Until recently, computer simulations of helicopter rotor dynamics have employed equations of motion that have been linearized or simplified. These modified equations of motion did not allow for the evaluation of nonlinear material properties in the rotor since higher order terms in the dynamics had been modified in the simplification process. With recent advances in both computer simulation hardware and symbolic mathematic manipulation software, the full nonlinear equations of motion may be utilized in helicopter rotor simulations. This dissertation reports on the use of the full nonlinear equations of motion in the analysis of rotor blade lead/lag motion and its effect on rotor hub and rigid body fulselage motion. Nonlinear modeling methods are implemented using Maple symbolic mathematic manipulation software and Matlab and Simulink computer simulation environments. Results are compared to the RAH- 66 Comanche Froude scale wind tunnel article and new methodologies evaluated in the search for a damperless rotor system that is free of ground and air resonance mechanical instabilities.
This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model. Curtiss, H. C., Jr. Ames Research Center
There has been significant interest for designing flight controllers for small-scale unmanned helicopters. Such helicopters preserve all the physical attributes of their full-scale counterparts, being at the same time more agile and dexterous. This book presents a comprehensive and well justified analysis for designing flight controllers for small-scale unmanned helicopters guarantying flight stability and tracking accuracy. The design of the flight controller is a critical and integral part for developing an autonomous helicopter platform. Helicopters are underactuated, highly nonlinear systems with significant dynamic coupling that needs to be considered and accounted for during controller design and implementation. Most reliable mathematical tools for analysis of control systems relate to modern control theory. Modern control techniques are model-based since the controller architecture depends on the dynamic representation of the system to be controlled. Therefore, the flight controller design problem is tightly connected with the helicopter modeling. This book provides a step-by-step methodology for designing, evaluating and implementing efficient flight controllers for small-scale helicopters. Design issues that are analytically covered include: • An illustrative presentation of both linear and nonlinear models of ordinary differential equations representing the helicopter dynamics. A detailed presentation of the helicopter equations of motion is given for the derivation of both model types. In addition, an insightful presentation of the main rotor's mechanism, aerodynamics and dynamics is also provided. Both model types are of low complexity, physically meaningful and capable of encapsulating the dynamic behavior of a large class of small-scale helicopters. • An illustrative and rigorous derivation of mathematical control algorithms based on both the linear and nonlinear representation of the helicopter dynamics. Flight controller designs guarantee that the tracking objectives of the helicopter's inertial position (or velocity) and heading are achieved. Each controller is carefully constructed by considering the small-scale helicopter's physical flight capabilities. Concepts of advanced stability analysis are used to improve the efficiency and reduce the complexity of the flight control system. Controller designs are derived in both continuous time and discrete time covering discretization issues, which emerge from the implementation of the control algorithm using microprocessors. • Presentation of the most powerful, practical and efficient methods for extracting the helicopter model parameters based on input/output responses, collected by the measurement instruments. This topic is of particular importance for real-life implementation of the control algorithms. This book is suitable for students and researches interested in the development and the mathematical derivation of flight controllers for small-scale helicopters. Background knowledge in modern control is required.
The state of hingless rotorcraft research and development in the NATO countries as of 1973 is described. The scope of this report is limited to flight dynamics (as defined in the Preface) since most of the hingeless rotorcraft problems have occurred in this area. In the Introduction, the special place of the hingeless rotorcraft within the family of rotorcraft is considered. The chapter on the history of hingeless rotorcraft describes the hingeless rotor research and development of the various rotorcraft manufacturers and the hingless rotor research at government laboratories and universities. A hierarchy of dynamic concepts from isolated blade dynamics to complete rotor/body dynamics is introduced. The effects of the basic rotor design parameters on flight dynamics are traced and certain hingeless rotorcraft problems are treated in some detail. A special chapter is devoted to the alleviation of hingeless rotor flight-dynamics problems by feedback control systems. Finaly, analytical modeling techniques, mathematical analysis techniques, and model and flight testing techniques for hingeless rotorcraft are discussed.
The rotor system is the primary source of vibratory forces on a helicopter. Vibratory forces result from the rotor system response to dynamic and aerodynamic loading. This thesis discusses sources of excitation, and investigates rotor system modeling methods. Computer models based on finite element and Mykiestad methods are developed and compared for the free and forced vibration cases of a nniform rotor blade. The modeling assumptions and the effects of non-iniform physical parameters are discussed. The Myklestad based computer model is expanded to include coupling effects isherent in modern rotor blades. This rotor modeling program is incorporated into the Dynamics section of the Joint Army/Navy Rotorcraft Analysis and Design (JANRAD) program currenfly used by the Naval Postgraduate School?s helicopter design course (AA43O6) for preliminary helicopter design and analysis. Computer programs are developed as tools to investigate the stabffity of a rotor system for the specfflc cases of rotor flapping and ground/air resonance. A rotor flapping stability model, based upon Floquet theory, provides a means of analyzing the effect of increasing advance ratio on the flapping stability of a rotor system. The ground/air resonance model uses a constant coefficient approximation of the rotor system to allow analysis of the effects of coupling between rotor lag motion and airframe motion.
Helicopter Dynamics Introduced in an Organized and Systematic Manner A result of lecture notes for a graduate-level introductory course as well as the culmination of a series of lectures given to designers, engineers, operators, users, and researchers, Fundamentals of Helicopter Dynamics provides a fundamental understanding and a thorough overview of helicopter dynamics and aerodynamics. Written at a basic level, this text starts from first principles and moves fluidly onward from simple to more complex systems. Gain Valuable Insight on Helicopter Theory Divided into 11 chapters, this text covers historical development, hovering and vertical flight, simplified rotor blade model in flap mode, and forward flight. It devotes two chapters to the aeroelastic response and stability analysis of isolated rotor blade in uncoupled and coupled modes. Three chapters address the modeling of coupled rotor–fuselage dynamics and the associated flight dynamic stability, and provide a simplified analysis of the ground resonance aeromechanical stability of a helicopter. Explains equations derived from first principles and approximations Contains a complete set of equations which can be used for preliminary studies Requires a basic first–level course in dynamics, as well as a basic first–level course in aerodynamics Useful for any student who wants to learn the complexities of dynamics in a flying vehicle, Fundamentals of Helicopter Dynamics is an ideal resource for aerospace/aeronautical, helicopter, and mechanical/control engineers, as well as air force schools and helicopter/rotorcraft manufacturers.
Modeling, Control and Coordination of Helicopter Systems provides a comprehensive treatment of helicopter systems, ranging from related nonlinear flight dynamic modeling and stability analysis to advanced control design for single helicopter systems, and also covers issues related to the coordination and formation control of multiple helicopter systems to achieve high performance tasks. Ensuring stability in helicopter flight is a challenging problem for nonlinear control design and development. This book is a valuable reference on modeling, control and coordination of helicopter systems,providing readers with practical solutions for the problems that still plague helicopter system design and implementation. Readers will gain a complete picture of helicopters at the systems level, as well as a better understanding of the technical intricacies involved.
The behaviour of helicopters is so complex that understanding the physical mechanisms at work in trim, stability and response, and thus the prediction of Flying Qualities, requires a framework of analytical and numerical modelling and simulation. Good Flying Qualities are vital for ensuring that mission performance is achievable with safety and, in the first edition of Helicopter Flight Dynamics, a comprehensive treatment of design criteria was presented. In this second edition, the author complements this with a new Chapter on Degraded Flying Qualities, drawing examples from flight in poor visibility, failure of control functions and encounters with severe atmospheric disturbances. Fully embracing the consequences of Degraded Flying Qualities during the design phase will contribute positively to safety. The accurate prediction and assessment of Flying Qualities draws on the modelling and simulation discipline on the one hand and testing methodologies on the other. Checking predictions in flight requires clearly defined ‘mission-task-elements’, derived from missions with realistic performance requirements. High fidelity simulations also form the basis for the design of stability and control augmentation systems, essential for conferring Level 1 Flying Qualities. The integrated description of flight dynamic modelling, simulation and flying qualities forms the subject of this book, which will be of interest to engineers in research laboratories and manufacturing industry, test pilots and flight test engineers, and as a reference for graduate and postgraduate students in aerospace engineering. The Author Gareth Padfield, a Fellow of the Royal Aeronautical Society, is the Bibby Professor of Aerospace Engineering at the University of Liverpool. He is an aeronautical engineer by training and has spent his career to date researching the theory and practice of flight for both fixed-wing aeroplanes and rotorcraft. During his years with the UK’s Royal Aircraft Establishment and Defence Evaluation and Research Agency, he conducted research into rotorcraft dynamics, handling qualities and flight control. His work has involved a mix of flight testing, creating and testing simulation models and developing analytic approximations to describe flight behaviour and handling qualities. Much of his research has been conducted in the context of international collaboration – with the Technical Co-operation Programme, AGARD and GARTEUR as well as more informal collaborations with industry, universities and research centres worldwide. He is very aware that many accomplishments, including this book, could not have been achieved without the global networking that aerospace research affords. During the last 8 years as an academic, the author has continued to develop his knowledge and understanding in flight dynamics, not only through research, but also through teaching the subject at undergraduate level; an experience that affords a new and deeper kind of learning that, hopefully, readers of this book will benefit from.
A mathematical model of a helicopter system with a single main rotor that includes rigid, hinge-restrained rotor blades with flap, lag, and torsion degrees of freedom is described. The model allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces, and inflow effects are accounted for by using a three-state nonlinear dynamic inflow model. The motion of the rigid fuselage is defined by six degrees of freedom, and an optional rotor rpm degree of freedom is available. Empennage surfaces and the tail rotor are modeled, and the effect of main-rotor downwash on these elements is included. Model trim, linearization, and time-integration operations are described and can be applied to a subset of the model in the rotating and nonrotating coordinate frame. A preliminary validation of the model is made by comparing its results with those of other analytical and experimental studies. This publication presents the results of research completed in November 1989.
