Dynamic Braking Control For Accurate Train Braking .

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Dynamic Braking Control for Accurate Train Braking DistanceEstimation under Different Operating ConditionsHusain Abdulrahman AhmadDissertation submitted to the faculty of the Virginia Polytechnic Institute and State University inpartial fulfillment of the requirements for the degreeofDoctor of PhilosophyInMechanical EngineeringMehdi Ahmadian (Chair)Muhammad R. HajjDaniel J. InmanCorina SanduSaied TaheriFebruary 20, 2013Blacksburg, VA, USAKeywords: Dynamic Braking, Traction Motors, Wheel/Rail Adhesion, Train Braking Distance,Longitudinal Train Dynamics, Model Reference Adaptive Control, Creep, Kalker’s Theory. Copyright 2013Husain Ahmad

Dynamic Braking Control for Accurate Train Braking DistanceEstimation under Different Operating ConditionsHusain Abdulrahman AhmadABSTRACTThe application of Model Reference Adaptive Control (MRAC) for train dynamic braking isinvestigated in order to control dynamic braking forces while remaining within the allowableadhesion and coupler forces. This control method can accurately determine the train brakingdistance. One of the critical factors in Positive Train Control (PTC) is accurately estimating trainbraking distance under different operating conditions. Accurate estimation of the brakingdistance will allow trains to be spaced closer together, with reasonable confidence that they willstop without causing a collision. This study develops a dynamic model of a train consist basedon a multibody formulation of railcars, trucks (bogies), and suspensions. The study includes thederivation of the mathematical model and the results of a numerical study in Matlab. A threerailcar model is used for performing a parametric study to evaluate how various elements willaffect the train stopping distance from an initial speed. Parameters that can be varied in themodel include initial train speed, railcar weight, wheel-rail interface condition, and dynamicbraking force. Other parameters included in the model are aerodynamic drag forces and airbrake forces.An MRAC system is developed to control the amount of current through traction motors undervarious wheel/rail adhesion conditions while braking. Minimizing the braking distance of a trainrequires the dynamic braking forces to be maximized within the available wheel/rail adhesion.Excessively large dynamic braking can cause wheel lockup that can damage the wheels and rail.Excessive braking forces can also cause large buff loads at the couplers. For DC traction motors,an MRAC system is used to control the current supplied to the traction motors. This motorcurrent is directly proportional to the dynamic braking force. In addition, the MRAC system isalso used to control the train speed by controlling the synchronous speed of the AC tractionmotors. The goal of both control systems for DC and AC traction motors is to apply maximumavailable dynamic braking while avoiding wheel lockup and high coupler forces. The results ofthe study indicate that the MRAC system significantly improves braking distance whilemaintaining better wheel/rail adhesion and coupler dynamics during braking. Furthermore,according to this study, the braking distance can be accurately estimated when MRAC is used.The robustness of the MRAC system with respect to different parameters is investigated, and theresults show an acceptable robust response behavior.

AcknowledgementsIn the Name of Allah, the Most Beneficent, the Most Merciful. All thanks and praise to Allah,the Lord of the worlds. Prayers and peace be upon His prophet Mohammed, the last prophet andmessenger of Allah.First of all, I thank Allah for giving me health, support, guidance, knowledge, and strength tocomplete this study. I would like to express my gratitude to my wonderful wife and children fortheir constant love, patience, and support to complete my PhD dissertation. I would also like toexpress my gratitude towards my parents for encouraging me and praying for me all my life.I would like to express my sincere gratitude to the Saudi Ministry of Higher Education forgranting me a fully-funded scholarship to complete my Ph.D. degree.I would like to express my sincere appreciation to my committee chair, Dr. MehdiAhmadian, for all his support, advice, help, and guidance. I would not have accomplished mywork without his vision and encouragement.I would also like to thank Dr. Corina Sandu, Dr. Saied Taheri, Dr. Muhammad Hajj, and Dr.Daniel Inman for serving on my committee.iii

ContentsAbstract . iiAcknowledgement . iiiTable of Contents . ivList of Tables . viiList of Figures . viiiNomenclature . xiiChapter 1: Introduction .11.1 Overview .11.2 Objectives .21.3 Research Approach .21.4 Main Contribution .31.5 Document Outline .3Chapter 2: Background .42.1 Introduction .42.2 Wheel/Rail Mechanics .42.2.1 Wheel/Rail Contact Ellipse .52.2.2 Creep Forces .82.2.3 Wheel/Rail Adhesion Coefficient .112.2.4 Wheel Lockup .122.3 Longitudinal Train Dynamics .122.3.1 Coupling Components .132.3.2 Dynamic Braking.142.3.3 Air Brake .192.3.4 Propulsion Resistance.192.3.5 Grade Resistance .222.3.6 Curving Resistance .232.4 Model Reference Adaptive Control .232.5 Review of Past Research .262.6 Research Justification .33iv

Chapter 3: Longitudinal Train Model .343.1 Introduction .343.2 Kinematics .343.3 Equations of Motion .363.3.1 Carbody Equations of Motion .363.3.2 Bogie Equations of Motion .393.3.3 Wheelset Equations of Motion .41Chapter 4: Parametric Study .434.1 Introduction .434.2 System Properties and Force Evaluation .434.2.1 Propulsion Resistance.444.2.2 Creep Force .454.2.3 Dynamic Braking .464.2.4 Air Brake .474.3 Coupler Slack Model Comparison .484.4 Model Verification .494.5 Parametric Study .534.5.1 Different Weights .534.5.2 Different Dynamic Braking Efforts .554.5.3 Different Initial Speeds .564.5.4 Aerodynamic Drag .584.5.5 Wheel/Rail Condition .584.5.6 Number of Railcars .60Chapter 5: MRAC of Dynamic Braking Forces .625.1 Introduction .625.2 Train Model .625.3 Control Model .635.3.1 Dynamic Braking.63v

5.3.2 Control Strategy.675.3.2 MRAC System .715.4 Simulation and Results .745.4.1 Case 1: MRAC Performance .745.4.2 Case 2: Adhesion Coefficient Change with Distance.84Chapter 6: Robustness of the MRAC System .926.1 Introduction .926.2 Simulations and Results .926.2.1 Coupler Stiffness and Damping .926.2.2 Primary Suspension Stiffness and Damping .946.2.3 Creepage .976.2.4 Wheel Normal Load .1006.2.5 Braking Torque .103Chapter 7: Final Discussion and Conclusions .1077.1 Summary .1077.2 Final Discussion .1077.3 Conclusions .108References .110Appendices .1151. Main Simulink block diagram for the parametric study .1152. Simulink block diagram for 3-car model in the parametric study .1153. Simulink locomotive block diagram (carbody, front & rear bogies, and six wheelsets) .1164. Simulink block diagram of the powered wheelset at the locomotive .1165. Simulink block diagram of the force evaluation at the powered wheelset .1176. Main Simulink block diagram of the MRAC system with DC traction motors .1187. Main Simulink block diagram of the MRAC system with AC traction motors .119vi

List of TablesTable 2.1 Coefficients m and n for different values ofTable 2.2 Kalker creepage coefficient.7for different b/a ratios and Poisson’s ratios .8Table 2.3 Normalized longitudinal and lateral Kalker’s coefficients .10Table 2.4 Different versions of the Davis formula for calculating propulsion resistance .21Table 2.5 C coefficient and areas for use with the Canadian National train resistance formula .22Table 4.1 System properties and coefficients .44vii

List of FiguresFigure 2.1 Creep forces and moments .5Figure 2.2 Principal radii of curvature for wheel and rail.7Figure 2.3 Kalker’s empirical theory .10Figure 2.4 Adhesion coefficient versus speed for different wheel/rail conditions .11Figure 2.5 Adhesion coefficient versus speed for EMD’s SD-45 locomotive .12Figure 2.6 Typical design of the coupler .13Figure 2.7 Conventional draft gear .14Figure 2.8 Example of dynamic braking versus speeds .15Figure 2.9 Dynamic braking forces for four control positions at a range of train speeds .15Figure 2.10 DC motor and applied dynamic braking torque to a wheelset .16Figure 2.11 Simple sketch of an AC motor .17Figure 2.12 Induction motor torque-slip curve for motor and generator region .18Figure 2.13 Tractive and braking effort diagrams for Siemens SD90MAC with 4300 hp .18Figure 2.14 Car weight resolved parallel and normal to the car .22Figure 2.15 Model Reference Adaptive System (MRAS) .24Figure 2.16 Block diagram of MRAC applied to a system .26Figure 3.1 Longitudinal train model .35Figure 3.2 Simple sketch of a train single car model .35Figure 3.3 Front view of the train model .36Figure 3.4 Free body diagram of the car body .36Figure 3.5 Free body diagram of the bogie .39Figure 3.6 Free body diagram of the wheelset .41Figure 4.1 Three-car model .43Figure 4.2 Kalker’s empirical theory applied to the longitudinal direction only. .46Figure 4.3 Assumed DC motor dynamic braking torque for model simulation .47Figure 4.4 Distance travelled by the train for cases with and without coupler slack .49Figure 4.5 Train speed for cases with and without coupler slack .49Figure 4.6 Three-railcar train model in SIMPACK .50viii

Figure 4.7 Air brake model in SIMPACK .51Figure 4.8 Dynamic braking model in SIMPACK .51Figure 4.9 Distance travelled and speed versus time from SIMPACK .52Figure 4.10 Distance travelled and speed versus time from Matlab .52Figure 4.11 Distance travelled by the train for different weight conditions .54Figure 4.12 Speeds versus stopping time for the train for different weight conditions .54Figure 4.13 Distance traveled

iii Acknowledgements In the Name of Allah, the Most Beneficent, the Most Merciful. All thanks and praise to Allah, the Lord of the worlds. Prayers and

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