A Cornputer Model of a Train Derailment Elton Edward Toma A thesis submitted to the Department of Mechanical Engineering in confonity with the requirements for the degree of Doctor of Philosophy Queen's University Kingston, Ontario, Canada October, 1998 copyright @Elton Edward Toma, 1998 National Library Bibliothêque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. rue Weliingîon OttawaON K1A ON4 OttawaON K1AW Canada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Librafy of Canada to Bibliothèque nationale du Canada de reproduce, loan, distriibute or sell reproduire, prêter, distribuer ou copies of this thesis in microfom, vendre des copies de cette thèse sous paper or electronic formats. la fome de microfiche/nlm, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantid extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. Abstract This thesis presents the development of a train derailment computer model. The planar model is based on coupled sets of 5 degree of freedom sub-system models for each rail car. and includes coupler body reaction forces, car-ground reaction forces. brake forces, and car-twcar collision forces. The mode1 allows constraint removal to model coupler failure and derailment conditions. The differentiai equations of motion for the train system are derived using Lagrange's equations with added multipliers. The cornplete cornputer model was validated against the well known Mississauga derailment of 1979. The model resulted in 24 derailed cars, identical to the actual event, and a -11.7% error in accident site area. The major collisions produced by the model correlate well with the damage which occurred at the actual event. The derailment model was also tested for sensitivity to parameter variation about a baseline train. The changes in the model outcome for variations of f20% and f-50% for CU mas, train length, train speed, braking force, ground reaction force. and derailment quotient (L/V ratio) were performed. The outcomes were compared by number of derailed cars, peak collision forces, and the length, width, and area of the accident scene. The results show the model to be numerically stable within the f50% boundaries, and to produce outcornes physicdy consistent with the variations in the parameters. Train speed, car mas, and train length were the parameters which had the greatest effect on the number of derailed cars and the peak collision force. Findy, the Mississauga derailment model was tested wit h alt erations to the brak- ing model. The results show that instantaneous application of brake forces approach- ing wheel lockup significantly reduced the severity of the Mississauga derailment model results. Recommended future research includes the study of the effects of braking, car placement, mass, and length, and the surrounding terrain near the rail lines on the severity of derailments. Acknowledgements This work was supewised by Dr. R.J. Anderson, P.Eng. d the Deportment of Mechanical Engineering. 1 thank him very much for the freedom given to pursue this research, and for his guidance and advice as the work progressed. His expertise. experience, and ability to quickly accept or reject ideas and theories was invaluable throughout the work. 1 am very grateful to my family for t heir encouragement and words of advice throughout my years at Queen's, and to the Vernooy family for their continued wmth and support. Thanks Andreas Schumann, Bruce Minaker, Geoff Rideout, and Rob Langlois for being thoroughly enjoyable Company in the Dynamics lab - 1 have never known a more diverse group of people. Thanks also to John Stewart and Kelly McKinley for their often needed words of advice and wisdom. A thank you goes to Hilary Richardson for the fun part-tirne work over several yearç at the Mechanicd Engineering Library, and to the staff of the Mechanical Engineering machine shop for being good Company and help throughout the years. 1 would also like to thank Dr. Anderson, the Department of Mechanical Engineering, the Naturd Sciences and Engineering Research Council, and the School of Graduate Studies at Queen's University for their financial assistance. Dedicated to my wife Cathy, for her continuous support, helpfd advice, and endless patience. Contents 1 Introduction 1 1.1 Railway Accidents in Canada ...................... 3. 1.2 RailEquipmentSurnrnary ........................ 6 1.2.1 Locomotives ............................ 6 7 1.2.2 Reight Cam ............................ I 1.2.3 Couplers .............................. 11 1.2.4 Trucks and Wheelsets ...................... 14 1.2.5 Brakes ............................... 15 1.3 Past Research Focusing on Derailments ................. 17 1.4 Previous Derailment Models ....................... 19 1.4.1 The Yang and Manos Mode1 (1972) .............. 20 1.4.2 Anderson Mode1 (1990) ...................... 22 1.4.3 Johnson Mode1 (1991); Guran Mode1 (1992) .......... 24 1.4.4 Gracie Mode1 (1991); Roorda and Gracie Model (1992) .... 26 1.5 Objectives of a State-of-the-Art Derailment Mode1 ........... 27 2 Theory 28 2.1 Solution Method ............................. 28 2.1.1 Development of the Specid Purpose Mode1 ........... 30 2.1.2 Lagrange's Equations with Added Multipliers ......... 32 2.2 The Rigid Body Model .......................... 36 2.2.1 Assumptions, Simplifications. and Characteristics ....... 37 2.2.2 Analysis of the Rigid Body Mode1 ................ 38 2.3 Rigid Body Equations of Motion ..................... 44 2.3.1 Sub-System Equations of Motion ................ 44 2.3.2 Car Rai1 Constraints: Straight Track .............. 17 2.3.3 Car Rail Constraints: Constant Radius Cwed Track ..... 49 2.3.4 Coupler-tecoupler Pivot Constraints .............. 52 2.3.5 Constraint Stabilization ..................... 53 2.3.6 Assembled Equations of Motion ................. 55 2.4 Generdized Forces ............................ 55 2.4.1 Brake Force Mode1 ........................ 55 2.4.2 Coupler Mode1 .......................... 59 2.4.2.1 StrikerReactionModel ................. 60 2.4.2.2 Coupler-tecoupler React ion Mode1 .......... 62 2.4.3 Ground Reaction Model ..................... 64 2.4.3.1 Basic Analysis of the Derailing Train System: Case 1. 66 2.4.3.2 Basic Andysis of the Derailing Train System: Case 2 . il 2.4.3.3 Basic Analysis of the Derailing Train System: Case 3. 74 2.4.3.4 Soi1 Mechanics Literature ............... 76 2.4.3.5 A Veloci ty Dependent Ground Reaction Force Funct ion . 78 2.4.3.6 Application of the Reaction Force ........... 81 2.4.4 Car Collision ........................... 53 2.5 Computer Program Implementation ................... 90 2.5.1 Input Data ............................ 94 2.5.2 Output Data ........................... 95 3 Results 96 3.1 Mode1 Validation: Modelling of the Mississauga Derailment ...... 96 3.1.1 Input Data ............................ 101 3.1.2 Results and Discussion ...................... 103 3.1.3 Conclusions: Mode1 Validation .................. 110 3.2 Variation of Parameters ......................... 111 3.2.1 Base System ............................ 113 3.2.2 Variation of Initial Train Speed ................. 115 3.2.3 Variation of Car Mass ...................... 118 3.2.4 Variation of Train Length .................... 122 3.2.5 Variation of Brake Force ..................... 126 3.2.6 Variation of the Derailment Quotient (L/V) ........... 129 3.2.7 Variation of Ground Reaction Force ............... 132 3.2.8 Cornparison of the Parameter Variation Results ........ 135 3.3.9 Conciusion: Variation of Parameters .............. 140 Mississauga Derailment: Brake Application Tests ........... 142 3.3.1 Results and Discussion of Brake Application Tests ....... 143 4 Summary and ConcIusions 146 4.1 Surnmary ................................. 136 4.1.1 Recommendat ions for Future Reseasch ............. 153 vii List of Tables CI 1.1 Power output and mass of typical locomotives .............. 1 1.2 Freight car weights and dimensions.................... Y 1.3 Dangerous goods tank car classification ................. 9 2.1 Coupler parameters used in the mode1.................. 62 3.1 Derailed freight car list . Mississauga derailment .[l1. .......... 99 3.2 lnput data for Mississauga mode1..................... 102 3.3 Peak coilision forces . Cornputer rnodel of the Mississauga derailment . 106 3.4 Resul ts of vrtriat ion of initial train speed ................. 115 3.5 Results of variation of car mass ...................... 119 3.6 Results of variation of train length .................... 122 3.7 Results of variation of brake force..................... 126 3.8 Results of variation of L/V ........................ 129 3.9 Results of variation of ground reaction force ............... 132 3.10 Results of brake application tests to the Mississauga mode1...... 144 List of Figures 1.1 Train speed influence on number of cars derailing per accident ..... 4 1.2 Train length influence on number of cars derailing Fer accident .... .5 1.3 LPGfAmmonia tank car .......................... 10 1.4 Vinyl chloride service tank cor ...................... 10 1.5