Recent Applications of Design Optimization to Rotorcraft-A Survey

Introduction T HE successful design of a helicopter relies, perhaps to a greater extent than for any other aerospace vehicle, on the tight integration of a variety of aeronautical engineering disciplines. An example of this is the design of the main rotor system. Rotor blades are slender, flexible beams. Even in normal operating conditions they may undergo elastic deformations in bending and torsion that can be beyond the limits of linear beam theories and, therefore, moderately large deformations need to be taken into account. Blade flexibility and related dynamic effects influence not only blade and hub stresses and fatigue life, but also interact with the aerodynamic loading, because the deformations of the blades substantially modify the effective angle of attack of each cross section. In turn, rotor-blade aerodynamics is coupled with structural dynamics because much of the damping in flap and lag bending and in torsion is of aerodynamic origin. With the partial exception of hovering flight, the structural and aerodynamic problems of a helicopter rotor blade are intrinsically unsteady. Even in steady cruise conditions, the blade can encounter airflow velocities that range from transonic or slightly supersonic to low speed, including stall, and reversed flow. The variations occur with a period of the order of 200 ms. Therefore, the calculation of aerodynamic forces and structural loads on a rotor blade is really an integrated aeroelastic problem. An even broader integration may be required when handling qualities considerations are brought into the design. Modern flight-control systems can modify the natural characteristics of the response of the helicopter to pilot inputs, in ways that make the helicopter easier to fly and reduce the pilot workload. For example, a flight-control system can make the helicopter react to a step input of lateral control with a step variation of roll angle, instead of the more natural step variation of roll rate. Experience has shown that the ability to achieve this kind of tailored handling quality characteristics can be limited by adverse dynamic interactions with the main rotor system. This way, the disciplines of flight dynamics and control-system design become closely coupled with structural dynamics and aerodynamics. These are but two of the many examples of helicopter engineering problems that require a multidisciplinary approach. This requirement has motivated the development of comprehensive analysis codes during the last two decades. Such codes attempt to integrate, in a single software program, the mathematical models required by each helicopter engineering discipline. 6 It is beyond the scope of the present paper to describe these codes in any detail. They are mentioned here as evidence that the design of a helicopter is intrinsically multidisciplinary, and perhaps more so than for any other aerospace vehicle. Design optimization appears to be an ideal methodology to help simplify helicopter design because it can provide a systematic way of integrating the various disciplines involved. However, despite considerable activity in this field, helicopter optimization has not yet reached the same maturity and acceptance as structural optimization. Therefore, the main objectives of the present paper are not only to review the current state of the art for rotorcraft applications of optimization, but also to identify issues that have impeded its progress. An extensive survey of multidisciplinary design optimization (MDO) applications to aerospace design has been recently presented by Sobieszczanski-Sobieski and Haftka. The present paper is meant to supplement it with a narrower focus on rotorcraft. Research in helicopter applications of optimization started in earnest in the early 1980s with the pioneering works of Refs. 8 — 12. Extensive research in this area was carried out throughout the 1980s. This research is reviewed in two papers by Friedmann and Adelman and Mantay; the first focuses on the use of optimization for vibration reduction, whereas the second addresses MDO applications. The present paper will focus primarily on developments in subsequent years. The words helicopter and rotorcraft will be used interchangeably. In fact, with the notable exception of tilt-rotor and tilt-wing aircraft, the rotorcraft of primary interest for optimization applications is the helicopter. Many practical helicopter optimization problems are not particularly different from those of other aerospace or ground vehicles. An example could be the minimum weight, structural optimization of a fuselage subject to preassigned harmonic loads, and with stress constraints. Therefore, the present paper will only address those design problems that are unique to the helicopter; in most cases this implies that the presence of the main rotor system is a dominant ingredient in the optimization. In general, no attempt will be made to extract specific design guidelines from the literature reviewed, such as, for example, ply orientations, airfoil shapes, or planform geometries of rotor blades. As pointed out later in this paper, many practical helicopter problems still cannot be modeled with the desired accuracy, and this affects negatively the reliability of the results obtained from optimization. The majority of the helicopter optimization studies have addressed some form of the rotor dynamic behavior, such as