Thomas R. McCarthy

Multilevel Decomposition Procedure for Efficient Design Optimization of Helicopter Rotor Blades

This paper addresses a multilevel decomposition procedure, for efficient design optimization of helicopter blades, with the coupling of aerodynamics, blade dynamics, aeroelasticity, and structures. The multidisciplinary optimization problem is decomposed into three levels. The rotor is optimized for improved aerodynamic performance at the first level. At the second level, the objective is to improve the dynamic and aeroelastic characteristics of the rotor. A structural optimization is performed at the third level. Interdisciplinary coupling is established through the use of optimal sensitivity derivatives. The Kreisselmeier-Steinhauser function approach is used to formulate the optimization problem when multiple design objectives are involved. A nonlinear programming technique and an approximate analysis procedure are used for optimization. Results obtained show significant improvements in the rotor aerodynamic, dynamic, and structural characteristics, when compared with a reference or baseline rotor.

A refined higher-order composite box beam theory

Abstract A three-dimensional theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Results presented for thick-walled box beams show the importance of including transverse shear in the formulation and the difficulty of defining a ‘beam’ twist for the entire cross-section.

A multidisciplinary optimization approach for vibration reduction in helicopter rotor blades

Abstract The paper addresses the integration of blade dynamics, aerodynamics, structures and aeroelasticity in the design of helicopter rotors using a formal optimization technique. The interaction of the disciplines is studied inside a closed-loop optimization process. The goal is to reduce vibratory shear forces at the blade root with constraints imposed on dynamic, structural and aeroelastic design requirements. Both structural and aerodynamic design variables are used. Multiobjective formulation. procedures are needed since more than one design objective is used. A nonlinear programming technique and an approximate analysis procedure are used for optimization. Substantial reductions are obtained in the vibratory root forces and moments while satisfying the remaining design criteria. The results of the optimization procedure using two multiobjective formulation procedures, are compared with a baseline or reference design.

An optimization procedure for the design of prop-rotors in high speed cruise including the coupling of performance, aeroelastic stability, and structures

An optimization procedure is developed to address the complex problem of designing prop-rotors in high speed cruise. The objectives are maximization of the aerodynamic efficiency in high speed cruise and minimization of the total rotor weight. Constraints are imposed on aeroelastic stability in cruise and rotor thrust. An isotropic box beam is used to model the principal load carrying member in the blade. Design variables include blade sweep and twist distributions, rotational velocity in cruise, and the box beam wall thickness. Since the optimization problem is associated with multiple design objectives, the problem is formulated using a multiobjective formulation technique known as the Kreisselmeier-Steinhauser function approach. The optimization algorithm is based on the method of feasible directions. A hybrid approximate analysis technique is used to reduce the computational expense of using exact analyses for every function evaluation within the optimizer. The results are compared to two reference rotors, unswept and swept. The optimum result shows significant improvements in the propulsive efficiency in cruise and reductions in the rotor weight without loss of aeroelastic stability or thrust, when compared to the reference unswept rotor. The swept reference rotor is initially unstable and the optimization procedure has been successful in producing a blade design which is fully stable with significant improvements in efficiency and blade weight. Off-design studies performed indicate that the optimum rotor maintains high propulsive efficiency over a wide range of operating conditions.

Design of high speed proprotors using multiobjective optimization techniques

A multidisciplinary optimization procedure is developed for the design of high speed proprotors. The objectives are to simultaneously maximize the propulsive efficiency in high speed cruise and the rotor figure of merit in hover. Since the problem involves multiple design objectives, multiobjective function formulation techniques are used. Two different multiobjective function procedures, the Kreisselmeier-Steinhauser function approach and the Minimum Sum β approach, are used. A detailed two-celled isotropic box beam is used to model the load carrying member within the rotor blade. Constraints are imposed on rotor blade aeroelastic stability in cruise, the first natural frequency in hover and total blade weight. Both aerodynamic and structural design variables are used. The results obtained using both objective function formulations are compared lo the reference rotor and show significant aerodynamic performance improvements without sacrificing dynamic and aeroelastic stability characteristics. The proced...

Structural optimization of high speed prop rotors including aeroelastic stability constraints

An optimization procedure is developed to address the problem of aeroelastic stability of high speed prop-rotor aircraft. A composite box beam is used as a perturbational stiffness model and the objective function to be minimized is the perturbational weight. An optimization algorithm, which used the method of feasible directions, is coupled with a hybrid approximate analysis to reduce the computational expense of exact analyses for every function evaluation. The results, compared to a reference rotor which is unstable in both hover and high speed cruise, show significant improvements in the aeroelastic stability without large weight penalties.

Investigation of composite ☐ beam dynamics using a higher-order theory

Abstract A higher-order composite ☐ beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.

A DESIGN OPTIMIZATION PROCEDURE FOR MINIMIZING DRIVE SYSTEM WEIGHT OF HIGH SPEED PROP-ROTORS

Abstract An optimization procedure is developed to address the problem of minimizing the drive system weight of high speed prop-rotor aircraft which are required to demonstrate fixed-wing-like efficiencies in high speed forward flight and maintain acceptable hover figure of merit similar to helicopters. The optimization is performed using the method of feasible directions. A hybrid approximate analysis procedure is also used to reduce the computational effort of using exact analysis for every function evaluation necessary within the optimizer. The results compared to a reference rotor show significant weight reductions. The aerodynamic performance of the optimized rotor, analyzed at “off-design” points to judge the strength of the optimization problem formulation and the validity of the resulting design, shows considerable improvements. The results are compared to the reference values and significant reduction in the weight is achieved.

Multidisciplinary optimization and design variable sensitivity of helicopter rotor blades using a composite box beam model

Abstract The paper addresses a fully integrated optimization procedure, for helicopter rotor blades, with the coupling of blade dynamics, aerodynamics, aeroelasticity and structures. The goal is to reduce vibratory shear forces at the blade root with constraints imposed on critical dynamic, aerodynamic, aeroelastic and structural design requirements. The blade is modeled with a composite box beam as the principal load carrying member. Nonlinear chord and twist variation are assumed. A wide range of both structural and aerodynamic design variables are used along with several subsets to determine the sensitivity of the design variables on the optimum design. The optimization problem is formulated with two objective functions and the Kreisselmeier-Steinhauser (K-S) function approach for multiple design objectives is used. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The procedure yields substantial reductions in the vibratory root forces and moments along with significant improvements in the remaining design requirements. Comparisons with previous work where isotropic beam elements were used indicate that the use of a composite box beam yields significant improvements in the blade design. Results are presented for several different cases of design variable vectors and are compared with a baseline, or reference blade.