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Handbook of Railway Vehicle 
 Dynamics
http://taylorandfrancis.com
Handbook of Railway Vehicle 
Dynamics 
Second Edition
Edited by
Simon Iwnicki
Maksym Spiryagin
Colin Cole
Tim McSweeney
CRC Press
Taylor & Francis Group
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v
Contents
Preface..............................................................................................................................................vii
Editors ...............................................................................................................................................ix
Contributors ......................................................................................................................................xi
Chapter 1 Introduction ..................................................................................................................1
Simon Iwnicki, Maksym Spiryagin, Colin Cole and Tim McSweeney
Chapter 2 A History of Railway Vehicle Dynamics .....................................................................5
A. H. Wickens
Chapter 3 Design of Unpowered Railway Vehicles .................................................................... 43
Anna Orlova, Roman Savushkin, Iurii (Yury) Boronenko, Kirill Kyakk, 
Ekaterina Rudakova, Artem Gusev, Veronika Fedorova and Nataly Tanicheva
Chapter 4 Design of Powered Rail Vehicles and Locomotives ................................................ 115
Maksym Spiryagin, Qing Wu, Peter Wolfs and Valentyn Spiryagin
Chapter 5 Magnetic Levitation Vehicles ................................................................................... 165
Shihui Luo and Weihua Ma
Chapter 6 Suspension Elements and Their Characteristics ...................................................... 197
Sebastian Stichel, Anna Orlova, Mats Berg and Jordi Viñolas
Chapter 7 Wheel-Rail Contact Mechanics ............................................................................... 241
Jean-Bernard Ayasse, Hugues Chollet and Michel Sebès
Chapter 8 Tribology of the Wheel-Rail Contact ....................................................................... 281
Ulf Olofsson, Roger Lewis and Matthew Harmon
Chapter 9 Track Design, Dynamics and Modelling .................................................................307
Wanming Zhai and Shengyang Zhu
Chapter 10 Gauging Issues ......................................................................................................... 345
David M. Johnson
Chapter 11 Railway Vehicle Derailment and Prevention ........................................................... 373
Nicholas Wilson, Huimin Wu, Adam Klopp and Alexander Keylin
vi Contents
Chapter 12 Rail Vehicle Aerodynamics ...................................................................................... 415
Hongqi Tian
Chapter 13 Longitudinal Train Dynamics and Vehicle Stability in Train Operations ............... 457
Colin Cole
Chapter 14 Noise and Vibration from Railway Vehicles ............................................................ 521
David Thompson, Giacomo Squicciarini, Evangelos Ntotsios and Luis Baeza
Chapter 15 Active Suspensions ................................................................................................... 579
Roger M. Goodall and T.X. Mei
Chapter 16 Dynamics of the Pantograph-Catenary System ....................................................... 613
Stefano Bruni, Giuseppe Bucca, Andrea Collina and Alan Facchinetti
Chapter 17 Simulation of Railway Vehicle Dynamics ............................................................... 651
Oldrich Polach, Mats Berg and Simon Iwnicki
Chapter 18 Field Testing and Instrumentation of Railway Vehicles........................................... 723
Julian Stow
Chapter 19 Roller Rigs ................................................................................................................ 761
Paul D. Allen, Weihua Zhang, Yaru Liang, Jing Zeng, Henning Jung, 
Enrico Meli, Alessandro Ridolfi, Andrea Rindi, Martin Heller and Joerg Koch
Chapter 20 Scale Testing Theory and Approaches ..................................................................... 825
Nicola Bosso, Paul D. Allen and Nicolò Zampieri
Chapter 21 Railway Vehicle Dynamics Glossary ....................................................................... 869
Tim McSweeney
Index .............................................................................................................................................. 879
vii
Preface
This is the second edition of the handbook. The first edition, published in 2006, has become the 
established text in this field, is used by many researchers and has over 800 citations. We have com-
pletely reviewed all the material and updated much of the text to recognise that some significant new 
theoretical, numerical and experimental approaches have been developed, and new designs of rail-
way vehicles and their components have been introduced since the publication of the first edition.
There  have been rapid developments in many areas, including the application of IT through 
digitisation and vastly increased access to data. Although many of the key tools and techniques 
presented in the first edition are still used, most have been modified or updated, and new methods 
and computer tools have been developed. In this edition, we have included new chapters covering 
design of powered rail vehicles, aerodynamics of railway vehicles, maglev and the dynamics of the 
pantograph-catenary system.
We hope that readers find this handbook useful. Railway transport is seeing a resurgence in 
many countries and can provide efficient passenger and freight operations, but higher demands 
for safe and reliable operation at higher loads and speeds mean that the dynamic performance of 
vehicles  and their interactionswith the track and other infrastructure must be well understood. 
Engineers and researchers working in this field face significant challenges and the tools and tech-
niques outlined in this handbook will assist in solving the problems faced in designing, operating 
and maintaining modern railway systems.
Simon Iwnicki
Maksym Spiryagin
Colin Cole
Tim McSweeney
http://taylorandfrancis.com
ix
Editors
Simon Iwnicki is professor of railway engineering at the University of Huddersfield in the UK, 
where he is director of the Institute of Railway Research (IRR). The  IRR has an international 
reputation for its research and support to industry, providing not only valuable practical solutions 
to specific problems in the industry but also making significant contributions to the understand-
ing of some of the fundamental mechanisms of the wheel-rail interaction on which the safe and 
economical operation of railways depends. Professor Iwnicki is the editor-in-chief of Part F of the 
Proceedings of the Institution of Mechanical Engineers (the Journal of Rail and Rapid Transit) 
and co-editor (responsible for railway matters) of the journal Vehicle System Dynamics. He was the 
academic co-chair of the Rail Research UK Association (RRUKA) from 2010 to 2014, and, from 
2014 to 2015, he was chair of the railway division of the Institution of Mechanical Engineers. He is 
a former member of the Scientific Committee of Shift2Rail.
Maksym Spiryagin is a professor of engineering and the deputy director of the Centre for Railway 
Engineering at Central Queensland University, Australia. He received his PhD in the field of rail-
way transport in 2004 at the East Ukrainian National University. Professor Spiryagin’s involve-
ment in academia and railway industry projects includes research experience in Australia, China, 
Italy, South Korea and Ukraine, involving locomotive design and traction, rail vehicle dynamics, 
acoustics and real-time and software-enabled control systems, mechatronics and the development 
of complex mechatronic systems using various approaches (co-simulation, software-in-the-loop, 
processor-in-the-loop and hardware-in-the loop simulations).
Colin Cole is a professor of mechanical engineering and the director of the Centre for Railway 
Engineering at Central Queensland University, Australia. His work history includes over 31 years 
in railway industry and research roles starting in 1984, with six years working in mechanised track 
maintenance in Queensland Railways. Since then, his experience has included both rolling stock 
and infrastructure areas. He has worked in railway research for the past 25 years, and his 1999 PhD 
thesis was on Longitudinal Train Dynamics. He has conducted a range of rail projects related to 
field testing of trains, simulation of dynamics, energy studies, train braking, derailment investiga-
tion, railway standards and innovations in measurement and control devices.
Tim McSweeney is an adjunct research fellow at the Centre for Railway Engineering (CRE) at 
Central Queensland University in Australia. He  has over 45 years of experience in the field of 
railway fixed infrastructure asset management, specialising particularly in track engineering in the 
heavy-haul environment. He was the senior infrastructure manager overseeing the Bowen Basin 
Coal Network for Queensland Rail from 1991 until 2001. He  then joined the CRE to follow his 
interest in railway research. Tim is a member of the Railway Technical Society of Australasia and a 
Fellow of the Permanent Way Institution. Central Queensland University awarded him an Honorary 
Master of Engineering degree in 2011. He has co-authored 2 books and 30 technical papers and 
consultancy reports on various aspects of railway engineering and operations.
http://taylorandfrancis.com
xi
Contributors
Paul D. Allen is a professor and assistant director of the Institute of Railway Research (IRR) at the 
University of Huddersfield. As a technical expert, his specialist fields are railway vehicle dynam-
ics and wheel-rail contact mechanics. He completed a PhD on the subject of error quantification of 
scaled railway roller rigs and led the concept design of the full-scale roller rig at the IRR. His wider 
research interests include train braking technologies, pantograph-overhead line dynamics and the 
promotion of innovation in the rail industry.
Jean-Bernard Ayasse is a retired research director. Before joining “The French Institute of Science 
and Technology for Transport, Development and Networks” (IFSTTAR), France, he worked at the 
Commissariat à l’Energie Atomique and obtained his PhD from the University of Grenoble in 1970 
and a state thesis in 1977 in solid state physics. He is a specialist in numerical simulations in the 
electromagnetic and mechanical domains. His research field goes from the modelling of linear 
induction motors to railway dynamics. He is the author of several innovations in the modelling of 
the wheel-rail contact and of the multibody formalism implemented in the VOCO code.
Luis Baeza is professor and chair at the Technical University of Valencia in Spain. From 2016 to 
2018, he was a full professor in the Institute of Sound and Vibration Research at the University of 
Southampton, UK. His research area comprises various fields of railway technology, including dynam-
ics of railway vehicles and the track, vibration, corrugation of rails and wheel-rail contact mechanics.
Mats Berg is professor and head of the Road and Rail Vehicles Unit at the Royal Institute of 
Technology (KTH) in Stockholm. Before joining KTH in 1993, he worked at ABB Traction in 
Västerås and at the University of California at Berkeley. He obtained his PhD from Lund Institute of 
Technology in 1987. His main research field is vehicle-track interaction, with emphasis on the aspects 
of structural dynamics, suspension dynamics, track dynamics and wheel-rail wear. Professor Berg 
has authored many papers and reports in this field and advised several PhD students. He teaches 
courses on rail vehicle dynamics and general railway engineering in degree programmes as well as 
for practising engineers of the railway sector (both in Sweden and internationally).
Iurii (Yury) Boronenko is professor and head of the Department of Railcars and Railcar 
Maintenance at the Petersburg State Transport University in St. Petersburg, Russia. Professor 
Boronenko is also the director of the Scientific Research Center ‘Vagony’. The centre is involved 
in many practical fields such as monitoring the fleet of freight wagons in Russia, evaluation of the 
technical condition of railway vehicles, design of new and modification of existing railcars and 
implementation of repair technologies, as well as in research and consultancy projects for Russian 
railways and industry. ‘Vagony’ is the testing centre certified by the Russian Federal Service to test 
railway vehicles and by the Russian Maritime Register to test containers. Professor Boronenko’s 
special interests include vehicle dynamics and modelling the motion of liquids in tank wagons. 
For his theoretical and practical contribution in developing railway vehicles, Professor Boronenko 
became a member of the Transport Academy of Russia.
Nicola Bosso is an associate professor at Politecnico di Torino. He gained his MA degree in 1996 
and his PhD in machine design in 2004. After experience at the strategic research group at Fiat 
Ferroviaria, he joined the railway research group at Politecnico di Torino, where he developed his 
research in the railway sector, primarily concerning wheel/rail contact, multibody simulation and 
experimental testing on prototypes and real vehicles. He teaches in several courses at Politecnico di 
Torino, including rolling stock design.
xii Contributors
Stefano Bruni is a full professor at Politecnico di Milano, Department of Mechanical Engineering, 
where he teaches applied mechanics and dynamics. He  is the leader of the ‘Railway Dynamics’ 
research group,carrying out research on rail vehicles and their interaction with the infrastructure, 
with a critical mass of senior research competence. Professor Bruni has authored over 240 scientific 
papers and has spent a large amount of time lecturing and consulting to industry in Italy and other 
countries. He has been lead scientist for several research projects funded by the industry and by 
the European Commission (EC). He is vice president of the International Association for Vehicle 
System Dynamics (IAVSD) and was chairman of the IAVSD’05 international conference held in 
Milano in 2005. He  is an editorial board member for some international journals in the field of 
railway engineering.
Giuseppe Bucca is an associate professor of applied mechanics at Politecnico di Milano, Department 
of Mechanical Engineering, where he teaches applied mechanics and mechatronics. His research 
activity is focussed on the dynamics and control of mechanical systems, with primary application to 
railway vehicles. In particular, his main research topics are the theoretical and experimental (labo-
ratory and on-track tests) studies of the dynamical interaction between pantograph and catenary 
and of the related electromechanical phenomena, and the study of railway and tramway vehicle 
dynamics focussing on the wheel-rail contact phenomena, passenger comfort and running safety. 
He has participated and continues to participate in several research projects funded by the EU and 
in research and technical projects funded by private companies.
Hugues Chollet is researcher at IFSTTAR, France. He graduated from Université de Technologie 
Compiègne (UTC) in 1984 and obtained a PhD in 1991 at Université Pierre et Marie Curie, Paris 6, 
on the experimental validation of Kalker’s theory for the use in wheel-rail contact. He carries out 
research and consultancy work on guided transportation systems, dealing with wheel-rail contact 
fatigue, derailment situations, instabilities, vibration and comfort problems.
Andrea Collina is a full professor at Politecnico di Milano, Department of Mechanical Engineering, 
where he teaches applied mechanics and dynamics. He is active in the field of railway dynamics, inter-
action with infrastructure and pantograph-catenary interaction, carrying out both simulation and labo-
ratory and field-testing activities. He has been involved in EU-funded projects. He has authored over 
140 scientific papers and acts as consultant to industry in Italy and other countries for railway topics.
Alan Facchinetti is an associate professor of applied mechanics at Politecnico di Milano. He grad-
uated in 2000 and received his PhD in 2004 from that same university before joining the academic 
permanent staff in 2005. His research focuses on the dynamics, stability and control of mechanical 
systems, with primary application to railway vehicles and to their interaction with the infrastruc-
ture. In this respect, his research activities address the dynamic behaviour of railway vehicles and 
tramcars, pantograph-catenary interaction, active control, monitoring and diagnostics in railway 
vehicles, and include the development of numerical and laboratory tools and the design and execu-
tion of on-track tests. He has participated and continues to participate in several research projects 
funded by EU or national grants and in research and technical projects funded by private compa-
nies. He is a member of various European Committee for Electrotechnical Standardization working 
groups dealing with current collection systems.
Veronika Fedorova is a researcher at the Department of Integrated Studies of Track-Train 
Interaction Dynamics at All-Union Research and Development Center for Transportation Technology 
(St. Petersburg, Russia). She graduated from Petersburg State Transport University in 2015. She is cur-
rently a postgraduate student working on a PhD thesis in the field of railway vehicle dynamics, develop-
ing wheel-rail wear and rolling contact fatigue (RCF) simulation models and designing advanced wheel 
profiles for freight wagons.
xiiiContributors
Roger M. Goodall spent 12 years at British Rail's Research Division in Derby, where he worked 
on a variety of projects, including Maglev, tilting trains and active railway suspension systems. 
Roger took up an academic position at Loughborough University in 1982, and he became professor 
of control systems engineering in 1994. He also has a part-time professorial role at the University 
of Huddersfield’s Institute of Railway Research. His research has been concerned with a variety of 
practical applications of advanced control, usually for high-performance electro-mechanical sys-
tems and, for many years, specifically on active railway vehicle suspensions. Roger has served in a 
variety of external roles such as a member of the board of the International Association for Vehicle 
System Dynamics (IAVSD), vice president of the International Federation of Automatic Control 
(IFAC) and chairman of the IMechE Railway Division. He has been a fellow of the Institution of 
Mechanical Engineers for a number of years, and he was elected a fellow of the Royal Academy of 
Engineering in 2007 and a fellow of IFAC in 2017.
Artem Gusev is a researcher at the Department of Integrated Studies of Train-Track Interaction 
Dynamics at All-Union Research and Development Center for Transportation Technology 
(St. Petersburg, Russia). He graduated from Petersburg State Transport University in 2014, com-
pleted postgraduate studies with a degree in railway rolling stock in 2018 and prepared the thesis 
for PhD viva examination. He carries out research in the area of improving rolling stock dynamics 
and developing freight bogies, using the finite elements method and computer simulation modelling 
of railcar movement.
Matthew Harmon is a research associate in the Department of Mechanical Engineering at 
The University of Sheffield where he studies tribology. He gained his PhD in 2019 which studied 
the application and mechanisms of lubricants and friction modifiers in the wheel-rail interface. 
This work developed a number of test methods in the laboratory as well as is developing an in situ 
method for measuring friction in interfaces. Since finishing his PhD he has continued to study the 
wheel-rail interface through a variety of projects. His current focus is on the verification of adhesion 
forecasts and the development of guidance for the rail industry.
Martin Heller is employed at Knorr-Bremse-Systeme für Schienenfahrzeuge, Munich, Germany, 
and directs the test department with the ‘Atlas’ Roller Rig. He completed a Dr.-Ing. in mechanical 
engineering on the subject of mathematical simulation of brake control systems of trains and rail-
way vehicles and has been engaged since then in R&D of railway brakes.
David M. Johnson has a BSc in civil engineering (University of Leeds) and a PhD in mechanical 
engineering (Imperial College London), where his research and thesis covered ‘The Simulation of 
Clearances between Trains and the Infrastructure’. His early career was at British Rail Research 
and in the USA, where he specialised in track, structure and soil mechanics disciplines. This led 
him to form his own business, specialising in technology development, particularly digital engi-
neering systems, through which he developed a number of laser-based measuring technologies 
and started his interest in gauging. David’s company, Laser Rail, specialised in the development 
of structure measuring technology, analysis of clearances and the management of gauging data. 
The  company is now  part of the Balfour Beatty Rail group. His latest venture, a partnership 
with his son, Colin, has developed gauging analysis technology to another level. Based upon 
mechanistic modelling of the complete gauging system (the topic of his PhD), DGauge specialises 
in matching clearance calculations to real life through processes of risk-based analysis (which 
they have commercially developedas Probabilistic Gauging™), high-definition and complex rail 
vehicle modelling and three-dimensional simulation, geometric swept envelope analysis of tran-
sitional curvature and other bespoke techniques. The Company’s Cloud-based gauging service 
provides near-instant results to a variety of rail vehicle and infrastructure clients, both in the UK 
and internationally.
xiv Contributors
Henning Jung, MSc, studied mechanical engineering at the University of Siegen. He  is now  a 
research assistant working in the Applied Mechanics group of Professor Claus-Peter Fritzen at the 
University of Siegen. His research activities are focussed on dealing with the development of mod-
ern structural health monitoring systems (SHM) for railway vehicles. Prior to this, he also worked 
as a research assistant in the field of rolling mill design at Achenbach Buschhütten.
Alexander Keylin is a senior engineer in the Vehicle-Track Interaction group at Transportation 
Technology Center, Inc. (TTCI) in Pueblo, Colorado. He holds a BSc in mechanical engineering 
from University of Pittsburgh (2011) and an MSc in mechanical engineering from Virginia Tech 
(2012). His work involves testing and characterisation of rail vehicles, modelling of special track 
work, conducting computer simulations of vehicle-track interaction, analysis of ride quality data 
and development of algorithms for processing of rail profiles and track geometry data.
Adam Klopp is a senior engineer at Transportation Technology Center, Inc. (TTCI) in Pueblo, 
Colorado, specialising in vehicle-track interaction and train dynamics. He has over 7 years of rail-
road research and engineering experience at TTCI. His research includes the characterisation, anal-
ysis and modelling of rail vehicles and trains. His testing experience includes static and dynamic 
vehicle and track tests, compressive end load tests and impact tests. He holds a BSc in mechanical 
engineering from Colorado State University (2012) and an MSc in engineering with emphasis in 
railroad engineering from Colorado State University-Pueblo (2016).
Joerg Koch is employed at Knorr-Bremse-Systeme für Schienenfahrzeuge, Munich, Germany. 
He has a university degree as Dipl.-Ing. in Mechanical Engineering. After university, he developed 
and built a range of test rigs for railway equipment. He has been responsible for the ATLAS test rig 
since 2010 and was involved in its concept, design, build, commissioning and now its operation.
Kirill Kyakk is executive director of PTK-Engineering LLC (Russia), the freight wagon fleet oper-
ating company introducing next-generation freight cars and heavy freight trains on 1520 mm gauge 
railways. He obtained the PhD in 2007 at Petersburg State Transport University in St. Petersburg, 
Russia. His field of scientific interest is railcar design theory and system engineering. Dr. Kyakk has 
16 years of experience in the railway industry, including leadership and participation in the develop-
ment of more than 120 new freight wagon models with improved technical characteristics for the 
railways of Russia, Europe, Africa and the Middle East.
Roger Lewis is a professor of mechanical engineering at the University of Sheffield, where he 
teaches design and tribology. He received his PhD from that university in 2000, before joining the 
academic staff in 2002. His research interests are split into three areas: solving industrial wear 
problems, application and development of a novel ultrasonic technique for machine element contact 
analysis and design of engineering components and machines. He has worked on a number of proj-
ects related to the wheel-rail interface, including understanding fundamental mechanisms and mod-
elling of wheel and rail materials, measurements of wheel-rail interface conditions and rail stress, 
friction management and understanding of low adhesion. In 2019, he was appointed as a Royal 
Academy of Engineering Research Chair in ‘Wheel/Rail Interface Low Adhesion Management’. 
In collaboration with the Rail and Safety Standards Board, he will now undertake a 5-year pro-
gramme of work in this area.
Yaru Liang is a PhD student at the State Key Laboratory of Traction Power, Southwest Jiaotong 
University, China. She  received her bachelor’s degree in vehicle engineering at Dalian Jiaotong 
University in 2010. She then continued her studies for the master’s degree course from 2010 to 2012 
and later became a PhD student. Her research interests are in vehicle dynamics simulation and roller 
rig testing.
xvContributors
Shihui Luo is a professor at the State Key Laboratory of Traction Power, Southwest Jiaotong 
University (SWJTU), China. He earned his BEng, MEng and PhD in 1985, 1988 and 1991, respec-
tively, from the Department of Marine Power Machinery Engineering, Shanghai Jiaotong University, 
China. He then joined SWJTU and started research on vehicle dynamics. During this period, he 
stayed 1 year in the Duewag Factory, Siemens VT, as a trainee. He teaches in postgraduate courses. 
He participated in dynamics simulation projects for the Shanghai maglev train in 2002 and has 
continued research since then for the development of maglev vehicles.
Weihua Ma is a researcher at the Traction Power State Key Laboratory (TPL), Southwest Jiaotong 
University (SWJTU), China. He was awarded a BEng degree in vehicle engineering from Shandong 
University, China, in 2002 and a PhD degree in vehicle engineering from SWJTU in 2008. He has 
worked at TPL since 2008 and completed his postdoctoral fellowship during this period in a joint 
project of CRRC-SWJTU at Qishuyan Co., Ltd. His research interests include locomotive and 
heavy-haul train dynamics as well as the maglev train. In recent years, he has focussed on develop-
ing maglev for regional applications, with an operational speed range of 160 ~ 200 km/h.
T.X. Mei is a professor in control engineering at the University of Salford, where he leads a research 
group at the School of Computing, Science and Engineering, carrying out leading-edge research in 
the area of control and systems study for railway vehicles. Professor Mei has a strong background 
in railway engineering and substantial expertise in vehicle dynamics and traction control. He has 
given invited research seminars at an international level and published many papers in leading 
academic journals and international conferences, which explore the application of advanced control 
techniques and the use of active components. Professor Mei is one of the most active researchers 
worldwide in the latest fundamental research into active steering and system integration for railway 
vehicles and has made significant contributions to several leading-edge research projects in the 
field. His educational background includes BSc (1982, Shanghai Tiedao), MSc (1985, Shanghai 
Tiedao), MSc (1991, Manchester) and PhD (1994, Loughborough).
Enrico Meli received his bachelor’s degree in mechanical engineering in 2004 and his master 
degree in mathematical engineering in 2006 from the School of Engineering of the University 
of Florence. He  received his PhD in mechanism and machine theory in 2010 from the School 
of Engineering of the University of Bologna. In 2014, Dr. Enrico Meli won the prestigious SIR 
2014 – Scientific Independence of Young Researchers Project, funded by the Italian Minister 
for Education, University and Research. He has been an assistant professor at the Department of 
Industrial Engineering of the University of Florence since 2015. Currently, his main research inter-
ests include vehicle dynamics, tribology, turbomachinery, rotor dynamics, robotics and automation. 
In these fields, Dr. Enrico Meli is the author of over 50 publications in international journals and 
over 120 publications in Proceedings of International Congresses.
Evangelos Ntotsios is a research fellow at the Institute of Sound and Vibration Research 
(ISVR), University of Southampton. Before joining the ISVR in 2013, he worked at the School of 
Architecture,Building and Civil Engineering at Loughborough University and obtained his PhD 
from the Department of Mechanical Engineering at University of Thessaly (Greece) in 2010. He has 
participated in EPSRC-funded research projects, including ‘MOTIV: Modelling of Train Induced 
Vibrations’ and ‘Track to the Future’. His research interests include ground-borne railway noise and 
vibration as well as structural vibration and system identification.
Ulf Olofsson has been professor in tribology at the Royal Institute of Technology (KTH) since 
2006. Before joining KTH, he worked at the Swedish National Testing and Research Institute 
with tribological material and component testing. He  obtained his Licentiate of Engineering 
degree from Chalmers University of Technology in 1994 and his PhD from the Royal Institute of 
xvi Contributors
Technology in 1996. Dr. Olofsson has 20 years of research experience on the tribology of the wheel-
rail contact. His main research interests include interfaces and especially simulation and prediction 
of friction and wear, mainly applied to problems in mechanical, automotive and railway engineer-
ing. New research interests include airborne particles from wear processes such as in disc brakes and 
the railway wheel to rail contact.
Anna Orlova is deputy director in scientific and technical development for Research and Production 
Corporation ‘United Wagon Company’ and CEO of its subsidiary, the All-Union Research and 
Development Center for Transportation Technology (St. Petersburg, Russia), working on the devel-
opment of innovative freight wagons and their components for CIS, North American, European 
and other markets. United Wagon Company carries out the full cycle of research and development 
of freight wagons, starting from marketing, design and prototype production, production technol-
ogy development, preliminary and operational testing, development of maintenance strategies and 
repair technology. Dr. Orlova’s special interests include optimisation of running gear parameters for 
dynamic performance, evaluation of design schemes and the development of simulation models and 
testing methods. Dr. Orlova is a supervisor of postgraduate students at Petersburg State Transport 
University and the author of several textbooks on bogie design and multibody dynamics simulation.
Oldrich Polach is an independent consultant and assessor, and an honorary professor at the Technische 
Universität Berlin. From 2001 to 2016, he was chief engineer dynamics in Bombardier Transportation, 
Winterthur, Switzerland, responsible for dynamics specialists in Business Unit Bogies Europe. He is 
a well-recognised expert in railway vehicle dynamics and wheel-rail contact. He acted for 20 years 
as a member of the working group ‘Interaction Vehicle-Track’ of the European Committee for 
Standardisation CEN TC 256 and is accredited by the Railway Federal Authority in Germany for the 
assessment of railway vehicles. Professor Polach teaches railway vehicle dynamics at the ETH Swiss 
Federal Institute of Technology Zürich and at the Technische Universität Berlin. He is a member of 
the editorial boards of the international journals Vehicle System Dynamics, the International Journal of 
Railway Technology and the International Journal of Heavy Vehicle Systems.
Alessandro Ridolfi is currently an assistant professor within the Department of Industrial 
Engineering (DIEF) at the University of Florence (UNIFI). He has also been an adjunct professor at 
Syracuse University in Florence since 2015, teaching dynamics. He graduated in mechanical engi-
neering from UNIFI in 2010 and received his PhD degree in industrial engineering from UNIFI in 
2014. At the beginning of his PhD, he worked on railway vehicle localisation and wheel-rail adhe-
sion modelling. His current research interests are underwater and industrial robotics, sensor-based 
navigation of vehicles, vehicle dynamics and bio-robotics. He is co-author of more than 80 journal 
and conference papers on vehicle dynamics, robotics and mechatronics topics.
Andrea Rindi received his PhD in 1999 from the University of Bologna, Italy. He  is currently 
associate professor in machine theory with the School of Engineering of the University of Florence. 
He is cofounder and coordinator of the Laboratory of Mechatronics and Dynamic Modelling (MDM 
Lab). His current research interests include vehicle dynamics, hardware in-the-loop (HIL) simula-
tion and automation in transport systems.
Ekaterina Rudakova is head of the Department of Integrated Studies of Track-Train Interaction 
Dynamics at All-Union Research and Development Center for Transportation Technology 
(St. Petersburg, Russia). She obtained her PhD in 2005 in railway rolling stock from Petersburg 
State Transport University. The department carries out science-based research in the area of estima-
tion of rolling stock dynamic characteristics, track forces and dynamic loading of railcar elements. 
xviiContributors
Theoretical research, coupled with testing and experimental results, allows to perfect simulation 
models of railcar movement and computational methods. Dr. Rudakova’s special interests include 
computer simulation modelling, design and developing of bogie suspensions.
Roman Savushkin is a member of the board of directors and CEO of Research and Production 
Corporation ‘United Wagon Company’ PJSC (MOEX: UWGN). He  received degrees from the 
Petersburg State Transport University and the University of Antwerp’s Management School. Roman 
Savushkin holds the scientific degree of PhD in technical sciences and is an acting professor at the 
Russian University of Transport (MIIT). His fields of research include theory, numerical simula-
tion and experimental evaluation of structural strength, durability, dynamic performance and track 
interaction of railway vehicles; structural fatigue theory and simulation of metal structures; theory 
and simulation of wheel-rail interaction; theory of casting and welding production processes includ-
ing automation and robotics; design of railway freight wagons and their major components; and the 
economics of railway transport. He is the author of multiple papers published in Russian national 
and international scientific journals.
Michel Sebès is research engineer at IFSTTAR, France. Prior to joining IFSTTAR, he spent 13 
years in the service industry, where he carried out studies in the fields of structural mechanics and 
numerical simulation. He obtained a Master of Science and Engineering degree from the Ecole 
Centrale de Nantes in 1989 in the field of structural mechanics. His main activities are centred on 
the development of the VOCO code, dedicated to guided transport dynamics, particularly the last 
wheel rail contact extensions.
Valentyn Spiryagin received his PhD in the field of railway transport in 2004 at the East Ukrainian 
National University at Lugansk. His research activities include rail vehicle dynamics, multibody 
simulation, control systems and vehicle structural analysis. He currently lives in Russia and works 
as a railway consultant on vehicle dynamics and design, including vehicle structural engineering, 
mechatronic suspension systems for locomotives, locomotive traction and embedded software 
development.
Giacomo Squicciarini is a lecturer at the Institute of Sound and Vibration Research (ISVR), 
University of Southampton. He joined the ISVR in 2012 after obtaining his PhD at Politecnico di 
Milano studying the acoustics of piano soundboards. His main areas of research are related to rail-
way noise and vibration, including rolling noise, curve squeal and measurement techniques. He is 
also active in vibroacoustics, structural vibration and musical instrument acoustics. He has written 
20 papers in refereed journals and co-authored various conference contributions. He teaches under-
graduate and master’s students at the University of Southampton.
Sebastian Stichel is professor in Rail Vehicle Dynamics and head of theDepartment of Aeronautical 
and Vehicle Engineering at KTH Royal Institute of Technology in Stockholm, Sweden. He is vice 
chairman of the European Rail Research Advisory Council. Since 2011, he has been director of the 
KTH Railway Group, a multidisciplinary research centre that deals with most aspects of Railway 
Technology. He holds a BSc (1989) and an MSc (1992) in vehicle engineering and a PhD (1996) 
in vehicle dynamics from Technische Universität Berlin. From 2000 to 2010, he was employed at 
Bombardier Transportation in Sweden, where, from 2003, he headed its Vehicle Dynamics depart-
ment with employees in Sweden, Germany, UK and France. Professor Stichel has a primary research 
interest in the dynamic vehicle-track interaction, mainly using multibody simulation; the main 
concerns are improved ride comfort and reduced wheel and track damage. He is also involved in 
research on the interaction between pantograph and catenary and active suspension for rail vehicles.
xviii Contributors
Julian Stow is assistant director at the Institute of Railway Research at the University of Huddersfield. 
He has 18 years of experience in the railway industry, specialising in rail vehicle dynamics and 
wheel-rail interface engineering, and has led a wide range of research and consultancy projects for 
the rail industry of Great Britain in these areas. These include investigating the causes of rolling 
contact fatigue and other wheel and rail defects, simulation for running acceptance, problem solving 
on current fleets, safety and maintenance standards development and wheel-rail interface manage-
ment for existing and new build light rail and metro systems. He is currently responsible for the 
delivery of a programme of research work under the strategic partnership between the Rail Safety 
and Standards Board and the University of Huddersfield. Julian is a chartered engineer and a Fellow 
of the Institution of Mechanical Engineers.
Nataly Tanicheva is a junior professor at the Department of Railcars and Railcar Maintenance at 
Petersburg State Transport University in St Petersburg, Russia, and a researcher at the Scientific Research 
Centre ‘Vagony’, with a special interest in design of rolling stock and its components. She obtained her 
PhD in 2013 in articulated railway flat wagons from Petersburg State Transport University.
David Thompson is professor of railway noise and vibration at the Institute of Sound and Vibration 
Research (ISVR), University of Southampton. Before joining the ISVR in 1996, he worked at British 
Rail Research in Derby, UK, and at TNO Institute of Applied Physics in Delft, The Netherlands, 
and obtained his PhD from the ISVR in 1990. He has written over 160 papers in refereed journals as 
well as a book on railway noise and vibration, which has also been translated into Chinese. He is the 
main author of the TWINS software for railway rolling noise. His research interests include a wide 
range of aspects of railway noise and vibration as well as noise control, vibroacoustics and structural 
vibration. He teaches undergraduate- and master-level courses.
Hongqi Tian is a professor of Central South University at Changsha in Hunan, Peoples Republic 
of China. She  is an academician of the Chinese Academy of Engineering. Professor Tian is cur-
rently president of Central South University and is a past vice president of the Chinese Academy 
of Engineering. She was awarded her bachelor’s degree and master’s degree in railway locomotive 
vehicles and a PhD degree in fluid mechanics. She has been engaged in the railway science and tech-
nology field over several decades. Under Professor Tian’s leadership, her research team exploited 
the research directions of railway vehicle aerodynamics and railway vehicle collision dynamics; 
established the aerodynamic design theory, technology and method system of high-speed trains; 
proposed the safety protection technology of train collision; and established the safety protection 
technology system for railway operations in windy environments. The team developed the 500 km/h 
moving model rig for the aerodynamic testing of high-speed trains and the actual vehicle impact test 
platform. These test qualifications are recognised in the relevant field around the world. In addition, 
the team developed the strong wind monitoring and warning system for the Qinghai-Tibet railway 
line, designed the shape of the first Chinese high-speed train and proposed the first crashworthiness 
and energy-absorbing vehicle design in China. The team has participated in the research and con-
struction of all high-speed railway lines in China, including the railway lines of Beijing-Shanghai, 
Beijing-Guangzhou and the Qinghai-Tibet railway line that is characterised by a frigid plateau.
Jordi Viñolas is dean and professor of the School of Engineering at Nebrija University. He has pre-
viously held positions as head of European Projects at Bantec and head of TECNUN (University of 
Navarra) and CEIT. His scientific interests are focussed on machine dynamics, noise and vibration, 
railway dynamics and infrastructure. He has published around 60 scientific papers in areas such as 
vehicle dynamics, rail/vehicle interaction and other topics linked to the performance optimisation 
of vehicle and machine components. He has directly supervised 16 PhD theses and more than 50 
MSc theses. His courses are machine elements design, noise and vibration and also mechanical 
fatigue analysis. Dr. Viñolas has worked as an evaluator for the European Commission and was one 
xixContributors
of the promoters of European Rail Research Network of Excellence (EURNEX). He is a member 
of the Editorial Board of the IMechE Journal of Rail and Rapid Transit and of the International 
Journal of Rail Transportation.
A. H. Wickens was educated as an aeronautical engineer at Loughborough and University of 
London. His 11 years in the aircraft industry culminated as head of Aeroelastics on the Avro Blue 
Steel missile. He joined British Railways Research in 1962 to carry out research into the dynam-
ics of railway vehicles. He was director of Research from 1971–1983 and director of Engineering 
Development and Research from 1983–1989. From 1987 to 1990, Alan Wickens was chairman of 
the Office for Research and Experiments of the International Union of Railways in Utrecht. He was 
professor of dynamics in the Department of Mechanical Engineering at Loughborough University 
in 1989–1992 and subsequently Visiting Industrial Professor, where his research interest was in the 
active guidance and dynamic stability of innovative railway vehicles. He is an honorary member of 
the Association for Vehicle System Dynamics.
Nicholas Wilson (BSME, Cornell University, 1980) is chief scientist at the Transportation 
Technology Center, Inc. (TTCI) in Pueblo, Colorado, where he has worked since 1980, specialis-
ing in rail vehicle dynamics and wheel-rail interaction. He leads TTCI’s Vehicle-Track Interaction 
group and the team of engineers developing TTCI’s NUCARS® multibody vehicle-track dynamic 
interaction software. Recently, he has been working on flange climb derailment research, derail-
ment investigations of rail vehicles, wheel-rail wear and RCF studies. He has also been working 
on developing rail vehicle dynamic performance specifications for, and analysing performance of, 
freight and passenger vehicles and trains to carry high-level radioactive material.
Huimin Wu (PhD, Mechanical Engineering, Illinois Institute of Technology, 2000) retired in 
May 2018 from her position as a scientist in the Vehicle-Track Interaction group at Transportation 
Technology Center, Inc. (TTCI) in Pueblo, Colorado. She worked for more than 26 years at TTCI in 
the simulation, analysis and testing of railway vehicles. Her research carried over into areas includ-
ing vehicle dynamics, vehicle-track interaction, wheel flange climb derailment criteria, computation 
methodology of studying wheel-rail contact, NUCARS development,wheel-rail profile design and 
rail grinding. She has presented papers at international conferences on vehicle-track interaction and 
published a number of reports on consultancy work carried out for the railways.
Qing Wu is a research fellow at the Centre for Railway Engineering, Central Queensland University 
(CQU), Australia. His research expertise and interests include parallel computing, 3D train system 
dynamics, track dynamics and multiobjective optimisations. Dr. Wu has authored more than 50 
journal articles and a simulation software. He has conducted a number of railway research and 
consultancy projects ranging from track dynamics to vehicle and train dynamics. His education 
background includes a BEng (2010) and MEng (2012) from Southwest Jiaotong University, China, 
and a PhD from CQU (2016).
Peter Wolfs is a professor of electrical engineering at Central Queensland University, Rockhampton, 
Australia. His research interests include railway power supply and traction systems, smart-grid 
technology, distributed renewable resources and energy storage and their impact on system capacity 
and power quality, the support of weak rural feeders and the remote-area power supply. Prof. Wolfs 
is a Fellow of Engineers Australia and a senior member of the Institute of Electrical and Electronics 
Engineers (IEEE).
Nicolò Zampieri is assistant professor at the Department of Mechanical and Aerospace Engineering 
of the Politecnico di Torino. He received his bachelor’s degree and master’s degree in mechanical 
engineering from that university in 2008 and 2010, respectively, and was awarded his PhD in 2014 
xx Contributors
for the dissertation regarding the development of monitoring systems for railway applications. His 
research interests are railway vehicle dynamics and monitoring, modelling of wheel-rail/roller con-
tact, wear and RCF. His current research activity concerns the design of test benches for railway 
applications and the development of specific applications for railway vehicle monitoring. Nicolò 
Zampieri is co-author of more than 30 scientific publications.
Jing Zeng is professor of railway vehicle system dynamics at the State Key Laboratory of Traction 
Power, Southwest Jiaotong University (SWJTU), China. He  obtained his PhD in Dynamic 
Simulation of Railway Vehicle Systems at SWJTU in 1991. His expertise covers novel bogie design, 
dynamic performance simulation and measurement techniques. In recent years, his research has 
mainly focussed on parameter optimal design, dynamic simulation and laboratory and field tests of 
high-speed trains. He has won two first-class and one second-class prizes of the State Scientific and 
Technological Progress Award.
Wanming Zhai is chair professor of railway engineering at Southwest Jiaotong University (SWJTU) 
in China and is an academician of the Chinese Academy of Sciences. Since 1994, Dr. Zhai has been 
a full professor and director of the Train and Track Research Institute, which is affiliated to the State 
Key Laboratory of Traction Power of SWJTU. In 1999, he was appointed Chang Jiang Chair Professor 
by the Chinese Ministry of Education. Currently, he is the chairman of the Academic Committee of 
Southwest Jiaotong University. Professor Zhai’s research activities are mainly in the field of railway 
system dynamics, focussing on vehicle-track dynamic interaction and train-track-bridge interac-
tions. He established a new theoretical framework of vehicle-track coupled dynamics and invented 
new methodologies for solving large-scale train-track-bridge interaction problems. His models and 
methods have been successfully applied to more than 20 large-scale field engineering projects for the 
railway network in China, mostly for high-speed railways. He is editor-in-chief of the International 
Journal of Rail Transportation and a trustee member of the International Association for Vehicle 
System Dynamics. He  also serves as the president of the Chengdu Association for Science and 
Technology, vice president of the Chinese Society of Theoretical and Applied Mechanics and vice 
president of the Chinese Society for Vibration Engineering.
Weihua Zhang is a distinguished professor of the ‘Cheung Kong Scholars’ Program of China, 
winner of the ‘National Science Funds for Distinguished Young Scholars’ and chief scientist of 
‘973 Program’, the National Basic Research Program. In  2012, he was awarded the Guanghua 
Award of Engineering Technology. His doctoral dissertation was listed among ‘National Top 100 
Outstanding Doctoral Dissertations’ in 2000. Professor Zhang served as an expert on the General 
Planning Group for Autonomous Innovation & Joint Action Plan for China’s High-Speed Trains and 
an expert of the General Planning Group for the China-standard Electrical Multiple Units (CEMU) 
Development Program.
Shengyang Zhu is an associate professor at the Train and Track Research Institute, affiliated to 
the State Key Laboratory of Traction Power, Southwest Jiaotong University (SWJTU) in China. 
He graduated from SWJTU with a PhD degree in rail transportation engineering in 2015. He had 
research experience at Rice University, USA, as an award holder from the China Scholarship 
Council for 18 months since 2012. Dr. Zhu has published more than 30 papers in refereed high-level 
journals, including 22 papers as the first author or corresponding author, and he has given several 
keynote or invited presentations in international conferences and seminars. His research interests 
include a wide range of aspects of train-track interaction as well as track vibration control, track 
damage mechanisms and structural health monitoring. He has worked on a number of national key 
projects related to long-term dynamic performance of train and track systems, as well as industry-
funded projects related to train induced vibration problems. He  supervises graduate students in 
railway system dynamics, and he is a PhD thesis (international) examiner for some universities.
1
1 Introduction
Simon Iwnicki, Maksym Spiryagin, Colin Cole 
and Tim McSweeney
The principal aim of this handbook is to present a detailed introduction to the main issues influenc-
ing the dynamic behaviour of railway vehicles, and a summary of the history and the state of the 
art of the analytical and computer tools and techniques that are used in this field around the world. 
The level of technical detail is intended to be sufficient to allow analysis of common practical situ-
ations, but references are made to other published material for those who need more detail in spe-
cific areas. The main readership will be engineers working in the railway industry worldwide and 
researchers working on issues connected with railway vehicle behaviour, but it should also prove 
useful to those wishing to gain a basic knowledge of topics outside their specialist technical area.
1.1 STRUCTURE OF THE HANDBOOK
The  topics covered in this handbook are the main areas that impact the dynamic behaviour of 
railway vehicles and are intended to present the existing solutions in this area from a multidisci-
plinary perspective. These include the numerical and tribological analysis of the wheel-rail inter-
face, general railway vehicle design and architecture, suspension and suspension component design, 
simulation and testing of electrical and mechanical systems, interaction with the surrounding infra-
structure and noise and vibration generation. The handbook is international in scope and draws 
examples from around the world, but several chapters have a more specific focus, where a particular 
local limitation or need has led to the development of specific techniques or tools.
For example, the chapter on longitudinal train dynamics and vehicle stability expands upon the 
longitudinal train dynamics chapter in the first edition and mainly uses Australian examples of the 
issues related to longitudinal dynamics on their heavy-haul lines, where very long trains are used 
to transport bulk freight.Similarly, the issue of structure gauging largely uses the UK as a case 
study, because it is there that historic lines through dense-population centres have resulted in a very 
restricted loading gauge. The desire to run high-speed trains in this situation has led to the use of 
highly developed techniques to permit full advantage of the loading gauge to be taken.
The history of the field is presented by Alan H. Wickens in Chapter 2, from the earliest thoughts 
of George Stephenson about the dynamic behaviour of a wheelset through the development of theo-
retical principles to the application of modern computing techniques. Professor Wickens was one of 
the modern pioneers of these methods and, as director of research at British Rail Research, played 
a key role in the practical application of vehicle dynamics knowledge to high-speed freight and pas-
senger vehicles.
Chapters 3 and 4 set out the basic structure of railway vehicles. In Chapter 3, Anna Orlova, 
Roman Savushkin, Iurii(Yury) Boronenko, Kirill Kyakk, Ekaterina Rudakova, Artem Gusev, 
Veronika Fedorova and Nataly Tanicheva outline and explain the basic structure of the railway 
coaches and wagons and the different types of running gear that are commonly used. Chapter 4 
covers the design of powered railway vehicles and locomotives. Maksym Spiryagin, Qing Wu, Peter 
Wolfs and Valentyn Spiryagin explain the type and structure of locomotives in service and the 
CONTENTS
1.1 Structure of the Handbook .......................................................................................................1
2 Handbook of Railway Vehicle Dynamics
different types of traction system used. Magnetic levitation vehicles are described in Chapter 5 by 
Shihui Luo and Weihua Ma. MagLev technology has been around for some time but does not yet 
seem to have achieved full commercialisation. The likely trends are explored in Chapter 5.
Chapter 6 explores the detail of the key suspension components that make up the running gear 
of typical railway vehicles. Sebastian Stichel, Anna Orlova, Mats Berg and Jordi Viñolas show how 
these components can be represented mathematically and give practical examples from different 
vehicles. The key area of any study of railway vehicle behaviour is the contact between the wheels 
and the rails. An understanding of all the forces that support and guide the vehicle pass through 
this small contact patch and of the nature of these forces is vital to any analysis of the general vehi-
cle behaviour. The equations that govern these forces are derived and explained by Jean-Bernard 
Ayasse, Hugues Chollet and Michel Sebès in Chapter 7. They  include an analysis of the normal 
contact that governs the size and shape of the contact patch and the stresses in the wheel and rail, 
and also the tangential problem, where slippage or creep in the contact patch produces the creep 
forces which accelerate, brake and guide the vehicle. The specific area of tribology applied to the 
wheel-rail contact is explained by Ulf Olofsson, Roger Lewis and Matthew Harmon in Chapter 8.
The track on which railway vehicles run is clearly a significant part of the dynamic system, and 
Wanming Zhai and Shengyang Zhu present the dynamics and modelling of various railway track 
structures in Chapter 9, as well as the interaction between track and train. Chapter 10 covers the 
unique railway problem of gauging, where the movement of a railway vehicle means that it sweeps 
through a space that is larger than it would occupy if it moved in a perfectly straight or curved path. 
Precise knowledge of this space or envelope is essential to avoid vehicles hitting parts of the sur-
rounding infrastructure or each other. David M. Johnson has developed computer techniques that 
allow the gauging process to be carried out to permit vehicle designers and operators to ensure 
safety at the same time as maximising vehicle size and speed, and he explains the philosophies and 
techniques in this chapter.
The  avoidance of derailment and its potentially catastrophic consequences are of fundamen-
tal concern to all railway engineers. In Chapter 11, Nicholas Wilson, Huimin Wu, Adam Klopp 
and Alexander Keylin explain how railway vehicle derailment is prevented. They explore the main 
causes and summarise the limits that have been set by standards to try to prevent these occurrences 
and cover the special case of independently rotating wheels and several possible preventative mea-
sures that can be taken.
In Chapter 12, Hongqi Tian explains the use of wind tunnels and computational fluid dynamics 
to improve the understanding of the effects of aerodynamics on the dynamic behaviour of railway 
vehicles.
Longitudinal train dynamics are covered by Colin Cole in Chapter 13. This is an aspect of vehi-
cle dynamics that is sometimes ignored, but it becomes of major importance in heavy-haul railways, 
where very long and heavy trains lead to extremely high coupling forces. This chapter also covers 
rolling resistance and braking systems.
Chapter 14 deals with noise and vibration problems. David Thompson, Giacomo Squicciarini, 
Evangelos Ntotsios and Luis Baeza explain the key issues, including rolling noise caused by rail 
surface roughness, impact noise and curve squeal. They outline the basic theory required for a study 
in this area and also show how computer tools can be used to reduce the problem of noise. The effect 
of vibrations on human comfort is also discussed, and the effect of vehicle design is considered.
In Chapter 15, Roger M. Goodall and T.X. Mei summarise the possible ways in which active 
suspensions can allow vehicle designers to provide advantages that are not possible with passive 
suspensions. The basic concepts from tilting bodies to active secondary and primary suspension 
components are explained in detail and with examples. Recent tests on a prototype actively con-
trolled bogie are presented, and limitations of the current actuators and sensors are explored before 
conclusions are drawn about the technology that will be seen in future vehicles.
Computer tools are now widely used in vehicle dynamics, and some specialist software pack-
ages allow all aspects of vehicle-track interaction to be simulated. In Chapter 17, Oldrich Polach, 
3Introduction
Mats Berg and Simon Iwnicki explain the historical development and state of the art of the methods 
that can be used to set up models of railway vehicles and to predict their behaviour as they run on 
typical track or over specific irregularities or defects. The material of previous chapters is drawn 
upon to inform the models of suspension elements and wheel-rail contact, and the types of analysis 
that are typically carried out are described. Typical simulation tasks are presented from the view-
point of a vehicle designer attempting to optimise suspension performance, and the key issue of 
validation of the results of computer models is reviewed.
In Chapter 18, Julian Stow outlines the key aspects of field testing, including the procedures 
typically used during the acceptance process to demonstrate safe operation of railway vehicles. An 
alternative to field testing is to use a roller rig on which a vehicle can be run in relative safety, with 
conditions being varied in a controlled manner. In Chapter 19, Paul D. Allen, Weihua Zhang, Yaru 
Liang, Jing Zeng, Henning Jung, Enrico Meli, Alessandro Ridolfi, Andrea Rindi, Martin Heller and 
Joerg Koch summarise the characteristics of the main types of roller rig and the ways in which they 
are used. Chapter 19 also reviews the history of existing roller rigs, summarising the key details 
of examples of the main types. Chapter 20 extends the theme to scale testing, which has been used 
effectively for research into wheel-rail contact. In  this chapter, Nicola Bosso, Paul D. Allen and 
Nicolò Zampieri describe the possible scaling philosophies that can be used and how these have 
been applied to scaled roller rigs. In Chapter 21, Tim McSweeneyprovides a glossary of terms 
relevant to railway vehicle dynamics.
http://taylorandfrancis.com
5
2 A History of Railway 
Vehicle Dynamics
A. H. Wickens
2.1 INTRODUCTION
The railway train running along a track is one of the most complicated dynamical systems in engi-
neering. Many bodies comprise the system, and so, it has many degrees of freedom. The bodies that 
make up the vehicle can be connected in various ways, and a moving interface connects the vehicle 
with the track. This interface involves the complex geometry of the wheel tread and the railhead and 
non-conservative frictional forces generated by relative motion in the contact area.
The technology of this complex system rests on a long history. In the late eighteenth and early 
nineteenth centuries, development concentrated on the prime mover and the possibility of traction 
using adhesion. Strength of materials presented a major problem. Even though speeds were low, 
dynamic loads applied to the track were of concern, and so the earliest vehicles adopted elements 
CONTENTS
2.1 Introduction .............................................................................................................................5
2.2 Coning and the Kinematic Oscillation ....................................................................................6
2.3 Concepts of Curving ...............................................................................................................8
2.4 Dynamic Response, Hunting and the Bogie ...........................................................................9
2.5 Innovations for Improved Steering ....................................................................................... 12
2.6 Carter .................................................................................................................................... 13
2.7 Wheel-Rail Geometry ........................................................................................................... 17
2.8 Creep ..................................................................................................................................... 18
2.9 Matsudaira............................................................................................................................. 19
2.10 The ORE Competition .......................................................................................................... 19
2.11 The Complete Solution of the Hunting Problem ................................................................... 21
2.12 Later Research on Curving ...................................................................................................23
2.13 Dynamic Response to Track Geometry ................................................................................26
2.14 Suspension Design Concepts and Optimisation ...................................................................26
2.14.1 Two-Axle Vehicles and Bogies ...............................................................................26
2.14.2 Forced Steering .......................................................................................................27
2.14.3 Three-Axle Vehicles ...............................................................................................28
2.14.4 Unsymmetrical Configurations ...............................................................................28
2.14.5 The Three-Piece Bogie ...........................................................................................28
2.14.6 Independently Rotating Wheels ..............................................................................29
2.14.7 Articulated Trains ...................................................................................................29
2.15 Derailment.............................................................................................................................30
2.16 Active Suspensions ................................................................................................................30
2.17 The Development of Computer Simulation .......................................................................... 32
2.18 The Expanding Domain of Rail Vehicle Dynamics ............................................................. 33
References ........................................................................................................................................34
6 Handbook of Railway Vehicle Dynamics
of suspension taken from horse carriage practice. Above all, the problem of guidance was resolved 
by the almost universal adoption of the flanged wheel in the early nineteenth century, the result of 
empirical development and dependent on engineering intuition.
Operation of the early vehicles led to verbal descriptions of their dynamic behaviour such as 
Stephenson’s description of the kinematic oscillation discussed later. Later in the nineteenth cen-
tury, Redtenbacher and Klingel introduced the first simple mathematical models of the action of the 
coned wheelset, but they had virtually no impact on engineering practice. In practice, the balancing 
of the reciprocating masses of the steam locomotive assumed much greater importance. At  this 
stage, artefacts, not equations, defined engineering knowledge.
A catastrophic bridge failure led to the first analytical model of the interaction between vehicle 
and flexible track in 1849.
The increasing size of the steam locomotive increased the problem of the forces generated in 
negotiating curves, and in 1883, Mackenzie gave the first essentially correct description of curving. 
This became the basis of a standard calculation carried out in design offices throughout the era of 
the steam locomotive.
As train speeds increased, problems of ride quality, particularly in the lateral direction, became 
more important. The introduction of the electric locomotive at the end of the nineteenth century 
involved Carter, a mathematical electrical engineer, in the problem, with the result that a realistic 
model of the forces acting between wheel and rail was proposed and the first calculations of lateral 
stability carried out.
Generally, empirical engineering development was able to keep abreast of the requirements of 
ride quality and safety until the middle of the twentieth century. Then, increasing speeds of trains 
and the greater potential risks arising from instability stimulated a more scientific approach to 
vehicle dynamics. Realistic calculations on which design decisions were based were achieved in the 
1960s, and, as the power of the digital computer increased, so did the scope of engineering calcula-
tions, leading to today’s powerful modelling tools.
This chapter tells the story of this conceptual and analytical development. It concentrates on the 
most basic problems associated with stability, response to track geometry and behaviour in curves 
of the railway vehicle, and most attention is given to the formative stage in which an understanding 
was gained. Progress in the last 20 years is not discussed, as the salient points are discussed later in 
the relevant chapters. As a result, many important aspects such as track dynamics, noise generation 
and other high-frequency (in this context, above about 15 Hz) phenomena are excluded.
2.2 CONING AND THE KINEMATIC OSCILLATION
The conventional railway wheelset, which consists of two wheels mounted on a common axle, has a 
long history [1] and evolved empirically. In the early days of the railways, speeds were low, and the 
objectives were to reduce rolling resistance (so that the useful load that could be hauled by horses 
could be multiplied) and to solve problems of strength and wear.
The flanged wheel running on a rail existed as early as the seventeenth century. The position of 
the flanges was on the inside, outside or even on both sides of the wheels and was still being debated 
in the 1820s. Wheels were normally fixed to the axle, though freely rotating wheels were sometimesused in order to reduce friction in curves. To start with, the play allowed between wheel flange and 
rail was minimal.
Coning was introduced partly to reduce the rubbing of the flange on the rail and partly to ease 
the motion of the vehicle round curves. It is not known when coning of the wheel tread was first 
introduced. It would be natural to provide a smooth curve uniting the flange with the wheel tread, 
and wear of the tread would contribute to this. Moreover, once wheels were made of cast iron, taper 
was normal foundry practice. In the early 1830s, the flange way clearance was opened up to reduce 
the lateral forces between wheel and rail, so that, typically, about 10 to 12 mm of lateral displace-
ment was allowed before flange contact.
7A History of Railway Vehicle Dynamics
Coning of the wheel tread was well established by 1821. George Stephenson in his observations 
on edge and tram railways [2] stated that ‘It must be understood the form of edge railway wheels 
are conical that is the outer is rather less than the inner diameter about 3/16 of an inch. Then from a 
small irregularity of the railway the wheels may be thrown a little to the right or a little to the left, 
when the former happens the right wheel will expose a larger and the left one a smaller diameter to 
the bearing surface of the rail which will cause the latter to lose ground of the former but at the same 
time in moving forward it gradually exposes a greater diameter to the rail while the right one on 
the contrary is gradually exposing a lesser which will cause it to lose ground of the left one but will 
regain it on its progress as has been described alternately gaining and losing ground of each other 
which will cause the wheels to proceed in an oscillatory but easy motion on the rails’.
This  is a very clear description of what is now called the kinematic oscillation, as shown in 
Figure 2.1.
The rolling behaviour of the wheelset suggests why it adopted its present form. If the flange is on 
the inside, the conicity is positive, and, as the flange approaches the rail, there will be a strong steer-
ing action, tending to return the wheelset to the centre of the track. If the flange is on the outside, 
the conicity is negative, and the wheelset will simply run into the flange and remain in contact as the 
wheelset moves along the track. Moreover, consider motion in a sharp curve in which the wheelset 
is in flange contact. If the flange is on the inside, the lateral force applied by the rail to the leading 
wheelset is applied to the outer wheel and will be combined with an enhanced vertical load, thus 
diminishing the risk of derailment. If the flange is on the outside, the lateral force applied by the 
rail is applied to the inner wheel, which has a reduced vertical load, and thus, the risk of derailment 
is increased.
As was explicitly stated by Brunel in 1838 [3], it can be seen that, for small displacements from 
the centre of straight or slightly curved track, the primary mode of guidance is conicity, and it is on 
sharper curves and switches and crossings that the flanges become the essential mode of guidance.
Lateral oscillations caused by coning were experienced from the early days of the railways. One 
solution to the oscillation problem that has been proposed from time to time, even down to modern 
times, was to fit wheels with cylindrical treads. However, in this case, if the wheels were rigidly 
mounted on the axle, very slight errors in parallelism would induce large lateral displacements that 
would be limited by flange contact. Thus, a wheelset with cylindrical treads tends to run in continu-
ous flange contact.
In 1883, Klingel gave the first mathematical analysis of the kinematic oscillation [4] and derived 
the relationship between the wavelength Λ the wheelset conicity λ, wheel radius r0 and the lateral 
distance between contact points 2l as 
 /( ) /Λ = 2 0 1 2π λr l (2.1)
Klingel’s formula shows that the frequency of the kinematic oscillation increases with speed. Any 
further aspects of the dynamical behaviour of railway vehicles must be deduced from a consider-
ation of the forces acting, and this had to wait for Carter’s much later contribution to the subject.
FIGURE 2.1 The kinematic oscillation of a wheelset. (From Iwnicki, S. (Ed.), Handbook of Railway Vehicle 
Dynamics, CRC Press, Boca Raton, FL, 2006. With permission.)
8 Handbook of Railway Vehicle Dynamics
2.3 CONCEPTS OF CURVING
The  action of a wheelset with coned wheels in a curve was understood intuitively early in the 
development of the railways. For example, in 1829, Ross Winans took out a patent that stressed the 
importance of the axles taking up a radial position on curves [5], a fundamental objective of running 
gear designers ever since, and W. B. Adams clearly understood the limitations of coning in curves 
in 1863 [6]. Redtenbacher [7] provided the first theoretical analysis in 1855, which is illustrated in 
Figure 2.2.
From the geometry in this figure, it can be seen that there is a simple geometric relationship 
between the outwards movement of the wheel y, the radius of the curve R, the wheel radius r0, the 
distance between the contact points 2l and the conicity λ of the wheels in order to sustain pure 
rolling.
The  application of Redtenbacher’s formula shows that a wheelset will only be able to move 
outwards to achieve pure rolling if either the radius of curvature or the flangeway clearance is suf-
ficiently large. Otherwise, a realistic consideration of curving requires the analysis of the forces 
acting between the vehicle and the track. In 1883, Mackenzie [8] gave the first essentially correct 
description of curving in a seminal paper (which was subsequently translated and published in both 
France and Germany). His work was suggested by an unintentional experiment in which the springs 
of the driving wheels of a six-wheeled engine were tightened to increase the available adhesion. 
The  leading wheel mounted the rail when the locomotive approached a curve. Mackenzie gave 
a numerical but non-mathematical treatment of the forces generated in curving. His discussion 
is based on sliding friction and neglects coning, so that it is appropriate for sharp curves, where 
flanges provide guidance. Referring to Figure 2.3, Mackenzie explains ‘If the flange were removed 
from the outer wheel, the engine would run straight forwards, and this wheel, in making one revolu-
tion, would run from A to B; but it is compelled by the flange to move in the direction of the line 
AC, a tangent to the curve at A, so that it slides sideways through a distance equal to BC. If this 
wheel were loose on the axle, it would, in making a revolution, run along the rail to F; but the inner 
wheel, in making a revolution, would run from H to K, the centre-line of the axle being KG; so that, 
if both axles are keyed on the axle, either the outer wheel must slide forwards or the inner wheel 
backwards. Assuming that the engine is exerting no tractive force, and that both wheels revolve at 
the speed due to the inner wheel, then the outer wheel will slide forwards from F to G. Take AL 
equal to BC, and LM equal to FG, the diagonal AM is the distance which the outer wheel slides in 
making one revolution’.
FIGURE 2.2 Redtenbacher’s formula for the rolling of a coned wheelset on a curve. (From Iwnicki, S. (Ed.), 
Handbook of Railway Vehicle Dynamics, CRC Press, Boca Raton, FL, 2006. With permission.)
9A History of Railway Vehicle Dynamics
He then applies similar reasoning to the other wheels, assuming various positions for the wheel-
sets in relation to the rails. Thus, Mackenzie’s calculations showed that the outer wheel flange exerts 
against the rail a force sufficient to overcome the friction of the wheel treads. Previously, centrifugal 
forces were regarded as the cause of many derailments. He also made the comment that ‘the vehicle 
seems to travel in the direction which causes the smallest amount of sliding’, which