Dynamic Analysis of Steering Bogies

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Dynamic Analysis of Steering Bogies
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DOI: 10.4018/978-1-5225-0084-1.ch021
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Cite this chapter as: A.K. Samantaray, S. Pradhan, Dynamic Analysis of Steering Bogies, Chapter 21,
pp. 524-580, In: Handbook of Research on Emerging Innovations in Rail Transportation and
Engineering, DOI: 10.4018/978-1-5225-0084-1.ch021.
Dynamic Analysis of
Steering Bogies
Arun K. Samantaray
Indian Institute of Technology Kharagpur, India
Smitirupa Pradhan
Indian Institute of Technology Kharagpur, India
ABSTRACT
Running times of high-speed rolling stock can be reduced by increasing running speed on curved por-
tions of the track. During curving, flange contact causes large lateral force, high frequency noises, flange
wears and wheel load fluctuation at transition curves. To avoid derailment and hunting, and to improve
ride comfort, i.e., to improve the curving performances at high speed, forced/active steering bogie design
is studied in this chapter. The actively steered bogie is able to negotiate cant excess and deficiency. The
bogie performance is studied on flexible irregular track with various levels of cant and wheel wear. The
bogie and coach assembly models are developed in Adams VI-Rail software. This design can achieve
operating speed up to 360 km/h on standard gauge ballasted track with 150mm super-elevation, 4km
turning radius and 460m clothoid type entry curve design. The key features of the designed bogie are
the graded circular wheel profiles, air-spring secondary suspension, chevron springs in the primary
suspension, anti-yaw and lateral dampers, and the steering linkages.
1. INTRODUCTION
Now-a-days, railway is one of the important transportation systems in most of the countries. To increase
the popularity of railway transport for further, improving speed, comfort and safety are some of the
important issues. However, heavy investment in infrastructure development, design and fabrication,
research, maintenance and operations, etc. is required to commission high-speed rails. When operating
speed increases up to 300-350 km/h, regular maintenance requirements and related economic issues
influence the decisions taken by railway operators. To minimize the wear in the wheels and rails, track
quality is the essential factor. The dynamic performance as well as ride comfort can be increased in the
DOI: 10.4018/978-1-5225-0084-1.ch021

straight track as well as curved track by taking care of bogie design as well as track design. To enhance
the performance in the straight track, optimization of bogie parameters is sufficient whereas; in curved
track, optimization of track design parameters as well as bogie parameters are necessary. Some of the
major parameters that influence performance (stability, comfort, etc.) and wheel/track wear in a curved
track are curve radius, cant given to the track, wheel-rail geometry, bogie parameters, axle load and the
tractive force between rails and the wheel.
For high speed rolling stock, running times can be reduced by increasing running speed on curved
portion of track. During curving, flange contact occurs on the gauge corner of the outer rail which causes
large lateral force, high frequency noises, wear of flanges and significant change of the wheel load at
transition curves. In extreme case, there is a chance of derailment. To avoid derailment and hunting,
and to improve ride comfort of the passengers, in the overall, to improve the curving performances at
high speed on curved path, two types of bogies have been implemented along with optimization of track
parameters: they are tilting bogie and steering bogie.
Running speed can be increased without reducing the ride comfort of passengers by using tilting bo-
gies. When a train enters a curve at high-speed, centripetal force can cause loss of balance of passengers
and luggage objects. Tilting is used to compensate this. When tilting is caused due to deformation of
suspensions only then it is called passive tilting. When actuators are using to force titling, it is called
active tilting. The amount of tilt including that from track super-elevation (much like banking of roads)
is usually restricted 6 or 8 degrees. Beyond this, on long distance travel, passengers may suffer from
a form of nausea resembling seasickness. This restriction does not allow for speed increase beyond a
certain range. Therefore, titling technology if often combined with other technologies.
With the help of steering bogie, speed increases on the curves by minimizing lateral force. Due to
high speed on the curve, wheel exerts large lateral force on the rails which causes wear of wheel flanges
and rails. Worn wheels or tracks affect the dynamic behavior of bogies. To reduce lateral force as well
as lateral displacement, steering mechanisms can be implemented. In fact, active steering mechanism
allows for a great deal of speed increase.
Primary steering of rail vehicles is achieved due to conical wheel profile. However, there is an inher-
ent conflict between curving performance (steering) and stability. Stability and curving performance
mostly depends on wheel-set guidance and bending stiffness and shear stiffness of primary suspension
in the horizontal direction. Generally hunting in the straight track occurs due to self-excited vibration of
wheel-sets. The critical speed of railway vehicles depends on the suspension parameters and equivalent
conicity of the wheel tread. To overcome the problems of the stability and curving performance (steering),
several developments have taken place in the form of implementation of passive steering, semi-active
controlled steering and active controlled steering.
This chapter discusses various steering bogies in details and their dynamic behavior is analyzed.
The steered bogie and its assembly (car body, front bogie and rear bogie) are modeled using multi-body
dynamics framework and run on a designed measured track. The dynamic performance of steered bogie
is investigated by changing the design parameters. The creep forces, wheel displacement, contact geom-
etry, accelerations and ride comfort are estimated against standards to ensure safe operation. The input
parameters are design parameters of bogie and different track irregularities in vertical as well as lateral
directions. Stability, curving behavior and comfort analysis is performed at various speeds. The dynamics
of the steered bogie is analyzed using multi-body system (MBS) simulation software ADAMS (VI-Rail).
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2. COMMON TERMINOLOGIES
The common terminologies which are used in the rail-vehicle dynamics are given below (The American
Public Transportation Association, 2007). Some of them are illustrated in Figure 1 to 3.
• Angle of Contact: The angle of a tangent line at the point of contact between the rail and wheel
with respect to axis of the wheel-set, i.e., the angle between the contact plane and the axle center
line.
• Angle of Attack: Angle between the leading outer wheels and outside rail (see Figure 3).
• Cant Deficiency: The difference between applied cant and a higher equilibrium cant.
• Cant Excess: The difference between applied cant and a lower equilibrium cant.
• Equilibrium Cant: The cant needed for the track to neutralize the horizontal acceleration due to
curving is called equilibrium cant.
• Flange Clearance: The maximum lateral distance by which the wheel-set can shift from its cen-
tered position between the rails at which the rail-wheel contact angle becomes 250 with respect to
the wheel axis.
• Grade: Slope of the track in longitudinal direction.
• Gauge: The minimum lateral distance between inner faces of the rails.
• Hunting: A self-excited lateral oscillation which is produced by forward speed of the vehicle and
wheel-rail interaction.
• Hunting Critical Speed: The speed above which persistent hunting typically occurs for a given
bogie or truck.
• Rolling Radius: perpendicular (radial) distance between the wheel/ axle center line and the point
of contact with the rail. Rolling radius may vary with respect to lateral location of the point of
rolling contact.
• Rolling Radius Difference: Different between rolling radius of left wheel and rolling radius of
right wheel of a wheel-set. As wheel-set is shifted laterally from its centered position between the
rails, rolling radius will vary with respect to lateral location of the point of rolling contact on each
wheel.
• Track Cant: Amount by which one running rail is raised above the other running rail in a curved
track. Track cant is positive when outer rail is raised above the inner rail. The angle made by the
track with horizontal plane is called track angle, which is expressed in radians.
• Super-Elevation: The vertical distance between left and right rail, same as cant.
• Tilt Angle: The angle between the car body floor plane and track plane.
• Tilting Train: The train that has the capacity to tilt the car body inward in the curve of the track
to reduce the lateral acceleration.
• Wheel Tread: The contact portion between the outer rim of the wheel and the rail.
Local or body-fixed reference system (see Figure 2):
• Roll: Rotation around the longitudinal axis of the car body.

• Pitch: Rotation around the lateral axis of the car body.
• Yaw: Rotation around the vertical axis of the car body.
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• Sway: Combination of the lateral displacement and rotation about the longitudinal axis of car
body as well as bogie frame. It occurs due to asymmetrical loading.
• Bounce: Vertical motion of rolling stock.
Figure 1. Wheel-rail geometry
Figure 2. Different types of motion
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Figure 3. Angle of attack of wheel-set
3. SOFTWARE FOR RAIL VEHICLE DYNAMICS STUDY
For railway vehicle dynamics study, several of software are available depending on the application areas
such as track design, rail-wheel interaction, vehicle dynamics and structural mechanics (Dukkipati &
Amyot, 1988). CONTACT, USETAB and FASTSIM are the software used to study rail-wheel interac-
tion (Polach et al., 2006). CONTACT is a program based on the complete theory of elasticity by which
tangential stresses and internal stresses are calculated. Based on simplified theory, Kalker developed
a program named as FASTSIM which is a FORTAN sub-routine. USETAB is a program designed by
Kalker for a general wheel-rail contact problem to find out creep forces.
We are concentrating on studying the dynamic behavior of the vehicles. Depending on the complexity
of the problem like linear or non-linear analysis, degrees of freedom etc., different types of methods are
used. In frequency domain, eigenvalue analysis is often used to evaluate critical speed, natural frequen-
cies, damping factors and mode shapes. But for most of the cases, non-linear models are deployed and
time-domain solution techniques are used to analyze the dynamic behavior of the vehicle. Dynamic
behavior studies, such as modal analysis, ride comfort, hunting stability and curving performances,
etc., are performed by multi-body software (MBS) like ADAMS, MEDYNA, SIMPACK, NUCARS,
VOCO, VOCOLIN, VAMPIRE and GENSYS. ADAMS/VI-rail provides a graphical interface which
allows developing a model similar to that in computer aided design (CAD) (Polach et al., 2006). This
software includes stability analysis, dynamic analysis as well wheel-rail contact model and animation.
A large number of computer codes have been developed by railway organizations to design as well as
optimize suspension systems, tracks parameters and vehicle parameters. The equations of motion for the
system are developed by multi-body dynamics theory, which are then processed by a solver. MATLAB /
Simulink can be used to design the control part of the railway vehicles whereas the mechanical part can
be modeled using ADAMS/ Rail. Finally MATLAB / Simulink and ADAMS/ VI-rail can be coupled
(called co-simulation) for mechatronic simulation. MEDYNA (Mehrkorper- Dynamika) was developed
by German Aerospace Research Organization (DLR) in collaboration with Technical University of Berlin.
SIMPACK was developed by the same team at DLR for analysis of road vehicles as well as rail vehicles
having nonlinear kinematics. In SIMPACK, equations of motion are formulated in terms of relative co-
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ordinates. This software package uses standard elements for primary and secondary suspensions having
linear spring and damper characteristics. In USA, Association of American Railroads (AAR) funded to
the development of a program to simulate the behavior of the railway vehicle negotiating a curve. To
analyze running behavior of vehicle, Schupp et al. (2004) built a mathematical model by using multi-
body system software, SIMPACK. NUCARS is another simulation package developed by Transportation
Technology Center, Inc. (TTCI). It is capable of predicting the response of different rail vehicles on dif-
ferent types of track geometry. VOCO (Voiture en Courbe) was developed by French National Transport
Research Institute (INRETS) to simulate multi-body dynamics with a reference frame on a long curve.
Initially it was used to simulate Y25 bogie. VOCODYM is the second version of VOCO. VOCOLIN
is used to simulate the wheel-rail contact with multi-Hertzian approach. VAMPIRE was developed by
British Rail Research for analyzing different dynamic behaviors as well as to predict the behaviors of
the worn wheels of railway vehicle (Pombo, 2012). Track data can be fed directly to the software from
the track recording coach and the behavior of that portion of the track can be predicted in the real time.
Derailment risk, passengers’ ride comfort and track creep forces can be calculated for different vehicle
models for track engineers. GENSYS is a new three dimensional railway vehicle analysis tool which
is used in Sweden for simulating track-vehicle interaction with all pre and post processing programs.
DIASTARS (Dynamic Interaction Analysis for Shinkansen train And Railway Structure) is a finite ele-
ment program which is developed for the simulation of Shinkansen train (Tanabe et al., 2003). Along
with DIASTARS, Visualization program (VIS) is used to generate animations.
For optimization of vehicle parameters such as those of suspension, sometimes it is easier to develop
models based on equations of motion (Cheng & Hsu, 2011). These equations of motion can be simulated
using different solvers such as Runge-Kutta method and used in optimization loops. These models are
free from software specific constraints and thus can be employed for various other studies. One such
study presented in Lee and Cheng (2005) evaluates the influences of several physical parameters on
critical speed by using Lyapunov’s indirect method. In Cheng et al. (2009), a heuristic nonlinear creep
model is used to derive nonlinear coupled differential equations of motion on the curved track.
In this chapter, the performance of different bogie models will be demonstrated through simulation
in Adams/ VI-Rail multi-body dynamics software. These studies can be as well performed with other
software like SIMPACK or NUCARS.
4. ANATOMY OF RAILWAY VEHICLES
Rolling stock along with track is a complex system having many degrees of freedom. In addition, in rail-
wheel interaction involves complex geometry. Forces between the rail and the wheel, inertia forces and
forces exerted by suspension system affect the dynamics of the railway vehicle. The dynamic behavior of
the rail and the wheel cannot be controlled but suspension design can be optimized to control the motion
of the railway vehicles for achieving good ride quality as well as to reduce the tendency of derailment.
Railway vehicles consists of wheel-sets, bogie frame, car-body and suspension systems (springs and
dampers), all of which affect dynamics of railway vehicles in a complex way. There is no definite way
of decoupling the dynamics of each subsystem of a railway vehicle. The main causes of critical hunting
and derailment are improper design or damaged suspension system and wheel. The coach is mounted on
several bogies. Bogies may be articulated, i.e., shared between adjacent coaches. The main components
of a bogie are given below:
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1. Wheel-Sets: It consists of two wheels with a common axle. The axle and wheels rotate with common
angular velocity. The contact portion between wheel and rail is called wheel tread (see Figure 4.).
Lower wheel tread gradient on a straight track increases the hunting stability and allows operating
the train at higher speed. However, curving requires difference in rolling radii at contact patches
between two wheels and rails. Thus, curving performance improves when the wheel tread gradient
is high. As a trade-off between these two contrasting requirements, wheel tread is usually conical
with 1:40 tread gradient/configuration (Okamato, 1998). To avoid flange contact, lateral displace-
ment is limited to ±7 to ±10 mm. For high speed bogie, graded circular wheel tread configurations
are mostly used. In such wheel tread configuration, large numbers of arcs are connected next to
each other.
2. Axle Boxes: An axle box permits the wheel-set to rotate relative to it. Primary suspension system
is mounted on the axle box which is attached to the bogie frame. The main function of an axle box
is to transmit the longitudinal, lateral and vertical forces from wheel-set to other bogie elements.
The bearing supporting the axle in the axle box can be cylindrical roller bearing, taper roller bear-
ing, conical bearing or ball bearings with cylindrical bearing (Okamato, 1999).
3. Suspension System: It consists of elastic elements, dampers and associated components (Orlova
& Boronenko, 2006). Generally, suspension system has two stages: A primary suspension which
connects the axle box to the bogie frame and a secondary suspension which connects the bogie
frame to the bolster or car body.
a. Primary Suspension: The main function of the primary suspension is to guide the wheel-
sets on straight as well as curved track and to isolate the dynamic loads produced due to track
irregularities from the bogie frame. To achieve high speeds, the longitudinal stiffness should
be high and lateral stiffness should be low. In curved track, high longitudinal stiffness leads
to increase in contact forces between wheel and rail which causes rapid wear and high lat-
eral stiffness leads to increase in dynamic force when negotiating lateral track irregularities.
Generally in a passenger bogie, different stiffness is provided in vertical, lateral, as well as
longitudinal directions. Coil springs with cylindrical rubber, traction links with resilient bushes,
and chevron (rubber-interleaved) springs are the different types of primary suspensions used
in different high speed bogies such as in Shinkansen, ETR-460 and X-2000, respectively.
b. Secondary Suspension: The main function of the secondary suspension is to reduce the
dynamic accelerations acting on the car-body which is responsible for ride comfort of pas-
sengers. The sources of these accelerations are excitation from track irregularities/ roughness
and natural oscillations of the bogie frame and car body. As passengers are more sensitive to
lateral oscillations, the stiffness in lateral direction should be as small as possible. Different
types of secondary suspensions used in different high speed trains are flexi-coil suspension,
air spring suspension and full active suspension (FSA).
4. Dampers: In bolster bogie (e.g., DT-200), side bearers (Okamato, 1998) give friction damping and
prevent hunting. Normally, yaw rotation of bogie relative to car body is controlled by longitudinal
yaw dampers. Yaw dampers are mounted between car body and outside of side beam of bogie
frame. Yaw damper is a part of the secondary suspension system. Redundant type yaw dampers
(called lateral dampers) are used to stabilize the running behavior in ICF3 high speed bogies. Lateral
dampers are also useful in reducing lateral disturbances.
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5. Bogie Frame: Different types bogie frames are there such as Z- shaped and H-shaped. Most of
the high speed bogies (Shinkansen, BT-41 and SF 400) are H-shaped. H-shaped bogies consist of
two side beams and two cross beams.
5. RAILWAY WHEEL-SET
The conical shaped wheel of the rolling stock helps to reduce rubbing of flange of the wheel on the
rail and improve the curving performance. The presence of flange on the wheel prevents derailment. In
the straight track, flanges are not in contact with the rail. In curved track, flange contact provides the
required guidance to the wheels. Though different types of wheel profiles are there, they have some
common features (Orlova & Boronenko, 2006): width of profile is 125-135 mm, the flange height is
28-30 mm, flange inclination angle is between 65 and 700 and the conicity is 1:10 or 1:20. But the co-
nicity for higher speed rolling stock is 1:40 for preventing hunting in straight track. If inside conicity is
positive and the flange moves towards the rail due to strong steering action, the wheel-set tries to return
to the center of the track. In this condition, the combination of the lateral force applied by the rail to the
outer wheel of the leading wheel-set and increased vertical load reduces the risk of derailment. When
outside conicity is negative, in the absence of steering action, flange is in contact with rail throughout
the track. The lateral force applied by the rail to the inner wheel reduces the amount of the vertical load
and increases the risk of derailment.
Figure 4. Different components of a Sinkansen 300 series motor bogie
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5.1. Hunting of Wheel-Set
In conventional wheel-set, wheels connect to each other through a rigid axle and angular speed of both
inner and outer wheels is same. There needs to be a difference in rolling radius between outer and inner
wheels on the curved track. The variation of rolling radius can be expressed by using lateral displacement
of a wheel in conventional wheel-set. For pure rolling motion, conical wheel-set occupy radial position
in the curved track. In the year 1855, Redenbacher derived the first theoretical formulation from the
simple geometrical relationship between lateral displacements of the wheel-set on the curve (y), radius
of curve (R), wheel radius (r0), conicity of wheel-set and lateral distance between two contact points on
the wheel set (2l).
By applying simple geometrical relationship (see Figure 5).
(r0 − λy ) (r0 + λy )
∆OAB ≅ ∆OCD ⇒ =
(R − l ) (R + l ) (1)
r0l
∵y=
Rλ
While a wheel-set moves on a track, if there is a slight displacement to one side then wheel on one
side runs on larger radius as compared to the other side. As two wheels are mounted on the common
axle, one wheel will move faster than other than other because of larger instantaneous rolling radius and
the wheel set would try to turn. This produces a centripetal force which forces the wheel set to the center
of the track and beyond it (due to inertia). The result is a kinematic oscillation called wheel hunting. In
the year 1883, Klingel derived the formula for kinematic oscillation with the parameters as wavelength
of hunting oscillation (Λ), wheel conicity (λ), wheel radius (r0) and lateral distance between two rail-
wheel contacts (2l) (Ayasse & Chollet, 2006). The distance along the track s=Vt, where V the forward
speed and t is time. Klingel’s formula (Ayasse & Chollet, 2006) considers Redtenbacher’s formulation
of pure rolling of a coned wheel-set on a curve (see Figure 6.):
1 d 2 y ω 2 y ω 2 r0l
= = 2 = 2 (2)
R ds 2 V V Rλ
Figure 5. Rolling of a coned wheel-set on a curve
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Figure 6. Kinematic oscillation of a wheel-set
r0l
Λ = 2π (3)
λ
By increasing the speed, the frequency of the kinematic oscillation also increases. This oscillation
damps out below a certain speed called the critical speed. Above the critical speed, this oscillation
increases and causes repeated flange contact on two sides of the wheel set which results in an uncom-
fortable ride and may lead to derailment. This simplified kinematic formulation ignores the inertial and
contact forces and the actual behavior is obtained through multi-body dynamics studies. In fact, simple
conical wheel sets are not used in modern trains.
Figure 7. Rail-wheel contact at different positions: in (a) normal operation; (b) flange contact (in curved
track); (c) tending to derailment; and (d) derailment or wheel jump
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5.2. Flange Climb and Derailment
Dynamic forces act in the frequency range of 0-20 Hz for sprung mass, 20-125 Hz for un-sprung mass
and 0-2000 Hz for corrugated, welded and flat wheels (Miura, 1998). The vertical forces in lower fre-
quency range are produced due to track geometry and irregularities. The forces in the higher frequency
range are due to discontinuities like rail joints, crossings, and rail and wheel surface irregularities. The
track is distorted due to lateral forces by wheel-set, which causes derailment in extreme cases. The lateral
forces consist of flange reaction, tread friction and lateral creep force on the rail. The combination of net
lateral and vertical forces acting on rail-wheel contact leads to mounting/climbing of the flange on the
rail which causes derailment. The derailment coefficient is defined as the ratio of instantaneous lateral
force and vertical force at the rail-wheel contact.
Several flange climb and derailment criteria have been proposed as guidelines for railway vehicle
engineers. The simplest criterion is Nadal’s single wheel L/V limit criterion which is related to instan-
taneous lateral and vertical forces (Ayasse & Chollet, 2006). Based on the static equilibrium of forces
between rail and wheel by considering single point contact at flange (see Figure 8.), the following equa-
tions can be derived.
F3 = V cos δ + L sin δ = V (cos δ + VL sin δ)

F2 = V sin δ − L cos δ = V (sin δ − VL cos δ) when V sin δ − L cos δ < µ × F3  (4)
 
F2 = µ × F3 when V (sin δ − VL cos δ) ≥ µ × F3 
 
The L/V ratio can be expressed as
F2
tan δ −
L F3
= (5)
V 1 + F2 tan δ
F3
Figure 8. Forces at flange contact location
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For the saturated condition, F2/F3=μ and the L/V ratio limiting criterion is given by
L tan δ − µ
= (6)
V 1 + µ tan δ
According to Nadal’s formula, derailment coefficient is 1.22 for friction coefficient μ=0.35 and
flange angle δ=700. Beyond that limiting value, derailment may occur. However, the time duration or
the distance for which the value of the derailment coefficient remains at critical value is another govern-
ing factor. In Japanese design, the limiting value of derailment coefficient is 0.04/t if t is less than 1/20
second and 0.8 if t is more than 1/20 second.
6. RAILWAY TRACKS: DESIGN AND DYNAMICS OF THE TRACK
6.1. Track Design
Track design parameters are important for the dynamic stability of vehicles. The most common parameters
are track gauge, track cant / super-elevation, transition length of the curve, radius of curvature (horizontal
and vertical), and track irregularities. These parameters are detailed in the following sections.
6.1.1. Track Gauge
In railway track, gauge is the least distance between the inner face of rails on the railway track (Figure 9).
Different countries use different types of gauges. They are classified into
• Standard Gauge: The lateral width of standard gauge is 1435mm.

• Broad Gauge: Track gauge is greater than standard gauge. The values of broad gauge are different
in different countries (Russia - 1520mm, United states - 1575mm, 1581mm, 1588mm, 1600mm,
1638mm etc., England- 1727mm, India - 1676mm, France - 1750mm).
• Narrow Gauge: Track gauge is smaller than standard gauge. The values of narrow gauge are dif-
ferent in different countries (United States - 508mm, 578mm, United Kingdom - 508mm, 578mm,
660mm, etc., Germany - 520mm,560mm, 860mm,1100mm, Japan - 838mm and 1067mm).
• Meter Gauge: Meter gauge is 1000mm.
Figure 9. Track gauge
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For high speed rolling stock, standard track gauge of 1435mm is universally adopted. This allows for
interchangeability between operators and standardization of such a safety critical system.
6.1.2. Track Cant
Track cant or super-elevation is defined as the difference between the levels of two rails (Figure 10) in
a curved path which is useful to compensate the unbalanced lateral acceleration. The cant angle can be
calculated as follows.
 h 
ϕt = sin−1  t  (7)
 2b0 
where 2b0= 1435mm on the standard gauge and ht is cant. The variation of track cant angle along a track
is shown in the Figure 11 (b).
Figure 10. Track cant
Figure 11. (a) Track curvature, (b) Track cant angle
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The track cant is designed based on the radius of curvature and the maximum running speed. More
track cant allows higher running speed. However, there is a chance of derailment due to large lateral
force and low vertical load on the outer track on a curve when a train runs at low speed on a track de-
signed for high speed. Therefore, there is a limit on the maximum value of cant. When a train runs on
a curve at a speed other than the designed speed, there can be cant deficiency or cant excess. These are
discussed later in this chapter.
6.1.3. Transition Length of the Curve
The radius of curvature (ρ) is defined as
ρ=1/R (8)
where, R is the curve radius. The variation of curvature at the entry and exit of a curved path is called
transition curve. Usually, it is of a clothoid type. It is used to join straight track to circular one or two
adjacent curves to allow a gradual change in curvature. In a clothoid (also called Euler spiral) the cur-
vature changes linearly with the curve length. The clothoid type of the transition curve (Figure 11 (a))
is given by Lindahl (2001)
s
ρ ( s) = ρ0 + (9)
A2
where, s=s0=0 at the start of the transition curve, ρ is the curvature at a distance s, and A is the clothiod
parameter. If a clothoid starts from straight line (ρ0 = 0) and ends in a circle with radius R with the total
transition length Lt then
A2 = LtR (10)
Figure 11. (a) shows different portions of a curved track where sections oa, ab and bc, respectively,
represent straight portion with infinite radius of curvature, transition portion with variable radius and
circular portion with constant radius. With the change in track curvature, the track cant is also varied
in proportion (see Figure 11(b)) where the proportionality constant depends on the designed operation
speed at which equilibrium cant is desired.
6.1.4. Tracks around the World
There is wide variation in track and speed parameters across railway networks in the world. This is pri-
marily because of different safety standards, guidelines, and demographics and geographic situations.
Table 1 gives an overview of the parameters across different railway networks.
537

Table 1. Speed and track operational parameters in some railway companies throughout the world
(Lindahl, 2001)
Organization TSI/ JR JR JR DB DB SNCF SNCF BV

CEN
Parameter Tokaido Sanyo Hannover- Koln- TGV TGV Botniaban
Shinkansen Shinkasen Wuzburg RheinMann Paris Atlantique (partly)
Sud Est
Maximum design 280 300 300 350 250
speed (kmph)
Maximum service 270 300 275 250 270 300 200a /250b
speed (kmph)
Max. cant (mm) 180 200 180 180 65 160 180 180 150
Max. cant 100 100 100 100 80 150 85 60 100/220
deficiency (mm)
Max. cant excess 110 50 100
(mm)
Minimum curve 2500 4000 4000 7000 3350 4000 6250 3200
radius (m)
Minimum vertical 10000 15000 15000 22000 12000 11000
curve radius (m) 14000
a: Conventional vehicles with older running gear and freight trains, b: Vehicles with improved running gear and car -body tilt system
6.2. Dynamics of the Railway Track
Irregularities of the track lead to oscillations or vibrations which cause human discomfort. Long wavelength
track irregularities give rise to low frequency oscillations of train which cause passenger discomfort and
can lead to derailment through resonance with different bending modes of the track. Short wavelength
irregularities cause vibration and noise which create unpleasant environment for passengers (Miura et
al., 1998). Before we proceed further, let us have a look at the track properties.
Figure 12. Different components of the track
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6.2.1. Track and Its Components
A railway track consists of rails, sleepers, rail pads, fastenings, ballast, sub-ballast and subgrade (Dahl-
berg, 2006). Super structure and sub-structure (sub-ground/ sub-grade) are two sub-systems of a ballasted
track. Super structure consists of rails, sleepers, ballast and sub-ballast and sub-structure is composed
of the formation layer and the ground. The main function of the track is to guide the train and to carry
load of the train and distribute the load over the sleepers and the ballast bed.
1. Rails: Modern steel rail has I-section with a flat bottom. The commonly used rail profile is UIC-
60, where 60 refers to mass of the rail in kg per meter. Standard rail length is 25m. To improve
ride quality and reduce noise as well as vibration, continuous welded rails (CWR) are used in
high-speed tracks. CWR carry vertical load (compression) of train, lateral forces from wheel-set,
longitudinal forces due to traction and breaking of train. A badly laid track may buckle causing
sharp lateral displacement. The above problem can be prevented by using sleepers, ballast and
fastening (Miura et al., 1998). Modern dedicated tracks for high-speed rails use fully concrete slab
tracks. Note that rail profile UIC 60 with inclination 1:40 has less guiding force as compared to
UIC60 with inclination 1:20.
2. Rail-Pads: Rail-pads are mainly used in railway track with concrete sleepers. They are placed
between steel rails and sleepers to protect the rails from wear and impact damage and also act as
electrical insulator. Soft rail pad permits larger deflection of rails, transmits axle load from train
to sleepers and also isolates high frequency vibration from rail to sleepers.
3. Sleepers: Sleepers provide support to rail. They transmit vertical, lateral and longitudinal forces
from the rail to the ballast. Generally wood and concrete sleepers are used. Due to good elastic
properties, light weight and ease of handling, timber sleepers are preferable to concrete sleepers.
But in case of wood, the service life is very short, especially in tropical and sub-tropical regions
and regions affected by termite and other pests. To overcome the drawback of wood, synthetic
sleepers made from polyurethane and glass fibers are used in Japan (Miura et al., 1998). Synthetic
sleepers have same physical properties as woods/timbers and give better life service. These sleep-
ers are generally used in the places such as steel girder bridge, switches and other places where
replacement as well as maintenance is difficult.
4. Rail Fastenings: Generally dog spikes are used to fasten timber sleepers to rails. In case of con-
crete sleepers, different types of springs are used for fastening purposes by using rubber pads. Leaf
springs are used in Japan and France, whereas wire springs are used in Germany for their better
adjustability, load bearing ability and fastening force.
5. Ballast: Coarse stones are used as ballast to support sleepers as well as rail and to transmit vertical
and lateral forces from trains to the sub-ballast. Standard depth of ballast is 0.3m and it is packed to
0.5m around sleeper ends to ensure lateral stability. Ballast dissipates the energy transmitted to it
through friction between the stones/pebbles. Loosely packed ballast can cause large rail deflection
and thus, derailment. Ballast is often covered with wire-mesh to stop the pebbles flying off due to
aerodynamic forces (referred to as the flying-ballast problem) as a train passes over it.
6. Sub-Ballast: Sub- ballast layer is the transition layer between ballast layers to lower layer of fine
graded sub grade. Any sand or gravel may serve as sub-ballast material.
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7. Subgrade: It is a portion of earth used for foundation of track bed. Sub-ballast and ballast layers
rest on subgrade portion. Track failure and poor track quality is mainly dependent on the subgrade
quality. Heavy rain or flood can cause damage to the sub-grade.
6.2.2. Dynamic Properties of the Track
For high-speed rails, ballasted tracks or concrete slab tracks are used. Under frequent use, ballast in
ballasted track loosens and deforms, causing minor track irregularities. Long wave track irregularity
mainly affects vertical and lateral body vibrations, and is the major source of ride discomfort. Rail sur-
face irregularities/short wave irregularities are due to rail welds and rail wear. Short wave irregularities
cause wheel vibration, fluctuation of the axle load, high frequency noise and increased dynamic/impact
load on track (Miura et al., 1998). Receptance is the ratio of the track deflection and force put on the
track. Receptance is the inverse of the track stiffness. The track stiffness is non-linear and depends on
the frequency of load. The receptance also depends on the preload on the track.
For soft subgrade, a resonance may occur at the frequency 20-40 Hz. When rail and sleepers vibrate
on the ballast bed, the frequency range is 50-300 Hz (Dahlberg, 2006). Here rail and sleepers provide
mass. Ballast acts as a spring and also provides large amount of damping. Another resonance can be often
found in the frequency range 200 to 600 Hz which is due to bouncing of the rail on rail pads. Sleepers
and rail provide masses and ballast provides most of the damping. Highest resonance frequency which
is also called pinned-pinned resonance frequency is approximately at 1000Hz. This frequency can be
excited when the wavelength of the bending waves of the rails is twice that of the sleepers’ spacing. The
nodes of the bending vibration of rails are at the support (sleeper) (Dahlberg, 2006).
6.3. Track–Vehicle Interaction
When the vehicle moves in a curved path, horizontal centrifugal acceleration and vertical gravitational
accelerations are act on the body as shown in the left side of Figure 13. The resultant acceleration can be
split into two components: ay parallel to the track plane and az perpendicular to the track (See right side
of Figure 13). The load difference between the inner and outer rails can be neglected at lower velocities.
Figure 13. Acceleration of the car-body during curving
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From the Figure 13, static equilibrium conditions give
v2 v2 h
ay = . cos ϕt − g. sin ϕt = . cos ϕt − g. t (11)
R R 2b0
v2
az = .sin ϕt + g .cos ϕt (12)
R
By assuming small cant angles (φi≤0.15rad), Equations (11-12) can be written as
v2 v2 h
ay = − g .sin ϕt = − g . t (13)
R R 2b0
az≈g (14)
The cant for which lateral acceleration is zero for a given radius and given speed is called equilibrium
cant (heq). The equilibrium cant is given by
2b0 v 2
heq = . (15)
g R
If speed is expressed in km/h and cant in mm then the equilibrium cant is given by
2b0, mm v2
heq ≈ . (16)
g 3.62 R
For a particular cant, if the speed of the vehicle gives zero acceleration for a given curvature, the
corresponding speed is called balanced speed or equilibrium speed. Equilibrium speed is given by
R.g.h t
veq = (17)
2bo
The net lateral acceleration along the plane of the track is not zero in every case. There is a chance
that train moves with low speed or stops in a curved path. Secondly, all the trains do not run at same
speed whereas the track remains fixed. So, it is impossible to get zero acceleration for all the trains. Cant
deficiency arises when actual cant is less than equilibrium cant. Cant deficiency (hd) is the difference
between equilibrium cant and actual cant (ht). Cant deficiency is given by
2b0 v 2
hd = heq − ht = . − ht (18)
g R
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When the actual cant is higher than the equilibrium cant, cant excess is caused. In this case, the vehicle
is running at a lower speed than designed speed of the track. Cant excess is the difference between the
actual cant and equilibrium cant and is given by
he = ht - heq (19)
Cant is somewhat helpful to reduce lateral acceleration as well as the creep force in lateral direction
in the curved track. So, the dynamic behavior of car-body is improved with the presence of cant in the
curved track. Some results are given at the end of this chapter showing the influence of cant on dynamic
behavior of the vehicle. The track parameters are cant 150mm (cant angle is 0.1047 radian), 460 m
transition curve and radius 4000m.
7. STEERING BOGIE
There is an inherent conflict between stability on the straight track and good curving behavior in the
curved track. Lower conicity helps to achieve high speed on the straight track whereas higher conicity
gives better curving performance. For the stability of vehicles, equivalent conicity is usually maintained
between 0.1 and 0.4. In low equivalent conicity (in case of new wheel), there is a possibility of creating
gravitational stiffness, i.e., wheel-sets cannot be returned back to the center of track when disturbed later-
ally from central position. To achieve both high speed as well as better curving performance, Shinkansen
bogies use conical wheel tread configuration with wheel gradient 1:40 at the nominal contact position on
straight track. Bending stiffness and shear stiffness are the two other parameters of primary suspension
that influence stability and curving performance. For better curving performance, low bending stiffness
in primary suspension is required whereas for better stability, shear stiffness of the primary suspension
should be increased. Shear stiffness helps to stabilize the vehicle and bending stiffness improves the
curving performance (steering action) of the wheel. The shear stiffness is responsible for critical speed
of the vehicle while bending stiffness determines the angle of attack of the wheel-set in curves.
The main purpose of using steering bogie is to reduce noise and wear during curving, improving dy-
namic performances and minimize the chance of derailment. During curve negotiation, tangential forces
are generated due to creepage (longitudinal and lateral) at the point of contact which plays a crucial role
in curving and stability of railroad vehicles. The longitudinal and lateral creepages of wheel-sets are
determined as (Shabana, et.al. 2008)
ζx =
(r P )
− rPr .t1r 
w
, 
V 

ζy =
( r
)
rP − rP .t2 
w r
,  (20)
V 
ϕ=
(w r
ω − ω .n  ) r 
,
V 
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where ξx, ξy, φ are the longitudinal, lateral and spin creepages, respectively; rPw and rPr are time deriva-
tive of wheel-rail contact position vector, respectively; t1r and t2r are orthogonal tangent vectors to the
rail at the contact point in longitudinal and lateral directions; nr is the normal vector unit to the surface
at the contact point and V is the wheel velocity in the longitudinal direction. The wheel and rail distort
due to compressive force at the contact zone. If two bodies (rail and wheel) move relative to each other,
tangential forces (shear traction) are generated at the contact zone due to Coulomb friction. Shear trac-
tion between two bodies is Ft=[Ftx,Fty]T. The longitudinal and lateral creep forces and the spin creep
moment, respectively, can be expressed by integrating local force components and moments over the
contact patch in the x-y plane:
Fx = ∫∫ Ftx dxdy 


Fy = ∫∫ Fty dxdy  (21)

M = ∫∫ ( xFty − yFtx ) dxdy 

By using elasticity theory based traction-displacement relation, linear relation between creepage,
creep forces and moment can be calculated as
 Fx  c11 0 0  ξ x 
 F  = −Gab  0 c22

abc23  ξ y  (22)
 y 
 M   
0 − abc23 abc33   ϕ  ,
where ξx, ξy, and φ are the longitudinal, lateral and spin creepages, respectively; a and b are, respectively,
the semi-axis dimensions in the rolling and lateral directions of the elliptical contact patch; G is the
modulus of rigidity and cij (i,j = 1..3) are creepage coefficients which depend on Poisson’s ratio and ratio
of the semi-axes lengths of the contact ellipse (Shabana, et.al., 2008; Kalker,1990). Kalker introduced
the equivalent modulus of rigidity and Poisson’s ratio to be used in Equation (22) as
1 1 1  ν ν w ν r 
G=  w
+ r , = + , (23)
2 G G  G  Gw Gr 
where G is an average shear modulus of wheel w and the rail r, and v is a combined Poisson’s ratio of
wheel and the rail. Generally, creepage, creep forces and creep moments are key aspects which affect
wear and noise in the curved track. While curving, speed of outer wheel is faster than inner wheel in
order to satisfy pure rolling of all wheels.
When the wheel-sets of bogies adapt or are forced to the radial position in the curved track as shown
in Figure (16), then the bogies are called radially steered bogies. In the case of steered bogie, the angle
of attack is small which reduces track creep forces and the resulting flange wear. Radially steered bo-
gies are classified depending on the control principle used. In case of passive/ self–steering, wheel sets
take up radial position due to low bending stiffness of primary suspension. The yaw of a wheel-set is
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induced by the wheel-rail contact forces or by the relative rotation between bogie frame and vehicle
body (either roll or yaw).
In both the above cases, the amount of yaw of the wheel-set depends on the radius of curvature. When
wheel-sets are forced to occupy radial position in the curved track, the corresponding steering mechanism
is called active steering. In an active steering bogie, electric, hydraulic or pneumatic actuators are used to
give yaw motion to the wheel-sets. Links, levers and sliders are used between wheel-sets and the bogie
frame to execute different types of forced/ active steering mechanisms.
7.1. Self-Steering
Wheel tread is helpful for the train to negotiate the curve and keep the vehicle in the mean position
while rolling on a straight track. Due to presence of conicity in the wheel and rigid connection between
wheels of wheel-sets, the bogie is self-steered. However, self-steering may not be sufficient while curv-
ing in small radius turn where large lateral forces exerted on wheels and rail cause wear of the both.
Self-steering/ passive steering is achieved due to difference in rolling radii between the left and right
wheels. If a wheel-set is moved laterally from its centered position, a difference in rolling radii arises
(Wickens, 2003). From Figure 14,
∆r
Equivalent conicity (γ e ) = (24)
2y
where ∆r is the instantaneous difference in rolling radii between left and right wheels and y is the lateral
displacement from the centered position. Rolling radius difference is a function of both the wheel and
Figure 14. Conicity of wheel profile
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rail shape and equivalent conicity is described by both rail and wheel profiles. The actual profiles are
similar to the shapes shown in Figure 15.
As the centrifugal force causes the center of axle to move towards the outside of the curve, the presence
of wheel-tread gradient leads to steering action in the curved portion of the track. The vehicle primary
suspensions are made more flexible in bending so that they can occupy more and less radial position on
the curves to improve curving performance.
Due to presence tread gradient, the effective outer wheel diameter increases and that of inner wheel
decreases on the curves (see Figure 16). This difference in the effective diameters leads to self -steer-
ing action. A common two-axle conventional bogie tends to turn outward with respect to tangent of
the curve. The corresponding angle between the tangent of the curve and direction of the leading outer
wheel is called angle of attack (see Figure 17). Due to the angle of attack, lateral creep force acts on the
outer wheel towards outer rail in the lateral direction. At the same time, the rear axle experiences op-
posite forces and tries to turn the opposite way. Longitudinal creep force between rail and wheel creates
high lateral force between rail and wheel which creates high lateral force on the front wheel-set towards
the outer rail. In steering action, wheelbase on the outer rail is longer than on the inner and axles turn
radially in the direction of the curve.
Figure 15. Wheel-rail profile
Figure 16. Self-steering characteristics of wheel-sets
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Figure 17. Behavior of self-steering on conventional bogie wheel-set
Self-steering / passive steering can be achieved in a number of ways such as
• Reducing the stiffness of the axle box suspension / primary suspension

• Increasing the tread gradient
• Interconnecting two wheel-sets by cross bracing
• Using three-axle vehicles with suitable linkage
By reducing the stiffness of the axle box suspension / primary suspension, wheels and axle can easily
move sideways in response to lateral forces. But excess reduction of stiffness of primary suspension can
affect running stability and ride comfort.
Increase in tread gradient/ conicity of the wheel set improves the curving behavior but simultane-
ously compromises stability on the straight track. To achieve both better curving performances as well
as stability on the straight track, tread gradient should be optimized. In modern high speed trains such
as in almost all bolster-less Shinkansen trains, graded circular wheel tread configurations are used in
which large numbers of arcs are joined next to each other (Okamato, 1998).
Circular graded profile reduces the contact area as well as contact bearing forces between wheel tread
and rail. Also, the contact points during curving are uniformly distributed over the tread and lead to
uniform wear instead of large localized wear. In this chapter, the circular tread profile with various levels
of wear has been considered (see Figure 18). In a worn wheel, the tread gradient is larger as compared
to a new wheel. As the centrifugal force causes the center of axle to move towards the outside of the
curve, the presence of wheel-tread gradient leads to steering action in the curved portion of the track. In
a worn wheel, self-steering effect is more pronounced as compared to a new wheel.
Excess tread wear leads may lead to contact with the fishplate bolt. With flange wear, flange angle
increases and flange thickness decreases which increases the chance of derailment. Dynamic performance
of the vehicle as well as steering effect increases up to certain depth of wear and after that the dynamic
behavior (comfort, critical speed, etc.) as well as stability deteriorates. When the center of wheel tread is
worn below the level of end of the tread, there can be significant deterioration of the vehicle’s dynamic
performance, i.e., stability and ride comfort. Different depths of worn profiles considered in this chapter
are given in Figure 19.
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Figure 18. Tread and flange wear
Figure 19. Original wheel profile and two worn profiles with different depths of wear
Self-steering or passive steering can also be achieved by interconnecting two wheels by different
ways as shown in Figure 20 (Wickens, 2006). Wheel-sets interconnected by cross-bracing (Figure 20(a))
is one of the oldest methods of self-steering. In a three-axle vehicle, central axle steers the outer one
through suitable linkage (Figure 20 (b)). Wheel sets of three-axle vehicle with suitable linkage can oc-
cupy the radial position in curved track and rearrange themselves on the straight track. In all the above
cases, passive/ self-steering is possible only through rigid linkages and pivots.
In conventional suspension arrangement, bending and shear stiffness are dependent to each other. So,
when shear stiffness is decreased, the bending stiffness also decreases. Thus, in conventional suspension
arrangement, improvement of curving performances reduces the stable operation speed on the straight
track. Therefore, in self- steering bogies, shear and bending stiffness are allowed to be independently
designed. This is achieved with use of cylindrical or conical laminated rubber springs. Material (rubber)
can be removed from certain portions of the spring to give directional properties to the spring’s stiffness
and damping parameters.
To enhance the curving–stability relationship, Scheffel proposed different types of inter-axle link-
age arrangements which are given in the Figure 20 (c), (d) and (e) (Orlova & Boronenko, 2006). These
bogie designs are based on the principle of three-piece bogie which consists of two side frames and one
bolster. In case of inter connected wheel-sets for self-steering of locomotives, transfer of tractive forces
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Figure 20. Passive steering (self-steering): (a) Direct connection between wheels by cross bracing; (b)
three axle vehicle; (c) Scheffel HS bogie with diagonal linkage between wheel-sets; (d) inter axle linkage
for Scheffel’s A-frame bogie; (e) inter axle linkage for Scheffel’s radial arm bogie
between the wheel-set to bogie frame should not influence the axle guidance. In this case, wheel-sets are
steered by inter-axle linkage instead of frame (as in conventional bogie design). To be more effective,
steering inter-axle links have low longitudinal as well as lateral primary suspension stiffness. Scheffel’s
bogies are usually double suspended.
Conicity of the wheels is responsible in natural/ self-steering action but at the same time conicity
creates instability. This problem can be overcome by using springs between wheel-sets and the bogie or
between the wheel-sets within the bogie. The additional springs interfere with natural steering action.
So it is necessary to optimize the mechanical components of the vehicles to give the best stability and
steering action. The excess reduction of stiffness of primary suspension can affect running stability and
ride comfort.
Generally in case of conventional steering bogies, both the wheel-sets are steered, so the mechanism
is bulky. To avoid that problem, a new concept, called single-axle steering, proposes that only one wheel-
set should be steered according to the requirement in the curved track. In this case, only rear wheel-set is
steered as explained in the Figure 21. When rear axle is steered, angle of attack of rear axle is increased
and consequently, large lateral creep force is generated towards the outer rail. By shifting the real axle
towards the outer rail, the difference between the diameters of rear wheels increases which helps the
bogie to be in radial position. As a result, angle of attack as well as lateral creep force of non-steered
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Figure 21. Behavior of single axle steering
axle (front) decreases. Longitudinal creep force of rear axle and lateral creep force of front wheel lead
to reduce creation of an anti-steering moment on the bogie (similar to self-aligning moment in steered
road vehicles). As railway vehicles run in both directions, for a coach supported on two bogies with four
axles, axles 1 and 4 are non-steered, whereas axles 2 and 3 are steered. When axle-3 (leading axle of rear
bogie) is steered, its angle of attack as well as lateral force on the outer rail decreases. This type of steer-
ing is used in SC101 bogie. It a link type passive actuation steering in which swing bolster, truck frame
and axle boxes are connected to the bogie through levers and links. When vehicle enters into a curve,
axle boxes change their position by changing the position of the linkage (Shimokawa & Mizuno, 2013).
To overcome the drawbacks of self-steering/passive steering, assist/ forced/ active steering principle
has been adopted in modern bogie designs.
7.2. Active/Assist/Forced Steering
Hunting motion and large centrifugal forces often lead to flange contact of wheel. Active steering is
used to control lateral displacement and yaw of wheel-set so that wheel contact patch is constrained to
the tread region. Active yaw damping and active lateral damping are two types of active damping which
gives stability for solid axle wheel-set. In active yaw damping, an actuator yaw torque is applied through
various means to the wheel-set in direct proportion to lateral velocity of the wheel-sets. In addition,
unstable modes are stabilized by active lateral damping control technique where the applied lateral force
is proportional to the yaw velocity of the wheel-set (Mei & Goodall, 2003a). Various sensors, actuators
and controllers are used for active stability control. Filters and estimators are used to measure the state
variables and local track reference so that natural curving action of the wheel-set is not affected by the
stabilization method. Note that it is impossible to realize such modification of the dynamics by purely
passive components. For cost effectiveness as well as better reliability, optimized passive components
are used for the improving stability of the vehicle. However, these affect steering action (curving per-
formance) of the vehicle and there is no means to improve both stability and curving performance with
passive components. Although directional properties can be modified (e.g., different stiffness in longi-
tudinal and lateral directions), the passive design still remains sub-optimal.
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7.2.1. Configuration of Active Primary Suspension
Various common forms of active steering configurations in bogie with active primary suspension system
are shown in Figure 22. The control system of actuated solid wheel-set (ASW) is designed for increasing
stability and enhancing the curving performances. In actuated independently rotating wheels (AIRW)
configuration, active control provides guidance and steering. Other types of actuations such as driven
independently rotating wheel (DIRW) and directly steered wheel (DSW) are possible through driving
and braking torque (Bruni, et.al. 2007). In some designs, control rod is used to enhance curving per-
formances without affecting stability (Shen & Goodall, 1999). To improve steering performances and
stability, closed loop control of solid axle wheel-set was designed in (Mei & Goodall, 1999; 2000b). Two
actuators termed lateral actuation and yaw actuation were used to control lateral force and yaw moment
or couple, respectively. It was found that less control force (actuator power) is required to achieve optimal
stability and ride comfort in yaw actuation as compared to lateral actuation. Actuation is introduced in
form of steering torque applied on the axle in AIRW. Control torque required to run DIRW vehicle is
less than the torque required for solid wheel-set (Mei & Goodall, 1999). Note that lateral creep force on
DIRW nearly reduces to zero. But in straight track, AIRW requires active guidance which may create
problems for sensor and controller implementations.
Figure 22. Different types of active steering actuation configurations: (a) yaw actuation of solid wheel-
set, (b) lateral actuation of solid wheel-set, (c) independently driven wheels, and (d) steered wheels with
separate axles.
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The wheels on the same axle are free to rotate in independently rotating wheel-set (IRW) which is used
largely in Spanish Talgo train. For long distance and high speed purposes, appropriate driving torques
are applied on IRWs with help of servo-meter which is connected to wheels through differential gear
box; this arrangement is named as driven independently rotating wheel (DIRW) as shown in Figure22
(c). Note that separate traction motors may produce differential torque without use of differential (Mei
& Goodall, 2003a). In IRW, guidance forces are provided by applying a differential torque on the two
traction motors of the wheel pair to obtain traction control and active guidance (Powel, 1999). Also,
differential braking may be used instead of differential traction on the trailing bogies (Goodall, et.al.
2006a). The combined use of AIRW and DIRW strategies have been implemented to improve steering
performances which is suitable for high speed and long distance application with conventional bogie
features. Such active system consists of one steering actuator and one traction motor for each wheel-set
(Perez, et.al. 2004). To obtain compact and light weight design, permanent magnet motors were used
inside wheel to implement DIRW control strategy. In Figure22 (d), wheels of IRW are mounted on the
wheel frame instead of axle which is actively steered to achieve guidance and curving (Aknin, et.al.
1992). A track rod is used to steer the wheels directly by producing lateral force between wheels and
frame. Stabilization, guidance and better curving performance were found in the curving track by using
lateral wheel displacement in a feedback loop (Wickens, 1993; 1994). Power steering control mechanism
is used to actuate track rod and enhance the curving performance. Power steering through DC motor
performs two roles: it acts as a passive magnetic damper (generator mode where power is dissipated)
to enhance damping of yaw oscillation in straight track and acts as a powered actuator to negotiate the
curve in the transition curves (Michitsuji & Suda, 2006). To improve stability and steering performance,
yaw torque is applied on the bogie; this is the basic concept of secondary yaw control. This control has
been used in tilting bogie/ high speed train where electro-mechanical actuator provides control force
(Diana, 2002). Active control takes place the role of passive yaw damper in straight track and yaw torque
is applied on the curved path. The yaw applied torque is computed as a function of cant deficiency and
curve radius. A longitudinal actuator may be used to control the amount of torque to the wheel-set in
yaw direction. This strategy is helpful to control lateral displacement and yaw motion by using laser
signals which are mounted on both ends of the wheel-sets to measure lateral displacement of front and
rear axles (Kim, et.al. 2008).
7.2.2. Control Strategies
During curving, both solid axle wheel-set and IRW have their own separate merits and demerits. In case
of solid axle wheel-set, passive suspension severely affects the curving performances; whereas IRW has
problem in guidance control both in straight and curve track, but no issue with stability.
7.2.2.1. Control Strategies for Stability

Kinematic instability mode of solid axle wheel-sets has been studied by different researchers. Stabilization
in case of IRW mounted on common axis can be achieved more easily than wheel-sets with solid axle.
The control strategy is called active lateral damping, where applied control force in lateral direction is
proportional to wheel-set yaw angular speed. For a two axle vehicle, active yaw damping strategy needs
less actuation forces and power and gives better ride comfort as compared to active lateral damping
(Mei & Goodall, 1999; Mei & Goodall, 2000b). In active yaw damping, control torque is proportional
551

to lateral velocity of the wheel-set with respect to car-body. The active yaw damping is more effective
due to its adaptability to speed variation and also due to its stabilizing action as compared to the passive
yaw dampers (Mei & Goodall, 2003b). To avoid the influence of the passive yaw stiffness on stability,
sky-hook/ absolute stiffness control strategy is used, where control torque is directly proportional to yaw
of the wheel-set rather than the relative yaw between the bogie and the wheel set. In sky-hook spring
control, actuators are attached between the wheel-set and bogie. Measurement or estimate of yaw angle
of each wheel-set is fed to the controller to control the corresponding actuator. The concept of sky-hook
damper is similar to sky-hook spring (Mei & Goodall, 2006). It is used in secondary suspension to
improve ride quality.
Two transfer functions, one between lateral displacement of wheel and control input and other between
yaw angle of wheel-set and control torque of single wheel-set were used to explain the stability of solid
axle wheel-set in (Mai & Li, 2008). In their study, two unstable and two stable poles were found. They
proposed to provide feedback signals of yaw angle and lateral movement in order to provide damping
effect on kinematic instability. The feedback method turned out to be equivalent to conventional passive
stabilization with yaw stiffness. To ensure better stability, (Mai & Li, 2008) have further proposed a
phase lead compensator to compensate the delays.
7.2.2.2. Control Strategies for Guidance

Guidance control is necessary in IRW to ensure that wheel-sets follow the track and do not contact the
flange. However, hunting may take place due to track irregularities and cause temporary flange contact.
To avoid flange contact, high band width control is necessary. Tracking error is the error of position of
the vehicle with respect track centerline. Active guidance is provided by steering the wheels in order to
reduce tracking error. Due to active guidance, the vehicle has the ability to follow on the curved path
without flange contact and minimize the lateral creep force. Direct guidance control uses wheel-rail deflec-
tion measurement (relative displacement between wheel-set and track) in a feedback control system. But
direct measurement of wheel–rail deflection is costly and difficult (Wickens, 1994). In another complex
approach, differential torque is applied with the help of a PID controller using linear combination of
measurements or estimates of leading and trailing wheel-sets’ lateral displacements and yaw velocity of
leading wheel-set (Gretzschel, 2002). In DIRW control strategy, direct control for guidance is possible
by controlling the traction torque (Perez, et.al. 2004).
7.2.2.3. Control Strategies for Steering

The key objective of steering control is to make sure that wheels/ wheel-set follow track and the wheel-
rail creep forces are reduced. Longitudinal creep (except during traction/ braking) is undesirable and can
cause unwanted yaw motion. However, lateral creep is somewhat essential to provide curving force to
compensate the cant deficiency, i.e., the amount of centrifugal force which cannot be balanced through
the given amount of track cant. Control strategies are responsible for reduction of unnecessary creep
forces and noise/ wear at rail-wheel interface during curving. The basic working principle of forced
steering is to control the relative angular displacement between car body and bogie or between bogie
and wheel-set. Forced steering control strategy can be perfectly implemented for zero cant deficiency.
But in normal operating conditions, zero cant deficiency is usually impossible. Hence, unwanted lateral
movement of wheels and creep forces appear at the rail-wheel interface. This problem can overcome by
controlling the wheels/ wheel-sets in order to achieve the desired angle of attack. Even distribution of
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curving force to each wheel is required for minimizing the wheel shifting on the curves. Active steering
bogie controls the wheel-set motion when it travels in curved track. In straight track, controller is off and
the bogie is equivalent to the conventional bogie provided that the steering mechanism is perfectly locked
(acts as a rigid connection). The conditions for perfect steering/ curving are (Goodall & Mei, 2006b):
1. The longitudinal creep forces in the wheels on the same axle are same,
2. The lateral creep forces of two wheel-sets are same,
3. The angle of attack of wheel-sets is same so that the entire bogie is in line with the track on the
curve.
Equal longitudinal forces on the wheels (perfectly distributed traction/braking force) leads to eliminate
wear and damage of the wheels and equal lateral forces are required to balance the centrifugal forces
caused by cant deficiency or cant excess. Same angle of attack on different wheel-sets is possible when
actuators control the yaw angle with respect to bogie. The required yaw angle is determined from the
radius of curvature of track, cant, velocity of vehicle and wheel base. In the other way, yaw torque can
be applied for cancelling the effect of longitudinal stiffness of primary suspension. Steering strategy
does not affect stability when the effect of longitudinal stiffness of primary suspension is cancelled at
frequencies lower than that of kinematic modes. Then relative yaw angle can be measured between the
wheel-set to the bogie using various sensors like encoders or geared potentiometers.
Perfect curving requires angle of attack and radial angular position of two wheel-sets to be equal and
the bogie to be in-line with the track, which is called yaw relaxation concept (Shen & Goodall, 1997).
For this, yaw motions of wheel-sets with respect to bogie frame need to be controlled through actuators.
The required yaw angle can be calculated by using track parameter (curve radius (R)) and parameters of
wheel-rail interaction (lateral creep force for each wheel-set (Fy) as calculated in Equation (21), creepage
coefficient (c22) (Kalker, 1990) and wheel base (lx)) (Shen et.al. 2004). The small desired yaw angles in
leading and trailing wheel sets, respectively, can be expressed as
 F  l  F l
ϕtrailing = sin −1  c  + sin −1  x  ≈ c + x
 2 f 22   R  2 f 22 R
 F  l  F l
ϕleadiing = sin −1  y  − sin −1  x  ≈ y − x , (25)
 2c22   R  2c22 R
 F  l  F l
ϕ trailing = sin −1  y  + sin −1  x  ≈ y + x .
 2c22   R  2c22 R
For positioning purpose, the relative yaw angle between individual wheel-set and bogie is measured
(Shen & Goodall, 1997; Perez, et.al. 2004). In AIRW control strategy, difference of angular speed between
inner and outer wheels are controlled by applied yaw torque in order to run the wheel-set on the center
position of the track (Perez, et. al. 2002). The guidance concept used in DIRW control strategy for low
speed curve (300 m) is helpful for controlling the wheel-set either in radial position or centered posi-
tion of the track (Gretzschel, et. al. 2002). In DSW control strategy, feed forward predictive control has
been proposed to enhance the performance along transition curves in which a control torque is applied
on each steered wheel pair depending upon the variation of track curve with time and track geometry
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(Michitsuji & Suda, 2006). In secondary yaw control (SYC) concept, feed forward control strategy is used
only for curving in which cant deficiency and bogie yaw rate are measured by using low pass filtered
lateral accelerometer signal from the bogie and gyroscope, respectively, and the steering torque applied
on the bogie is estimated from track curvature and level of wheel and track wear (Diana, et. al. 2002).
Actuators are mounted on the bogie and car-body to generate yaw torque. Different wheel-sets have
different conditions, mostly due to level of wear and local track irregularities. So the individual wheel-
sets should be controlled separately to optimize the steering performances (Park, et.al. 2010). In forced
steering, the axle needs to yaw relative to the bogie frame. According to Goodall & Mei (2006b), the
assist/forced steering can be achieved in the following different ways:
1. Axles can be connected by suitable linkage which can be actuated to achieve different radial posi-
tions on curved tracks.
2. Control torque can be applied to the wheel-set in the direction perpendicular to the plane of the
wheel-set.
3. Actuators can be used in the lateral direction of wheel-set, but ride quality is affected by this
arrangement.
4. Wheel-set can be controlled by active torsional coupling between the wheels.
Active primary suspension (actuators with primary suspension) along with passive components can
be used in the same way as an active secondary suspension. Passive stiffness can be used to stabilize the
kinematic oscillations (hunting instability) and actuator is used to provide steering action in the curved
track. In the case of active steering, stability and steering actions are designed separately.
To improve the curving performances by active steering, different types of control strategies are
developed. They are (Perez, et. al. 2004):
1. Lateral position of wheel-set may be controlled in such a way that only pure rolling will take place
which reduces longitudinal creep force.
2. Yaw moment which is dependent on lateral wheel-rail displacement is to be controlled by using
traction motors to run the wheel in central position of the track.
3. The relative angle between wheel-sets is to be controlled by using traction motors to implement
differential torque control or yaw actuation for IRW steering control strategy.
By implementing above three strategies, wheel lateral displacement, angle of attack and lateral contact
forces can be reduced; thereby reducing material loss/wear of wheel. In some designs, anti-yaw dampers
are replaced by actuators to steer the bogie against car body in active steering bogie (Matsumoto, et.al.
2005). Radial steering is the most well-known steering mechanism which consists of mechanical link-
ages with joints. Park et.al. (2010) proposed a link type steering, which consists of two driving links, two
steering links, a transverse link and a linear actuator. The driving links, which are on both sides of the
bogie frame, are connected to each other by transverse link. Due to presence of revolute joint between
bogie frame and driving links, the links can rotate easily depending on the movement of the linear ac-
tuator. Steering links act as the bridge between the axle box and driving links through universal joints.
Axle boxes are pulled or pushed according to the movement of the driving links. Left steering link of
front wheel-set is connected to the end of left driving links, whereas right steering link is attached to
the middle of the right driving link. In addition, there is a transverse link to transmit linear motion and
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actuator force to driving link. Steering mechanism for rear and front wheel-sets are diagonally sym-
metrical. In this type of active steering, four PID controllers are used to control the lateral displacement.
Control gains are selected in such a way that the generated control forces remain within the allowable
actuator force range.
Controller design is an important factor for active steering of railway systems. Linear quadratic optimal
control is suitable for both solid axle wheel-set and IRW. To avoid flange contact between wheel and rail,
it is necessary to control both the lateral displacement and yaw angle (angle of contact) of wheel with
respect to track. Generally controllers severely interfere in natural curving in case of solid axle wheel-set,
but it is less critical in IRW due to its extra degree of freedom. Adequate weighting factors are used in
optimal control to avoid interference in performance of solid axle wheel-set. In both the cases of solid
axle and IRW, optimal controller needs to implement integral action to reduce steady state error (Mei &
Goodall, 2003b). Due to simplicity and well known design method, classic PID control is often used. But
in these approaches, measurements of angle of contact and wheel deflection are required for feedback.
However, it is difficult to directly measure these variables in practice. Full state feedback control with
ideal condition of the track, i.e. no irregularities, avoids use of such complicated measurements, but
requires a well-developed vehicle model. The complete vehicle model has multiple inputs and outputs.
Modal control is another approach where lateral and yaw motions of the body/ bogie are decoupled using
certain transformations to yield decoupled subsystems. Separate controllers can be then independently
designed for these subsystems and inverse transformation is performed to transfer the desired control
actuations to the coupled system. For example, outputs from decoupled lateral and yaw controllers are
recombined to control two actuators for the wheel-set (Mei & Goodall, 2003a).
7.2.3. Sensors and Actuators
Measurement of wheel-set movement with respect to track is used in all the above discussed controllers.
But mounting sensors on the wheel-sets is costly and difficult. Model based estimation techniques such
as Kalman filters and observers are often used for indirect measurement. The outputs from the sensors
are compared with output from a mathematical model (observer model) and the deviation is used to
produce corrective action through gain matrix to compensate for the inaccuracy in the model output.
Estimated state variables from the observer model are then used as feedback signals for controllers. Iner-
tial sensors on the wheel-sets and bogies have been shown to provide excellent results (Mei & Goodall,
2000a). In modern designs, these sensors have been replaced by more accurate bogie based displacement
sensors which provide the primary suspension deflection (Pearson, et.al. 2004) and observer models
are used to estimate other states from the displacement measurements. Note that application of such
type of control strategies needs the track data at the exact position of the vehicle. Usually, track data is
stored in a database and the positions of different wheel-sets are computed with respect to a reference
on the train. The position of the reference point is obtained through GPS or other trackside tracking and
relaying devices. Communication infrastructure is vital to implementation of such type of active steer-
ing principle. Another way of obtaining track data is to sense the track through sensors such as through
optical sensors and then applying image processing or other techniques to determine the track curvature.
Usually, a constant correlation is assumed between the track curvature and cant.
Different types of actuators such as servo-hydraulic, servo-pneumatic, electro-hydraulic and electro-
mechanical are used in active suspensions. Though servo-hydraulic actuators are compact and easy
to handle, but along with power supply, the whole system tends to be heavy. Pneumatic actuators are
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basically used in air-spring for many rolling stocks, but compressibility of air causes actuation delay
and undesired low frequency oscillations. Electro-mechanical actuators offer quick response and high
efficiency. However, they are less compact and careful attention is required for reliability and life of
mechanical components. Electro-magnetic actuators give extremely high reliability and better perfor-
mance, but they are heavy (Goodall & Mei, 2006b).
7.2.4. Controller Set-Point Specification
We can increase the curving performance and reduce the lateral creep force by inserting steering mecha-
nism. As a result, wear and tear of wheel (especially, in the flange portion) reduces significantly. Steering
effect can be improved in the presence of cant/ super elevation on the curved portion of the track. But
excess cant or deficient cant affect the steering mechanism, so optimization of cant angle in the curved
portion of the track is required to improve the steering performance at a given operating speed.
Link type forced steering can reduce the lateral force to one-half or one–third than a conventional
bogie on conventional tracks (Okamato, 1999). For a given radius of track at a particular position, the
steering angle is defined by the angle by which each axle has to be turned to make its wheels’angle of
attack with the track zero and align the axle with the radius of the track. Perfect steering can be achieved
when the angle of attack for all wheel sets is the same, so that the bogie center line is tangent to the
mean track circle. The controller tries to align the wheel sets to a desired angle called a set point. The
set point depends on the local curvature of the track.
This steering angle/ yaw movement may be calculated as (see Figure23)
W 1 
α = sin−1  b ×  , (26)
 2 R 
where Wb is the wheel-base, α is the required steering angle and 1/R = ρ is the radius of curvature of
the track.
However, the above formulation does not consider the existing cant in the track and hence can result
in under or over steering leading to yaw oscillations of the wheel set. Also, the vehicle encounters large
centrifugal force in high speed and needs more steering angle. Thus, steering angle in presence of cant
angle may be calculated in terms of cant deficiency or cant excess depending on speed of the train.
Then using Equation (25), the instantaneous steering angle/ yaw movement at leading and trailing axles,
respectively, can be modified to
 F  W 1  F W
α l = sin −1  c  − sin −1  b ×  ≈ c − b
 2 F22   2 R  2 F22 2 R
(27)
−1  Fc  −1  Wb 1 Fc Wb
α t = sin   + sin  × ≈ +
 2 F22   2 R  2 F22 2 R
where Fc=M(v2/R–gsinϕ) is the lateral force due to cant deficiency, v is the velocity, g is the acceleration
due to gravity, M is the mass corresponding to static axle load, ϕ is cant angle in radians and F22 is a
creep coefficient. The calculated steering angle depends on track design parameters such as curve radius
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Figure 23. Steering angle of wheel set, Wb is distance between two axles of the wheel-set in a bogie
and cant angle and running velocity of the vehicle. However, the computed angle goes out of bounds for
large magnitude of cant excess or deficiency, i.e., at very low and very high speeds. Thus, the steering
angle is restricted to a specified limit.
In the following, the performance of steering systems would be demonstrated through simulation
studies performed with Adams VI-Rail multi-body dynamics simulations.
8. DYNAMIC ANALYSIS
Though a large number of components are present in railway vehicle, we are interested only on the dy-
namic behavior of the main components such as body components and suspension systems. The main
body components are car-body, bogie frame, wheel-set, primary and secondary suspensions, and the axle
box. Dynamic performance is analyzed here through multi-body simulation (ADAMS/VI-Rail) software.
A bogie template is created as shown in Figure 24. The bogie template is then assembled with car body
to produce an integrated coach model (Figure 25). We analyze the dynamic behavior when the train
runs at a constant speed. Note that aerodynamic load is not significant on a coach (except for crosswind)
and thus a single coach model is sufficient to approximate the behavior of a whole train. Although we
have performed analysis with integration of a few coaches, the results are similar and hence only results
from the single coach model are presented here. It may however be noted that if variable speed run is
to be analyzed, such as during acceleration and braking, then the complete train model with assembly
of coaches is required.
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Figure 24. Bogie template (without steering mechanism)
Figure 25. Bogie assembly (with steering)
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The mass inertia properties are essential for simulation and they are obtained from solid modeling
software. Generally track is separately modeled and track parameters are taken as input parameters for
simulation. Here, we have considered flexibility of track (lateral, vertical and roll) as well as track irregu-
larities. Track flexibility introduces variable track stiffness as wheels move on a rail (beam) supported
at regular intervals on sleepers. Between two sleepers, the track flexibility varies and the frequency of
the change in flexibility (a parametric excitation) depends on the sleeper spacing and the train speed.
The flexible track also assumes the presence of ballast. Track irregularities are generally given in the
lateral and vertical directions in terms of the deviations from the track centerline, track cant and track
gauge. The track parameters for the straight track are length of the track, track irregularities, rail incli-
nation and nature of the track (rigid and flexible) and those for the curved track are length of the track,
curve radius, cant, track irregularities, rail inclination and nature of the track (rigid and flexible). For
the analysis, curve radius is taken as 4000m, cant angle is 0.1047 radian (cant height is 150 mm), rail
inclination is 1:40 of rail profile UIC60. At nominal contact, the tread conicity of s1002 wheel profile
is 1:20 and accounting for the 1:40 rail inclination/tie plate angle, the equivalent conicity is 1:40. The
types of track irregularities are sinus, ramp, DIP, power spectral density (PSD) and measured type. The
results shown in this are for measured type track irregularities as shown in Figure 26.
The outputs of the analysis are the critical speed, derailment speed, creep forces between rail and
wheel, wheel lateral displacement, acceleration of the wheel-set and the ride comfort.
The bogie template shown in Figure 24 was modified with implementation of various passive steer-
ing mechanisms (Figure 27). The simulation results for these passive mechanisms showed improved
performance up to 270 km/h speed on curved tracks.
We present the results for the active steering mechanism whose bogie template is shown in Figure
28. The proposed link type active steering consists of steering beam, steering link and steering lever.
Figure 26. Measured type track irregularities
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Figure 27. Bogie templates (with passive steering mechanism)
Steering beam and steering levers are connected by revolute joints, and steering levers and steering
links are connected by spherical joints. An actuator is placed in the center of the bogie frame to rotate
the steering beam (actuated revolute joint). Generally in this design, yaw torque is applied through the
actuator at the center of the steering beam.
Figure 28. Bogie template (Link type active steering mechanism)
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We need to control the steering angle (Equation 26) at center of axle-box which is attached to the
axle of wheel-set. The correlation of yaw movement between center of steering beam and at the axle
box is calculated from analysis of steering linkage mechanism in ADAMS (Figure 29). This correlation
of steering beam and axle box steering angles is shown in Figure 30. For a specific set of chosen link
lengths, this correlation can be curve fitted as
αb = 17αW3 − 20αW2 + 15αW (28)
where αb and αW are the desired steering beam angle and desired axle steering angle. The steering linkage
applies forces directly on the axle-box and the rear and front axles turn in opposite directions. The angle
of steering is in fact very small (less than ±0.01 radian). It is computed based on the operating speed
and existing cant in the track at the given location of the bogie. The steering angle varies linearly from
0 to a steady value as the train transits from the straight track to the constant radius of curvature track.
For vehicle stability, track stresses as well as dynamic analysis, it is very essential to understand the
behavior of lateral and vertical forces developed between rail and wheel. Basically forces acting on the
rail as well as wheel can be classified as static forces, quasi-static forces and dynamic forces. Static
forces arise due to static load of wheel on the rail. Several factors are responsible for quasi-static forces:
centrifugal forces caused by cant excess or deficiency, crossing of rails and crosswind. Dynamic forces
are produced due to stiffness of primary suspension, track geometry and irregularities of tracks as well
as discontinuities like rail joints and crossings. Before starting any dynamic simulation, it is necessary
to allow the vehicle to settle to its equilibrium position due to static loads. This process develops the
necessary forces in suspension elements and contacts to support the static load of the vehicle. These
static deflections automatically work as initial conditions for dynamic simulation.
Figure 29. Analysis of steering linkage in ADAMS
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Figure 30. Correlation between yaw angle at axle box and steering beam
8.1. Wheel-Rail Contact Animation
When wheel is in contact with rail, elastic deformation occurs in the form of contact area which trans-
mits normal load from wheel to rail. The contact area or contact patch is very small as compared to
the dimensions of wheel as well as rails. The shape and orientation of contact patch depends on the
transverse radius of curvature of wheel tread, radius of curvature of rail head at the point of contact and
wheel radius. The contact area is large at the flange throats and corners of the rail.
The wheel-rail interaction is very crucial for dynamic analysis of the vehicle. In the multi-body simu-
lation (MBS) software VI-rail (ADAMS), it is necessary to run time-domain simulations with short time
steps (in the order 1ms). The contact parameters are calculated in a preprocessor program. The input
parameters are wheel-rail geometry, rail inclination and track gauge. Normally it is assumed that all the
parameters are kept constant throughout the simulation. Two wheel-rail elements (one for the left side
and the other for the right side) consist of a wheel-set model. Contact angle, conicity and roll angle are
the parameters necessary for the dynamic analysis of vehicle and these are computed from specialized
algorithms devoted to contact determination.
In tread contact, the radii of curvature are change slowly with position and contact patch is almost
elliptical shape depending up on the position of the contact patch, velocity and track properties. If the
contact is conformal or the radii are changing suddenly, the contact patch is quite different from elliptical
shape. As the rail-wheel contact is a non-linear type, multi-Hertzian method is used to find the nature
of contact patches. Some animation contact graphics for s1002 wheel profile and UIC60 rail profile are
given in Figure 31. The contact patches are both elliptical and non-elliptical. In Figure 31(a), the train
is taking a curve at slow speed and the elliptical contact patches at the tread are stable throughout the
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uniform track curvature zone. In Figure 31(b), the speed is close to maximum designed operating speed
on curved track. There is a multi-point contact in one wheel at the tread as well as the flange, and the
contact patches are still elliptical. Figure 31(c) shows the case when the train is curving at a speed very
close to the derailment limit. There is repeated flange contact and rebound at this speed and sometimes
one of the wheels loses contact from the rail and then suddenly falls back on the rail. The contact forces
are large due to impacts. Figure 31(d) shows the situation when the one of the wheel climbs over the
rail and leads to derailment.
8.2. Critical Speed and Derailment
Critical speed is the speed at which vehicle becomes unstable on straight track and the hunting vibrations
persists either with or without flange contact. Above critical speed, in addition to lateral vibrations, twist
and roll, and resonance type of motions in which car body oscillates about the longitudinal axis take
Figure 31. Different types of contact patches for s1002 wheel profile and UIC60 rail profile
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place. Derailment takes place at some speed above the critical speed. For critical speed analysis, inputs
are vehicle design parameters, stiffness and damping values of suspension system and moment of inertia
(MI). The simplest form of analysis of critical speed is performed using a linearized model about fixed
wheel conicity. The minimum speed at which at least one of the eigenvalues of the linearized model has
a positive real part is the critical speed. The linearized model employs Kalker’s linearized model for
rail-wheel contact forces. The critical speeds for the coach with the considered bogie design at various
levels of wheel conicity with flexible track and with no rail inclination are shown in Figure 32. The
contact angle is taken as 85 λ, where λ is the equivalent conicity. It is found that the critical speed at the
conicity of 1:40 (which is equivalent conicity in our case with 1:20 conicity of s1002 wheel profile and
1:40 UIC60 rail inclination) is 102 m/s (367 km/h).
However, the linear analysis only gives a ballpark value and the actual critical speed should be evalu-
ated through full transient simulation of the non-linear model with non-linear contact force formulation.
The linear analysis assumes constant conicity throughout the tread. In graded circular wheel, the change
in rolling radius due to lateral shift is different for both wheels. Thus, the actual critical speed of trains
with graded circular wheels is much higher than the value predicted from linearized model’s eigenvalue
analysis.
Hunting motion of wheels is a self-excited vibration. The initial excitation can be caused by any
form of disturbance such as by track irregularities (Dukkipati & Amyot, 1988). For simulation in Adams
VI-Rail, we have used a small amplitude ramp type discontinuity in vertical direction. The same results
are obtained for other forms of small disturbance. The results in Figure 33 show the lateral displace-
ment of the wheel-set on a curved track at various operating speeds. As is evident that after the initial
Figure 32. Stability range of vehicle with steered bogies from linear stability analysis with different
values of conicity
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disturbance the hunting vibrations stabilize for a speed below the critical speed, persist at the critical
speed and grow (leading to flange contact) above the critical speed. There is no derailment, though, on
the straight flexible track.
While a train operates below the critical speed, irregularities of track can still excite other modes of
the vehicle. Symmetric track irregularities can give pitch and bounce. Asymmetric irregularities excite
roll and yaw modes. Occasionally, these two types of motions are responsible for derailment in which
the wheel climbs over the flange. Derailment may be caused at speeds lower than the critical speed due
to bad track conditions such as loose ballast, rail waviness, rail discontinuity and any other form of large/
abnormal excitation. Even when there is no derailment, temporary wheel separation from one rail causes
large vertical impact forces and passenger discomfort. When the speed exceeds the critical speed by a
small amount, self-excited yaw and sway motions are sustained and there is a good chance of derailment
under sufficiently large disturbance.
Usually, high-speed rail tracks are so well laid out that there is practically no chance of derailment
on straight tracks. The derailment can only occur on curved tracks and turnouts. The limiting speed at
which derailment occurs in curved track is dependent upon the track radius of curvature, entry curve
length, cant/super-elevation, track irregularities and other track parameters, and bogie design parameters.
For the considered bogie design with forced steering, the derailment occurs above the speed of 114m/s
(410 km/h) on 4km radius track with 460m long entry/transition curve, and flexible track condition
with measured irregularities. An animation frame grab from Adams VI-Rail during good curving of a
coach on a flexible curved track is shown in Figure 34. The wheel jump and derailment scenarios are
shown in Figure 35.
Figure 33. Hunting behavior at various speeds with an initial disturbance
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Figure 34. A coach with non-steered bogie approaching the entry curve
Figure 35. Derailment of coach within the entry curve
8.3. Influence of Worn Wheel
Wheels and rails wear due to the friction between them. Generally, rail wear is less as compared to the
wheel wear. The places where wheel wear takes place is determined from the contact patch location.
On straight runs, wheels wear in the nominal contact position. On curves, wheels wear near the flanges.
In general, some points on the wheel wear out at a much faster rate. A wear evolution model based on
forces and locations at the contact patch is used to produce worn wheel profiles (see Figure 19). If a train
traverses the same path in both forward and backward directions then both the wheel on the inside of a
curve during forward run also remains on the inside of the curve on the reverse run. Thus, wheels wear
out at flanges in an asymmetric manner whereas tread wear is faster (due to longitudinal creep forces)
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and symmetric. Since the purpose of this chapter is about steering of rail vehicles, we will consider that
the train mostly operates on straight track and few curves. Thus, we consider symmetric wheel wear.
Two worn wheel profiles and the original new wheel profile as shown in Figure19 are used in this study.
Figures 36 and 37 show the influence of wheel wear on the hunting behavior of the vehicle on a
straight flexible track with irregularities. All the simulation results shown here are at the same speed as
the critical speed of the vehicle with new wheels. The results reveal that wheels with small wear tend
to increase the critical speed and reduce the lateral creep forces. This happens due to flattening of the
nominal contact patch (reduction of the conicity) on the wheel tread. Also, the reduction in creep forces
indicates that the rate of wear decreases in marginally worn wheels. It is evident that the wheels wear
out at a faster rate in the beginning (new wheel) and then start wearing at a smaller rate till a critical
level of wear is reached. At this critical level of wear, the critical speed of the vehicle starts to reduce
and the contact forces and wheel wear start to increase rapidly.
Small level of wear reduces the wheel conicity near the nominal contact patch. As a result, when the
vehicle has to take a turn, wheels have to be displaced more to produce the desired level of difference
in radius of curvature on inside and outside rails (see Figure 38). However, small level of wear surpris-
ingly reduces the lateral creep forces during curving as shown in Figure 39. This happens due to stiffer
tread gradient near the worn flanges.
When the tread wear level is very high (the rolling radius at nominal tread contact becomes 5mm less
than the radius at tread end) then there is a negative cant effect. This causes the bogie to move at a very
fast rate towards the flange. Although the worn flanges provide steeper gradient, the lateral momentum
is sufficient to cause derailment. Thus, wheel wear levels for safe running are determined from simula-
tions. Those results are out of the scope of this chapter.
Figure 36. Lateral displacement (hunting behavior) of wheels of various levels of wear on straight track
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Figure 37. Lateral creep forces of wheels of various levels of wear on straight track
Figure 38. Lateral displacement of wheels of various levels of wear on curved irregular and flexible
track of 4km radius
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Figure 39. Lateral creep forces of wheels of various levels of wear on curved irregular and flexible
track of 4km radius
Worn wheels also change the passenger comfort. Comfort level is described in terms of the Sperling
ride index, which must be less than 2.5 and preferably less than 2 (see Table 2). Small to moderate wear
causes better passenger comfort on straight tracks and slightly lower comfort on straight tracks (Table
3). However, note that the comfort levels in Table 3 are given for very high-speed operation on irregular
track (worst case scenario) and the actual comfort level is much better at smaller speed ranges and/or
on more regular tracks.
Table 2. Different ranges of ride comfort (The Table 3. Ride comfort with worn wheels
American Public Transportation Association,
2007). Type of Track Wheel Ride Ride
and Operating Profile Comfort In Comfort in
Speed Y-Direction Z-Direction
Ride Comfort Subjective Ride Comfort
(Wz) Straight track Profile-1 2.5030 2.0465
with measured
1 Just noticeable Profile-2 2.4450 2.0457
irregularity
2 Clearly noticeable (100 m/s or 360 Profile-3 2.2900 2.0490
km/h)
2.5 More pronounced but not unpleasant
Curved track Profile-1 2.0740 1.9397
3 Strong, irregular but still tolerable with measured
Profile-2 2.3564 2.2020
irregularity
3.25 Very irregular
(100 m/s or 360 Profile-3 2.2611 2.1130
3.5 Extremely irregular, unpleasant, annoying, km/h)
prolonged exposure intolerable
4 Extremely unpleasant, prolonged, exposure
harmful
569

8.4. Influence of Steering
Proper cant is helpful in reducing lateral accelerations as well as creep forces in lateral direction in the
curved track. The cant adds to the self-steering action. If one needs to increase the operating speed
around the curves then the track cant has to be increased. However, that causes excess cant for low speed
operation on that same track. Therefore, it is not possible to increase the cant beyond a certain limit.
Thus, to improve the dynamic behavior of vehicles on curved portions of the track, forced steering will
be required. Actuation from the active steering mechanism has to counter the cant deficiency in order
to increase the speed on the curves.
The dynamic behavior of the vehicle with forced-steering mechanism is improved in the presence
of cant in the curved track. Forced-steering effect is more pronounced in the presence of cant/ super-
elevation on the curved portion of the track. Figures 40 and 41 show the influence of cant in a well-
designed track when the vehicle with bogies having active steering linkage takes a turn of 4km radius
at the recommended speed (270 km/h).
Forced/active steering is effective not only when the train needs to operate with cant deficiency on the
track but also when it needs to operate with cant excess. Excess cant is nullified by steering the wheels
in opposite direction to the track curvature. Incorrect actuation of the self-steering mechanism can lead
to severe problems like derailment due to instability of the feedback control loop. Therefore, precise
measurement of location, correct correlation with track geometry at that location, proper selection of
controller gains and minimization of controller and actuator delay are some of the important factors in
mechatronic implementation of the active steering system.
The control algorithm turns the wheel-sets of each bogie in a coach in opposite directions to mini-
mize the angle of attack. The controller is based on a proportional feedback system where the wheel-set
orientation and vehicle speed are measured variables. The local cant deficiency/excess at the given speed
is used to compute the desired steering angle and the error with the measured wheel steering angle is
Figure 40. Comparison of the lateral displacement of the left front wheel with track cant (150mm super
elevation) and without cant at 75 m/s (270km/h) with forced steering
570

Figure 41. Comparison of the creep force in the left front wheel with track cant (150mm super elevation)
and without cant at 75 m/s (270km/h) with forced steering
used to provide the additional amount of steering. The controller gains are kept small in order to avoid
feedback delay induced instability problems.
Figures 42 and 43 show some results for active steering bogie operating beyond the recommended
speed on the curved track (100 m/s as compared to 75 m/s considered in Figs. 40 and 41). Because of
steering action, the lateral displacement is reduced and the frequency of lateral accelerations is less.
Likewise, creep forces are smaller. With no steering, the wheel on the outer side remains continuously in
flange contact whereas with steering action, there is continuous oscillation with no flange contact. The
oscillations are result of simple proportional feedback control. With implementation of proportional-
integral-derivative (PID) control through co-simulation in Matlab/Simulink and Adams VI-rail software
(block diagram as shown in Figure 44), the oscillations in lateral displacement and creep forces become
much less. Those results are not presented here.
8.5. Ride Comfort
The steering effect influences the ride comfort to a great extent. The effect of vibration on a person riding
the vehicle is measured in terms of ride comfort which depends on carbody acceleration and the person’s
physical structure. Here, ride comfort for different tracks (with measured irregularities) is calculated by
Sperling’s ride index method. The weighting function B is different for vertical and horizontal direc-
tions. These weighting functions represent the average human body’s vibration transmissibility models.
The weighting factor for transmissibility in horizontal (lateral) direction is given by (Chandra & Roy,
2002; Gangadharan et al., 2004)
1/ 2
 
1.911 × f 2 + (0.25 × f 2 ) 2
Bh = 0.737 ×   (29)
 (1 − 0.277 × f 2 )2 + (1.563 × f − 0.0368 × f 3 )2 
 
571

Figure 42. Lateral left wheel displacement of front wheel of front bogie at 100m/s (360 km/h) on an ir-
regular flexible track with 150mm super-elevation
Figure 43. Lateral creep force in left wheel of front wheel of front bogie at 100m/s (360 km/h) on an
irregular flexible track with 150mm super-elevation
572

Figure 44. Block diagram of PID control of steering angle calculation.
where f is the frequency in Hz. Likewise, the weighting factor for transmissibility in vertical direction
is given by
Bv = Bk/1.25 (30)
These weighting functions are graphically shown in Figure 45. It is seen that the low frequency content
in the range of 1 to 10 Hz is most uncomfortable to the human beings. The suspension systems should
be designed to isolate this frequency range so that they are not transmitted to the car-body.
The ride comfort (Sperling’s ride index) in respective directions is expressed as
Wz = (a2B2)1/6.67 (31)
where a is the amplitude of acceleration in cm/s2. This amplitude is obtained from Fourier transform
(frequency response) of experimental/simulated car-body acceleration data. The ride index factor is
determined for each individual frequency, and cumulative ride index (for n frequency components) is
calculated as
Wz _ total = (Wz16.67 + Wz2 6.67 + Wz36.67 + Λ + Wzn 6.67 )1/ 6.67 (32)
The continuous vibration spectrum of vehicle can be used to obtain the correct cumulative ride index
(ride comfort) by integrating the convoluted transmissibility and acceleration frequency responses over
a frequency range of interest:
573

Figure 45. Weighting factors (frequency weighting curves) in difference directions
1/ 6.67
 f2 
Wz =  ∫ a 2 B 2 df  , (33)
f 
 1 
where f1 and f2 are the lower and upper bounds of the frequency range.
The ride comfort for the forced steering bogie at different speeds and regular and irregular track
conditions with various levels of cant are given in Table 4. It is found that at the designed operating
speed of 75 m/s (270 km/h) on the curved track, the ride comfort is good for cant values between 0.05
and 0.1047. The steering bogie does not give good ride comfort when there is no cant in the track. Also,
the ride becomes very uncomfortable when the operating speed is increased to 100 m/s (360 km/h) on
the curved track. Up to 50 m/s (180 km/h) speed on curved track, the ride comfort is exceptional.
9. CONCLUSION
The design of a mechatronic railway bogie with passive and forced/active steering mechanisms is pre-
sented in this chapter. Influence of various track parameters on the vehicle performance is evaluated
through simulations performed using Adams VI-Rail software. It was shown that the forced steering
bogie is able to adapt to cant excess and cant deficiency on curved tracks. In addition, it has been shown
that the bogie performance remains good even for small to moderate levels of wheel tread and flange
wears. The forced steering bogie also gives exceptional ride comfort up to 270 km/h speed on irregular
flexible curved tracks.
574

Table 4. Ride comfort at different speed, track condition and cant for vehicle with forced steering bogies
Cant Track Condition Speed in m/s (km/h) Ride Comfort

Lateral Direction Vertical Direction
0 Smooth 25 (90) 0.81214 0.3519
50 (180) 1.10692 0.31017
75 (270) 2.98507 0.9612
100 (360) 1.79949 0.61052
Irregular 25 (90) 1.1047 1.6875
50 (180) 1.602 1.3874
75 (270) 3.3177 1.7834
100 (360) 2.5026 1.9753
0.05 Smooth 25 (90) 0.8179 0.7643
50 (180) 1.16873 0.4988
75 (270) 1.4455 0.688
100 (360) 2.5566 1.02169
Irregular 25 (90) 1.113 1.81398
50 (180) 1.47 1.389
75 (270) 1.763 1.777
100 (360) 2.5569 1.0217
0.075 Smooth 25 (90) 0.822 0.366
50 (180) 1.13 0.47
75 (270) 1.44 0.625
100 (360) 3.199 0.973
Irregular 25 (90) 1.137 1.68
50 (180) 1.465 1.389
75 (270) 1.788 1.67
100 (360) 3.116 1.988
0.1047 Smooth 25 (90) 0.8216 0.715
50 (180) 1.0767 0.5837
75 (270) 1.2927 0.86023
100 (360) 1.54 1.0520
Irregular 25 (90) 1.1744 1.678
50 (180) 1.4693 1.39
75 (270) 1.7886 1.78454
100 (360) 3.54 3.30866
10. ACKNOWLEDGMENT
The Adams VI-Rail software used in this research has been procured with financial support from Center
for Railway Research (CRR), Indian Institute of Technology, Kharagpur. Some validations have been
575

performed with Simpack Rail which has been procured with financial support from Department of Me-
chanical Engineering, Indian Institute of Technology, Kharagpur. We also acknowledge help from Mr.
Sital Singh of Research, Design & Standards Organization (RDSO), Ministry of Railways, Lucknow,
for his help during initial stages of software learning.
REFERENCES
Aknin, P., Ayasse, J. B., & Devallez, A. (1991). Active steering of railway wheel sets. Proceedings of
the 12th IAVSD Conference, Lyon, August 1991.
Ayasse, J.-B., & Chollet, H. (2006). Wheel-Rail Contact. In S. Iwnicki (Ed.), Handbook of railway
vehicle dynamics (pp. 86–120). Boca Raton, FL: CRC Press.
Bruni, S., & Goodall, R. M., Mei, T.XTsunashima, H. (2007). Control and monitoring for railway vehicle
dynamics. Vehicle System Dynamics, 45(7-8), 743–779. doi:10.1080/00423110701426690
Chandra, K., & Roy, D. G. (2002). A technical guide on oscillation trial (p. 334). MT: RDSO.
Cheng, Y. C., & Hsu, C. T. (2012). Hunting stability and derailment analysis of car model of a railway
vehicle system. Rail and Rapid Transit, 226(2), 187–202. doi:10.1177/0954409711407658
Cheng, Y. C., Lee, S. Y., & Chen, H. H. (2009). Modeling and nonlinear hunting stability analysis of high
speed railway vehicle moving on the curved track. Journal of Sound and Vibration, 324(1-2), 139–160.
doi:10.1016/j.jsv.2009.01.053
Dahlberg, T. (2006). Track issues. In S. Iwnicki (Ed.), Handbook of railway vehicle dynamics (pp.
143–179). Boca Raton, FL: CRC Press. doi:10.1201/9781420004892.ch6
Diana, G., Bruni, S., Cheli, F., & Resta, F. (2002). Active control of the running behavior railway ve-
hicle: Stability and curving performances. Vehicle System Dynamics, 37(Suppl.), 157–170. doi:10.108
0/00423114.2002.11666229
Dukkipati, R. V., & Amyot, J. (1988). Computer aided simulation in railway dynamics. New York:
Marcel Dekker. Inc.
Gangadharan, K. V., Sujata, C., & Ramamurti, V. (2004), Experimental & analytical ride comfort evalu-
ation of a railway coach. Proc. IMAC-XXII, Dearborn, Michigan.
Goodall, R. M., Bruni, S., & Mei, T. X. (2006). Concepts and prospects for actively controlled railway
running gear. Vehicle System Dynamics, 44(Suppl.), 60–70. doi:10.1080/00423110600867374
Goodall, R. M., & Mei, T. X. (2006). Active Suspensions. In: S. Iwnicki (Ed.), Handbook of railway
vehicle dynamics (pp. 327-357). Boca Raton, FL: CRC Press.
Gretzschel, M., & Bose, L. (1999). A mechatronic approach for active influence on railway vehicle run-
ning behaviour. Vehicle System Dynamics, 33(Suppl.), 418–430.
Gretzschel, M., & Bose, L. (2002). A new concept for integrated guidance and drive of railway running
gears. Control Engineering Practice, 10(9), 1013–1021. doi:10.1016/S0967-0661(02)00046-1
576

Kalker, J. J. (1990). Three Dimensional Elastic Bodies in Rolling Contact. Dordrecht, Netherlands:
Kluwer. doi:10.1007/978-94-015-7889-9
Kim, M.S., Park, J.H. & You, W.H. (2008). Construction of active steering system of scaled railway
vehicle. International journal of systems applications, engineering and development, 4(2), 217-226.
Lee, S. Y., & Cheng, Y. C. (2005). Hunting stability analysis for high-speed railway vehicle trucks on
tangent tracks. Journal of Sound and Vibration, 282(3-5), 881–898. doi:10.1016/j.jsv.2004.03.050
Lindahl, M. (2001), Track geometry for high speed railways: A literature survey & simulation of dynamic
vehicle response.
Matsumoto, A., Sato, Y., Ohno, H., Suda, Y., Michitsuji, Y., Komiyama, M., & Nakai, T. et al. (2005),
Multi-body dynamics simulation and experimental evolution for active steering bogie. Proc. Int’l sym-
posium on speed up and service technology for railway and maglev systems (pp. 103-107).
Mei, T. X., & Goodall, R. M. (1999). Wheelset control strategies for a two axle railway vehicle. Vehicle
System Dynamics, 33(Suppl.), 653–664.
Mei, T. X., & Goodall, R. M. (2000). LQG solution for active steering of solid axle railway vehicles.
IEE Proceedings. Control Theory and Applications, 147(1), 111–117. doi:10.1049/ip-cta:20000145
Mei, T. X., & Goodall, R. M. (2000). Modal controller for active steering of railway vehicles with solid
axle wheel-sets. Vehicle System Dynamics, 34(1), 25–41. doi:10.1076/0042-3114(200008)34:1;1-K;FT025
Mei, T. X., & Goodall, R. M. (2003). Recent development in active steering of railway vehicles. Vehicle
System Dynamics, 39(6), 415–436. doi:10.1076/vesd.39.6.415.14594
Mei, T. X., & Goodall, R. M. (2003). Practical strategies for controlling railway wheel-sets with inde-
pendently rotating wheels, Transactions of the ASME Journal of Dynamic Systems, Measurement and
Control, 125, 354–360.
Mei, T. X., & Goodall, R. M. (2006). Stability control of railway bogies using absolute stiffness–sky-
hook spring approach. Vehicle System Dynamics, 44(Suppl.), 83–92. doi:10.1080/00423110600867440
Mei, T. X., & Li, H. (2008), Control design for the active stabilization of rail wheel-sets. Proceedings
of theTransactions of the ASME Journal of Dynamic Systems, Measurement and Control.
Michitsuji, Y., & Suda, Y. (2006). Running performance of power-steering railway bogie with indepen-
dently rotating wheels. Vehicle System Dynamics, 44(Suppl.), 71–82. doi:10.1080/00423110600867416
Miura, S., Takai, H., Uchida, M., & Fukada, Y. (1998). The mechanism of railway track. In Japan Rail-
way & Transport Review (pp. 38-45).
Okamato, I. (1998). How bogies work. Japan Railway & Transport Review, 18, 52–61.
Okamato, I. (1999). Shinkansen bogies. Japan Railway & Transport Review, 19, 46–52.
Orlova, A., & Boronenko, Y. (2006). The Anatomy of Railway Vehicle Running Gear. In S.
Iwnicki (Ed.), Handbook of railway vehicle dynamics (pp. 42–83). Boca Raton, FL: CRC Press.
doi:10.1201/9781420004892.ch3
577

Park, J. H., Koh, H. I., Hyun, H. M., Kim, M. S., & You, W. H. (2010). Design and analysis of active
steering bogie for urban trains. Journal of Mechanical Science and Technology, 24(6), 1353–1362.
doi:10.1007/s12206-010-0341-4
Pearson, J. T., Goodall, R. M., Mei, T. X., & Shen, S. (2004). Kalman filter design for high speed bogie
active stability system. Proceedings of UKACC control, Bath, UK
Perez, J., Busturia, J. M., & Goodall, R. M. (2002). Control strategies for active steering of bogie based
railway vehicles. Control Engineering Practice, 10(9), 1005–1012. doi:10.1016/S0967-0661(02)00070-9
Perez, J., Busturia, J. M., Mei, T. X., & Vinolas, J. (2004). Combined active steering and traction for
mechatronic bogie vehicles with independently rotating wheels. Annual Reviews in Control, 28(2),
207–217. doi:10.1016/j.arcontrol.2004.02.004
Perez, J., Mauer, L., & Busturia, J. M. (2002). Design of active steering systems for bogie-based railway
vehicles with independently rotating wheels. Vehicle System Dynamics, 37(Suppl.), 209–220. doi:10.1
080/00423114.2002.11666233
Polach, O., Berg, M., & Iwnicki, S. (2006). Simulation. In S. Iwnicki (Ed.), Handbook of railway vehicle
dynamics (pp. 359–421). Boca Raton, FL: CRC Press.
Pombo, J. (2012). Application of computational tool to study influence of worn wheels on railway ve-
hicles. Journal of software engineering and application, 5, 51-61.
Powell, A. J. (1999). On the dynamics of actively steered railway vehicles. Vehicle System Dynamics,
33(Suppl.), 442–452.
Schupp, G., Weidemann, C., & Mauer, L. (2004). Modeling the contact between wheel and rail within
multi-body system, Vehicle System Dynamics. International Journal of Vehicle Mechanics and Mobil-
ity, 41(5), 349–364.
Shabana, A. A., Zaazaa, K. E., & Sugiyama, H. (2008). Rail road Vehicle Dynamics: A Computational
Approach. Boca Raton, FL: CRC Press.
Shen, G., & Goodall, R. M. (1997). Active yaw relaxation for improved bogie performance. Vehicle
System Dynamics, 28(4-5), 273–289. doi:10.1080/00423119708969357
Shen, S., Mei, T. X., Goodall, R. M., Pearson, J., & Himmelstein, G. (2004). A study of active steering
strategies for railway bogie. Vehicle System Dynamics, 41(Suppl.), 282–291.
Shimokawa, Y., & Mizuno, M. (2013). Development of new concept steering bogie. Nippon Steel &
Sumitomo Metal Technical Report No. 105, Osaka.
Standard for Definition and Measurement of Wheel Tread taper (Publication No. APTA PR-M-S-017-06).
(2007The American Public Transportation Association. Washington, DC: APTA Press.
Tanabe, M., Komiya, S., Wakui, H., Matsumoto, N., & Sogade, M. (2003). Simulation and visualization
of high speed Shinkansen train on the railway structure. Japan J. Indust. Appl. Math, 17(2), 309–320.
doi:10.1007/BF03167350
578

Wicken, A. H. (1993), Dynamic stability of articulated and steered railway vehicles guided by lateral
displacement feedback. Proceedings of the13th IAVSD symposium, Chengdu, China.
Wickens, A. H. (1994). Dynamic Stability of articulated and steered railway vehicles guided by lateral
displacement feedback. Vehicle System Dynamics, 23(Suppl.), 541–553. doi:10.1080/00423119308969539
Wickens, A. H. (2003). Fundamentals of rail vehicle dynamics. Lisse, The Netherlands: Swets &
Zeitlinger. doi:10.1201/9780203970997
Wickens, A. H. (2006). A History of Railway Vehicle Dynamics. In S. Iwnicki (Ed.), Handbook of
railway vehicle dynamics (pp. 5–38). Boca Raton, FL: CRC Press. doi:10.1201/9781420004892.ch2
579
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Dynamic Analysis of Steering Bogies

Chapter · May 2016

Smitirupa Pradhan Arun Kumar Samantaray

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Local or body-fixed reference system (see Figure 2):

• Roll: Rotation around the longitudinal axis of the car body.

Figure 1. Wheel-rail geometry

Figure 2. Different types of motion

Figure 3. Angle of attack of wheel-set

3. SOFTWARE FOR RAIL VEHICLE DYNAMICS STUDY

4. ANATOMY OF RAILWAY VEHICLES

Figure 4. Different components of a Sinkansen 300 series motor bogie

5.1. Hunting of Wheel-Set

Figure 5. Rolling of a coned wheel-set on a curve

Figure 6. Kinematic oscillation of a wheel-set

5.2. Flange Climb and Derailment

F3 = V cos δ + L sin δ = V (cos δ + VL sin δ)

The L/V ratio can be expressed as

Figure 8. Forces at flange contact location

6. RAILWAY TRACKS: DESIGN AND DYNAMICS OF THE TRACK

6.1. Track Design

6.1.1. Track Gauge

• Standard Gauge: The lateral width of standard gauge is 1435mm.

Figure 9. Track gauge

6.1.2. Track Cant

Figure 10. Track cant

Figure 11. (a) Track curvature, (b) Track cant angle

6.1.3. Transition Length of the Curve

The radius of curvature (ρ) is defined as

6.1.4. Tracks around the World

Organization TSI/ JR JR JR DB DB SNCF SNCF BV

6.2. Dynamics of the Railway Track

Figure 12. Different components of the track

6.2.1. Track and Its Components

6.2.2. Dynamic Properties of the Track

6.3. Track–Vehicle Interaction

Figure 13. Acceleration of the car-body during curving

From the Figure 13, static equilibrium conditions give

By assuming small cant angles (φi≤0.15rad), Equations (11-12) can be written as

Figure 14. Conicity of wheel profile

Figure 15. Wheel-rail profile

Figure 16. Self-steering characteristics of wheel-sets

Figure 17. Behavior of self-steering on conventional bogie wheel-set

Self-steering / passive steering can be achieved in a number of ways such as

• Reducing the stiffness of the axle box suspension / primary suspension

Figure 18. Tread and flange wear

Figure 21. Behavior of single axle steering

7.2. Active/Assist/Forced Steering

7.2.1. Configuration of Active Primary Suspension

7.2.2. Control Strategies

7.2.2.1. Control Strategies for Stability

7.2.2.2. Control Strategies for Guidance

7.2.2.3. Control Strategies for Steering

7.2.3. Sensors and Actuators

7.2.4. Controller Set-Point Specification