AEROMECHANICAL STABILITY AUGMENTATION OF HELICOPTERS USING ENHANCED ACTIVE CONSTRAINED LAYER DAMPING TREATMENT ON ROTOR FLEX BEAMS

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical Engineering AEROMECHANICAL STABILITY AUGMENTATION OF HELICOPTERS USING ENHANCED ACTIVE CONSTRAINED LAYER DAMPING TREATMENT ON ROTOR FLEX BEAMS A Thesis in Mechanical Engineering by Asari Badre Alam Asari Badre Alam Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December

2 We approve the thesis of Asari Badre Alam. Date of Signature Kon-Well Wang William E. Diefenderfer Chaired Professor in Mechanical Engineering Thesis Co-Advisor Co-Chair of Committee Farhan Gandhi Assistant Professor of Aerospace Engineering Thesis Co-Advisor Co-Chair of Committee Asho Belegundu Professor of Mechanical Engineering Edward C. Smith Associate Professor of Aerospace Engineering George A. Lesieutre Professor of Aerospace Engineering Richard C. Benson Professor of Mechanical Engineering Head of the Department of Mechanical Engineering

3 ABSTRACT iii This thesis presents a study conducted to explore the feasibility of employing Enhanced Active Constrained Layer (EACL) damping treatment in helicopter rotor systems to alleviate aeromechanical instability. The central idea is to apply the EACL treatment on the flexbeams of soft in-plane bearingless main rotors (BMRs) and increase the damping of the first lag mode. In helicopters, if the damping in the first lag mode of the rotor is increased above a minimum design requirement (usually 4-5%), the ground and air resonance problem can be eliminated. In this research, it is explored whether EACL damping treatment can provide sufficient damping in rotor system without exceeding the physical design limits of actuators. To study the feasibility of the EACL damping treatment for damping augmentation, a finite element based mathematical model of a rotor with EACL treatment on the flexbeam is developed. In this study, energy method, Hamilton s Principle, in combination with the GHM viscoelastic modeling method is used to derive the equations of motion. A bench top experiment is conducted to verify the mathematical model. It is shown that the experimental results correlate well with the analytical results. A derivative controller, with control voltage based on the flexbeam tip transverse velocity, is used in this investigation. In this study, it is demonstrated that high damping in forward flight can only be provided if a filter is used in the feedbac loop that removes /rev component of the signal. Such a filter is designed and implemented. An optimization study is conducted to understand the influence of EACL design parameters on the performance of the damping treatment. A design chart is developed using the results of the optimization study that can be used to efficiently design EACL treatments for various design requirements. It is demonstrated that the EACL damping treatment on helicopter flex beams can provide sufficient damping to alleviate aeromechanical stability in helicopters.

4 iv In multilayered structures, it is nown that the interlaminar shearing and peeling stresses can be very high due to discontinuities in the material properties. These interlaminar stresses are usually concentrated near the free ends and can cause the layers to delaminate. Because the conventional EACL treatments are applied on the surface of a structure, lie flexbeams, there are a number of free edges that are susceptible to high interlaminar stresses. In this study, the interlaminar stresses in EACL damping treatment are analyzed and techniques are developed to reduce them. The mathematical models that are commonly used to analyze the performance of constrained layer damping treatments cannot predict the interlaminar stresses. Hence in this study, a new finite element model is developed. This model is capable of accurately predicting both, the performance of the constrained layer damping treatment as well as the interlaminar stresses. The new model is derived using the concept of the built-up-bar (BUB) theory originally presented by Mirman [99b]. However, the mathematical model developed in this thesis includes some fundamental modifications and improvements in the original concept. In this model, three types of materials can be used for the layers, namely, elastic, viscoelastic (VEM), and PZT. Due to the time dependent characteristics of the VEM, a modified concept of interlaminar stiffness is proposed and the GHM method is employed to model it. The mathematical model is verified using two sets of published data, [Mirman 99b, Robbins and Reddy 99]. The study of interlaminar stresses in the constrained layer damping treatments is conducted in three stages. First the passive constrained layer treatment (PCL) is analyzed, then the active constrained layer treatment (ACL) is studied and finally EACL damping treatment is investigated. The interlaminar stresses, peeling and shearing, in the PCL treatment are studied and it is demonstrated that the peeling stress has an area of high stress concentration near the free edge of the treatment. In this study, it is found that the configurations that provide high damping (thic constraining layer and relatively thin VEM layer) also have high stresses.

5 v Therefore, a new configuration of PCL damping treatment is developed by tapering the constraining layer at the free ends. As compared to a conventional ACL, this configuration has lower interlaminar stresses and similar damping performance. There are two issues that are addressed in the ACL treatment analysis. First, a study is conducted to analyze the type of feedbac signal that should be used for active damping. It is nown that the ACL damping treatment can provide damping with either displacement or velocity feedbac. However, the mechanism of damping in these two control schemes is different and the selection of control scheme is usually based on the voltage requirements for these two cases (lower voltage). In this study, a system with proportional and the derivative control scheme is analyzed for the interlaminar stresses. It is shown that for the system under consideration, derivative control has lower voltage requirements and lower interlaminar stresses. Next, a study is conducted to compare ACL with purely active configuration. In general, the treatment that provides damping with lower control voltage is usually preferred. In this study, the interlaminar stresses in these two configurations are analyzed, and a new criterion is developed for comparison (treatment with lower interlaminar stress). It was shown that in ACL configuration, the interlaminar stresses are an-order-of-magnitude lower than the purely active configuration. In this thesis a new configuration of ACL treatment is presented that has lower interlaminar stresses as compared to a conventional ACL configuration. This new configuration is designed by changing the poling direction of the PZT constraining layer close to the free edge (-5 coupling). It is found in this research that if the poling direction of the PZT close to the free edge is changed (-5 coupling), the control voltage would actuate a small portion of the PZT close of the free edge in shear mode. Thus, the tip of the PZT would press on the structure and the interlaminar peeling stresses would reduce. However, the peeling stresses at a location inboard of the free edge could increase. An extensive study was conducted to analyze the mechanics of this system. It

6 vi was demonstrated that the interlaminar stresses could be reduced by 6-7% by using this new configuration. The EACL damping treatment utilizes the edge elements at the end of the treatment to transfer some of the control forces to the host structure. These edge-elements have a strong influence on the performance of the treatment and it has been shown previously that EACL treatment has better performance than both active and ACL configurations. In this research, the influence of the edge-elements on the interlaminar stresses was studied and it was demonstrated that the transverse edge-element stiffness (normal to the structure) does not have a strong effect on the interlaminar stresses. However, increasing the axial edge-element stiffness reduces the pea interlaminar peeling stresses. The physics of this phenomenon was studied in detail and is documented in this thesis. Also, the physical design of the edge-element was studied and recommendations are made on the selection of design parameters to minimize the interlaminar stresses in the edgeelement itself. The last part of this research focuses on utilizing the concepts developed in the interlaminar stress study to reduce the interlaminar stresses in EACL treatment on the helicopter flexbeam.

7 vii TABLE OF CONTENTS LIST OF FIGURES... xi LIST OF TABLES...xxiii ACKNOWLEDGEMENTS... xxiv CHAPTER INTRODUCTION.... BACKGROUND.... LITERATURE REVIEW Literature Review on Aeromechanical Stability Augmentation Literature Review on Constrained Layer Damping Treatment Literature Review on Delamination RESEARCH OBJECTIVE PROBLEM STATEMENT THESIS OUTLINE... 4 CHAPTER MATHEMATICAL MODEL OF A HELICOPTER ROTOR WITH EACL TREATMENT ON THE FLEXBEAM SYSTEM DESCRIPTION Disturbance Forces Feedbac Filter Control Law ASSUMPTIONS MATHEMATICAL MODEL DEVELOPMENT Kinematic Relations Strain-Displacement Relations Velocity Field Potential Energy Kinetic Energy External Virtual Wor Finite Element Equations... 35

8 viii.4 EXPERIMENTAL VERIFICATION MODEL REDUCTION SYSTEM ANALYSIS Stresses in PZT Electrical Field in PZT SUMMARY CHAPTER 3 DESIGN OF EACL TREATMENT on HELICOPTER FLEXBEAMS DESIGN OF THE FEEDBACK CONTROL SYSTEM Filter Design Closed Loop System OPTIMIZATION OF THE EACL TREATMENT SUMMARY CHAPTER 4 INTERLAMINAR STRESSES IN MULTILAYERED STRUCTURES WITH VEM SYSTEM DESCRIPTION Assumptions MATHEMATICAL MODEL DEVELOPMENT Kinematic Relationship Strain-Displacement Relationship Stress-Strain Relationships Potential Energy Kinetic Energy Virtual Wor CONCEPT OF INTERLAMINAR STIFFNESS INVOLVING VEM LAYERS Interlaminar Stiffness involving VEM Layers FINITE ELEMENT EQUATIONS VERIFICATION OF THE MATHEMATICAL MODEL Transistor Stac... 8

9 ix 4.5. Cantilevered Beam with PZT Actuators Experimental Verification SUMMARY... 3 CHAPTER 5 DAMPING PERFORMANCE AND INTERLAMINAR STRESSES IN PASSIVE CONSTRAINED LAYER TREATMENT MODEL DESCRIPTION MODEL REDUCTION ANALYSIS IMPROVED DESIGN CONCEPT SUMMARY... 8 CHAPTER 6 DAMPING PERFORMANCE AND DELAMINATION IN AN ACTIVE CONSTRAINED LAYER DAMPING TREATMENT MODEL DESCRIPTION MATHEMATICAL MODEL Modal Reduction ANSLYSIS SUMMARY... 5 CHAPTER 7 A NEW ACTIVE CONSTRAINED LAYER DAMPING TREATMENT FOR GOOD PERFORMANCE AND LOW INTERLAMINAR STRESES DESCRIPTION OF THE INNOVATION MATHEMATICAL MODEL AND SYSTEM DESCRIPTION APPROACH AND PROCEDURE ANALYSIS Static stress analysis and proof of concept Closed Loop Control Quasi Static analysis... 46

10 x Resonance analysis Viscoelastic shear layer SUMMARY CHAPTER 8 INTERLAMINAR STRESSES IN ENHANCED ACTIVE CONSTRAINED LAYER DAMPING TREATMENT APPROACH MATHEMATICAL MODEL OF A BEAM WITH EACL DAMPING TREATMENT ANALYSIS OF EDGE-ELEMENT STIFNESS Important observations Displacement field in EACL damping treatment Discussion on interlaminar stress EDGE-ELEMENT STIFNESS DESIGN System description Mathematical Model System Analysis Parametric Study SUMMARY CHAPTER 9 A DISCUSSION ON HIGH DURABILITY EACL TREATMENT FOR HELICOPTER ROTOR SYSTEM... CHAPTER SUMMARY AND FUTURE WORK... REFERENCES... 8 APPENDIX... 39

11 xi LIST OF FIGURES Figure - Enhanced active constrain layer concept with edge elements... 3 Figure - Schematic of idealized model of rotor... 9 Figure - Schematic of lag flexure with EACL treatment, discretized into a number of elements... 9 Figure -3 Lag flexure in deformed configuration Figure -4 Single finite element of lag flexure with nodal degrees of freedom Figure -5 Schematic of experimental setup... 4 Figure -6 Finite element discretization of the lag flexure in the experimental setup... 4 Figure -7 Frequency response of the lag flexure (without the rotor blade), solid line : experiment, dashed : analytical Figure -8 Frequency response of the rotor (Lag flexure and rotor blade combination), solid line : experiment, dashed : analytical Figure 3. PZT electrical field as a function of available lag damping in presence of periodic excitations Figure 3. Feedbac filter... 5 Figure 3.3 Frequency response function of the feedbac filter... 5 Figure 3.4 Performance for Case Figure 3.5 Performance for Case Figure 3.6 Performance for Case Figure 3.7 Inboard edge element stiffness for Case-6 (N-m)... 6 Figure 3.8 Optimized design space (solid passive damping, dashed hybrid damping) Figure 3.9 Axial stress in the PZT actuators (MPa) Figure 3. Electrical field on the PZT actuators Figure 4- A Multilayered Structure Comprised of n Layers and n- Bonds... 7 Figure 4- Schematic of the transistor stac and the mode of modeling Figure 4-3 Interlaminar peeling stress in the transistor stac (Si-BeO interface)... 85

12 xii Figure 4-4 Interlaminar peeling stress in the transistor stac (BeO-Solder interface) Figure 4-5 Interlaminar peeling stress in the transistor stac (Solder-Cu interface) Figure 4-6 Interlaminar peeling stress in the transistor stac (Cu-Al interface) Figure 4-7 Interlaminar shearing stress in the transistor stac (Si-BeO interface) Figure 4-8 Interlaminar shearing stress in the transistor stac (BeO-Solder interface) Figure 4-9 Interlaminar shearing stress in the transistor stac (Solder-Cu interface) Figure 4- Interlaminar shearing stress in the transistor stac (Cu-Al interface) Figure 4- Axial force at the neutral axis of each layer... 9 Figure 4- Rate of change of axial force calculated at the neutral axis of each layer... 9 Figure 4-3 Shear angle for each layer in the stac... 9 Figure 4-4 Bending moment for each layer in the stac... 9 Figure 4-5 Rate of change of bending moment for each layer in the stac... 9 Figure 4-6 Total bending moment in the strcurure as defined by equation 4.3j... 9 Figure 4-7 Schematic of the cantilever beam with PZT actuators Figure 4-8 Distribution of peeling and shearing stress at the aluminum and adhesive interface Figure 4-9 Distribution of axial and shear stress at the neutral axis of adhesive layer Figure 4- Distribution of peeling and shearing stress between two PZT layers Figure 4- Normalized interlaminar peeling stress between layers Figure 4- Normalized interlaminar shearing stress between layers Figure 4-3 Axial force at the neutral axis of various layers Figure 4-4 Rate of change of axial force at the neutral axis of various layers Figure 4-5 Shear angle in different layers... Figure 4-6 Bending moment in various layers... Figure 4-7 Rate of change of bending moment in various layers...

13 xiii Figure 4-8 Total bending moment in the strcurure as defined by Equation 4.3j... Figure 4-9 Frequency response of the cantilever beam, solid line: experimental result, dashed line: analytical result... Figure 5- Cantilever beam with constrained layer damping treatment covering 5% of the length... 9 Figure 5- Distribution of interlaminar peeling stress along the length of the treatment... 9 Figure 5-3 Distribution of interlaminar shearing stress along the length of the treatment... Figure 5-4 Pea interlaminar peeling stress for various VEM and constraining layer thicnesses at CL/VEM interface... Figure 5-5 Pea interlaminar shearing stress for various VEM and constraining layer thicnesses at CL/VEM interface... Figure 5-6 Damping in the first transverse mode for various VEM and constraining layer thicnesses... Figure 5-7 Modified constrained layer for reduced interlaminar stresses... Figure 5-8 Graphic description of taper ratio and thicness ratio... Figure 5-9 Cantilever beam with modified constrained layer thicness... 3 Figure 5- Pea interlaminar peeling stress for various taper ratios... 3 Figure 5- Damping ratio for the first transverse mode for various taper ratios... 4 Figure 5- Pea interlaminar peeling stress for various thicness ratios... 4 Figure 5-3 Damping ratio for the first transverse mode for various thicness ratios.. 5 Figure 6- Structure under consideration... 6 Figure 6- Open loop damping as a function of viscoelastic material layer thicness (3MISD)... 7 Figure 6-3 Interlaminar peeling stress for a unit tip force (3MISD)... 7 Figure 6-4 Interlaminar shearing stress for a unit tip force (3MISD)... 8 Figure 6-5 Frequency response function of beam tip displacement for unit tip transverse load (3MISD)... 8

14 xiv Figure 6-6 Frequency response function of control voltage for tip transverse load (3MISD)... 9 Figure 6-7 Amplitude of peeling stress between constraining layer and VEM layer for unit tip transverse load (3MISD)... 9 Figure 6-8 Amplitude of peeling stress between VEM layer and beam for unit tip transverse load (3MISD)... 3 Figure 6-9 Amplitude of shearing stress at both interfaces, constraining layer- VEM and VEM-beam, for unit tip transverse load (3MISD)... 3 Figure 6- Voltage requirements for derivative and proportional control schemes (3MISD)... 3 Figure 6- Interlaminar peeling stress for derivative and proportional control schemes (3MISD)... 3 Figure 6- Interlaminar shearing stress for derivative and proportional control schemes (3MISD)... 3 Figure 6-3 Axial PZT actuator stress for derivative and proportional control schemes (3MISD)... 3 Figure 6-4 Open loop damping as a function of viscoelastic material layer thicness (DYAD66) Figure 6-5 Frequency response function of beam tip displacement for unit tip transverse load (DYAD66) Figure 6-6 Frequency response function of control voltage for tip transverse load (DYAD66) Figure 6-7 Amplitude of peeling stress between constraining layer and VEM layer for unit tip transverse load (DYAD66) Figure 6-8 Amplitude of peeling stress between VEM layer and beam for unit tip transverse load (DYAD66) Figure 6-9 Amplitude of shearing stress at both interfaces, PZT-VEM and VEMbeam, for unit tip transverse load (DYAD66) Figure 6- Control voltage requirements for various damping ratios Figure 6- Interlaminar peeling stress in active and ACL configuration... 36

15 xv Figure 6- Interlaminar shearing stress in active and ACL configuration Figure 6-3 Pea axial stress in PZT actuator for active and ACL configuration Figure 7- Schematic of sheartip activation in modified contained layer damping treatment... 5 Figure 7- Control scheme for the modified contained layer damping treatment... 5 Figure 7-3 Length of the elements in finite element discretization... 5 Figure 7-4 Interlaminar stress in the conventional ACL treatment for a unit voltage applied on the PZT actuators (static)... 5 Figure 7-5 Interlaminar stress in the conventional ACL treatment for unit tip force on the beam and voltage on PZT such that the tip displacement is zero (static)... 5 Figure 7-6 Static interlaminar stress in the modified ACL treatment for a unit voltage applied on the PZT actuators (Length ratio = 5, voltage ratio =)53 Figure 7-7 Static interlaminar stress in modified ACL treatment for unit tip force on beam and voltage on PZT to cancel tip displ. (Length ratio = 5, volt. ratio =) Figure 7-8 Static interlaminar stress at certain locations in the modified ACL damping treatment for various length ratios (Voltage actuation) Figure 7-9 Pea static interlaminar stress in the modified ACL damping treatment for various length ratios (Voltage actuation) Figure 7- Static interlaminar stress at certain locations in the modified ACL damping treatment for various length ratios (Force and voltage actuation) Figure 7- Pea static interlaminar stress in the modified ACL damping treatment for various length ratios (Force and voltage actuation) Figure 7- Static interlaminar stress at certain locations in the modified ACL damping treatment for various voltage ratios (voltage actuation) Figure 7-3 Pea static interlaminar stress in the modified ACL damping treatment for various voltage ratios (voltage actuation)... 56

16 xvi Figure 7-4 Static interlaminar stress at certain locations in the modified ACL damping treatment for various voltage ratios (force & voltage actuation) Figure 7-5 Pea static interlaminar stress in the modified ACL damping treatment for various voltage ratios (force & voltage actuation) Figure 7-6 Interlaminar stress at the free end of conventional ACL treatment for all four interfaces (f = rad/s, K p =, K d = ) Figure 7-7 Interlaminar stress at the inboard location in conventional ACL treatment for all four interfaces (f = rad/s, K p =, K d = ) Figure 7-8 Interlaminar stress at the free end of modified ACL treatment for all four interfaces (f = rad/s, K p =.56x 6, K d = ) Figure 7-9 Interlaminar stress at the inboard location in modified ACL treatment for all four interfaces (f = rad/s, K p =.56x 6, K d = ) Figure 7- Interlaminar stress at the free end of conventional ACL treatment for all four interfaces (f = ωn ξ, K p =, K d = )... 6 Figure 7- Interlaminar stress at the inboard location in modified ACL treatment for all four interfaces (f = ωn ξ, K p =, K d = )... 6 Figure 7- Interlaminar stress at the free end of modified ACL treatment for all four interfaces (f = ωn ξ, K p =.4x 6, K d = )... 6 Figure 7-3 Interlaminar stress at the inboard location in modified ACL treatment for all four interfaces (f = ωn ξ, K p =.4x 6, K d = )... 6 Figure 7-4 Interlaminar stress at the free end of conventional ACL treatment for all four interfaces (f = ωn ξ, K p =, K d = 75)... 6 Figure 7-5 Interlaminar stress at the inboard location in conventional ACL treatment for all four interfaces (f = ωn ξ, K p =, K d = 75)... 6 Figure 7-6 Tip displacement of the beam partially covered with conventional ACL damping treatment (f = ωn ξ, K p =, K d = 75)... 63

17 Figure 7-7 Interlaminar stress at the free end of conventional ACL treatment for xvii all four interfaces (f = ωn ξ, K p =.8x 6, K d = 75) Figure 7-8 Interlaminar stress at the inboard location in conventional ACL treatment for all four interfaces (f = ωn ξ, K p =.8x 6, K d = 75) Figure 7-9 Tip displacement of the beam partially covered with modified ACL damping treatment (f = ωn ξ, K p =.8x 6, K d = 75) Figure 7-3 Interlaminar stress at the free end of conventional ACL treatment for all four interfaces (f = ω ξ, K p =, K d =, material: n 3MISD) Figure 7-3 Interlaminar stress at the inboard location in conventional ACL treatment for all four interfaces (f = ωn ξ, K p =, K d =, material: 3MISD) Figure 7-3 Tip displacement of beam partially covered with conventional ACL damping treatment (f = ω ξ, K p =, K d =, material: n 3MISD) Figure 7-33 Interlaminar stress at the free end of modified ACL treatment for all four interfaces (f = ω ξ, K p =.x 6, K d =, material: n 3MISD) Figure 7-34 Interlaminar stress at an inboard location in modified ACL treatment (f = ω ξ n, K p =.x 6, K d =, material: 3MISD) Figure 7-35 Tip displacement of beam partially covered with modified ACL damping treatment (f = ω ξ, K p =.x 6, K d =, material: n 3MISD) Figure 7-36 Interlaminar stress in conventional ACL treatment for all four interfaces (f = ωn ξ, K p =, K d = 75, material: 3MISD)... 68

18 Figure 7-37 Interlaminar stress at an inboard location in conventional ACL xviii treatment (f = ωn ξ, K p =, K d = 75, material: 3MISD) Figure 7-38 Tip displacement of beam partially covered with conventional ACL damping treatment (f = ω ξ, K p =, K d = 75, material: n 3MISD) Figure 7-39 Interlaminar stress at the free end of modified ACL treatment for all four interfaces (f = ω ξ, K p =.7x 6, K d = 75, material: n 3MISD) Figure 7-4 Interlaminar stress at an inboard location in modified ACL treatment (f = ω ξ n, K p =.7x 6, K d =, material: 3MISD)... 7 Figure 7-4 Tip displacement of beam partially covered with modified ACL damping treatment (f = ω ξ, K p =.7x 6, K d = 75, material: n 3MISD)... 7 Figure 8- Schematic of EACL treatment on a cantilever beam and description of edge-element lumped model Figure 8- Beam static tip transverse displacement when PZT s are activated with unit static voltage Figure 8-3 Beam static tip transverse displacement when PZT s are activated with unit voltage Figure 8-4 Beam static tip transverse displacement for unit tip force Figure 8-5 Beam static tip transverse displacement for unit tip force Figure 8-6 Open loop modal damping ratio for various values of edge-element axial stiffness... 9 Figure 8-7 Open loop modal damping ratio for various values of edge-element transverse stiffness... 9 Figure 8-8 Pea interlaminar peeling stress for various axial edge-element stiffness values when unit voltage is applied on the PZT actuators... 9 Figure 8-9 Pea interlaminar peeling stress for avrious transverse edge-element stiffness values when unit voltage is applied on the PZT actuators... 9

19 xix Figure 8- Pea interlaminar peeling stress for avrious axial edge-element stiffness values when unit force is applied at the tip of the beam... 9 Figure 8- Pea interlaminar peeling stress for avrious transverse edge-element stiffness values when unit force is applied at the tip of the beam... 9 Figure 8- Transverse displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = Keq w = ) Figure 8-3 Transverse displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = Keq w = ) Figure 8-4 Slope of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = Keq w = ) Figure 8-5 Slope of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = Keq w = ) Figure 8-6 Axial displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = Keq w = ) Figure 8-7 Shear deformation in the system plotted against the normalized axial position for unit voltage on the actuators (Keq u = Keq w = ) Figure 8-8 Transverse displacement of the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8-9 Transverse displacement of the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8- Slope of the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8- Slope of the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8- Axial displacement of the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8-3 Shear deformation in the system plotted against the normalized axial position for unit tip force (Keq u = Keq w = ) Figure 8-4 Graphic description of the deformation field in the system for unit voltage in the PZT actuators (Keq u = Keq w = )... 99

20 xx Figure 8-5 Graphic description of the deformation field in the system for unit tip transverse force (Keq u = Keq w = )... Figure 8-6 Transverse displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = )... Figure 8-7 Transverse displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = )... Figure 8-8 Slope of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = )... Figure 8-9 Slope of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = )... Figure 8-3 Axial displacement of the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = ) 3 Figure 8-3 Shear deformation in the system plotted against the normalized axial position for unit voltage on the PZT actuators (Keq u = x, Keq w = ) 3 Figure 8-3 Transverse displacement of the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 4 Figure 8-33 Transverse displacement of the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 4 Figure 8-34 Slope of the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 5 Figure 8-35 Slope of the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 5 Figure 8-36 Axial displacement of the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 6 Figure 8-37 Shear deformation in the system plotted against the normalized axial position for unit tip force (Keq u = x, Keq w = )... 6

21 xxi Figure 8-38 Schematic of edge-element model with design parameters... 7 Figure 8-39 Deformation field in the edge-element model (all dimensions in m)... 8 Figure 8-4 Interlaminar peeling stress plotted against the axial position... 8 Figure 8-4 Interlaminar shearing stress plotted against the axial position... 9 Figure 8-4 Edge-element stiffness for various values epoxy thicness... 9 Figure 8-43 Maximum interlaminar peeling stress for various values epoxy thicness... Figure 8-44 Maximum interlaminar shearing stress for various values epoxy thicness... Figure 8-45 Edge-element stiffness for various overlap lengths (L )... Figure 8-46 Maximum interlaminar peeling stress for various overlap lengths (L )... Figure 8-47 Maximum interlaminar shearing stress for various overlap lengths (L )... Figure 8-48 Edge-element stiffness for various free length values (L )... Figure 8-49 Maximum interlaminar peeling stress for various free length values (L )... 3 Figure 8-5 Maximum interlaminar shearing stress for various free length values (L )... 3 Figure 8-5 Edge-element stiffness for various values of vertical section thicness (t e )... 4 Figure 8-5 Maximum interlaminar peeling stress for various values of vertical section thicness (t e )... 4 Figure 8-53 Maximum interlaminar shearing stress for various values of vertical section thicness (t e )... 5 Figure 8-54 Edge-element stiffness for various values of horizontal section thicness (t e )... 5 Figure 8-55 Maximum interlaminar peeling stress for various values of horizontal section thicness (t e )... 6 Figure 8-56 Maximum interlaminar shearing stress for various values of horizontal section thicness (t e )... 6 Figure 8-57 Edge-element with taper free ends... 7

22 xxii Figure 8-58 Edge-element stiffness for various taper ratio values... 7 Figure 8-59 Maximum interlaminar peeling stress for various taper ratio values... 8 Figure 8-6 Edge-element stiffness for various values of modulus of elasticity of the edge element... 8 Figure 8-6 Maximum interlaminar peeling stress for various values of modulus of elasticity of the edge element... 9 Figure 8-6Maximum interlaminar shearing stress for various values of modulus of elasticity of the edge element... 9 Figure A- Frequency response function of beam tip displacement and tip force... 4 Figure A- Frequency response function of beam tip displacement and tip force... 4 Figure A-3 Frequency response function of beam tip displacement and tip force... 4 Figure A-4 PZT voltage requirement for a unit tip transverse force... 4 Figure A-5 PZT voltage requirement for a unit tip transverse force... 4 Figure A-6 Pea interlaminar peeling stress between PZT/VEM... 4 Figure A-7 Pea interlaminar peeling stress between PZT/VEM... 4 Figure A-8 Pea interlaminar peeling stress between PZT/VEM... 4 Figure A-9 Pea interlaminar peeling stress between VEM/Beam Figure A- Pea interlaminar peeling stress between VEM/Beam Figure A- Pea interlaminar peeling stress between VEM/Beam Figure A- Pea interlaminar shearing stress Figure A-3 Pea interlaminar shearing stress Figure A- Pea interlaminar shearing stress... 44

23 xxiii LIST OF TABLES Table - A Classification of Aeromechanical Stability Augmentation Techniques... 6 Table - System parameters of the reduced scale experimental setup Table - Lag flexure configuration of the reduced scale experimental setup Table 3. System parameters of the full scale rotor system Table 3. Lag flexure configuration of the full scale rotor system Table 3.3 Optimized designs Table 4- Physical properties of the transisor stac Table 4- Physical properties of the cantilevered beam with PZT actuators Table 5- System Parameters... 5 Table 5- Element length in FEM discretization... 6 Table 6- System Parameters Table 6- Interlaminar Stiffness at ω Table 7- System parameters... 5 Table 7- Element length in FEM discretization... 7 Table A- System Parameters... 39

24 xxiv ACKNOWLEDGEMENTS The fact that my name is the only name that appears on the binding of this thesis is misleading in the extreme. I would have never been able to complete my research and this thesis without the support and guidance I received from everybody during my stay at the Pennsylvania State University. I would lie to express my heartfelt thans to my advisors Dr. Kon-Well Wang and Dr. Farhan Gandhi for their endless encouragement and supervision throughout my research. They were always available when I needed help and I do not have enough words to express my gratitude for that. I also want to than my committee for providing valuable insight and suggestions at various stages of this research. I would lie to acnowledge Dr James Wang from United Technologies Siorsy Aircraft and, Dr. Young Yu from National Rotorcraft Technology Center for providing the financial support to complete this research. I would lie to than all my family and friends for their constant support. Special thans to Errol Fernandes and Sajjad Badre Alam for proof reading my comprehensive proposal and my thesis. My lab mates deserve a special mention for their constant help and stimulating discussions. My acnowledgements would never be complete without recognizing Dr. Edward Smith for his help with my job search and my career decisions. He has been a good mentor and I would always be thanful to him for his valuable suggestions Although several sources contributed to this thesis, the responsibility for any errors or omission, however, rests solely on my shoulders.

25 CHAPTER INTRODUCTION. BACKGROUND Over the last couple of decades, increasing effort has been devoted to the design and development of bearingless main rotors (BMR) for helicopters. The main advantages of such rotor systems compared to the articulated ones are mechanical design simplification, reduced drag, lower weight, parts and maintenance cost, higher moment capability and hence better handling qualities [Reichert and Huber, 973]. In these types of rotors, the flap and lag hinges as well as the pitch bearings are replaced by compliant flexures nown as flexbeams. The flexbeam undergoes elastic bending and twist to accommodate the flap, lag and pitch motions. It is surrounded by a torsionally rigid casing nown as the torque tube. Pitch control is achieved by rotating the torque tube that in turn elastically twists the flexbeam. The helicopter rotor systems are usually classified into two categories depending on the lag natural frequency: soft-inplane rotors with ω ξ /Ω < and stiff-inplane with ω ξ /Ω >. Research has shown that low in-plane hub loads can only be achieved by using softinplane rotors [Johnson, 994]. Hence, modern bearingless/hingeless rotors are designed to be soft-inplane to reduce the dynamic stresses. However, such designs are nown to be susceptible to aeromechanical instabilities such as ground- and air-resonance [Chopra, 99]. The reason for these instabilities is the coupling of the low frequency regressing lead-lag mode with body pitch and roll [Johnson, 994]. These instabilities are generally alleviated by introducing sufficient lead-lag damping. Hence, helicopters have traditionally been equipped with passive elastomeric or hydraulic lag dampers at the rotor hub. However, these dampers have a number of drawbacs. They result in hub complexity, weight, and aerodynamic drag. Additionally, passive damper performance could significantly degrade due to environmental changes and variations in operating

26 conditions. A review of the conventional passive damping techniques for aeromechanical stability augmentation of helicopters is presented in Section... In view of the drawbacs associated with current passive lag dampers, considerable efforts have been devoted to the development of damperless rotors [Ormsiton, 996, Gandhi, 997] and/or adaptive damping treatments. These efforts include the exploitation of aeroelastic coupling [Bousman, 98; Nagabhushanam et al., 983; Gandhi & Hathaway, 998], the use of active blade pitch control via the swashplate [Straub, 987; Taahashi, 99; Weller, 996; Gandhi and Weller, 997], the use of active control of individual blade pitch [Hathaway and Gandhi, 998; Kessler 998] and the development of magneto-rheological (MR) fluid based lag dampers [Marathe et al., 998]. Most of the techniques mentioned above are at the development stage. A more detailed review of these investigations is presented in Section... In this research, a new active-passive hybrid approach is developed for rotor lag damping. Compared to the traditional passive lag dampers, this new technique reduces hub complexity and compensates for variations in operating environment. The proposed approach utilizes the enhanced active constrained layer (EACL) damping treatment idea [Liao and Wang, 996, 998] (Figure -) for rotor stability augmentation. The EACL configuration was developed to improve the performance of the original active constrained layer (ACL) treatment [Plump and Hubbard, 986; Agnes and Napolitano, 993; Baz and Rao, 994; Shen, 996; Van Nostrand 994; Azvine et al.; 995; Lam et al.; 995; Liao and Wang, 997; Huang et al., 996; Lesieutre and Lee, 996]. ACL generally consists of a viscoelastic material (VEM) sandwiched between the host structure (e.g., the flexbeam) and a piezoelectric (PZT) cover sheet (active constraining layer). As the host structure undergoes bending, the viscoelastic layers undergos shear and hence provides damping. Based on sensor feedbac, the controller actuates the PZT layers (by application of an electric field) to further enhance the shear in the VEM layer as well as to exert active control forces onto the host structure. It has

27 3 Controller OR Sensor Viscoelastic Layer Active PZT Layer Structure Voltage Source Edge-element Figure - Enhanced active constrain layer concept with edge elements

28 4 been shown that the ACL treatment can increase the system damping when compared to a baseline passive system. However, it is also recognized that the viscoelastic layer reduces the direct active control authority from the active constraining layer to the host strucure, when compared to a purely active design (no VEM). To address this issue, the EACL idea is to add a pair of edge elements at the ends of the PZT layer and directly connect the active source (i.e., PZT) to the host structure (Figure -). Such edge elements could greatly increase the transmissibility between the actuator electrical field input and the active control force output to the host structure. It is found that the EACL could be designed to produce significant active control actions while still maintaining a fair amount of passive damping [Liao and Wang, 996, 998; Liu and Wang, 999]. A more detailed review of the constrained layer damping treatment is provided in Section... The advantage of an active-passive hybrid damping approach for rotor stability augmentation is apparent it contains the merits of both the purely active and passive designs. It is superior to purely passive treatments, as the active component can be used to compensate for operating condition variations and environmental changes. Further, purely passive dampers are generally over-designed and provide high damping levels to stabilize the most critical condition. However, such large levels of damping may be required only over a very small percentage of the operational range and produce excessive periodic damper loads in forward flight, leading to premature fatigue. The proposed design can provide a modest amount of passive damping and increase damping actively on an as-needed basis. Such a hybrid configuration is also superior to a purely active approach since the passive component increases fail-safe reliability. This research also explores the implementation issues of EACL damping treatment on helicopter flexbeams. Since helicopter flexbeams are subjected to very large aerodynamic and inertial forces, the EACL treatment flexbeam is susceptible to delamination. The delamination of the EACL damping treatment has never been studied before and the current research addresses this issue in detail.

29 . LITERATURE REVIEW 5 This section contains a more formal and comprehensive literature review. The literature review is separated into three sections corresponding to the three main aspects of this research, namely: aeromechanical stability augmentation of helicopters, active constrained layer damping treatment, and the interlaminar stresses in the multilayered structures... Literature Review on Aeromechanical Stability Augmentation The phenomenon of ground resonance has been investigated extensively ever since this problem was identified in the early helicopters. It was found that ground resonance could be eliminated by introducing a certain amount of damping either in the rotor system or in the landing gear of the fuselage [Johnson, 994; Ormiston, 99]. It is customary in helicopter design to use passive lag dampers to increase the lag damping of the rotor blades [Johnson 994]. There are numerous techniques available to introduce this damping including hydraulic dampers, viscoelastic dampers, and the fluid-filled elastomeric dampers (Fluidlastic ). Most of these dampers are currently used in helicopters. But these dampers still face some performance limitations and the design of the lag dampers remains a challenging tas. There are a number of new adaptive damping techniques being explored, but they are currently at a development stage. Considerable effort is also being devoted towards the development of damperless rotors as they offer significant simplification in rotor design. As mentioned before, there are several techniques available to eliminate the aeromechanical stability problem in helicopter rotor systems. Based on how instability is eliminated, these techniques may be classified in one of the three categories presented in Table -. These include: () conventional damper systems, () damperless rotors, (3) advanced adaptive damping techniques. All of these categories have several approaches. The recent developments in these categories are discussed in the following sections in more detail.

30 Table - 6 A Classification of Aeromechanical Stability Augmentation Techniques Aeromechanical Stability Augmentation Conventional Damper Systems Damperless Rotors Advanced Adaptive Damping Techniques Elastomeric Aeroelastic Coupling MR Dampers Fluid Filled Active Blade Control ACL/EACL Damping Hydraulic Rotor Blade Anisotropy Elastomeric Dampers Recent developments in the area of material science have led to the development of very high loss factor elastomers. These elastomers are rapidly gaining popularity as a solution for designing lag dampers with high damping capability, and have been utilized for both articulated and BMR rotor systems; e.g., Boeing AH-64 Apache, Boeing CH-47F Chinoo, Bell model 4, Siorsy RAH-66 Comanche, McDonnell Douglas Explorer. The elastomeric dampers have gained increasing popularity for the damping enhancement in the BMR s due to the ease of implementation. In a BMR, an elastomeric snubber/damper is introduced at the inboard section of the flexbeam [Huber, 99]. The damper, which is connected between the flexbeam and the torque tube, undergoes shear strains due to blade lag motions and hence provides the required damping which is -4 percent of the st lag mode critical damping [Huber, 99]. But the design of these elastomeric dampers is not simple because of the complex behavior of the elastomeric material including: () nonlinear amplitude and frequency dependence, () blade limit cycle oscillations, (3) large variations of properties due to variation in temperature, including significant degradation in performance at extreme temperatures. As mentioned earlier, the main problem with elastomeric dampers is associated with the complexity in behavior. This problem was first addressed by McGuire [976] when he conducted the ground resonance studies at the Lord Corporation. He used a rather simple

31 7 model but drew attention to the highly nonlinear stiffness and damping properties of the elastomeric dampers. Huber [99] has provided a comprehensive review of the advancements in the area of BMR and the programs pursued by various companies including Bell, Aerospatiale, Hughes Helicopter, Siorsy, MBB Germany and McDonnell Douglas Helicopter Systems. He has outlined the problems associated with the damper deformation amplitude, frequency and temperature. He has also provided review of the analytical techniques available for handling these problems. In his paper, he has emphasized that the industry needs to further improve the life-time of snubber dampers, improve the definition of replacement criteria, and advance failure analysis. Recently, Gandhi et al. [994a] developed a nonlinear viscoelastic solid model comprising of a combination of a quadratic softening leading spring in series and a linear Kelvin element. The model adequately mimics the nonlinear behavior of elastomer under large amplitude deformations for various equilibrium conditions and multi-frequency excitations with a single nonlinear differential equation. The effect of the damper model on the aeromechanical stability was studied by Gandhi [994a, 994b, 996a]. The quadratic spring and Kelvin chain model was extended to capture the reduction of loss factor at low strains and the resulting limit cycles associated with it [Gandhi and Chopra, 996a, b]. The results showed that the elastomeric dampers can stabilize ground resonance as well as eliminate the air resonance in hover and in forward flight. Their wor also drew attention to the effects of the static offset strains on the behavior of elastomeric materials in hover, and the periodic lag response in forward flight. The effect of the material stiffness on the lag frequency was also studied and it was concluded that the dampers increase the lag natural frequency. A time domain analytical model to analyze the aeroelastic response of helicopter rotor systems incorporating the elastomeric dampers has been developed by [Smith et al., 996a, b]. The elastomeric damper is modeled using the Anelastic Displacement Fields (ADF) method [Lesieutre and Bianchini, 995] which preserves the frequency dependent

32 8 behavior of the material and can be integrated in time domain. The model is configured by determining the ADF parameters using the experimental results at two strain rates for two different materials. It is validated with the experimental stress and strain hysteresis loops for various strain amplitudes. This model can also account for the static strain offset resulting from various operating conditions (e.g. drag in hover). In this study, both soft and stiff in-plane rotors are analyzed for hover and forward flight. It was found that the nonlinear behavior of the material has a significant effect on rotor stability. Also, the damping in the rotor system increases with the periodic lag response in forward flight. A recent study conducted by Hebert et al. [998] utilized a set of distributed, tuned vibration absorbers to introduce lag damping in the rotor system. This technique can be implemented on both articulated as well as bearingless rotors. In this study, it is assumed that multiple individual vibration absorbers that are distributed both in space and in frequency are embedded in the leading edge of the blade. Preliminary studies show that by replacing only 3% of the existing blade mass, these absorbers can provide the necessary lag damping. Sela and Rosen [99, 994] studied the influence of interconnected blades on lag damping in articulated rotor systems. They showed that if the lag dampers are connected between adjacent blades rather than blade and the hub, higher lag damping could be obtained for certain rotor configurations. Boeing Helicopters have been involved in developing and improving a nonlinear model of elastomeric dampers using a Coulomb friction model. A review of the efforts in this area and the bacground of this model have been discussed by Tarzanin and Panda [995]. They have shown that their model matched very well with the experimental data they obtained for various design configurations.