Nonlinear dynamics of helicopter with slung load analysis by continuation methods

Application of helicopters to transport of heavy and bulky loads creates the stability problems specially of hovering with hanging loads. The presence of an external load modifies the flight dynamics and handling qualities characteristics of a helicopter because the load behaves like a pendulum, and it can change natural frequencies and mode shapes of the low frequency modes of the helicopter. Additionally, the aerodynamic characteristics of the load may make it unstable in certain flight conditions, with obvious repercussions on the stability and the safety of the entire helicopter/load system. The paper presents a study of the fight dynamics of an articulated rotor helicopter carrying a suspended load. The rotorcraft model includes rigid body dynamics, individual flap and lag blade dynamics, and inflow dynamics. The load is modelled as pendulum with a single suspension point. Helicopter with suspended load is the inherently non-linear and time varying system. Manoeuvrability of this system in wide flight regimes involves non-linear aerodynamics and inertial coupling. Dynamical systems theory provides a methodology for studying non-linear systems of ordinary differential equations. Bifurcation theory is a part of that theory which is considering changes in the stability lead to qualitatively different responses of the system. Results from dynamical systems theory were used to predict the nature of the instabilities caused by bifurcations and the response of the rotorcraft and suspended after a bifurcation was studied. INTRODUCTION Carrying external suspended loads has always been one of the traditional missions of the helicopter. Both military and commercial operators have exploited the capability of the helicopter to rapidly move heavy loads to locations where the use of ground based equipment would be impractical or impossible. The presence of an external load can *Division Manager, PhD. **Deputy Commandant, PhD. ***Assoc. Professor, PhD, D. Sc, Member AIAA + Senior Scientist, PhD. Senior Engineering Specialist. Copyright © 2001 The American Institute of Aeronautics and Astronautics Inc. All rights reserved. modify the fight dynamic and handling qualities characteristics of a helicopter because the load behaves like a pendulum, and it can change natural frequencies and mode shapes of the low frequency modes of the helicopter. Additionally, the aerodynamic characteristics of the load may make it unstable in certain fight conditions, with obvious repercussions on the stability and the safety of the entire helicopter/load system. The dynamics of a helicopter with external suspended loads received considerable attention in the late 1960's and early 1970's. Two reasons for this interest were the extensive external load operations in the Vietnam war, and the Heavy-Lift Helicopter program (HLH). This interest has been renewed recently, prompted by the re-evaluation and extension of the ADS-33 Helicopter Handling Qualities Specifications to transport helicopters, and in the expectation of new cargo helicopter procurements. One of the first theoretical studies of the dynamics of a helicopter with a slung load is due to Lucassen and Sterk. A simple 3-degree of freedom modelled the hover longitudinal dynamics of the helicopter and the angular displacement of the load. A single suspension point was assumed and the aerodynamic forces and moments on the load were neglected. In general, the pole associated with the load pendulum mode was stable; the phugoid remained unstable, but its frequency decreased with increasing cable length. For some combination of parameters the helicopter mode became unstable while the load mode was stabilised. Szustak and Jenney pointed out that a conventional stability augmentation system was not adequate for precision hover and load release, and could result in pilot-induced oscillations (PIO). A more effective solution consisted of an inner loop in which the relative motion of aircraft and load was fed back to cyclic, and an outer loop in which the aircraft position above ground was fed back, again to cyclic. Dukes studied the basic stability characteristics of a helicopter with a slung load, and possible feedback stabilisation schemes, and appropriate piloting strategies for various manoeuvres. A 3-degree of freedom longitudinal helicopter/load model was used. Positive pitch damping, whether provided by the rotor alone or also by a fight control system, did not