Modelling and Nonlinear Analysis of Aircraft Ground Manoeuvres ec1099/ECoetzee_PhD_   Modelling

download Modelling and Nonlinear Analysis of Aircraft Ground Manoeuvres ec1099/ECoetzee_PhD_   Modelling

of 123

  • date post

    29-Jun-2018
  • Category

    Documents

  • view

    212
  • download

    0

Embed Size (px)

Transcript of Modelling and Nonlinear Analysis of Aircraft Ground Manoeuvres ec1099/ECoetzee_PhD_   Modelling

  • Modelling and Nonlinear Analysis of AircraftGround Manoeuvres

    Etienne Coetzee

    Department of Engineering Mathematics

    University of Bristol

    A dissertation submitted to the University of Bristol in

    accordance with the requirements of the degree of

    Doctor of Philosophy in the Faculty of Engineering.

    February 2011

  • Abstract

    Recent studies in the USA and Europe show that passenger numbers are doubling every 15years, with a consequent increase in traffic and a demand for new airframes. More efficient sur-face movements will alleviate congestion due to this growth. An understanding of the grounddynamics of different sized aircraft is therefore essential. The objective of this thesis is to clas-sify the ground dynamics of different sized aircraft across the entire operational and designenvelope. The nonlinear nature of the problem generally adds to the complexity of such dy-namics, where small perturbations in velocity, steering angle or brake application may lead tosignificant differences in the performance that can be achieved. The use of industrially testedmodels of the A320 and A380 are an important aspect of this work. Good agreement is shownbetween simulation results and flight test data, underpinning the validity of the models. Thesemodels are constructed in the MSC.Adams and SimMechanics software environments, whereall relevant information in terms of steering angles, clearance distances, and tyre forces areprovided. The computational challenges related to multibody simulations are highlighted, andconsequently alternative analysis methods are explored. The most widely employed analysismethods that can be used to study aircraft ground manoeuvres consist of geometric, kinematic,dynamic, and bifurcation methods. To allow for the nonlinear analysis of industrially-testedmodels in a user-friendly environment, AUTO has been integrated with Matlab in the form of aDynamical Systems Toolbox. The SimMechanics aircraft models are coupled to AUTO withinthis new toolbox, where AUTO has direct access to the states, even though the model equationsare a black-box to the user. This is an important capability that allows one to integrate exist-ing validated models with the bifurcation software, avoiding significant effort in redevelopingmodels for bifurcation analysis.

    We show that widely used geometric methods for the calculation of turn widths are not applica-ble to large aircraft such as the A380, due to the asymmetric thrust and braking inputs that arerequired for the U-turn manoeuvre. Bifurcation and continuation methods, on the other hand,are shown to be effective for the analysis of this type of manoeuvre at a fraction of the costof simulations. The presence of a fold bifurcation provides new insight into the dynamics ofU-turn manoeuvres, which is not easily observed from simulation data. Kinematic equationsare used to analyse the stability of an aircraft that is being towed, where we conclude that jack-knifing can be avoided by maintaining a towing radius that is larger than the wheel base. Theyalso form the basis of the runway exit studies, from which empirical formulas are derived forsteering angle and clearance predictions. The results of the empirical method compare verywell with kinematic studies, as well as detailed dynamic model simulations, as is demonstratedwith a test case example of an A380 model. The empirical formulas can be used to great effectduring the early design phases of an aircraft programme for the prediction of steering anglesand clearance distances, when very little data is available. The greatest advantage of the pro-posed method is that any aircraft configuration or runway exit can be analysed. The steady-stateforce values that are provided from continuation methods can be used to evaluate the FAA 0.5ghigh-speed lateral ground loads regulation. A strong correlation exists between the results fromthe analysis and the measurements from an operational loads test campaign. We show that theA380 can only generate a load that is half the value stipulated by the regulation. This is due tothe nonlinear nature of the tyre properties and the overwhelming influence of the aerodynamicsat higher velocities. This analysis provides additional evidence that a lateral load factor of 0.5cannot be reached for such a large aircraft.

  • Acknowledgements

    I would like to thank my supervisors, Prof. Bernd Krauskopf and Dr. Mark Lowenberg, for theircontinued support and encouragement. Without their guidance and expertise this PhD wouldnot have been possible. I would also like to thank my industrial supervisor at Airbus, SanjivSharma, who has supported all the nonlinear dynamics activities at Airbus since 2003. He hasbeen instrumental in advocating their use within an industrial context. I owe Airbus immensegratitude for allowing me to pursue this PhD, and I hope the results speak for themselves. I alsowould like to thank Bob Thompson at Airbus for his valuable inputs, especially with regardsto the explanation of some of the operational usage scenarios. Thanks also to James Rankinand Phani Thota who helped to lay the foundations for many of the projects that have followed.I would like to thank my family in South Africa and in the United Kingdom, who have beenright behind me every step of the way. Lastly, I would like to thank my lovely wife Sarah forher patience, and our eight week old daughter, Elana, for giving me some added incentive tocomplete this work before she was born.

  • Science is built up with facts, as a house is with stones.But a collection of facts is no more a science than a heap of stones is a house.

    Henri Poincar

  • Authors Declaration

    I declare that the work in this dissertation was carried out in accordance with the regulations ofthe University of Bristol. The work is original except where indicated by special reference inthe text and no part of the dissertation has been submitted for any other degree.

    Any views expressed in the dissertation are those of the author and in no way represent thoseof the University of Bristol.

    The dissertation has not been presented to any other University for examination either in theUnited Kingdom or overseas.

    Signed:

    Dated:

  • Contents

    1 Introduction 11.1 Research Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . 11.2 Review of Existing Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2 Models and Hierarchy of Analysis Methods 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Kinematic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Dynamic Methods - Modelling and Simulation . . . . . . . . . . . . . . . . . 15

    2.3.1 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Normal and Towing Operations . . . . . . . . . . . . . . . . . . . . . 192.3.3 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.4 Computational Challenges of Simulations . . . . . . . . . . . . . . . . 20

    2.4 Bifurcation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.1 Bifurcation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.2 Dynamical Systems Toolbox AUTO Integration into Matlab . . . . . 222.4.3 Application to Ground Manoeuvres . . . . . . . . . . . . . . . . . . . 23

    3 Low-Speed: U-turn Manoeuvres 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 The U-turn Manoeuvre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 The Geometric Approach to the U-turn . . . . . . . . . . . . . . . . . . . . . . 283.4 U-turn Results from Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 U-turn Performance Using the Bifurcation Approach . . . . . . . . . . . . . . 313.6 Turn Centre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    4 Low- and Medium-Speed: Towing 374.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Kinematic Towing Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Load Factors due to Towing . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    5 Medium-Speed: Runway Exit Manoeuvres 455.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2 Steering Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    5.2.1 Steering Angle Variation During Circular Section of Exit . . . . . . . . 48

    i

  • ii CONTENTS

    5.2.2 Steering Angle Variation on Horizontal Section of Exit . . . . . . . . . 505.2.3 Steering Angle Predictions from Continuation Methods . . . . . . . . . 515.2.4 Steering Angle Comparisons for the Different Methods . . . . . . . . . 51

    5.3 Clearance Distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.4 Load Factors During Runway Exit Turns . . . . . . . . . . . . . . . . . . . . . 55

    5.4.1 Runway Exit Design Velocities . . . . . . . . . . . . . . . . . . . . . 575.4.2 Load Factors for an A320 . . . . . . . . . . . . . . . . . . . . . . . . 585.4.3 Load Factors for an A380 . . . . . . . . . . . . . . . . . . . . . . . . 60

    5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    6 High-Speed: Ground Loads Requirements 656.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2 Side Loads Requirements . . . . . . . . . . . . . .