapping displacement between figure 3.20 and table 3.4 are due to modeling a tab with a width of 10% span, rather than a small strip 0.16% of the span. The displacement measurements are still from a 0.75R span position. All four variations will be compared amongst each other. The active displacement of the 0.15c, single-ply shim is 6.6, over a degree greater than predicted considering just a strip equivalently a 12% increase in tip displacement. This increase in active displacement is dependent on spanwise length and a 10% span does have a slight variation of tip displacement along the span direction. However, the variation is concentrated near the two corners of the trailing edge and varies by +2% or 4% of the midpoint value. The increase in displacement is closer to the tip than the

149 121 Figure 3.19: Isometric views of the first three mode shapes for tab Figure 3.20: Tip deflection due to actuation, blade flapping, and various aerodynamic loading

150 122 decrease in displacement which is within the first or last 5% of the tab s spanwise width, depending on whether inboard or outboard. The use of a two-ply shim reduces the active deflection to 5. The 0.2c tab with a two-ply shim, necessary to limit both flapping induced and aerodynamic deflections, deflects actively 6. Doubling the shim to four plies reduces the active deflection to 3.8. The response to flapping for the 10% span tab is reduced compared to the strip (first row table 3.4), 0.42 versus 0.49 for the single ply shim, 0.15c configuration. A shim twice as thick reduces the flapping induced motion to The longer tab requirs a thicker shim to reduce the flapping induced response, deflecting 0.43 for a two-ply shim and 0.25 for a four-ply shim. All four configurations resist flapping induced motions beyond the design requirement of 0.5. Four different aerodynamic conditions have been selected for modeling aerodynamic loads. These four cases were selected based on figure The rationale behind these cases is presented in section The pressure difference plots from the TURNS results are shown in figure A positive value indicates an upward load. For a positive AOA value, these positive values indicate loads causing the tab to deform upward. However, because of the point at the tip of the TURNS airfoil (figure 3.22), a reversal in the pressure difference occurs at the tip (starting at 80% of the tab chord length). This reversal is an artifact of the tip imposed by the internal meshing software used in TURNS. This region of pressure reversal is only over 2.5% of the total airfoil chord and any impact is diminished when the entire airfoil is considered. However, when considering only the loads on the tab, this opposing load, concentrated at the tip imposes a greater bending moment than the rest of the pressure difference acting on the tab. The net result is a reversal of the tab deformation direction, illustrated in figure This pressure reversal is a manifastation of the tip shape and a blunt tip (as would be expected in a practical application) would not produce the same result. Figure 3.24 plots the applied chordwise pressure loads for both the 0.15c and 0.2c configurations for a blunt tab tip(shown in figure 3.22). These pressure distributions were generated with the computation fluid dynamics code FLUENT. This code was used instead of TURNS, because it is able to model a blunt tip (Appendix C) presents details of this analysis). The three positive AOA values have positive chordwise pressure distributions,

151 123 (a) 0.15c (b) 0.20c Figure 3.21: Tab s 2D chordwise pressure distribution, pointed tip 0.02 y/c 0 Fluent TURNS x/c Figure 3.22: Outline of the bluntly tipped (TURNS) tab versus sharply tipped (Fluent) airfoil

152 124 (a) 0.15c (b) 0.20c Figure 3.23: Tab s 2D chordwise, centerline displacement distribution, pointed tip Figure 3.20, whereas the negative AOA value has a negative chordwise pressure distribution. A positive pressure indicates a lifting force, whereas a negative value is in the opposite direction. These pressure difference distributions are more appropriate and do not exhibit the pressure reversal. The pressure difference at Mach 0.3 imposes the smallest chordwise pressure loads, whereas the highest are the Mach 0.6 and Mach 0.7 cases. For both tab chord lengths, the two middle Mach numbers are very similar, with Mach 0.7 having slightly larger chordwise pressure values when the shorter tab is considered. At Mach 0.8 with an AOA value of 2, the applied load is between the Mach 0.3 case and the Mach 0.6 and Mach 0.7

153 125 (a) 0.15c (b) 0.20c Figure 3.24: Tab s 2D chordwise pressure distribution, positive pressure results in a lifting force, blunt tip cases. The Mach 0.3 case causes little tab deflection, being below 0.4 for all four configurations. At Mach 0.6, the chordwise pressure loads are much greater and this is evident in the resulting tab deflections shown in figure The two-ply shim, 0.2c configuration has the greatest deflection, 3.2, which is reduced to 1.3 when a four-ply shim is used. For the 0.15c tab, the single-ply shim configuration deflects 1.8 and the two-ply shim configuration deflects 1. At Mach 0.7, the twoply shim, 0.2c tab again displaces the greatest amount, 2.9, reducing to 1.2 for the four-ply shim configuration. The 0.15c, single-ply shim configuration deflects

154 126 (a) 0.15c one-ply shim (b) 0.15c two-ply shim (c) 0.20c two-ply shim Figure 3.25: Tab s 2D chordwise, centerline displacement distribution, blunt tip

155 127 2, but this reduces to 1 using a two-ply shim. At Mach 0.8, the negative AOA value results in the tabs deforming in the opposite direction. In all cases, the tab deforms away from the incoming flow. This aerodynamic case, as previously stated, imposes moderate chordwise pressure loads. Both the 0.15c, single-ply shim and the 0.2c, two-ply shim configurations deform 1.6. The two-ply, 0.15c configuration reduces to 0.9 and the four-ply shim, 0.2c configuration deflects 0.7. The chordwise displacement due to the various aerodynamic cases are plotted in figure 3.25a-c. The figures show the thick root resisting the aerodynamic loading, deflecting little. Also, the tip shows little curvature, due to the reduced aerodynamic loading at the tip, the tab undergoes little bending. The middle portion of the tab undergoes the greatest bending in all three configurations. The deflection due to aerodynamic loads can be reduced to 1 or less, but are an important consideration, along with flapping induced motion and active displacement Rotating environment and blade pitching and flapping angles: 0.15c tab The rotation of the blade results in a large body force which the tab experiences. The majority of the loading is aligned along the span (figure 3.26). With the blade rotating without any flapping or pitching, the centrifugal force (an acceleration resulting from blade rotation, ie the body force) acts in the same plane as the tab, resulting in in-plane loads only. This load aligned with the chord and acting rearward, stiffening the beam. The rotor blade itself experience a stiffening due to blade rotation. Because the tab is bending in the chordwise direction, only a small component of the centrifugal force acts to stiffen. At the tip of the tab, located at a span location of 0.7R, this component is As a result, the amount of stiffening of the tab is much less than a rotor blade would experience. For example, using simple Rayleigh-Ritz formulation and an assumed displacement of x 2, the stiffness due to the centrifugal force can be estimated. Based on the same energy formulation used of a buckled beam [152] the stiffness contribution of the tab structure is found in equation 3.4 and the stiffness contribution of the centrifugal force is in equation 3.5. Unlike a buckled beam, the force is tensile, not compressive, and various with location. The tension force must remain in

156 128 the integral of equation 3.5. The tension force is found in equation 3.6. Both the radial distance from the rotor mast and the angle the centrifugal force makes with the blade are functions of x, or chordwise position on the tab. R tot [x] = (0.75R)2 +(0.75c+x) c+x and sin(θ[x]) = EI Ltab 0 (0.75R) 2 +(0.75c+x) 2 (w ) 2 dx (3.4) Ltab 0 T(w ) 2 dx (3.5) Ltab T = Ω 2 ρar tot [x]sin(θ[x])dx (3.6) x For this example, a simple bimorph is modeled. The bimorph has three layers, the outer layers being MFCs of thickness 0.3 mm and the middle layer is the shim with a thickness of 0.4 mm and is assumed Aluminum. For the purpose of calculating the centrifugal load, the tab is located at the 0.75R span location and located 0.75c aft of the feathering axis. The bending stiffness of the tab is 2.71 N/m 2. For the tab, the stiffness resulting from the centrifugal force is estimated at N/m 2. In this configuration, the centrifugal force does not stiffen the system. However, if the tab were aligned with the centrifugal force, its contribution to stiffening would be 1.42 N/m 2. Results from the finite element solution show similar trends. For a tab with a one-ply shim, L 1 /L = 0.8, L 2 /L = 0.32 and L 3 /L = 0.1, with centrifugal stiffening the system actively deflects 6.6. Accounting for centrifugal stiffening, the tab deflection reduces to For the same tab, but with a two-ply shim, with centrifugal stiffening the system actively deflects 5. Accounting for centrifugal stiffening, the tab deflection reduces to As expected, the stiffening due to the centrifugal force is minimal. As a result of the tab orientation relative to the centrifugal force, stiffening due to the centrifugal force is negligible. When the blade is flapped or the tab deflects, a small component of the centrifugal force acts as a bending moment on the tab. The flapping angle is not the only way the centrifugal force acts on the tab. The tab being located behind the feathering axis of the rotor blade experiences a rearward component of the

157 129 centrifugal force, this is shown in figure This force acts to deform the tab towards the plane of rotation, the x-y plane. When the blade undergoes pitching, the chordwise of the centrifugal force acts to deform the tab in the direction of the x-y plane, deflecting upwards when the nose pitches upward and deflecting downward when the nose pitches downward. This load makes up the propeller moment [153]. The centrifugal force can act either together or in opposition to the tab deflection. Ideally, the tab design should show little to no response due to these loadings. Table 3.6 shows the tab of the first row of table 3.4 (single-shim ply, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1) at various blade pitch and flapping angles. Table 3.5 shows the results for the same tab, but with a two shim tab. As expected, flapping results in larger deflections than blade pitching. While the flapping angle is small, nearly all the CF loading is aligned spanwise. With blade pitching, the smaller chordwise component of the centrifugal force acts on the tab via the pitching angle. Even acting via large angles, the chordwise centrifugal force component itself is much smaller than the spanwise component as shown in figure The analysis conducted was static, with the system undergoing a 27 rad/s rotation. To properly account for the centrifugal force, the tab starts 0.75c behind the feathering axis. This is based on the feather axis being located at the quarter chord. For both flapping and pitching, the tab is rotated about the appropriate axis. Tab deflection is measured from a plane parallel to the root of the tab and is converted to an angular measurement of the tab tip with respect to the plane. This was done so that the results can be compared to the active tip displacements. At a 20 pitch attitude, the tab deflects 0.19 for a single-layer shim and 0.13 for a two-layer shim. With a nose up pitch attitude, the tab will deflect upwards, opposite for a nose down attitude. Recall, the centrifugal force seeks to align the tab with the x-y plane. At a 6 flap angle, the tab with a single-ply shim undergoes a 0.78 deflection and the tab with a two-ply shim undergoes 0.47 of deflection. When the blade is flapped upwards, the tab deflection due to the centrifugal force is downwards and vice versa. From this result, it is clear that the centrifugal force acting through the blade flapping angle is of importance. But the levels of deflection due to aerodynamic loads are higher. To fully understand the importance of the centrifugal force acting via flapping and pitching the actual pitching and

158 130 top view y y-component of CF x x-component of CF CF y + z root view y-component of CF Figure 3.26: The centrifugal force acting on an airfoil selection on the rotor Table 3.5: Active tip displacement in the rotating environment at various pitching or flapping angles (single-shim ply, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1) Pitching Angle Tip Deflection Angle Flapping Angle Tip Deflection Angle flapping motions are useful. This will permit the designer to understand at what blade azimuth locations these loads are most critical. The addition of stiffness will reduce the response, but will adversely affect the active displacement. 3.5 Assessment of Design Achieving Objectives At the beginning several design objectives were proposed as design guides. These objectives involved both active and passive deflections, the bulk of consideration. While not an objective, the overall thickness is considered, as a check for the feasibility of the system. The maximum thickness of the tab, with a single composite Table 3.6: Active tip displacement in the rotating environment at various pitching or flapping angles (two-shim ply, L 1 /L = 0.8, L 2 /L = 0.32, and L 3 /L = 0.1) Pitching Angle Tip Deflection Angle Flapping Angle Tip Deflection Angle

159 131 layer shim and six layers of MFC, is 2 mm. With just four actuators through the thickness, the value is 1.4 mm. Lastly, with just two MFCs, the thickness is 0.8 mm. The overall tab thickness is small, resulting from the improved active deflections achievable by keeping the actuators close to each other. The goal active tab deflections is ±6, which was achieved using the ±1000 V maximum voltage capability of the actuation. However, to achieve this, the tolerable aerodynamic induced displacement is as high as 2. For such a design, the flapping induced motion is 0.4. The deflections due to the CF are also around the 1 mark for a single-ply shim or 0.5 fir a two-ply shim. The use of a two ply shim reduces the aerodynamic response to 1, accompanied with an active response reduced to 5. The designer must trade between tolerable passive deflections and desired active deflection, as both small passive deflections and large active deflections cannot be achieved simultaneous.

160 Chapter 4 Benchtop Tab Demonstrator The building and testing of a prototype was pursued to experimentally verify that the piezoelectric actuators produce the tab bending deformations predicted in Chapter 3, and to understand any issues that arise. The goal was to build tab that is full-scale in the chordwise direction and test the dynamic response of the system at various voltages and frequencies. This will allow validation of the finite element predictions. 4.1 Design of Experimental Tab The prototype was based on the tab dimensions found in table 3.4. This configuration was selected as having a low response to flapping and over 5 of active displacement. This is a 3 layer tab, with a total length of 0.15c (79.1 mm), based on SC-1094R8 airfoil with a chord of m. The IAL has a length of 63.3 mm, the MAL 25.3 mm, and OAL 7.6 mm. While these lengths represent an optimal value, based on the objectives of maximum active displacement and minimum flapping displacement, consideration is now given to commercially available piezoelectric actuator lengths. The actuator chosen for the prototype is the macro fiber composite actuator. This actuator, described in Section 1.2, takes advantage of a piezoelectric material s best electromechanical coupling. Also, MFC actuators come in thin sheets, giving the actuator great flexibility not seen with other piezoelectric actuator configurations, like stack actuators. The MFC was developed by NASA, but is now made by Smart Materials Corporation [150]. The active

161 133 Table 4.1: Dimensions and capacitance for MFC actuators [150] Model Active Length Active Width Total Length Total Width M2814-P1 28 mm 14 mm 38 mm 20 mm M5628-P1 56 mm 28 mm 67 mm 37 mm lengths available commercially from Smart Materials Corp. are: 85 mm, 56 mm, 43 mm, 40 mm, 28 mm, and 25 mm. The overall dimensions of the actuators are greater than the dimensions of the active material. Each actuator has passive material surrounding the active material. Based on the minimum length available, the outer most layer was dropped in favor of two layers on either side of the shim. The available length of 56 mm offers the closest match to the optimal length for the inner layer (63.3 mm), and was chosen. This actuator has an active width of 28 mm (table 4.1). Smart Materials Corp. offers a MFC with an active length of 25 mm, closely matching the optimal middle layer length (25.3 mm). This MFC is offered with an active width of only 3 mm. One of the offered 28 mm active length actuators has an active width of 14 mm, half that of the inner layer. For this reason, the 28 mm long actuator was selected. The actuators used are shown in figure 4.1. The left hand figure, 4.1(a), is the larger MFC and the right hand figure, 4.1b, is the smaller actuator. The MFC actuators have two electrodes at their bases, with the positive electrode on the left side and the negative electrode on the right side looking from the base to the tip. Also visible in the figure is the inactive material at the perimeter. Another design choice was selection of the shim material. Previous analysis found that a composite shim performed best of the materials considered. This material had a stiffness of 64 GPa in both principal directions and a thickness of mm (0.008 in). It was decided to use a material that could be obtained commercially and ready to use simplifying the experiment. This also removed the need to measure the material properties of the shim. Table 4.2 includes the composite material as well as three other candidate materials considered, displaying the material properties and expected performance. The most critical parameter was thickness, as too thick a shim would result in a stiffer system. Such a system would have reduced active displacement. However, too thin and soft a system

162 (a) (b) Figure 4.1: Smart Materials macro fiber composites: (a) 56 mm by 28 mm active and (b) 28 mm by 14 mm active Table 4.2: Shim materials t (mm/in) E (GPa) ρ (kg/m 3 ) Material,act,flap / composite / aluminum / polyester / steel would result in large uncommanded deformations caused by aerodynamic and inertial forces, as discussed in Chapter 3. The goal was to select a thickness close to that of the composite material. Stiffness and density where also important, but secondary to thickness. Based on the active and flapping induced motion, the aluminum shim was selected. Although the polyester shim provided similar performance to the aluminum, the material properties were not known as accurately and would required material characterization (various polyesters have different stiffness values). Using the aluminum shim, the initial estimated active tip displacement is 5.65 and the flapping induce tip displacement is Figure 4.2 shows the aluminum shim with the doubler on the tip. The doubler was added to the tip to stiffen the beam, as the shim material has low flexural stiffness.

163 135 Figure 4.2: Aluminum shim with doubler bonded at one end 4.2 Experimental Setup Testing equipment Requirements In order to determine the requirements for the high voltage amplifiers the peak current must be calculated. Piezoelectric materials are capacitive in nature [5] and are analyzed as such. The capacitance of the two MFC actuators used are found in table 4.1. For the tab to undergo bending motion, the upper surface MFC actuators must be driven 180 out-of-phase. The simplest setup would only elongate one side at a time. But additional active tip displacement is achieved if one side contracts and the other side elongates, even if the relative amounts are different. Therefore, two separate amplifiers were used, so maximum current and voltage only needs to be computed for each side. As the same voltage needs to be applied across all three actuators on a side, they are connected in parallel. To compute the total capacitance in parallel, the individual values are simply added as in equation 4.1 from [154] indicates. The total capacitance for each side is 4.43 nf. C = C 1 +C 2 +C (4.1) For a harmonic voltage input, current is given by equation 4.2 [154]. This equation was derived for a general resistor-inductor-capacitor system. Assuming that the capacitance dominates, the relation can be simplified to equation 4.3. This equation shows that the current required depends on the voltage, capacitance, and the driving frequency. The expected maximum current is 0.81 ma, based on a peak

164 Small Actuator 0.30 Outer Actuator Inner Actuator Shim DETAIL A SCALE 20 : 1 Shim 0.20 Large Actuator Doubler A Figure 4.3: Schematic of tab prototype, units in millimeters voltage of 1500 V and a 4/rev actuation frequency (corresponding to Hz). Another important consideration in selecting a high voltage amplifier is slew rate, or the rate at which the voltage can be changed with time. This value, typically given in V/µs is a specification on how quickly the amplifier can change the voltage. This is particularly important for square waves, which theoretically require an infinite slew rate. This value is related to the slope of the sinusoidal curve and has a peak value of V p ω. The maximum required slew rate expected is V/µs. I p = V p R 2 + ( ) (4.2) Lω 1 2 Cω I p = V p Cω (4.3) The high voltage amplifiers were driven with a harmonic input, such that the

165 137 Figure 4.4: The maximum voltage input to the MFCs actuators high voltage output is -500 V to 1500 V, as in figure 4.4. The upper and lower actuators were driven 180 out-of-phase, with 2,000 V pp and a 500 VDC offset. The use of a DC offset was used for the trailing edge flap first by Koratkar [16] The signal to the amplifiers was provided by a signal generator Equipment specifications Two Trek 609 series high voltage amplifiers were used to drive the MFC actuators and are pictured in figure 4.5. Each amplifier drove one set of three actuators (in parallel), either the top or the bottom. The specifications for the latest high voltage amplifier in the series, the model 609E-6, are as follows [155]: a voltage range of 0 V to ± 4000 V DC or peak AC, an output current of 0 to ± 20 ma for either DC or peak AC, an input voltage range of 0 V to ± 4 V with a DC voltage gain of V/V (noninverting). The input impedance of the amplifiers is 50 kω. The slew rate is greater than 30 V/µs. These amplifiers met all the requirements for driving the MFCs as calculated above. The amplifiers also provide a voltage monitor that divides the output voltage by In the back, the amplifiers provide a high voltage output as well as a grounding post for the test specimen. The signal generator was a Tektronix AFG3022B, two channel signal generator, shown in figure 4.6. The signal generator specifications are as follows [156]. The frequency range for sine waves is 1µHz to 25MHz, with an accuracy of ± 1 ppm. The phase resolution is The output voltage range is 20 mv pp to 20 V pp into an open circuit (high impedance) load. The accuracy of the output signal is 0.1

166 138 (a) (b) Figure 4.5: Trek 609c/b-6 series high voltage amplifiers: (a) front view with control input and voltage monitor output and (b) back view with high voltage output and ground mv pp. The signal generator was operated up to a 2 V pp sine wave with a 0.5 V DC offset. Thesecondchannelwas180 out-of-phasewiththefirstchannel. Duetothe high input impedance of the voltage amplifier, the signal generator was operating in high impedance load mode on both channels. The signal generator was also used to produce just a DC offset, a square wave, and a sine sweep. The velocity of the tab s traiing edge was measured via a Polytec OFV 534 compact senor head connected to a Polytec OFV-2500 Vibrometer controller [157, 158]. Thissystemisshowninfigure4.7. Thecontrollercanmeasureapeakvelocity of 500 mm/s. The frequency range is 0 Hz to 350 khz. The controller provides an analog output scaled by 50 mm/s per V. The laser consists of two components,

167 139 Figure 4.6: The Tektronix AFG3022D signal generator Figure 4.7: The Polytec vibrometer controller (bottom) and laser unit (top) the laser unit and a sensor head. The laser light is generated in the laser unit and travels along a fiber optic cable to the sensor head. The sensor head is mounted on a tripod and was positioned over the tab. Reflective tape was attached to the tab to improve signal strength. The tape had negligible mass and was not expected to change results, particularly in comparison to the alternative, an accelerometer. The data acquisition system used was a National Instruments DAQ Pad-6020E.

168 140 This system connects to a computer via USB. The analog input was received via BNC connectors. A time trace program written in LabView was used to aquire and store the voltages. This program allowed the user to record multiple channels and three was the maximum number used. The channels were used to capture the voltage monitors of the two amplifiers and the output of the vibrometer. In certain tests, one amplifier s voltage and current monitor outputs were captured, in addition to the vibromter output. An Ametek/Vision Research Phantom Miro M310 high-speed camera was used to obtain video footage. The camera has a maximum resolution of 1280 x 800 at 3,260 frames per second [159]. The camera was operating at a resolution of 1024 x 768 at 1000 fps. This was selected so that the frames would be at the same rate that data was collected Test specimen The testing of the tab required various components to be assembled, including the test specimen as well as a testing fixture. The test specimen consisted of an aluminum shim and the MFC actuators, the design of which is described in Section 4.1. The various components were bonded using Loctite E-120HP Hysol, a two-part epoxy. The epoxy was one of the two recommended by the manufacturer of the MFC actuators. All pieces were cleaned with a 70% Ethyl rubbing alcohol solution before bonding. All pieces were cured at room temperature and were left under compression for at least 24 hours. The aluminum shim and doubler were cut from a larger piece using compoundaction snips. First, the doubler was bonded to the tip of the shim material. Second the inner MFC actuators figure 4.1a were individually bonded to either side of the shim. After being cured, high voltage lead wire was soldered to both terminals of the MFCs. This was done because part of the inactive material of the outer MFCs where the electrodes are located overlap with the lower MFC. The wire used has insulation rated to 4,000 V. The top actuators were bonded edge to edge lengthwise such that the active region starts at the same location as the lower MFC. Each of the two upper actuators has wire soldered to the leads. Each side has three positive and three ground leads.

169 141 Figure 4.8: The terminal block with input leads and output leads To simplify connection to the voltage amplifiers, a terminal block was built, using non-conductive polymer. The terminal block is shown in figure 4.8. The terminal block has four posts, two for each side. Each post has three wires connected via ring connectors, where all three wires require the same voltage. The connector block then allows each amplifier to be connected with only a high voltage and a ground line. The high voltage line required a special adapter whereas the ground line used lead wire. Both had fork connectors attached to the terminal block side. Due to the high voltages involved, the testing fixture was designed to be mostly non-conducting and protective. Figure 4.9 shows the clamping mechanism. The clamping mechanism serves to hold that tab at the root and attach it to the rest of the testing fixture. The tab is gripped by non-conducting polymer as in figure 4.9. These grips isolate the tab electrically from the rest of the clamp, one of several design choices to reduce risks associated with testing at high voltages. The clamping force is provided by an angle aluminum on one side and an aluminum strip on the other, forced together by four machine screws, two on each side. These three components consist of the clamp. The polymer grips are reversibly bonded to the aluminum. This was done to ensure the two clamps remain aligned when the tab is fitted for clamping. The angle aluminum is bolted to the acrylic box that surrounds the tab, shown in figure This ensures that the clamping mechanism is electrically isolated from the rest of the testing fixture. The acrylic

170 142 (a) (b) Figure 4.9: Testing Fixture: (a) front view of clamp and (b) rearview of clamp box is a cm (6 in) cube with 0.32 cm (1/8 in) thick acrylic walls. The box is held together with aluminum hinges, which allow for easier access to the inside. The box itself rests on polymer feet to ensure that the conductive hinges do not touch any table surface. As the tab prototype was aligned horizontally, the laser was positioned above, requiring the top panel to be open during testing. Two images of the tab clamped are in figure Due to the location of the electrodes to the active portion of the MFC, the grips overlap the active portion. Due to the insulation thickness of the leads, it was best to keep them straight or slightly curved. Figure 4.10b shows the leads traveling straight out the back of the box through a slot. 4.3 Experimental Results and Discussion Testing objectives The goal of testing was to verify the finite element predictions conducted and used in the design study. Since the application of the tab is dynamic, the primary focus was dynamic testing. However, static displacement was also of interest. Initial testing was conservative and based around the unknown robustness of the system. Previous experience with piezoelectric materials (although not MFCs)

171 143 (a) (b) Figure 4.10: Testing fixture with tab: (a) view from trailing edge and (b) side view

172 144 Table 4.3: Test frequencies 1/rev 2/rev 3/rev 4/rev 5/rev 6/rev rad/s Hz Table 4.4: The voltage ramping steps used during testing Voltage Range (V) V pp (V) V DC (V) 0 : : : : : : : : : : : showed tendencies to fail in conditions within the operational envelope. Another concern was the risk of debonding of the MFC layers from each other or from the aluminum shim. With these concerns in mind, the testing started at low voltage and frequency, increasing frequency first, then voltage. This was to ensure the greatest amount of data collected in the event of a failure. The frequencies that were considered are in table 4.3. The frequencies considered are based on the rotor speed of the UH-60, 27 rad/s. The 4/rev frequency is the frequency of which the design work was conducted. A sinusoid wave form was used in all these cases. The voltage ranges considered are in table 4.4. The MFCs are designed for -500 V to 1500 V. To use this full voltage range, a DC offset is required. The voltage variation occurs about this offset, which allows a ±1000 V range, as opposed to ±500 V range without the offset. Various intermediate steps were used before any testing at the maximum voltage was conducted, both with and without the DC offset. In addition to testing at all the frequencies in table 4.3, static displacement was also measured.

173 145 In addition to the frequencies and the sinusoidal waveform described above, lower frequencies and different waveforms were also considered and will be described where their results are provided. A frequency response curve, showing up to the first natural frequency was also obtained. This would allow assessment of the structural portion of the finite element model, relative to the measured behavior of the prototype Finite element model of experimental tab A finite element model was developed to closely match the actual experimental tab. This finite element model differs from the simulations used throughout this dissertation in two ways. First, due to the location of the electrodes and the finite thickness of the clamp grips, the usable tab length is 77 mm the grips reduce the length by 3 mm, overlapping with a portion of the active material. Second, the MFCs bonded to the prototype do not cover the entire width of the tab. Therefore, the finite element model of the prototype accounts for this difference, whereas the simulations in Chapter 3 assume the actuators cover the entire width or span of the tab. Figure 4.11 contains a depiction of the modeled surface features for the prototype finite element model. The three actuators are all in the lower 2/3 of the tab. The small actuators overlay both the large actuators and, at the edges, the shim itself. The regions where the actuators layer are darker illustrate the overlap. The lighter region is modeled only as a single layer. The major difference between the prototype and the finite element model was that neither the nonactive regions of the MFC or the bondline of the epoxy are considered. The nonactive regions were considered of negligible stiffness and mass. The bondline was neglected as reliable information about the bondline was unavailable, although estimates were made for the consideration of the frequency response only. The actual width of the tab was measured at 40.5 mm. The active lengths of the large and small MFC actuators, not covered by the grips, were 52.5 mm and 24 mm respectively. In all other aspects, the model used the same element type (SHELL281) and material properties as the design analysis.

174 146 Figure 4.11: Layout of the tab used for finite element analysis Testing results and discussion The results of the experiment are compared with the results calculated via finite element analysis. Various inputs and outputs are presented. The primary inputs areadcinput, aharmonicinputwithadcoffset, andaharmonicinputwithouta DC offset. The most important output considered is the peak-to-peak displacement of the tab tip. Other outputs include tip velocity or direct voltage output of the vibrometer, voltage and current output of the amplifier DC input The static results are discussed first. These measurements were made with the function generator outputting a DC signal essentially the system was either on or off. Since the laser vibrometer could not be used, a ruler measuring in millimeters was placed next to the tab tip and a picturewas taken. Using the pixel information of the centimeter marks on the ruler, greater accuracy could be obtained. The number of pixels corresponding to 1 cm was about 430, leading to a resolution of less than 0.03 mm per pixel. The camera was placed in front of the tab, with the ruler aligned with the tip. The camera was mounted on a tripod and a small aperture setting was selected to maximize depth-of-field. The images were taken withacanoneosrebelt1iusingaefs18-35mmlens. Thefocallengthwas36 mm and with a lens aperture of F/28.1. The camera was used in aperture priority mode, such that the exposure time is calculated automatically. The original image

175 147 Table 4.5: Percent error between the experimentally measured displacement and the finite element predicted displacement Voltage Range (V) Percent Error Voltage Range (V) Percent Error 0 : % ±100 V -54% -100 : % ±200 V -40% -200 : % ±300 V -26% -300 : % ±400 V -18% -400 : % ±500 V -12% -500 : % is 4752 pixels by 3168 pixels (15 MP). The maximum and minimum deflection pictures at the rated voltage are figures 4.12(a and b). These images have been cropped and desaturated, but all analysis on the images were done on the originals. The results are compiled in table 4.6. The maximum deflection was 5.2 peak amplitude (10.4 peak to peak), although peak-to-peak amplitude was measured directly. The finite element peak amplitudes are found in table 4.7. The expected deflection was 5.35, a percent error of less than -3%. The other percent errors are found in the first two columns of table 4.5. The lower voltages show greater differences than the higher voltages. But the high voltage static displacement matching is more important and shows that the actuators are able to produce the strains expected. Static results were also recorded for symmetrically applied DC voltage, that the upper actuators are equal but opposite of the lower actuators. These displacement results correspond to the harmonic input without any DC offset. At the highest symmetric voltage range possible (while following the manufacturer s recommendation), ±500 V, displaces 2.36, as found in table 4.8. Even though this is half of the peak-to-peak voltage, the displacement is less than half of the -500 V to 1500 V case. Compared to the expected result, the difference is -12 %. Another interesting comparison between the DC and no DC offset results is -100 V to 500 V and ±300 V, with both have a 600 V peak-to-peak voltage. With a DC offset, the tab displaces 1.2, without it displaces 1.19, essential the same value. This is not unexpected, as the DC offset should not hurt the performance of the actuators, rather it should inhance the performance. Likewise the estimated displacements are the same, 1.61, or a percent error of -26%. The remaining percent errors are

176 148 (a) -500 V to 1500 V up (b) -500 V to 1500 V down (c) -400 V to 1250 V up (d) -400 V to 1250 V down (e) -300 V to 1000 V up (f) -300 V to 1000 V down Figure 4.12: Static deflection of the tab found in the last two columns of table 4.5. As before, experimental results with high voltages are closer to the estimated value, with the experiment falling further below with reductions in voltage. Figure 4.19 compiles the measured tip displacements and plots them versus the applied peak-to-peak voltage. The dashed line, the static displacement curve, is linear from 250 V to 1650 V. The rate the displacement increase with voltage reduces above a voltage of 1650 V. Overall, the tip response is linear with the input voltage for static displacements.

177 149 (g) -200 V to 750 V up (h) -200 V to 750 V down (i) -100 V to 500 V up (j) -100 V to 500 V down (k) 0 V to 250 V up (l) 0 V to 250 V down Figure 4.12: Static deflection of the tab Tab frequency response To characterize the structural dynamics of the tab, a sine sweep was conducted at low voltage. To avoid any potential issues with current limits at higher frequencies, the input voltage was -50 V to 50 V. This also assured tip velocity remained below the 500 mm/s limit of the laser vibrometer. The sine sweep spanned from 1 Hz to 250 Hz with a 2.5 s rise and fall time. The instantaneous frequency of the sweep varied linearly with time. This signal was generated using the signal generator. The power spectrum was calculated using GNU Octave s spectral_xdf function

178 150 and used with a hanning window. The power spectrum was calculated for both the input sine sweep and the output from the laser vibrometer. The vibrometer output was kept in volts, keeping units consistent. The frequency response was calculated by taking the output power spectrum and dividing it by the input power spectrum. The result was scaled so that the initial response was one. The response curve, figure 4.13 shows twin peaks at 138 Hz and 152 Hz. As the sine sweep cannot be phased, the upper and lower actuators were tested separately. The two curves match well except below 10 Hz. The cause of the two experimentally measured natural frequencies is unknown. Due to the low voltage imposed by the high frequencies resulting from power limitations of the amplifiers, the use of the high speed camera to image the mode shape was infeasible. Another feature of the measured response is a drop in the initial response with frequency. A similar phenomena associated with the actuators is observed in the experimentally measured active tab results and is discussed in detail in Section The natural frequency from the finite element model was between 135 Hz and 142 Hz (figure 4.14 and mode shape in figure 4.15), depending on the thickness of the bond layer, which was considered in the analysis. This thickness was estimated from the actual prototype thickness compared to expected thickness of the various components. The average bond layer thickness is estimated to be between 0.05 mm and 0.07 mm, Young s modulus of 4 GPa, and a shear Modulus of 1.23 GPa. The stiffness values were estimated from an aggregate of epoxy material properties. The finite element model has a frequency independent (structural) damping of 5% to prevent infinte displacement at resonance, this damping is added via the finite element software. The damping matrix is created via the stiffness matrix multiplied by the damping ratio divided by applied frequency [149]. The percent difference between the lowest peak and the estimated peak is about -2% and 3%. The model shows no double peak and shows a greater dropoff after the resonant peak. The finite element model predicts a flat response at low frequencies, which was the expected outcome. The frequency range of interest is 4 Hzto25Hzandiswellbelowtheresonancefrequencyandwasexpecttobeinaflat portion of the response curve. However the results in figure 4.13 contridict this expectation and the experimentally measured active displacement results agree, although reveal an even greater drop in actuator performance with frequency.

179 151 Figure 4.13: The output power spectrum over the input power spectrum for -50 V to 50 V input via a 1 Hz to 250 Hz Sine sweep Figure 4.14: The displacement response versus frequency from the finite element model Figure 4.15: Fundamental mode of the finite element model

180 152 Voltage (V) V, 1 out V in, 1 V out, 2 V in, 2 V out, 3 V, 3 in time/period Figure 4.16: Plots of laser vibrometer output and amplifier voltage monitor versus time, 1=[0 V : 250 V & 27 rad/s], 2=[0 V : 250 V & 162 rad/s, and 3=[-500 V : 1500 V & 27 rad/s]] Example time trace of output subjected to harmonic loading The laser vibrometer was used to acquire the velocity of the tab resulting from a sinusoidal voltage input to the piezoelectric actuators. The output from the laser vibrometer was converted to a direct velocity measurement which was integrated to obtain displacement. From the displacement time trace, the peak-to-peak amplitude was obtained. Examples of vibrometer output are found in figure Both the vibrometer output and the voltage monitor on the amplifier are plotted for three cases: 0 V to 250 V at 27 rad/s (blue curves), 0 V to 250 V at 162 rad/s (red curves), and -500 V to 1500 V at 27 rad/s (green curves). The x-axis is the normalized by the period, so that the shape of the higher frequency input can be compared to the lower frequencies. The voltage monitor plotted is that of the top actuator, so a positive voltage leads to a downwards deflection. The amplifier does a good job outputting the proper voltage and all three dashed waveforms appear sinusoidal. The velocity of the low frequency and voltage case solid blue line is also sinusoidal. At a higher frequency of 162 rad/s (red curve), the wave form is not truly sinusoidal. The peaks and valleys are still rounded, but in between the trace deviates, developing a slight kink. At the high voltage, but low frequency (curve in green), the vibrometer output (proportional to velocity) develops a slight s-bend when crossing zero velocity. Across this bend the rate of voltage change with time decreases, then increases. While speculative, it might be related to the

181 153 switching of the amplifier from a source to a sink or vice versa. Or this kink could be related to the direction change of the tab. However, the amplifier voltage monitor does not display any deviation from the prescribed sinusoidal input across 0 volts. The localized spikes in velocity measurements (green curve) are likely erroneous measurements from the vibrometer as such a sudden increase in velocity seems unlikely Harmonic input with DC offset The experimentally measured peak amplitudes (half the peak-to-peak displacement) for the various frequencies and applied voltages with DC offset are in table 4.6. At the higher frequencies and voltages, the tip velocity exceeded the limits of the laser vibrometer. The finite element results are presented in table 4.7. Looking at these results first, the expectation was a slight increase in displacement with frequencies compared to static. The frequency response curves lead to a similar conclusion. Considering table 4.6, the 1/rev responses are about half or slightly greater than experimentally measured static displacement. Also, as frequency increases, the displacement decreases. The finite element results of table 4.7 does not show a reduction in amplitude with frequency like table 4.6. Figure 4.17a shows the experimentally measured amplitudes versus the finite element amplitudes at various frequencies and amplitudes. At the low frequencies, figure 4.17a shows the experimental results being about 60% of the estimated value. This was an unexpected result, given that the quoted frequency range for use as an actuator at high electric field is 0 Hz to 10 khz [150]. The expectation was that the actuator would be able to respond quickly at the given frequencies without any attenuation Harmonic input without DC offset The experimentally measured displacements at various frequencies for voltage inputs without DC offset also show a large reduction, relative to static results. Tables 4.8 and 4.9 summarize the displacement results of both the experiment and the finite element analysis. Even at the highest applied voltage, the 4.3 Hz harmonic output (1.26 is about half of the static response (2.36 ). The results in those two tables are plotted in figure Figure 4.18a shows the dramatic reduction

182 154 Table 4.6: Experimentally measured (peak amplitude) of the benchtop tab ( denotes data acquired via high speed camera) Frequency (Hz Voltage Range (V) : : : : : : ±0.15 Table 4.7: (peak amplitude) calculation from finite element model of the benchtop tab Frequency (Hz) Voltage Range (V) : : : : : : Experiemntal/Simulated, Displacement [0:500] V [ 100:500] V [ 200:750] V [ 300:1000] V [ 400:1250] V [ 500:1500] V Frequency (Hz) (a) Experiemntal Displacement (deg) [0:500] V [ 100:500] V [ 200:750] V [ 300:1000] V [ 400:1250] V [ 500:1500] V Frequency (Hz) (b) Figure 4.17: Experimental results with DC offset: a) ratio of experimental over estimated and b) experimental displacement

183 155 Table 4.8: Experimentally measured (peak amplitude) of the benchtop tab without any DC offset Frequency (Hz Voltage Range (V) : : : : : Table 4.9: (peak amplitude) calculation from finite element of the benchtop tab without any DC offset Frequency (Hz) Voltage Range (V) : : : : : in performance, compared to the expected performance. Particularly at the lower voltages, with the ±100 V being around a quarter of the expected result. Even when comparing amongst the experimental results 4.18b, the drop in displacement between DC and AC input is clear. However, with increasing frequency, at any of the applied input voltage level only a small further drop in output displacement is measured. Since both the ±300 V and -100 V to 500 V cases have the same peak-topeak voltage, 600 V, it is natural to compare. With just a DC voltage, these two cases produced the same output displacement amplitude (half peak-to-peak amplitude of 1.2 ). Dynamically, the two cases also agree well. The maximum percent error between the two is under 4%. Both exhibit a sharp reduction in response amplitude going from 0 Hz to 4.3 Hz and a minor reduction in amplitude with increasing frequency there after. The agreement shows that the use of a DC offset does not adversely affect the response when compared to no DC offset, while allowing an increase in the peak-to-peak voltage input.

184 156 Experiemntal/Simulated, Displacement ± 100 V ± 200 V ± 300 V ± 400V ± 500 V Frequency (Hz) (a) Experiemntal Displacement (deg) ± 100 V ± 200 V ± 300 V ± 400V ± 500 V Frequency (Hz) (b) Figure 4.18: Experimental results without DC offset: a) ratio of experimental over estimated and b) experimental displacement In figure 4.19, the amplitude versus peak-to-peak applied voltage is plotted. The two curves representing frequencies of 4.3 Hz and Hz are similar. Compared to the static curve, the dynamic deflection has lower slope. The two dynamic curves are nearly linear, appearing slightly quadratic, but with low curvature. The slope of these two curves increases slightly with applied voltage. Overall, this figure supports using a linear relation between applied voltage and actuator response, as was used in all the finite element models Amplifier voltage and current output In order to determine if the amplifier was unable to generate sufficient current, the current monitor was captured along with velocity and the amplifier voltage monitor. These results are compiled in figure The voltage output of the vibrometer (velocity output in figure 4.20) is plotted in volts on the left vertical axis with the amplifier voltage monitor. The current monitor has been converted to current (2 ma/v) and plotted on the right vertical axis. The output current has a waveform of similar shape as the velocity output. Also of importance is that the maximum current is 1 ma, well below the limit of 20 ma. It is safe to conclude that the limited actuator response is not due to the amplifier hitting its current limit.

185 157 Tip Deflection (deg.) ω=0 Hz ω=4.3 Hz ω=17.16 Hz Peak to Peak Voltage Amplitude (V) Figure 4.19: The displacement versus voltage of the experimental results at 0 Hz, 4.3 Hz, and Hz Table 4.10: Experimentally measured (peak amplitude) of the benchtop tab Frequency (Hz) Voltage Range (V) : Low frequency response Forthe-500Vto1500Vcases, threeadditionallowerfrequencieswerecaptured: 2, 1, and 0.5 Hz. This was done to explore how frequency changes the displacement over a range lower than that originally considered. Table 4.10 compiles these results and shows that even at 0.5 Hz, the deflection is still 1 less than the static result. The conclusion as the frequency increases is that the peak amplitude rapidly decreases. These results seem to indicate that even at low frequencies, below those of interest the actuator is unable to achieve the levels of deflection of the static displacement case.

186 158 Figure 4.20: Laser vibrometer output, amplifier voltage monitor, and amplifier current monitor versus time for -500 V : 1500 V & 27 rad/s High-speed camera results The high-speed camera allowed for the capture of motion at velocities exceeding thatofthelaservibrometer. Thelensonthecameraisalongfocallengthtelephoto zoom, as a result the camera had to be placed several meters from the tab so that it could focus on the tab. A result of this setup, is that the number of pixels per millimeter is much lower than that obtained with still shots. The average distance a pixel covered was 0.1 mm to 0.2 mm, compared to 0.02 mm to 0.03 mm using the Cannon T1i. The use of the high speed camera enabled displacement to be captured for two cases the laser vibrometer was unable: the square wave input and the 4/rev sinusoidal input, both at -500 V to 1500 V. The sinusoidal displacement is in figure The software to view the camera output files, CV-Cine Viewer Application, allows the user to set a gauge length in terms of pixels. The ruler located next to the tip was used to set this gauge. The software allows the user to track points over time, but requires the user to select the tracking point in each frame. This method was used to obtain one cycle of the sine wave figure This data was used to obtain tip displacement and figure 4.21 shows the camera and software extracted the expect tip displacement shape with time. The total tip displacement is 8.77 mm which corresponds to a value of 3.2 ±0.15. The resolution of the displacement measurement is quite

187 159 Figure 4.21: Displacement via the high speed camera at -500 V : 1500 V & 108 rad/s low compared to the other methods used. The 4/rev result from the camera is near the 3/rev measurement taken by the laser vibrometer within the limits of accuracy. A square wave input and the tab s response were measured to better understand the response of the actuator. Having observed the step response of the actuator, its time response to a sudden application of voltage was investigated. The results from the square wave are compiled in figure Figure 4.22a shows half the period (1.25 s), whereas figure 4.22b shows the initial 0.1 s. Not only is displacement plotted, but on the right vertical axis the output of the current monitor and voltage monitor are plotted. Recall the current output needs to be scaled by 2 ma/v and the voltage monitor by 1000V/V. While both the current and voltage have been shifted on the time scale to match the output data, there is no way of determining iftheyarebothfromthesamecycle, likewisethecurrentandvoltagecanbe±1ms out-of-phase. This is because the data collection did not start simultaneously with the camera. Looking at figure 4.22b, the initial response is quick, achieving a total displacement of 12 mm in 8 ms. After this point the tab undergoes oscillations due to the impulsive motion until about 60 ms of elapsed time. The initial response occurs at about 250 Hz (assuming the measured quantity is half a cycle), whereas waiting for the transient oscillations to dampen out as a half cycle, the frequency drops to 33 Hz. The current monitor shows similar oscillations, that continue for a greater time than looking at displacement alone. These oscillation correspond with

188 160 (a) (b) Figure 4.22: Displacement resulting from a square wave (-500 V to 1500 V) going fromdeflecteddowntodeflectedup: a)theentire1.25shalfperiodandb)temporal zoom from 0 s to 0.1 s the beam s motion after the step input. An estimate natural frequency of 143 Hz based on the period of the oscillation compares favorably with the measured 138 Hz natural frequency. Figure 4.22a shows that even after these initial oscillations, the tabcontinuestodisplaceupto1.25sofelapsedtime, atwhichtimethesquarewave cycles. Both the voltage and current output from the amplifier remain constant during this time. Although difficult to see from the figures, the current steadies at a value of ma, although such a low value may simply be noise. Overall, this investigation showed the actuators exhibit a quick initial response, followed by a slow creep-like response with a step voltage input.

189 Exploration of frequency response Three likely explanations for the poor dynamic response are: 1) the amplifiers are unable to provide sufficient current, 2)additional electrical dynamics are occurring, and3)themfcsareunabletoresponsefastenough. Thepossibleimpactofdamping on the system is addressed in Appendix E. Explanation one has been examined previously and it is clear that the high voltage amplifiers are not exceeding their current limits when the sinusoidal wave is being used. The second explanation proposes that additional electrical dynamics are occurring, perhaps between the various elements between the high voltage line and the ground. The most likely sources for these dynamics involve the three MFC actuators in parallel. The MFCs are mostly a capacitance load. The voltage across a capacitor subjected to a step voltage, V emf, is [154]: ( ) V(t) = V emf 1 e t RC (4.4) This equation has been simplified to assume no initial voltage across the capacitor, that is no charge intially stored. The entire system has a capacitance of 4.4 nf, which would reach 95% voltage in 13.2 ns to 133 ns depending on a resistance of 1 to 10 ohms. Clearly the actuators should be able to charge quickly, based on theses assumptions. One way to test whether interactions between the actuators was causing the reduced dynamic performace is having only the bottom actuators driven, with the upper actuators disconnected. Testing in this manner prevents any current or voltage reaching the top actuators via the high voltage and ground leads. In this configuration both the static displacement with -500 V to 1500 V and the same voltage with a sinusoidal input at 4/rev (17.16 Hz) were tested. The static displacement was 3.1 whereas the dynamic response was 2.3. The percentage in displacement with respect to the finite element displacement is less than experienced with all actuators functioning, 74% versus about 60%, but still represents a reduction. The source of the poor dynamic performance does not depend on interaction between the actuators via the connecting leads. The third explanation, based on published specifications, also seems unlikely, relative to the low frequencies the system is operating given the actuators bandwidth of 0 Hz to 10 khz [150]. However, a careful search of the literature for a

190 162 similar issues turned up three relevant papers. The first paper is by NASA Langley and presents new benchtop testing results of their active-twist blade [160]. The blade is designed with layered MFCs, two on the upper surface and two on the lower surface. The blade has a total of 9 MFC radial stations. The authors conducted a frequency sweep from 0.2 Hz to 100 Hz, by 0.2 Hz steps. The authors consider a 0.2 Hz input as steady. The response measured is show in figure The frequency range of interest, 0.2 Hz to 20 Hz is below the first twist natural frequency, which is around 60 Hz. The authors comment on the reduction in active twist when going from quasi-steady to 5 Hz [160]. The authors conclude the response is not modal, but related to a creeplikeeffectintheblade. Theresultsinfigure4.23seemtoshowthatforhighvoltages the effect is greatest, whereas the ±75 V case shows little reduction. The measured ratio of reduced magnitude over quasi-static magnitude in amplitude for the 500 V caseis68%, the350 Vcaseis66%, the200vcaseis61%, andthe75vcaseis79%. So, with the exception of the lowest voltage, the ratio between dynamic response and quasi-static response increases with decreasing voltage. As a comparison, the results from the tab experiment, dynamic over static is found in figure Recall, that static in this case truely means static, with the tab having at least 30 s to achieve full displacement. At the highest voltage, the ratio is between 60% to 65%. With decreasing voltage, the ratio of dynamic response to static response is smaller the difference between the two is greater. The dynamic displacement decreases with frequency, with some voltage levels showing a leveling of at the higher frequencies and other continues to decrease. Although the reductions are slightly greater, the general trends are quite similar. Figure 4.25 contains the experimental results without a DC offset. There is little difference between having a DC offset or not. At the highest voltage, the ratio between dynamic and the corresponding static result is lower, between 60% and 55%. But the lower voltage ratio floor is at the same value, just under 45%. The major difference between the presented experimental results and that of Kreshock et al [160]. is the difference in static versus quasi-static. The authors do not present experimental results of a truly static result, but do offer a prediction, This is predicted by their CAMRAD II model and the predicted frequency response is plotted in figure Considering the predicted static displacement

191 163 Figure 4.23: Tip twist frequency response of NASA s active-twist rotor at ±75 V, ±200 V, ±350 V, and ±500 V, [160] Experiemntal Displacement (dynamic/static) Frequency (Hz) [0:500] V [ 100:500] V [ 200:750] V [ 300:1000] V [ 400:1250] V [ 500:1500] V Figure 4.24: Experimental dynamic results over static results with DC offset

192 164 Experiemntal Displacement (dynamic/static) Frequency (Hz) ± 100 V ± 200 V ± 300 V ± 400V ± 500 V Figure 4.25: Experimental dynamic results over static results without DC offset and comparing it to the measured 10 Hz displacement, the ratio of dynamic response to static response is 61%. This value is closer to the range measured for the tab. It seems likely that the creep-like effect reducing the dynamic performance of the active-twist rotor is the same affecting the tab. Figure 4.26 shows that the difference between predicted and measured response extends beyond the low frequencies, up to the maximum measured frequency reponse. The CAMRAD II predictions for the active-twist rotor show and initially flat response at low frequencies, with an increase in response up to the first natural torsion frequency. The CAMRAD II model also picks up a small change in response corresponding with the second flapping frequency (16 Hz). Nagata et al. [161] from The University of Electro-Communications in Tokyo, Japan testing a cantilevered beam using MFC actuators for use in microelectromechanical systems. The focus is on both actuation and sensing via the MFC. The authors provide relevant experimental results, found in figure Figure 4.27a has the results from a quasi-steady test using a 0.1 Hz sine wave at voltages from -500 V to 1000 V. This result shows the hysteresis present in the MFC actuators. This figure also provides the quasi-steady displacements to compare with dynamic results. Although this quasi-static result is specifically for V,

193 165 Figure 4.26: Estimated and measured tip twist frequency response of NASA s active-twist rotor at ±75 V, ±200 V, ±350 V, and ±500 V, [160] the linear curve fit will be used to approximate the steady values at other voltages. The dynamic experimental results in figure 4.27b show an initially flat response, which then increases towards the first natural frequency. However, note that the lowest frequency is 10 Hz. Comparing the 10 Hz responses for the various voltages, the reductions at 10 Hz are: 52% at 930 V, 53% at 760 V, and 40% at 572 V. These reductions are in the range measured for the tab. The trend of increasing reduction with voltage is mixed with these results. The authors never compare their static results and dynamic results and so do not comment on it or consider any causes. However, the observations agree with the notion that the creep-like behavior is the cause. The previous two papers presented results in terms of the frequency domain, Schröck et al. [162] of the Automation and Control Institute in Vienna, Austria, present time domain results. The authors main goal was considering the compensation of hysteresis and creep phenomena in an MFC actuator beam for use in positioning tasks. The authors experimentally record the beam tip displacement response to a step input of 500 V (figure 4.28). Figure 4.28b, shows the initial response to the step input, with damped transient oscillations resulting from the initial motion evident. This response was also recorded for the tab after the appli-

194 166 (a) (b) Figure 4.27: Measured tip displacement of a cantilevered beam for a) quasi-static and b) dynamic voltage [161] cation of a step input figure 4.22b. However, this is an expected response and not related to the issue of creep. However, figure 4.28 continues for a much longer time interval and shows a pronounced creep-like motion. The initial creep is greater than towards the end of the time trace. The total creep distance is about 0.8 mm based on the beam s displacement after the transient oscillations have stopped to when the step input is removed. This creep-like response is the same response measured from the tab s response to a step input 4.22a.

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