Design Sensitivity Analysis for Helicopter Flight Dynamic and Aeromechanic Stability

Abstract

An ef cient technique is described to calculate the sensitivities of bandwidth and phase delay (de ned according to the ADS-33 speci cation) and poles of a helicopter with respect to the blade torsion stiffness GJ. The technique is based on the derivation of expressions for the sensitivities using chain rule differentiation of appropriate portions of the equations of motion. Two con gurations are studied, similar to the Eurocopter BO-105 and the Sikorsky UH-60. The study shows that the semi-analytical sensitivities are in excellent agreement with the corresponding nite difference-based sensitivities and that they are far less sensitive to step size. For the BO-105 con guration, phase bandwidth, gain bandwidth, phase delay, and poles are only weakly nonlinear functions of the torsion stiffness GJ, and therefore, linear approximations are accurate for broad variations of GJ. The same is mostly true for the UH-60 con guration, except that move limits are recommended for linear approximationsto the phase delay at low GJ. The new technique is computationally very ef cient. The additional cost of calculating the sensitivities is 4% of that of a complete linearized analysis, regardless of rotor con guration and ight speed. The gure is expected to apply also to sensitivities with respect to ap and lag stiffness. Nomenclature A= state matrix A nr = state matrix in nonrotating frame B = control matrix B nr = control matrix in nonrotating frame C = output matrix D = distance from level 1 boundary in ADS-33 requirement charts E I 2 , E I 3 = blade lag and ap bending stiffnesses G.i !/ = frequency-responsematrix G J = blade torsion stiffness M t , M l , M f = elastic moment components acting on the blade section p = generic design parameter p, q, r = fuselage roll, pitch, and yaw rates T = multiblade coordinate transformation matrix u = control vector v, w, Á = blade elastic displacements x = state vector y = output vector µ G = geometric pitch angle of the cross section (pitch control angle plus builtin twist) ¿ p = time delay ! BW = bandwidth

Helicopter Flying Qualities Sensitivity Analysis with Respect to Aerodynamic Configuration

“…Using vortex theory, the isolated rotor induced velocity that is activized by zero-and first-order circulations (second and higher order circulations are neglected) can be expressed by a Fourier series [5] .…”

“…In order to investigate expediently the impact of aerodynamic layout changing on flying qualities, the rotor-fuselage downwash coefficient is expressed as follow [5] : In Eq.2, χ is rotor wake angel, rotor-stabilizer downwash coefficient is 1.0, rotor-tail rotor downwash coefficient is 1.8.…”

Survey on Flight Control Technology for Large-Scale Helicopter

“…To cope with this problem, the engineering tool CONDUIT uses multiobjective optimization, which allows the relative importance of each design specification to be determined, to ensure that the best feasible solution of the proposed control system is achieved within all robustness constraints. Besides, other techniques being developed are also applied to study multidisciplinary design optimization of FCS parameters [38] and automated procedure for gain-scheduled flight control law design [39]. Future development of the engineering toolset will directly provide designers rapid insight on control system response and accelerate the R&D process for helicopter industry.…”