Rail Vehicles: the Resistance to the Movement and the Controllability
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S.Yu. Sapronova, V.P. Tkachenko, O.V. Fomin, I.I. Kulbovskiy, E.P. Zub RAIL VEHICLES: THE RESISTANCE TO THE MOVEMENT AND THE CONTROLLABILITY monograph Dnipro 2017 UDC 629.4.072:629.1.072 C 19 This monograph is recommended for printing by the Science Council of DUIT STATE UNIVERSITY OF INFRASTRUCTURE AND TECHNOLOGY (protocol No 1 dd 8.12.2017). Reviewers: Miamlin S.V. – doctor of Technical Sciences, Professor, Vice-Rector on Scientific Work of Dnipropetrovsk National University of Railway Transport named after academician V. Lazaryan Gorbunov M. I. – doctor of Technical Sciences, Professor, Head of Railway Transport, Automobile Transport and Lifting-Transporting Machines of Volodymyr Dahl East Ukrainian National University S.Yu. Sapronova, V.P. Tkachenko, O.V. Fomin, I.I. Kulbovskiy, E.P. Zub. C19 Rail Vehicles: The Resistance to the Movement and the Controllability: Monograph. Dnipro: Ukrmetalurginform STA, 2017. – 160 p. ISBN 978-966-921-163-7 The monograph substantiates the existence and determines the origin of the constituent element of the resistance to the movement within rail carriages; the constituent is determined by the control of the wheel pairs within the railway track. In this book, we suggest the method to analyze closed power circuit in mechanical power transmission applied to rolling stock. The method of mathematical modeling for two- point contact of the wheel with the rail has also been developed. The characteristics of the kinematic resistance to the movement for a number of types of rolling stock have been obtained. There are power factors which control the rail carriages and their analysis is very important, therefore we address to it in the book as well. Based on the decrease in the circulation ratio within the closed power circuits of the control system created for carriages by the railway track, we also suggest the principles of designing the rolling stock truck arrangement with low resistance to the movement. The monograph is intended for scientists, engineers and technicians working in the field of design and research for railway transport as well as for masters and postgraduate students of specialty 273 - «Railway transport». UDC 629.4.072:629.1.072 ISBN 978-966-921-163-7 © S.Yu. Sapronova, V.P. Tkachenko, O.V. Fomin, I.I. Kulbovskiy, E.P. Zub, 2017 © DUIT STATE UNIVERSITY OF INFRASTRUCTURE AND TECHNOLOGY, 2017 CONTENTS INRODUCTION .............................................................................................6 1. STUDY ON THE RESISTANCE TO THE MOVEMENT OF THE ROLLING STOCK ..............................................................9 1.1. Historical Review on the Studies of the Movement Resistance with the Railway Rolling Stock .............................................................9 1.2. Structure of the Resistance to the Movement of Rail Carriages ...........30 1.2.1. Resistance in the Axle Equipment .......................................................30 1.2.2. Loss of Power in the Traction Drive ....................................................33 1.2.3. Resistance to Wheels Rolling on Rails .................................................33 1.3. The Choice on the Calculation Schemes for Simulating the Carriages Control by the Railway Track ........................................39 1.3.1. The Nature of the Resistance to the Movement Based on the Control of the Wheel Pairs by the Railway Track ............................................39 1.3.2. Closed Power Circuits in the Contacts of Wheels with Rails ..............40 1.3.3. Closed Power Circuits of Wheel Pairs .................................................41 2. STUDY ON CONTROLLABILITY AS THE PROCESS OF GUIDANCE FOR THE CARRIAGE BY THE RAILWAY TRACK ................................................................................................44 2.1. The Concept of Controllability in the Railway Transport ....................44 2.2. The Study on the Guidance Force Generated by the Track for Wheel Pairs .....................................................................................48 2.3. Theories of Wheel-Rail Adhesion ........................................................49 2.4. Study of Adhesion Characteristics ........................................................51 2.5. The Guidance of the Carriage by the Railway Track ...........................56 2.5.1. The Role of Wheel Flange Reactions in the Wheel Pairs Control and the Coefficient of the Derailment Resistance .................................56 2.5.2. The Kinematics of the Wheel Pairs Contact with Rails .......................61 2.5.3. Power Interaction of the Wheel Flanges and the Rail ..........................63 2.5.4. The Criterion of the Derailment Prevention ..........................................64 3. THEORETICAL STUDY ON RESISTANCE TO THE MOVEMENT ASSOCIATED WITH THE CONTROL OF THE CARRIAGE BY THE RAILWAY TRACK ....................66 3.1. The Choice on the Calculation Schemes for Modeling the Carriages Control by the Railway Track ........................................66 3 3.1.1. The System of Coordinates and the Simulation Features for the Rail Carriages ............................................................................66 3.1.2. The Calculation Models of the Carriages under the Study ...................69 3.2. Differential Equations of the Carriage Movement ...............................73 3.2.1. Equations of the Wheel Pairs Movement .............................................73 3.2.2. Equations of the Truck Frame Movement ............................................75 3.2.3. Equations of the Body Movement ........................................................76 3.3. Mathematical Models of Locomotives .................................................76 3.3.1. Mathematical Models of Frame Locomotives ......................................77 3.3.2. Locomotives with Linked Carriages .....................................................79 3.3.3. Six-Axle Carriages with the Axial Formula of 3о-3о ..........................84 3.3.4. Multiaxial Locomotives Based on Two-Axle Carriages ......................87 3.4. Models of Electric Trains, Diesel Trains, Passenger Carriages, Trams and Underground Carriages .....................................93 3.5. Mathematical Models of Freight Carriages ..........................................96 3.6. Simulation of the Contacting Parts of the Carriage ............................100 4. SIMULATING THE EXTERNAL CONTROL ACTION ...........103 4.1. Generalized Contact and Axle Equipment Reactions .........................103 4.2. Analysis on the Control of Power Factors ..........................................108 4.2.1. Structure of the Power Factors Affecting Wheel Pairs .......................108 4.2.2. Power Factors for Rolling Stocks Control when Interaction between Wheel Pairs and Tracks ........................................................109 5. MODELING THE KINEMATIC RESISTANCE TO THE MOVEMENT ....................................................................................114 5.1. The Nature of the Resistance to the Movement Associated with the Control of the Wheel Pairs by the Railway Track ..............................114 5.2. Mathematical Modeling for Carriages Control by Rails in the Curve ..118 5.2.1. Calculation Scheme of Truck Guiding into the Curve of the Track ...118 5.2.2. The System of Equations for Truck Equilibrium when Guided into the Curve .....................................................................................121 5.2.3. Calculation Results of the Resistance to the Movement Associated with the Control of Wheel Pairs by Rail Tracks: A Study on the Carriages of 18-100 Type ...................................................................122 5.3. Method to Calculate the Kinematic Resistance to the Movement ......126 5.3.1. Reduction of Forces and the Moments of the Movement Resistance ...........................................................................................126 5.3.2. Impact of Carriage Truck Parameters on the Kinematic Movement Resistance .........................................................................127 4 6. WAYS TO IMPROVE CONTROLABILLITY AND REDUCE THE RESISTANCE TO THE MOVEMENT OF RAIL CARRIGES ............................................131 6.1. Linked Carrieges Design Development .............................................132 6.2. Carriages with Radial Installation of Wheel Pairs .............................133 6.2.1. HTCR-II Trucks Locomotives Developed by Electro-Motive Diesel ..................................................................................................134 6.2.2. Truck of 2TE25k Locomotive Being Studied ....................................134 6.2.3. Wheel Blocks of Talgo High-Speed Spanish Electric Trains .............136 6.2.4. Technical Solutions for Designs of Wheels with Radial Installation of Wheel Pairs ..................................................................137 CONCLUSIONS AND RESULTS .............................................................147 REFERENCES .............................................................................................150 5 INRODUCTION For more than 30 years, one of the main and most resource-intensive problems of railway transport is the problem of heavy wear of wheels rolling surfaces and rails in curved sections of tracks. Significantly greater wear of wheels and rails in curves in comparison with straight lines is explained by the fact that the rolling stock in the curves is guided by the horizontal forces, which are necessary