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NASA NTRS2000

Improving Tiltrotor Whirl-Mode Stability with Rotor Design Variations

Further increases in tiltrotor speeds are limited by coupled wing/rotor whirl-mode aeroelastic instability. Increased power, thrust, and rotor efficiency are not enough: the whirl-mode stability boundary must also be improved. With current technology, very stiff, thick wings of limited aspect ratio are essential to meet the stability requirements, which severely limits cruise efficiency and maximum speed. Larger and more efficient tiltrotors will need longer and lighter wings, for which whirl-mode flutter is a serious design issue. Numerous approaches to improving the whirl-mode airspeed boundary have been investigated, including tailored stiffness wings, active stability augmentation, variable geometry rotors, highly swept tips, and at one extreme, folding rotors. The research reported herein began with the much simpler approach of adjusting the chordwise positions of the rotor blade aerodynamic center and center of gravity, effected by offsetting the airfoil quarter chord or structural mass with respect to the elastic axis. The research was recently extended to include variations in blade sweep, control system stiffness, and pitch-flap coupling (delta(sub 3)). As an introduction to the subject, and to establish a baseline against which to measure stability improvements, this report will first summarize results. The paper will then discuss more advanced studies of swept blades and control-system modifications.

Acree, C. W., Jr.↗

NASA NTRS2009

An Overview of Prognosis Health Management Research at Glenn Research Center for Gas Turbine Engine Structures With Special Emphasis on Deformation and Damage Modeling

Herein a general, multimechanism, physics-based viscoelastoplastic model is presented in the context of an integrated diagnosis and prognosis methodology which is proposed for structural health monitoring, with particular applicability to gas turbine engine structures. In this methodology, diagnostics and prognostics will be linked through state awareness variable(s). Key technologies which comprise the proposed integrated approach include (1) diagnostic/detection methodology, (2) prognosis/lifing methodology, (3) diagnostic/prognosis linkage, (4) experimental validation, and (5) material data information management system. A specific prognosis lifing methodology, experimental characterization and validation and data information management are the focal point of current activities being pursued within this integrated approach. The prognostic lifing methodology is based on an advanced multimechanism viscoelastoplastic model which accounts for both stiffness and/or strength reduction damage variables. Methods to characterize both the reversible and irreversible portions of the model are discussed. Once the multiscale model is validated the intent is to link it to appropriate diagnostic methods to provide a full-featured structural health monitoring system.

Arnold, Steven M.↗

NASA NTRS2009

An Overview of Prognosis Health Management Research at Glenn Research Center for Gas Turbine Engine Structures With Special Emphasis on Deformation and Damage Modeling

Arnold, Steven M.↗

NASA NTRS2009

An Overview of Prognosis Health Management Research at GRC for Gas Turbine Engine Structures With Special Emphasis on Deformation and Damage Modeling

Herein a general, multimechanism, physics-based viscoelastoplastic model is presented in the context of an integrated diagnosis and prognosis methodology which is proposed for structural health monitoring, with particular applicability to gas turbine engine structures. In this methodology, diagnostics and prognostics will be linked through state awareness variable(s). Key technologies which comprise the proposed integrated approach include 1) diagnostic/detection methodology, 2) prognosis/lifing methodology, 3) diagnostic/prognosis linkage, 4) experimental validation and 5) material data information management system. A specific prognosis lifing methodology, experimental characterization and validation and data information management are the focal point of current activities being pursued within this integrated approach. The prognostic lifing methodology is based on an advanced multi-mechanism viscoelastoplastic model which accounts for both stiffness and/or strength reduction damage variables. Methods to characterize both the reversible and irreversible portions of the model are discussed. Once the multiscale model is validated the intent is to link it to appropriate diagnostic methods to provide a full-featured structural health monitoring system.

Arnold, Steven M.↗

NASA NTRS1985

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Majda, G.↗

NASA NTRS1981

Application of a local linearization technique for the solution of a system of stiff differential equations associated with the simulation of a magnetic bearing assembly

A digital local linearization technique was used to solve a system of stiff differential equations which simulate a magnetic bearing assembly. The results prove the technique to be accurate, stable, and efficient when compared to a general purpose variable order Adams method with a stiff option.

Kibler, K. S.↗

NASA NTRS1980

Full scale wind tunnel investigation of a bearingless main helicopter rotor

A stability test program was conducted to determine the effects of airspeed, collective pitch, rotor speed and shaft angle on stability and loads at speeds beyond that attained in the BMR/BO-105 flight test program. Loads and performance data were gathered at forward speeds up to 165 knots. The effect of cyclic pitch perturbations on rotor response was investigated at simulated level flight conditions. Two configuration variations were tested for their effect on stability. One variable was the control system stiffness. An axially softer pitch link was installed in place of the standard BO-105 pitch link. The second variation was the addition of elastomeric damper strips to increase the structural damping. The BMR was stable at all conditions tested. At fixed collective pitch, shaft angle and rotor speed, damping generally increased between hover and 60 knots, remained relatively constant from 60 to 90 knots, then decreased above 90 knots. Analytical predictions are in good agreement with test data up to 90 knots, but the trend of decreasing damping above 90 knots is contrary to the theory.

Source record↗

NASA NTRS1984

Skin-stiffener interface stresses in composite stiffened panels

A model and solution method for determining the normal and shear stresses in the interface between the skin and the stiffener attached flange were developed. An efficient, analytical solution procedure was developed and incorporated in a sizing code for stiffened panels. The analysis procedure described provides a means to study the effects of material and geometric design parameters on the interface stresses. These stresses include the normal stress, and the shear stresses in both the longitudinal and the transverse directions. The tendency toward skin/stiffener separation may therefore be minimized by choosing appropriate values for the design variables. The most important design variables include the relative bending stiffnesses of the skin and stiffener attached flange, the bending stiffness of the stiffener web, and the flange width. The longitudinal compressive loads in the flange and skin have significant effects on the interface stresses.

Wang, J. T. S.↗

NASA NTRS1987

Prediction and experimental observation of damage dependent damping in laminated composite beams

The equations of motion are developed for laminated composite beams with load-induced matrix cracking. The damage is accounted for by utilizing internal state variables. The net result of these variables on the field equations is the introduction of both enhanced damping, and degraded stiffness. Both quantities are history dependent and spatially variable, thus resulting in nonlinear equations of motion. It is explained briefly how these equations may be quasi-linearized for laminated polymeric composites under certain types of structural loading. The coupled heat conduction equation is developed, and it is shown that an enhanced Zener damping effect is produced by the introduction of microstructural damage. The resulting equations are utilized to demonstrate how damage dependent material properties may be obtained from dynamic experiments. Finaly, experimental results are compared to model predictions for several composite layups.

Allen, D. H.↗

NASA NTRS1989

On equivalence of discrete-discrete and continuum-discrete design sensitivity analysis

Developments in design sensitivity analysis (DSA) method have been made using two fundamentally different approaches as shown. In the first approach, a discretized structural finite element model is used to carry out DSA. There are three different methods in the discrete DSA approach: finite difference, semi-analytical, and analytical methods. The finite difference method is a popular one due to its simplicity, but a serious shortcoming of the method is the uncertainty in the choice of a perturbation step size of design variables. In the semi-analytical method, the derivatives of stiffness matrix is computed by finite differences, whereas in the analytical method, the derivatives are obtained analytically. For the shape design variable, computation of analytical derivative of stiffness matrix is quite costly. Because of this, the semi-analytical method is a popular choice in discrete shape DSA approach. However, recently, Barthelemy and Haftka presented that the semi-analytical method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. They found that accuracy problems occur even for a simple cantilever beam. In the second approach, a continuum model of the structure is used to carry out DSA.

Choi, Kyung K.↗

NASA NTRS1991

Scale effects in buckling, postbuckling and crippling of graphite-epoxy Z-section stiffeners

The buckling, postbuckling and crippling of Hercules Inc. AS4/3502 graphite-epoxy Z-section stiffeners is investigated as a function of specimen structural parameters. Variables addressed are flange and web widths, flange-to-web corner radius, thickness and stacking sequence. Analytical, numerical and experimental results are discussed. Nondimensional parameters have been obtained from an analytical model which effectively normalize the initial local buckling data reported herein and in the references. The nature of the load redistribution after buckling and its impact on postbuckling stiffness is related to the geometric variables. A normalized total width concept is used to unify the crippling data.

Wieland, Todd M.↗

NASA NTRS1984

Sizing-stiffened composite panels loaded in the postbuckling range

Stiffened panels are widely used in aircraft structures such as wing covers, fuselages, control surfaces, spar webs, bulkheads, and floors. The detailed sizing of minimum-weight stiffened panels involves many considerations. Use of composite materials introduces additional complexities. Many potential modes of failure exist. Analyses for these modes are often not trivial, especially for those involving large out-of-plane displacements. Accurate analyses of all potential failure modes are essential. Numerous practical constraints arise from manufacturing/cost considerations and from damage tolerance, durability, and stiffness requirements. The number of design variables can be large when lamina thicknesses and stacking sequence are being optimized. A significant burden is placed on the sizing code due to the complex analyses, practical constraints, and number of design variables. On the other hand, sizing weight-efficient panels without the aid of an automated procedure is almost out of the question. The sizing code postbuckled Open-Stiffener Optimum Panels (POSTOP) has been developed to aid in the design of minimum-weight panels subject to the considerations mentioned above. Developed for postbuckled composite panels, POSTOP may be used for buckling resistant panels and metallic panels as well. The COPES/CONMIN optimizer is used in POSTOP although other options such as those in the ADS system could be substituted with relative ease. The basic elements of POSTOP are shown. Some of these elements and usage of the program are described.

Biggers, S. B.↗

NASA NTRS1990

An enhanced integrated aerodynamic load/dynamic optimization procedure for helicopter rotor blades

An enhanced integrated aerodynamic load/dynamic optimization procedure is developed to minimize vibratory root shears and moments. The optimization is formulated with 4/rev vertical and 3/rev inplane shears at the blade root as objective functions and constraints, and 4/rev lagging moment. Constraints are also imposed on blade natural frequencies, weight, autorotational inertia, centrifugal stress, and rotor thrust. The 'Global Criteria Approach' is used for formulating the multi-objective optimization. Design variables include spanwise distributions of bending stiffnesses, torsional stiffness, nonstructural mass, chord, radius of gyration, and blade taper ratio. The program CAMRAD is coupled with an optimizer, which consists of the program CONMIN and an approximate analysis, to obtain optimum designs. The optimization procedure is applied to an advanced rotor as a reference design. Optimum blade designs, obtained with and without a constraint on the rotor thrust, are presented and are compared to the reference blade. Substantial reductions are obtained in the vibratory root forces and moments. As a byproduct, improvements are also found in some performance parameters, such as total power required, which were not considered during optimization.

Chattopadhyay, Aditi↗

NASA NTRS1990

An enhanced integrated aerodynamic load/dynamic approach to optimum rotor blade design

An enhanced integrated aerodynamic load/dynamic optimization procedure is developed to minimize vibratory root shears and moments. The optimization is formulated with 4/rev vertical and 3/rev inplane shears at the blade root as objective functions and constraints, and 4/rev lagging moment. Constraints are also imposed on blade natural frequencies, weight, autorotational inertia, contrifugal stress, and rotor thrust. The Global Criteria Approach is used for formulating the multi-objective optimization. Design variables include spanwise distributions of bending stiffnesses, torsional stiffness, nonstructural mass, chord, radius of gyration, and blade taper ratio. The program CAMRAD is coupled with an optimizer, which consists of the program CONMIN and an approximate analysis, to obtain optimum designs. The optimization procedure is applied to an advanced rotor as a reference design. Optimum blade designs, obtained with and without a constraint on the rotor thrust, are presented and are compared to the reference blade. Substantial reductions are obtained in the vibratory root forces and moments. As a byproduct, improvements are also found in some performance parameters, such as total power required, which were not considered during optimization.

Chattopadhyay, Aditi↗

NASA NTRS2002

Vibration Reduction of Helicopter Blade Using Variable Dampers: A Feasibility Study

In the report, the investigation of controlling helicopter-blade lead-lag vibration is described. Current practice of adding passive damping may be improved to handle large dynamic range of the blade with several peaks of vibration resonance. To minimize extra-large damping forces that may damage the control system of blade, passive dampers should have relatively small damping coefficients, which in turn limit the effectiveness. By providing variable damping, a much larger damping coefficient to suppress the vibration can be realized. If the damping force reaches the maximum allowed threshold, the damper will be automatically switched into the mode with smaller damping coefficient to maintain near-constant damping force. Furthermore, the proposed control system will also have a fail-safe feature to guarantee the basic performation of a typical passive damper. The proposed control strategy to avoid resonant regions in the frequency domain is to generate variable damping force in combination with the supporting stiffness to manipulate the restoring force and conservative energy of the controlled blade system. Two control algorithms are developed and verified by a prototype variable damper, a digital controller and corresponding algorithms. Primary experiments show good potentials for the proposed variable damper: about 66% and 82% reductions in displacement at 1/3 length and the root of the blade respectively.

Lee, George C.↗

NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗

NASA NTRS1986

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

Majda, George↗

NASA NTRS1994

A new look at the simultaneous analysis and design of structures

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

Striz, Alfred G.↗