NUMERICAL OPTIMIZATION OF HELICOPTER ROTOR BLADE DESIGN FOR ACTIVE TWIST CONTROL

The vibration of a helicopter has several different sources, such as the rotor, engine and transmission system. This creates a number of problems with performance, for example poor manoeuvrability, discomfort of the pilot, low fatigue life of the structural components, and, consequently, high operating costs. At the present time there are in existence various methodologies for vibration reduction, such as Higher Harmonic Control (HHC), Individual Blade Control (IBC), Active Control of Structural Response (ACSR), Active Twist Blade (ATB), and Active Trailing-edge Flap (ATF). The goal of the presented work is the development of an active twist actuation concept based on the application of Macro Fiber Composite (MFC) actuators. These actuators consist of polyamide films with IDE-electrodes. They are glued on the top and the bottom of piezoceramic ribbons and oriented at ±45 to the spar axis of the rotor blade. The interdigitated electrodes deliver the electric field required to activate the piezoelectric effect in the fibers and this, in turn, creates a stronger longitudinal piezoelectric effect along the length of the fibers. The properties and orientation of piezoelectric actuators cause the MFC actuators to induce shear stresses and thus distribute a twisting movement along the blade. The design methodology, based on the planning of experiments and response surface technique, has been developed for an optimum placement of Macro Fiber Composite (MFC) actuators in helicopter rotor blades. The optimisation problem for the optimum placement of actuators in helicopter rotor blades has been formulated on the results of parametric study. The investigated helicopter has a rotor blade which is equipped with NACA23012 airfoil and has a rectangular shape with an active part radius of 1.56 m and a chord length of 0.121 m. The blade also consists of D-spar. This is made of unidirectional fiberglass, reinforced plastic (UD GFRP), a skin made of ±45 GFRP, a foam core, balancing weight and MFC actuators placed on the top and bottom of the skin. The 3D finite element model of the rotor blade has been built by ANSYS. The rotor blade skins are modelled with linear layered structural shell elements (SHELL99), balancing weights and foam with 3D 20node structural solid elements (SOLID186). The spar is modelled with shell and solid elements. The optimisation results have been obtained for design solutions, connected with an application of active materials, and checked by the finite element calculations.


Introduction
The vibration of a helicopter has several different sources, such as the rotor, engine and transmission system. This creates a number of problems with performance, for example poor manoeuvrability, discomfort of the pilot, low fatigue life of the structural components, and, consequently, high operating costs. Traditional helicopter vibration control methods are based on the application of Higher Harmonic Control (HHC) and Individual Blade Control (IBC). However, because of the recent development of smart materials, a new active control technique has begun to be implemented for the control of rotor blade vibration, noise reduction and enhanced performance. Recently, several active control approaches have been investigated. These have used smart material actuation to achieve individual blade control without the need for complex mechanisms in the rotating frame. The application of such materials for control has resulted in the production of two innovative designs: the trailing edge flap rotor and active twist rotor. Early studies on the concept of an active twist rotor were done by Chen and Chopra in 1996 [1,2]. According to their designs, the rotor blade incorporated discrete dual-layer monolithic piezopatch elements embedded at +45 0 under the upper skin and -45 0 under the lower skin of the rotor blade. Experiments were conducted on a two bladed, hingeless rotor with a 6 foot diameter and built to a 1/8 Froude scale. Different piezoceramic arrangements were analyzed along with different rotation speeds. The maximum tip twists at resonance frequencies were 0.35 0 and 1.1 0 . Later, in 1998, Bernhard and Chopra [3,4] developed an active, on blade vibration-reduction system which used smart, active blade tips (SABT) and was driven by a piezo-induced, bending-torsion coupled actuator. The beam was designed specifically to fit within the rotor blade profile and was used essentially as a pure torsional actuator. The beam lay-up was selected so that if the inboard end was clamped, the outboard end resulted in a twist. This twist was measured by the deflection of the SABT. A Mach-scale active twist rotor was fabricated and tested using the SABT concept. The rotating twist amplitudes with SABT are similar to the tip twist amplitudes reported by Chen and Chopra [8,9]. In 1998 a new approach to smart materials was adopted by Rodgers and Hagood [5,6]. They attempted to develop an integral, twist-actuated rotor which would allow for individual blade control. Active fiber composites (AFC) were integrated within a composite rotor blade to induce a twisting movement. These were active plies oriented at 45 0 angles to the blade span in order to induce shear stresses and the distribution of a twisting movement along the blade. A CH-47D blade was designed to a 1/6 Mach-scale and was then fabricated and tested in hover at the MIT hover test facility. Good correlation was obtained between theory and the results of experiments. The goal of the present work is the development of an active twist actuation concept based on the application of Macro Fiber Composite (MFC) actuators [7,8]. A Macro Fiber Composite was developed at NASA Langley Research Center. The actuators consist of polyamide films with interdigited electrodes that are glued on the top and bottom of piezoceramic fibres ( Fig. 1,2).  The interdigitated electrodes deliver the electric field required to activate the piezoelectric effect in the fibers. This then allows for the creation of stronger longitudinal piezoelectric effects along the length of the fibers. In contrast with MFC, the circular cross-section PZT fibers of the AFC had very little contact area between the interdigitated electrodes and the fibers. This resulted in the transfer of the electric field into the PZT fibers inefficiently. The rectangular PZT fibers of the MFC improved the maximum contact area between the PZT fibers and the interdigitated electrodes and, as a result, increased the angle of twist [9]. The aim of the present study is to describe the methodology, based on the planning of experiments and response surface technique, for the optimal design of active rotor blades using MFC actuators. The reason for this is to obtain high piezoelectric actuation forces and displacements with the minimal actuator weight and energy applied. The structural static analysis with a thermal load is carried out to characterize an active twist of the helicopter rotor blade. Design solutions for an application of active materials are studied to estimate the effectiveness.

Helicopter rotor blade
An investigated helicopter rotor blade (Fig. 3) is equipped with NACA23012 airfoil and has a rectangular shape with active part radius R =1.56 m and chord length c=0.121 m.

Finite element analysis
The 3D finite element model of the rotor blade is produced by ANSYS (Fig. 5). The rotor blade skin and spar "moustaches" are modelled with linear layered, structural shell elements (SHELL99). The spar and foam, however, are produced using 3D 20 node structural solid elements (SOLID186). The clamped boundary conditions are applied from one end-side of the rotor blade. The thermal analogy based on the analogy between the piezoelectric effect and thermoelastic effect. An applied electric field is modelled as a thermal load. The correspondence between piezoelectric strain and thermal strain is obtained by taking: where d ij is the effective piezoelectric constant and ∆ ES is the electrode spacing taken as ∆ ES =0.5 mm. Then, steady-state thermal analysis is carried out to determine a torsion angle of the rotor blade (Fig. 6), static torsion analysis is employed to determine a location of the elastic axis and modal analysis is used to determine the first torsion eigenfrequency of the rotor blade.

Parametric study
Before the formulation of the optimisation problem, the parametric study has been carried out with the purpose to decrease a number of design parameters (Fig. 7). By doing this the accuracy of the obtained optimal results will be increased. The findings of parametric study have been investigated in previous work [10]. The skin thickness is examined as a discrete value design parameter with the step ∆t (+45/-45) = 0.25 mm. The smallest influence has been shown by spar "moustaches" length, web length and web thickness. The influence on the torsional angle of the spar "moustaches" thickness and web thickness together is better than only the spar "moustaches" thickness. The voltage has influence on the strain. But this influence is less than permissible. For this reason, web thickness, web length, voltage and spar "moustaches" thickness have been excluded from the set of design parameters used in this optimisation.

Optimal design
Due to the large dimensions of the numerical problem to be solved, the non-direct optimisation technique should be applied. Indeed, the application of direct minimisation algorithms and multiple finite element analysis is too expensive from a computational point of view. For this reason, an optimisation methodology is developed employing the method of experimental design and response surface technique.

Formulation of optimisation problem
An optimisation problem for the optimum placement of actuators in helicopter rotor blades (Fig. 8) has been formulated based on the results of parametric study [10] and taking into account the producer's requirements:   In the previous work [10] the application of active material has been investigated when it is applied on the top of the skin. Later studies of parametric research for two different applications of the active material ( Fig. 9) have been studied to determine their effectiveness. As can be seen from the graphs (Fig. 10), variant 2 is considerably more effective than variant 1 in relation to active twist of the helicopter rotor blade. For this reason, the second variant of application of smart material has been chosen as a solution to the optimization problem, when active materials apply on the top and bottom of skin.

Experimental design and FEM simulations
The program EDAOpt [11] was used for the generation of the experimental design. D-optimal experimental design is formulated for 4 design parameters and 30 experiments. Then, in the points of the plan of experiments, both the structural static analysis with a thermal load and modal analysis are carried out to determine the torsion angles in the rotor blade and the first torsion eigenfrequency respectively. As with additional parameters, a location of the centre of gravity and rotor blade mass are found from the finite element model. Determining the elastic axis location is a more complicated problem and requires a solution to the additional static torsion problem. This involves the application of two forces independently from both sides of the sought elastic centre [12].

Response surfaces.
At the time of the present study a form of the equation of regression was previously unknown [13]. There are two requirements for the equation of regression: accuracy and reliability. Accuracy is characterised as a minimum of standard deviation of the   Accordance between approximation function and control points for frequency and MFC chord-wise length.

Optimisation results
The non-linear, global optimisation problem is executed by the Improved Multistart Random Search [14] using the response surfaces obtained. In the first stage, the design problem has been solved with the purpose of obtaining a maximum torsion angle. The optimisation is given in Tables 1-3 together with the finite element solutions obtained in the optimal point. As can be seen in the tables, the difference between finite element and response surface solutions is reasonable.

Conclusions
An optimisation problem for the optimum placement of actuators in helicopter rotor blades has been formulated on the results of parametric study using the finite element method. The methodology, based on the planning of experiments, the response surface technique, and parametric study, has been developed for the optimum placement of actuators in helicopter rotor blades. To describe the behaviour of a twisted rotor blade, the finite element method has been applied in the sample points of experimental design. For this purpose the structural static analysis with a thermal load, using a 3D finite element model, has been developed by ANSYS. Minimisation problems have been solved by the Improved Multistart Random Search, using the approximating functions instead of the original functions.
From the optimisation results of the present study, and in comparison with previous studies, it was observed that the 2nd variant arrangement of MFC is more effective than the 1 st in the production of a maximum torsion angle under voltage on 26%. From the approximation function and using the obtained optimal results there can be found a compromise between the necessary solutions.