![Comparison of contact patch semi-axes ratio of contact model (top) and Gensys model (bottom) from [25]](https://www.researchgate.net/profile/Sundar-Shrestha/publication/338005959/figure/fig1/AS:837373210402821@1576656739931/Comparison-of-contact-patch-semi-axes-ratio-of-contact-model-top-and-Gensys-model_Q320.jpg)
Content uploaded by Sundar Shrestha
Author content
All content in this area was uploaded by Sundar Shrestha on Jul 23, 2021
Content may be subject to copyright.
11th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems
(CM2018), Delft, The Netherlands, September 24-27, 2018
1
WHEEL-RAIL CONTACT MODELLING FOR REAL-TIME ADHESION ESTIMATION SYSTEMS WITH
CONSIDERATION OF BOGIE DYNAMICS
Sundar Shrestha1,*, Qing Wu 1, Maksym Spiryagin1
1 Centre for Railway Engineering, Central Queensland University, Rockhampton, Australia
* s.shrestha@cqu.edu.au
Abstract: Information about the adhesion condition in
wheel-rail contact during railway operations is required
to characterise the braking and traction which are key
factors in railway performance and safety issues.
Adhesion estimation is a methodical process which
requires mathematical models of crucial processes. As a
part of this development, the wheel-rail interface process
needs to be modelled at the initial stage. A real-time
multipoint wheel-rail contact model is developed in the
Matlab software environment using a modular approach.
Additionally, a simplified friction condition estimation
algorithm is implemented to determine friction condition
between wheels and rails. The friction condition
information is further implemented in a Matlab contact
model to determine the actual adhesion coefficient.
Finally, a bogie test rig is developed in the Gensys
multibody simulation tool to validate the Matlab contact
model. The contact model gives realistic results during
numerical investigations. The friction condition
algorithm is able to handle the change in slip under
varying friction conditions which indicates the robustness
of the algorithm.
Keywords: wheel-rail contact; adhesion estimation; real-
time; inverse model; slip.
1. Introduction
Adhesion estimation at the wheel-rail contact interface is
a multifaceted process because it is dependent on several
operational factors such as processes at the wheel-rail
nonlinear contact interface, distribution of load
conditions acting on small contact patches, speed of the
vehicle; operational rail self-cleaning mechanism, track
irregularities and axle load distributions. Moreover,
environmental factors also have a significant influence on
the adhesion estimation. Some of these are
unintentionally spilled contaminations, deliberately used
friction modifiers, weather condition and contact surface
temperature. Hence, adhesion is dependent on many
parameters and the analytical dependency on some of
them may not be easy to define. Moreover, adhesion
estimation requires carefully selected methodological
processes and a wheel-rail interface process is one of
them, which is modelled in this work.
For the adhesion estimation process, several model-based
methods have been implemented. The first is based on the
inverse method as described in the patent [1]. In this
method, the wheel-rail contact forces are predicted from
vehicle dynamic behaviour without incorporating the
wheel-rail contact algorithm [2,3]. The result may not be
sufficiently accurate in some cases as explained in paper
[4]. Different Kalman filter methods have been used in
adhesion estimation. In [5,6], an Extended Kalman Filter
is used in the online estimation of low adhesion condition
by using vehicle response to lateral track irregularities in
normal (no traction or braking) running condition. In [7],
the Kalman-Bucy filter is used to detect lateral creep
force for local adhesion condition determination.
Multiple Kalman filters are used in [8] based on wheelset
dynamics and a fuzzy logic observer to identify the
operating condition of the wheelset at the wheel-rail
interface. Recently, a multiple model approach based on
swarm intelligence to estimate friction at the wheel-rail
interface was proposed in [9]. The artificial neural
network method was also used to predict wheel-rail
contact force [10] and to estimate adhesion condition
[11]. However, these approaches do not consider many
significant parameters such as wheel and rail profile
change, friction conditions, etc. In this case, it is better to
use classical wheel-rail contact algorithms [12] that are
used for multi-body software packages which provide
results with good accuracy.
However, the classical contact models become
impracticable for implementation in real-time due to the
low computational speed. To achieve real-time
simulation by satisfying the requirements mentioned in
literature [13], the fast approximation model seems to
produce reasonable accuracy, however, it is unable to
consider contact profile change and requires user-defined
coefficients in models. In [14,15], the real-time model is
implemented in field-programmable gate array (FPGA)
hardware including Hertz and Fastsim modules to
describe contact laws between wheels and rails. The
contact geometry, creepages and normal forces are
extracted from a precalculated lookup table. Furthermore,
a real-time contact model for a scaled test rig has been
developed at Politecnico di Torino, Italy [16,17] which
considers single point contact.
This paper presents a methodological development of a
multipoint wheel-rail contact model for the purpose of
real-time adhesion estimation. The model has potential to
consider multiple wheel-rail contact points.
2. Contact model in MATLAB
The proposed model considers multiple point wheel-rail
contact. It is created in the MATLAB platform. The
model consists of the following modules:
2
2.1. Profile generation module
In this work, the S1002 new (unworn) wheel profile and
UIC60 new rail profile are used. The profiles for both
right and left side wheel and rail are initialised separately
by loading stored prm-files as ASCII data to ensure a
modular approach.
Since it is a two dimensional (2D) contact model, the
profiles can be defined on the x-plane (profile in y and z
coordinates) to their local reference. To define the wheel
and rail surface in a global reference system, a rotary-
translation subroutine is defined based on the 2D
rotational matrix algorithm. The wheel profile is first
translated in the lateral direction of wheelset (). A rotary
translation is then performed in the vertical direction ()
and along the roll angle () to achieve the defined contact
condition in an iterative process.
(1)
For faster execution, it considers only that part of the
wheel profile which has a projection of rail profile
on a horizontal plane and interpolates using the common
abscissa to calculate distance function between
the two profiles as shown in Figure 1.
(2)
Figure 1: Interpolation for wheel-rail contact geometry
2.2. Geometrical module
It is possible to determine the entire area in which there
is interpenetration between wheel and rail profiles and the
point of contact corresponds to the point in that area that
has the maximum penetration value. If the penetration is
greater than a specified tolerance value, or in the case
of no contact, rotary translation is applied to the wheelset
to reach the desired value. Relatively more iterative
process is required in the case of non-linear profiles
(i.e.) as compared to a linear
profile (i.e.). Here is
wheel roll angle, is rail roll angle and is yaw angle.
For at least single contact point detection on both sides of
the wheel and rail interaction, the requirements specified
in Equation (3) need to be fulfilled.
(3)
where is the interpolated distance between wheel
and rail profiles on the left side and is the
interpolated distance between wheel and rail profiles on
right side. The suggested penetration for a 50 kN wheel
load is in the order of 10-2 mm approximately, hence a
specified tolerance value of 10-4 mm is used here to
meet the accuracy requirements.
Figure 2: Penetrated sections after interpolation- collinear contact
points (top), non-collinear contact points (bottom)
To determine if there is multi-point contact, the
requirements specified in Equation (3) need to be fulfilled
first. If the requirements are satisfied, there exists one or
more contact point(s). In Figure 2, there are five extreme
points which satisfy the requirements, however, and
are not probable contact points. An additional essential
condition for multi-point contact is that each independent
contact point must be adequately far from each other and
separated by at least one extreme point (such as or in
Figure 2) as specified in Equation (4).
x
y
z
0
y
’
x
z
0
y
x
z
ϴ
x
y
z
0
x
z
0
y
3
(4)
where is the penetration depth of the potential contact
point. The number of probable contact point(s) is.
If, multi-point contact exists and if, single
point contact occurs.
Figure 3 shows one case of the wheel-rail profiles not in
contact. In this case, the vertical distance of the wheel is
lower by and rotated clockwise by. The value of
differs on the right and left sides which is calculated
as in Equation (5). The value of is calculated as in
Equation (6).
(5)
Figure 3.Potential contact points on both sides of the wheel-rail
profiles
(6)
Here are slopes of the lines connecting potential
contact points on wheel and rail respectively.
denote right and left sides of wheelset
respectively. denote rail/roller and
wheelset respectively. The radii of curvature is calculated
using the Frenet formula, which requires first and second
derivatives of contact points. The contact angle is the
arctangent of the first derivative at the point of contact.
2.3. Vertical force calculation
The vertical force acting on the bogie was evaluated
based on the simplified inverse modelling presented in
the study by Sun et al. [18]. The following simplified
expressions were used, assuming constant train
acceleration/deceleration and tangent track.
(7)
(8)
where, is vertical force acting on bogie, is
vertical force acting on each wheelset, is carbody
mass, is bogie mass, is axle mass, is train
acceleration, is acceleration due to gravity.
2.4. Normal task module
The normal problem is solved by using the theory of
Hertz [19]. For faster calculation, an approximation
function reported by Ayasse and Chollet [20] is
implemented in this work. Suppose that each body has
two principal rolling radii, one in the y-z plane
(,) and the other in the x-z plane (,).
The separation for this case can be written in terms of
coefficients C and D,
(9)
where
and are non-dimensional coefficients tabulated as a
function of the ratio or the angle . When 0 <
g <∞, in all the cases, . Hence, the
Hertz table can be rewritten as Table 1. C/D can be used
directly as the input to the table, instead of [20]. The
coefficient is determined from the Piecewise Cubic
Hermite Interpolating Polynomial (PCHIP) method [21].
(10)
(11)
(12)
where normal load at the point of contact is, is
Young’s Modulus and is Poisson’s Ratio.
Table 1: Hertz Coefficients for =0 to 180 degrees.
ϴ
0 5 10 30 60 90 120 150 170 175 180
C/D 0 0.002 0.01 0.07 0.333 1 3 13.93 130.6 524.6 Inf
m Inf 11.24 6.61 2.73 1.486 1 0.72 0.493 0.311 0.238 0
2.5. Creepage module
In this module the longitudinal, lateral, and spin
creepages are calculated.
(13)
(14)
(15)
where for the right wheel and left wheel
respectively; is the longitudinal translation velocity;
,
)
, )
, )
, )
4
is the nominal velocity in the longitudinal direction; is
the nominal spin velocity; is the nominal radius of a
wheel for the central position of a wheelset; is the yaw
angle of a wheelset; is a geometrical parameter based
on the contact patch dimensions; is the actual rolling
radius; is the contact angle; is the actual distance
from the centreline of the track to the wheel contact point
in the lateral direction; is the velocity of a wheelset in
the lateral direction.
2.6. Tangential task module
This module is used to calculate the value of creep force
based on the Polach algorithm [22] which is described as:
(16)
(17)
(18)
(19)
(20)
where is wheel load, is proportionality coefficient
characterising the contact shear stiffness, and are the
semi-axes of the elliptic contact patch, and are
longitudinal and lateral creepages, is the longitudinal
creepage force and are model parameters
for different friction conditions which are defined in
Table 2.
Table 2: Creep force model parameters
Parameters
Dry
Wet
Low
0.47
0.25
0.1
0.44
0.40
0.40
0.60
0.20
0.20
1.0
1.0
0.6
0.4
0.4
0.2
3. Adhesion coefficient detection algorithm
The algorithm is based on the approach presented in [23].
First, the adhesion-slip curve is created to define the
relationship between the adhesion in dry, wet and low
conditions with respect to slip. The adhesion coefficient
is calculated for the longitudinal slip range from zero to
one at step size of 0.001.
(21)
where represents the probable adhesion coefficients in
all conditions for a given slip value, is preliminary
estimated adhesion coefficient and is friction condition
represented numerically (i.e., for dry, wet and
low). The schematic of the algorithm is presented in
Figure 4. The predicted adhesion condition is provided to
the real-time contact model to determine the actual
adhesion coefficient as shown in Figure 5.
Figure 4: Schematic diagram of adhesion condition detection
algorithm [23].
Figure 5: Adhesion coefficient calculation from contact model
Vertical
force
Braking/
Traction
force
Estimated
adhesion
coefficient
Adhesion condition
detection algorithm
Slip
Adhesion
condition
Geometrical
module
Normal
contact
problem
Wheel-rail
profile
generation
Contacts
Curvature
Contact area
dimensions
Creepage
module
Rolling radii;
Contact angles
Adhesion
condition
from
algorithm
Adhesion coefficient
calculation
Tangent
contact
problem
Bogie test rig model
(Gensys)
Slip
Vertical
wheel load
calculation
Creep forces
Wheelsets:
State vector
Contact Model
Actual adhesion coefficient
5
4. Bogie test rig model in Gensys
For the simulation process, the two axle wagon bogie test
rig model as shown in Figure 6 is designed based on the
model provided from the real-time bogie test rig model
[24]. It uses the new ENS1002 wheel on new UIC60
roller profiles identical to the profiles used in Matlab
contact model. The car body is modelled as a single mass
with six degrees of freedom (DOFs) considering
longitudinal, roll and pitch DOFs as zero. The bogie
frame consists of two side frames and a bolster each with
four DOFs. The connection between masses is shown in
Figure 7 with the relevant number of DOFs.
The connection between car body and bolster include 10
couplings;
two vertical coil springs with longitudinal,
lateral and vertical stiffness;
one anti-roll stiffness element, two lateral bump
stops, one lateral damper, two vertical viscous
dampers;
one damping element and one stiffness element
working in parallel in the longitudinal direction
for the traction rod.
The connection between bolster and side frames includes:
14 couplings;
six damper and six stiffness elements for
longitudinal, lateral and vertical directions;
two yaw dampers.
Each wheelset is modelled as a single mass with six
DOFs. The connection between the bogie side frames and
each wheelset includes:
24 couplings;
twenty-four stiffness and damping elements for
longitudinal, lateral and vertical directions;
four vertical and four lateral bump stops.
The bogie masses and inertia are shown in Table 3.
Figure 6: Default view of bogie test rig in Gensys
Table 3: The bogie mass and inertia parameters
Parameter
Value
Unit
Car body
Centre of gravity, vertical
1.4
m
Mass
8000
kg
Moment of inertia, roll
1.50e5
kg m2
Moment of inertia, pitch
1.44e5
kg m2
Moment of inertia, yaw
1.44e5
kg m2
Bolster frame
Mass
661.9818
kg
Centre of gravity, vertical
0.4445
m
Moment of inertia, roll
311.8392
kg m2
Moment of inertia, pitch
50
kg m2
Moment of inertia, yaw
311.8392
kg m2
Side frame
Centre of gravity, vertical
0.4572
m
Mass
521.87
kg
Moment of inertia, roll
50
kg m2
Moment of inertia, pitch
154.7897
kg m2
Moment of inertia, yaw
154.7897
kg m2
Wheelset
Centre of gravity, vertical
0.4572
m
Mass
1100.735
kg
Moment of inertia, roll
665.4830
kg m2
Moment of inertia, pitch
282.4631
kg m2
Moment of inertia, yaw
665.4830
kg m2
Roller
Mass
2000
kg
Radius
1.0
m
Moment of inertia, roll
1789
kg m2
Moment of inertia, pitch
1200
kg m2
Moment of inertia, yaw
1789
kg m2
Figure 7: Bogie test rig model with mass, force element, constraints
and joints with degrees of freedom.
Side frame
1
Ground
Bolster
Car body
Name
1
Rigid body with
label
Force
element
Joint with number
of DOFs
Constraint
4
Wheelset
Roller set
6
6
1
1
1
Wheelset
bearing
Rollerset
bearing
Wheelset
bearing
Rollerset
bearing
6
5. Simulation and results
5.1. Validation of the contact model
Both the Gensys bogie test rig model and the contact
model consider the same wheel and roller profiles. In
order to validate the geometrical and normal problem,
results provided by Gensys [25] are compared. Results
can be seen for variation in the contact patch semi-axes
ratio due to lateral wheelset displacement in Figure 8. A
significant discrepancy between results is seen in the area
of contact switching from wheel tread to the flange and
in the flange region because the yaw angle is not taken
into account in the contact model. To validate the tangent
module of the contact model, the Polach creep force
model [22] is used in both models. The state vectors from
the Gensys model were used in the contact model. The
comparisons of the results from the Gensys bogie model
against the real-time contact model are presented in
Figure 9.
Figure 8: Comparison of contact patch semi-axes ratio of contact
model (top) and Gensys model (bottom) from [25]
5.2. Cases
Two simulation cases are performed in this study. The
first case is required to validate the real-time contact
model and friction condition detection algorithm. In this
case, the longitudinal slip value has been adjusted for
each friction condition, namely ‘dry’, ‘wet’ and ‘low’, by
means of a simple traction controller. Each condition
remains for 5 seconds in an order of dry-low-wet. The
bogie model was run on the roller rig under varying
friction conditions with a constant speed of 20km/h.
Figure 9: Comparison of results from Gensys bogie test rig model
(orange line) and real-time wheel-rail contact model (blue line)
Subplot [a]
Subplot [b]
Subplot [c]
Subplot [d]
7
The second case is required to validate the friction
condition detection in a braking mode. In this case, the
friction condition is ‘wet’ for the first 30 seconds, ‘low’
for the next 30 seconds and then remains ‘dry’ until the
test rig stops. The initial braking speed is 90km/h.
The result of the first case simulation is presented in
Figure 9. The adhesion condition detected from the
algorithm is displayed in subplot [a]. The longitudinal
creepage obtained by the contact model is slightly higher
as compared to the Gensys bogie test rig model which can
be seen in subplot [b]. The longitudinal creep force is
marginally higher and adhesion coefficient is slightly
lower in the contact model in a dry condition which can
be seen in subplots [c] and [d] respectively. The
algorithm is able to handle the change in slip under
variations of friction condition, which shows that the
algorithm is robust.
The results for the second case simulation are presented
in Figure 10. The speed of the roller and wheel are
presented in subplot [a]. The slope gradient between 30
to 60 seconds is the lowest among all, which indicates the
‘low’ friction condition. The estimated slip value has
highest fluctuation when the friction condition is changed
which is noticeable in subplot [b].
Figure 10: Results for friction condition detection in braking mode
Based on these simulation results, the contact model
gives realistic results during numerical investigations.
Moreover, the adhesion estimation algorithm provides
the anticipated result in both traction and braking
conditions which indicates the robustness of the
algorithm.
6. Conclusion
At this stage, the algorithm uses a simplified adhesion
estimation method which will be further advanced by
using dedicated input observers. In the next stage, the
contact model and the adhesion estimation algorithm will
be experimentally validated using test rig data. In this
study, vertical force and braking/traction force are used
to determine the preliminary results. To achieve more
realistic initial results, an approach such as rolling noise
analysis [26] could be used in combination.
Acknowledgments
The authors greatly appreciate the financial support from
the Rail Manufacturing Cooperative Research Centre
(funded jointly by participating rail organisations and the
Australian Federal Government’s Business Cooperative
Research Centres Program) through Project R1.7.1 –
“Estimation of adhesion conditions between wheels and
rails for the development of advanced braking control
systems”.
References
[1] Xia F, Wolfs PJ. Estimation of wheel rail
interaction forces. United States Patent US
7,853,412 B2. 2010.
[2] Xia F, Cole C, Wolfs P. An inverse railway
wagon model and its applications. Vehicle
System Dynamics. 2007;45:583–605.
[3] Xia F, Cole C, Wolfs P. Grey box-based inverse
wagon model to predict wheel–rail contact forces
from measured wagon body responses. Vehicle
System Dynamics. 2008;46:469–479.
[4] Xia F, Cole C, Wolfs P. A method for setting
wagon speed restrictions based on wagon
responses. Vehicle System Dynamics.
2006;44:424–432.
[5] Charles G, Goodall R, Dixon R. Model-based
condition monitoring at the wheel–rail interface.
Vehicle System Dynamics. 2008;46:415–430.
[6] Charles G, Goodall RM. Low adhesion
estimation. The Institution of Engineering and
Technology International Conference on
Railway Condition Monitoring. Birmingham,
UK; 2006. p. 96–101.
[7] Ward CP, Goodall RM, Dixon R, et al. Adhesion
estimation at the wheel–rail interface using
advanced model-based filtering. Vehicle System
Dynamics. 2012;50:1797–1816.
[8] Mei TX, Hussain I. Multi Kalman filtering
approach for estimation of wheel-rail contact
conditions. UKACC International Conference on
CONTROL 2010. Coventry, UK: Institution of
Engineering and Technology; 2010. p. 459–464.
Subplot [a]
Subplot [b]
Subplot [c]
8
[9] Altan O, Voltr P. Swarm intelligence based
multiple model approach for friction estimation
at wheel-rail interface. The 5th International
Symposium on Engineering, Artificial
Intelligence and Applications (ISEAIA 2017).
Kyrenia, Cyprus; 2017.
[10] Hossein-Zadeh N, Dhanasekar M, Sun YQ. ANN
application to predict the wheel–rail impact
forces due to the short wavelength defects in rail.
The second international conference on artificial
intelligence in science and technology (AISAT
2004). Hobart, Australia; 2004. p. 212–217.
[11] Gajdar T, Rudas I, Suda Y. Neural network based
estimation of friction coefficient of wheel and
rail. IEEE International Conference on Intelligent
Engineering Systems. Budapest, Hungary; 1997.
p. 315–318.
[12] Meymand SZ, Keylin A, Ahmadian M. A survey
of wheel–rail contact models for rail vehicles.
Vehicle System Dynamics: International Journal
of Vehicle Mechanics and Mobility.
2016;54:386–428.
[13] Belanger J, Venne P, Paquin J-N. The what,
where and why of real-time simulation. Transient
Analysis of Power Systems: Solution
Techniques, Tools, and Applications. 2011.
[14] Mei TX, Zhou YJ. Systems-on-chip approach for
real-time simulation of wheel–rail contact laws.
Vehicle System Dynamics. 2013;51:542–553.
[15] Zhou Y, Mei TX, Freear S. Real-time modeling
of wheel-rail contact laws with system-on-chip.
IEEE Transactions on Parallel and Distributed
Systems. 2010;21:672–684.
[16] Bosso N, Spiryagin M, Gugliotta A, et al.
Mechatronic modeling of real-time wheel-rail
contact. Springer. Springer Berlin Heidelberg;
2013.
[17] Bosso N, Gugliotta A, Zampieri N.
RTCONTACT: An efficient wheel-rail contact
algorithm for real-time dynamic simulations.
2012 Joint Rail Conference (JRC2012).
Philadelphia, Pennsylvania, USA; 2012. p. 1–10.
[18] Sun YQ, Cole C, Spiryagin M. Monitoring
vertical wheel–rail contact forces based on
freight wagon inverse modelling. Advances in
Mechanical Engineering. 2015;7:1–11.
[19] Hertz H. Ueber die Beruehrung fester elastischer
Koerper. Journal fur die Reine und Angewandte
Mathematik. 1881;156–171.
[20] Ayasse J-B, Chollet H. Wheel-rail contact. In:
Iwnicki S, editor. Handbook of Railway Vehicle
Dynamics. Boca Raton, Florida: CRC Press;
2006. p. 85–120.
[21] Chawla MM, Jayarajan N. A generalization of
Hermite’s interpolation formula in two variables.
Journal of the Australian Mathematical Society.
1974;18:402.
[22] Polach O. Creep forces in simulations of traction
vehicles running on adhesion limit. Wear.
2005;258:992–1000.
[23] Spiryagin M, Cole C, Sun YQ. Adhesion
estimation and its implementation for traction
control of locomotives. International Journal of
Rail Transportation. 2014;2:187–204.
[24] Spiryagin M, Sun YQ, Cole C, et al.
Development of a real-time bogie test rig model
based on railway specialised multibody software.
Vehicle System Dynamics. 2013;51:236–250.
[25] DEsolver. Users manual for program KPF
[Internet]. [cited 2017 Sep 3]. Available from:
http://www.gensys.se/doc_html/kpf.html.
[26] Spiryagin M, Lee KS, Yoo HH, et al.
Experimental and theoretical investigation of
adhesion based on analysis of wheel-rail noise.
15th International Congress on Sound and
Vibration 2008, ICSV2008. 2008;2:942–949.
