Sathyamangalam Ramanarayanan Viswamurthy

Optimal placement of trailing-edge flaps for helicopter vibration reduction using response surface methods

This study aims to determine optimal locations of dual trailing-edge flaps to achieve minimum hub vibration levels in a helicopter, while incurring low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithm to determine the flap time history for vibration minimization. The reduced hub vibration levels and required flap control power (due to flap motion) are the two objectives considered in this study and the flap locations along the blade are the design variables. It is found that second order polynomial response surfaces based on the central composite design of the theory of design of experiments describe both objectives adequately. Numerical studies for a four-bladed hingeless rotor show that both objectives are more sensitive to outboard flap location compared to the inboard flap location by an order of magnitude. Optimization results show a disjoint Pareto surface between the two objectives. Two interesting design points are obtained. The first design gives 77 percent vibration reduction from baseline conditions (no flap motion) with a 7 percent increase in flap power compared to the initial design. The second design yields 70 percent reduction in hub vibration with a 27 percent reduction in flap power from the initial design.

Using the Complete Authority of Multiple Active Trailing-edge Flaps for Helicopter Vibration Control

In the current work, the application and advantages of multiple active trailing-edge flaps for helicopter vibration control in forward flight are investigated. Small active flaps of this type can be actuated using smart materials. A comprehensive aeroelastic analysis is used to model a helicopter with multiple trailing-edge flaps. The objective function containing the hub vibratory loads and flap control effort is minimized by an optimal controller. The control effort is differentially weighted for different flaps, such that all trailing-edge flaps are exploited to their full authority and limited to ±2 degrees peak deflection. Numerical results are obtained for one, two and three flaps and their optimal locations identified. A reduction of 76% in the hub vibration level is achieved at an advance ratio (nondimensional forward speed) of 0.3 using three flaps. For the four-bladed, soft-inplane, hingeless rotor considered in this work, it is observed that the extent of hub vibration reduction is directly related to the effect of trailing-edge flap motion on the contribution of the second flapwise bending mode to blade motion. It is also shown that multiple flaps can effectively modify the participation of second flapwise bending mode at a much lower control power than is needed with single and dual flap configurations. Furthermore, multiple flaps are shown to allow redundancy in operation and are considerably more effective than single flaps in low speed transition flight regimes because of their capability in distributing the airloads.

Optimization of Helicopter Rotor Using Polynomial and Neural Network Metamodels

This study aims to determine optimal locations of dual trailing-edge flaps and blade stiffness to achieve minimum hub vibration levels in a helicopter, with low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithmtodeterminethe flaptimehistoryforvibrationminimization.Usingtheaeroelasticanalysis,itisfoundthat the objective functions are highly nonlinear and polynomial response surface approximations cannot describe the objectives adequately. A neural network is then used for approximating the objective functions for optimization. Pareto-optimal points minimizing both helicopter vibration and flap power are obtained using the response surface and neural network metamodels. The two metamodels give useful improved designs resulting in about 27% reduction in hub vibration and about 45% reduction in flap power. However, the design obtained using response surface is less sensitive to small perturbations in the design variables.

Effect of Piezoelectric Hysterisis Nonlinearity on Helicopter Vibration Control Using Trailing Edge Flaps

This study deals with the effect of piezoelectric actuator hysteresis on helicopter vibration control using trailing edge flaps. An aeroelastic analysis is used represent the helicopter with trailing edge flaps. A compressible unsteady aerodynamic model is used to predict the incremental airloads due to trailing edge flap motion. The material and mechanical hysteresis in the piezoelectric actuator is modeled using the classical Preisach model. Experimental data from the literature is used to estimate the weighting function through geometric interpretation and numerical implementation. Results are obtained from vibration control studies performed using trailing edge flap with (1) linear actuator, (2) nonlinear actuator with hysteresis modeled and (3) nonlinear actuator approximated with a linear model. Results indicate that the actuator with hysteresis performs comparably to the actuator without hysteresis at both low and high speed steady forward flight, provided the controller is designed using an aeroelastic analysis including the hysteresis effects. In high speed forward flight, multicyclic control input gave 90 and 81 percent reduction in hub vibration in case(1) and case(2), respectively. However, in case(3), the controller performance deteriorated, yielding only 69 percent reduction in hub vibration. In low speed flight, multicyclic control input gave 99, 96 and 77 percent vibration reduction for case(1), case(2) and case(3), respectively. It is therefore important to account for hysteresis effects when designing controllers for trailing edge flap actuation.

Preliminary Studies with Active Flaps

There are primarily two types of flaps that are suitable to be mounted on helicopter blades: plain flaps and servo-flaps. The servo-flap design consists of auxiliary airfoil sections that are located aft of the trailing edge of the main blades, thereby resulting in high drag due to the exposure of hinges and supporting structure. In comparison, plain flaps are aerodynamically efficient since the flap is integrated into the blade structure, but are located closer to the blade elastic axis and their capability to generate pitching moments is correspondingly reduced. The plain flap configuration is used in this book. In this chapter, a simple aerodynamic model of the trailing-edge flap is used to obtain an idea about the advantages of 1, 2, and 4 trailing-edge flaps. Section 3.1 gives a brief description of the trailing-edge flap aerodynamic model and the flap control law. Section 3.2 explains formulation of optimization problem. Section 3.3 gives the numerical results. Section 3.4 gives the summary of this chapter.

Airfoil-Section Rotor Blades

The work done in the previous chapter is further extended to the design of a two-cell airfoil cross-section which is a more realistic model of the helicopter rotor blade. Optimum actuator placement, the effect of the current active twist concept on key characteristics such as blade loads, aeromechanical stability and trim controls is investigated. Aeroelastic analysis of the rotor blade is very important in the case of any refinement in the structural or aerodynamic model. Since the incorporation of piezoceramic changes the blade structural characteristics, it is important to ensure that the benefits gained due to the refinement should not be detrimental to the other aspects of the rotor such as performance, trim, and stability.

Box-Beam Active Rotor Blades

The previous chapter clearly showed that shear-based piezoceramic actuation using \(d_{15}\) is feasible for obtaining active twist. The current chapter dwells more on the development and validation of the concept of induced-shear-based piezoceramic actuation in helicopter rotor blades considering a simple two-cell box cross section. It is known that two-cell cross-section model is closer approximation to a realistic rotor blade section and is a good model for preliminary design studies.

Active Flap Controller Evaluation

The performance of a global and a local controller is studied in this chapter. It is well-known that the global controller yields optimal control input in a single step for a linear system. For a nonlinear system, however, the global controller gives only a suboptimal solution, since the transfer matrices (\(\mathbf{T_{i}}\)) are determined only once. Section 5.1 provides a comparison of the performance of global controller with a local controller. Section 5.2 presents the control law sensitivity studies. Section 5.3 explains the noise in hub loads measurements. Section 5.4 gives the summary of this chapter.

Trailing-Edge Flap Placement

The optimal location of flaps for multiple-flap configuration shown in Chap. 4 was obtained through parametric studies and the objective was to minimize only the hub vibration levels. These trailing-edge flaps are typically operated using piezoceramic actuators placed inside the blade section.

Flap Configuration and Control Law

Preliminary results obtained in Chap. 3 indicate that multiple trailing-edge flaps have great potential in helicopter vibration control. However, the aerodynamic model used in that chapter did not include the unsteady effects due to the motion of trailing-edge flaps. Also, the effects of the rotor wake were captured using a simple linear inflow model. In this chapter, a two-dimensional unsteady aerodynamic model for a flapped airfoil in compressible, subsonic flow is used to calculate the incremental aerodynamic loads due to flap motion. The free wake model described is utilized to obtain the inflow distribution over the rotor disk. Also, in this chapter, a control algorithm based on optimal control theory is used to determine the flap control input. Sections 4.1 and 4.2 give brief description of the flap inertial and aerodynamic load calculations. The flap control algorithm is explained in Sect. 4.3. Section 4.4 provides a comparison of differential versus uniform weighting method. The effect of trailing-edge flap motion on the blade motion is discussed in Sect. 4.5 and its effect on the optimal location of flaps is examined in Sect. 4.6. In Sect. 4.7, trailing-edge flap actuation power is explained. Section 4.8 explains trailing-edge flap hinge loads. Section 4.9 considers the performance of the multiple-flap system in the event of failure of one or more flaps. Section 4.10 gives the summary of this chapter.