This paper identifies the desirable attributes of a flexible skin of a morphing wing. The study is conducted using airfoil camber morphing as an example. The ideal flex-skin would be highly anisotropic, having a low in-plane axial stiffness but a high out-of-plane flexural stiffness. Reduced skin axial stiffness allows morphing at low actuation cost. However, for some substructure and actuation designs, a lower limit on the skin's in-plane axial stiffness may be required to prevent unacceptable global camber deformation under aerodynamic loads. High flexural stiffness prevents local deformation of skin sections between supports due to aerodynamic pressure loads, and avoids buckling of skin sections under compression as the airfoil cambers under actuation force. For the camber morphing application the strain levels in the flex-skin are not expected to exceed around 2%. If the axial stiffness of the flex-skin is reduced significantly, it may be necessary to consider aerodynamic stiffness (negligible vis-à-vis structural stiffness for classical airfoils) to accurately calculate deformation under loading. The approach followed in the study can be used to identify specifications for the skin and then reverse engineer and design highly anisotropic composite skins that meet the specifications.
This study analytically examines the influence of cyclic variations in flap-, lag-, and torsion-stiffness of the blade root region (at harmonics of the rotational speed), for reduction of vibratory hub loads of a helicopter in forward flight. The results indicate that considerable reduction in hub vibrations is possible using small-to-moderate amplitude cyclic variations in stiffness (no greater than 15% of the baseline stiffness value). Torsion stiffness variations produced moderate reductions in vertical hub force, lag stiffness variations produced substantial reductions in all hub forces and the hub yaw moment, and flap stiffness variations produced very significant reductions in all hub forces and the hub roll and pitch moments. The amplitude of the cyclic stiffness variations required generally increase with increasing forward speed, for comparable reductions in vibration. At any given forward speed, if the amplitudes of cyclic stiffness variation are too large, the hub vibrations can actually increase. The stiffness variations that reduce the vibratory hub loads could produce increases in certain vibratory blade root load harmonics. Vibration reductions are achieved due to a decrease in the inertial contribution to the hub loads, or a change in relative phase of various contributions.
In the present study, a design methodology is developed for determining the optimal distribution of a limited amount of piezoelectric material and optimal skin for a conformable rotor airfoil section. The objective of the design optimization is to generate a conformable airfoil structure that produces significant trailing edge deflection under actuation loads, but minimal airfoil deflection under aerodynamic loads. Energy functions, Mutual Potential Energy (MPE) and Strain Energy (SE), are used as measures of the deflections created by the actuation and aerodynamic loads, respectively. The design objective is achieved by maximizing a multi-criteria objective function that represents a ratio of the MPE to SE. Several design optimization techniques are evaluated including geometry and concurrent geometry-topology optimizations. The results of the study indicate that the optimized conformable airfoil section obtained using the concurrent geometry-topology optimization can produce a significant downward trailing edge deflection, and the airfoil deformation due to the aerodynamic loads alone is small. However, the optimized airfoil design is extremely complex and contains intricate network of actuators, which may be difficult to fabricate. Systematic simplification of the structure is performed to obtain a conformable airfoil design that is simple and may be easy to build. Further parametric optimization is used to find optimal values of the skin axial and bending stiffness for an optimal conformable airfoil design. The airfoil can produce a downward trailing edge deflection equivalent to 3.7° of Effective Flap Angle from the actuation loads, with the peak-to-peak deflection being nearly twice the downward deflection, and the airfoil deformation due to the airload loads is less than 1°. The optimal skin should have less axial stiffness and much more bending stiffness as compared to a conventional skin.
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