Abstract and Figures

This study focuses on the quantification of the influence of rolling stock failures (RSFs) on railway infrastructure. Taking the wheel flat, a common RSF, as an example, we introduce four quantification indexes to evaluate the influence on the following four deterioration mechanisms: track settlement (TS), track component fatigue (TCF), abrasive wear (AW), and rolling contact fatigue (RCF). Our results indicate that TS, TCF, and AW increase sharply with the increase of the wheel flat length and the vehicle speed, and this increasing trend becomes more acute with the increase of the wheel flat length and the vehicle speed. At low speeds, RCF increases gradually as the wheel flat length increases; at high speeds, it increases sharply at first and then decreases gradually. The influence of the wheel flat on TCF and AW is the most obvious, followed by TS and RCF. These findings can help infrastructure managers (IMs) to better understand infrastructure conditions related to RSFs and can aid them in managing problems with vehicle abnormality in track access charging.
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Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
783
Quantification of the influence of rolling stock
failures on track deterioration*
Yun-guang YE1, Da-chuan SHI†‡1, Sara POVEDA-REYES2, Markus HECHT1
1Institute of Land and Sea Transport Systems, Technical University of Berlin, Berlin 10587, Germany
2AITEC, Parque Tecnológico, Valencia 46980, Spain
E-mail: dachuan.shi@tu-berlin.de
Received Jan. 21, 2020; Revision accepted Aug. 28, 2020; Crosschecked Sept. 27, 2020
Abstract: This study focuses on the quantification of the influence of rolling stock failures (RSFs) on railway infrastructure.
Taking the wheel flat, a common RSF, as an example, we introduce four quantification indexes to evaluate the influence on the
following four deterioration mechanisms: track settlement (TS), track component fatigue (TCF), abrasive wear (AW), and rolling
contact fatigue (RCF). Our results indicate that TS, TCF, and AW increase sharply with the increase of the wheel flat length and
the vehicle speed, and this increasing trend becomes more acute with the increase of the wheel flat length and the vehicle speed. At
low speeds, RCF increases gradually as the wheel flat length increases; at high speeds, it increases sharply at first and then de-
creases gradually. The influence of the wheel flat on TCF and AW is the most obvious, followed by TS and RCF. These findings
can help infrastructure managers (IMs) to better understand infrastructure conditions related to RSFs and can aid them in managing
problems with vehicle abnormality in track access charging.
Key words: Rolling stock failure (RSF); Track deterioration; Quantification; Track charging; Wheel flat
https://doi.org/10.1631/jzus.A2000033 CLC number: U270
1 Introduction
1.1 Quantification of track deterioration
Deterioration of rail tracks is an inevitable
phenomenon of the railway infrastructure affected by
traffic and climate and is one of the main concerns for
train operators and throughout infrastructure sectors
(Smith et al., 2017). In terms of running safety, even a
small geometric deviation may pose a risk of serious
disasters. In 2015, the failure of track geometry was
the second leading cause of freight wagon derail-
ments in the USA (Higgins and Liu, 2018). The de-
terioration of rail tracks and related vehicle compo-
nents (e.g. bearings, axles, and wheelsets) and infra-
structures (e.g. rails, sleepers, and fasteners) signifi-
cantly increases the frequency of needed maintenance
and decreases the service life of related components
(Soleimanmeigouni et al., 2018). In addition, poor
conditions of rail tracks increase noise, energy con-
sumption, and running costs (Odolinski and Nilsson,
2017). More detailed quantitative descriptions of the
process of track deterioration may aid infrastructure
managers (IMs) to improve running safety, mainte-
nance strategies, and track access charging across rail
systems.
To date, track deterioration mechanisms are
mainly classified into four categories: track settle-
ment (TS), track component fatigue (TCF), abrasive
wear (AW), and rolling contact fatigue (RCF), and
Corresponding author
* Project supported by the Assets4Rail Project Funded by the
Shift2Rail Joint Undertaking under the EU’s H2020 Program (No.
826250) and the China Scholarship Council (No. 201707000113).
Open access funding provided by Projekt DEAL
ORCID: Yun-guang YE, https://orcid.org/0000-0002-2921-8420;
Da-chuan SHI, https://orcid.org/0000-0002-9296-7213; Sara POVEDA-
REYES, https://orcid.org/0000-0002-4869-5134
© The Author(s) 2020
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)
ISSN 1673-565X (Print); ISSN 1862-1775 (Online)
www.jzus.zju.edu.cn; www.springerlink.com
E-mail: jzus@zju.edu.cn
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
784
each category has a corresponding quantitative index
depending on vehicle characteristics and generated
wheel-rail (WR) forces (Öberg and Andersson, 2009).
At present, the combination of these indexes has two
functions: (1) estimating the marginal cost for railway
tracks (track charging model) and (2) evaluating the
track friendliness for railway vehicles (track friend-
liness evaluation model).
(1) Track charging model
Currently, three strategies are adopted to analyze
railway costs, as detailed by Wheat and Smith (2008):
engineering simulations and econometric estimation
(bottom-up model); econometric estimation of a cost
function (top-down model); cost allocation model
(top-down model). The bottom-up model, or two-
stage approach, relies on engineering simulation in-
cluding (1) engineering simulation methods that es-
timate the track deterioration caused by vehicles and
(2) econometric methods that estimate the relation-
ship between the actual maintenance costs and the
different deterioration mechanisms. Wheat and Smith
(2008) proposed this model to estimate the marginal
cost of different types of vehicles on the rail infra-
structure. In the engineering simulation, three deteri-
oration mechanisms (TS, AW, and RCF) were con-
sidered. The econometric results indicated that TS is
the most expensive of the three mechanisms in terms
of the maintenance cost, followed by RCF and AW.
Öberg and Andersson (2009) developed a bottom-up
track charging model, considering TS, TCF, AW, and
RCF in the context of Swedish mainline traffic and
vehicles; additional similar studies have also been
conducted (Smith et al., 2015, 2016).
(2) Track friendliness evaluation model
This is the first stage of the bottom-up charging
model. Bruni et al. (2016) used TS, TCF, AW, and
RCF to assess the track friendliness of passive and
active steering in railway bogies, in which five con-
cepts of the bogie for a Co-Co locomotive were in-
vestigated: passive steering using mechanical link-
ages (EMD), passive hydraulic steering (PHS), active
steering using secondary yaw control (SYC), active
hydraulic steering (AHS), and self-steering secondary
yaw control (SS-SYC). The survey showed that the
EMD, AHS, and SS-SYC concepts could signifi-
cantly reduce RCF and AW, and the SS-SYC and
EMD concepts could significantly reduce TS and
TCF.
In these studies, researchers considered charac-
teristics such as vehicle type, bogie structure, and
curve radius as variables, studying changes in quan-
tification indexes (TS, TCF, AW, and RCF), which
are used to evaluate track deterioration. However, the
abnormal interaction between rolling stock and in-
frastructure, which could be caused by RSFs such as
wheel flats, brake failure, and suspension faults, was
not considered. More information concerning the
influence of WR interface on track deterioration can
be found in (Smith, 2003; Falomi et al., 2011; Halama
et al., 2011; Liang et al., 2013; Ye et al., 2020a).
1.2 Rolling stock failures (RSFs)
RSFs, including carbody failures (CBFs) and
rolling gear failures (RGFs), have a great impact on
running safety and may increase the risk of derailment.
According to a report of the D-RAIL project (Andreas
et al., 2012), between 2005–2010 derailment accidents
caused by RSFs accounted for the highest proportion
of accidents (38%) followed by infrastructure failures
(34%), in 14 European countries (Austria, France,
Germany, the UK, Sweden, Switzerland, Belgium,
Bulgaria, Czech Republic, Hungary, Italy, the Neth-
erlands, Poland, Slovenia), as shown in Fig. 1a. In
fact, RSFs directly affect the infrastructure and may
accelerate track deterioration, thereby increasing the
probability of infrastructure failures.
Among RSFs, rolling gear failure (RGF) usually
has the greatest impact on track deterioration due to
more severe WR interactions. In our previous work
(Hecht et al., 2018), we conducted a statistical analy-
sis on the RSFs of three European railway companies.
The data provided by the three companies indicated
that there were approximately 95 500 damaged vehi-
cles with a total of approximately 244 500 RSFs in a
year, including CBFs and RGFs. Specifically, we
conducted a separate analysis on the RGFs (Fig. 1b),
and the results showed that the four leading failures
were wheel flat, axlebox failure, material deposition,
and thermal overload, with wheel flat failure ac-
counting for the highest proportion (19%) followed
by axlebox failure (18%). In another project (Regazzi
et al., 2019) based on the data provided by
Havelländische Eisenbahn AG (HVLE), Germany,
researchers used the failure mode and effect analysis
(FMEA) method to analyze the likelihood of seven
RSFs including axle crack, wheel out-of-round, wheel
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785
crack, wheel build-up material, wheel thermome-
chanical crack, wheel flat, and wrong tread profile.
The results showed that among these seven failures,
the occurrence probabilities of the wheel out-of-round
and the wheel flat are the highest, both are approxi-
mately 0.06.
Due to limited data and a limited range of vehi-
cle types, these statistics may not reflect the status of
the entire railway industry. However, they do show
that the wheel flat is one of the most critical RSFs: the
large impact force induced by structural discontinuity
on the wheel flat area will accelerate the deterioration
of infrastructure elements such as rails, sleepers, fas-
teners, and other components (Appel and Hecht, 2017;
Mitusch and Hecht, 2017; Bosso et al., 2018).
1.3 Motivation
Current simulation-based track charging models
and track friendliness evaluation models are based on
the quantitative indexes of track deterioration mech-
anisms such as TS, TCF, AW, and RCF. However, the
abnormal interaction between rolling stock and in-
frastructure, which could be caused by RSFs, are not
considered. Our work, which was initiated by the
Assets4Rail Project, focuses on quantifying specific
RSF effects on railway infrastructure to help IMs
better understand the influence of RSFs on infra-
structure deterioration and vehicle abnormalities on
track access charge.
The wheel flat is a common RSF with well-
established length standards for operational limits
(e.g. the 40-mm standard specified by the Italian
railways (Belotti et al., 2006)). However, in actual
operation, the size of wheel flats can be smaller than
the specified criteria, and such flats are difficult to be
completely erased by normal wheel-rail wear, re-
sulting in a long-term cyclic WR impact, in turn ex-
acerbating track deterioration. Quantifying the in-
fluence of wheel flats on track deterioration allows
better safety management and investment decisions,
ultimately benefiting the competitive success of
railways.
1.4 Quantification method
1.4.1 Quantification indexes
The first stage in our methods involves a multi-
body dynamics simulation (MBS) in which we built a
Bo-Bo locomotive with a wheel flat failure and op-
erated it on a straight track to produce estimates of the
four damage mechanisms (TS, TCF, AW, and RCF).
We used four indexes (qTS, qTCF, qAW, and qRCF) to
quantify the severity of these damage mechanisms.
1.4.2 Surrogate modeling
The second stage involves the creation of a
quantitative model to describe the influence of vehi-
cle speed and wheel flat length on track deterioration,
where the Kriging surrogate model (KSM) technique
is introduced.
Simulations involving parametric studies are
often based on repetitive modeling, which signifi-
cantly increase the calculation complexity and load;
these calculations are in fact so complex that the
railway industry is reluctant to do many deterministic
analyses. Part of the research goal was to find a
high-efficiency and reliable method to simplify sim-
ulation procedures to reduce the number of uncer-
tainties and decrease the probability of errors (Ye et
al., 2020b, 2020c). KSM, as a regression model, is
introduced to reduce simulation times (Chowdhury
and Adhikari, 2012).
Fig. 1 Derailment causes and their percentages (a) and
most frequently discovered defects in the rolling gear (b)
(a)
(b)
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2 Locomotive/track coupled dynamics
model
2.1 Locomotive model
The Bo-Bo locomotive (Tao et al., 2018) mod-
eled in this section includes three substructures: one
car body and two bogies. The bogie has two stages of
suspensions, i.e. the primary suspension and the
secondary suspension (Fig. 2).
The primary suspension includes:
1. Two flexi-coil springs (each axlebox) to
provide the vertical stiffness;
2. A vertical damper to slow down the impact;
3. A longitudinal rod to provide the main
longitudinal stiffness and transmit the traction and
braking force from the wheelset to the bogie frame;
4. A lateral bump stop to limit the lateral
displacement of the axlebox;
5. A vertical bump stop to limit the vertical
displacement of the axlebox.
The secondary suspension includes:
1. Six flexi-coil springs arranged in the middle of
the bogie frame (three for each side) to provide the
stiffness in three directions (longitudinal, lateral, and
vertical).
2. Two lateral dampers located at the two ends of
the bogie frame (one for each end) to reduce the
lateral vibration of the carbody. These dampers also
provide anti-rotary torque to limit the yaw motion of
the bogie and have a similar function of the anti-yaw
damper that is not included in this bogie.
3. Two vertical dampers arranged at the two
sides of the bogie (one for each side) to reduce the
vertical vibration from the bogie to the carbody.
4. A traction rod to transmit the longitudinal
force.
5. A lateral bump stop to limit the lateral
displacement of the bogie.
6. A vertical bump stop to limit the vertical
displacement of the bogie.
2.2 Wheelset-track model
Wheelset structural flexibility and track flexi-
bility are two main factors that contribute to high-
frequency WR forces and affect track deterioration
(Chaar and Berg, 2006). In addition, the wheel
flat-induced forces may contribute to the elastic de-
formation of the wheelset (Wu et al., 2018; Ye et al.,
2020a). Therefore, the wheelset is modeled as a
flexible body on the basis of the finite element
method (FEM), and the first 26 eigenmodes belong-
ing to eigen-frequencies below 1 kHz are imported
into SIMPACK. Fig. 3 presents some of the flexible
mode shapes of the wheelset together with the cor-
responding frequencies. The detailed derivation pro-
cess of the motion equation to describe the flexible
wheelset refers to Baeza et al. (2008) and Han et al.
(2018).
For the modeling of the track, on one hand,
simulating the track according to the real situation (i.e.
the form of rail+sleeper+track bed+subgrade) will
involve many degrees of freedom, thereby increasing
the calculation amount especially when coupled with
flexible wheelsets. On the other hand, track flexibility
contributes to high-frequency WR forces. For these
reasons and others (Chaar and Berg, 2006), we sim-
plified the track model as a moving track with a form
of rail+sleeper+ground (Fig. 4), which is convenient
for simulating long travel distances. This simplifica-
tion is acceptable because the required outputs are the
WR lateral force, longitudinal force, and wear num-
ber, and the internal forces of the track are not con-
sidered. The ERRI B176 spectrum integrated in
SIMPACK is applied as the track irregularities.
In this model, the power spectral density
(PSD) of the typical European spectrum (ERRI B176)
defined in SIMPACK is applied as the track
irregularities.
Fig. 2 Side elevation of the bogie
1: primary suspension flexi-coil spring; 2: primary suspensio
n
vertical damper; 3: axlebox longitudinal rod; 4: secondary
suspension flexi-coil spring; 5: secondary suspension lateral
damper; 6: secondary suspension vertical damper; 7: tractio
n
rod. Reprinted from (Tao et al., 2018), Copyright 2018, wit
h
permission from Springer
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
787
.
2.3 Wheel flat model
As mentioned in Section 1.2, the wheel flat is
one of the most common RSFs. It is therefore intro-
duced as a case to study the influence of RSFs on
track deterioration. Referring to Lyon (1972), the
wheel flat (Fig. 5a) is modeled as a haversine wheel
flat and expressed as
f
f
f
12
=1cos,
2
x
dd L

 


(1)
where Δd denotes the variation in radius, Lf denotes
the flat length, xf denotes the distance along the flat,
2
ff
=/(16)dL R denotes the flat depth, and R denotes
the wheel radius. In Fig. 5a, Ψ denotes the angular
size of the wheel flat, and ω denotes the angular co-
ordinate. In this paper, eight different wheel flats
lengths (Lf) are simulated (Fig. 5b), which are 5 mm,
10 mm, 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, and
40 mm, respectively.
The final vehicle model, as well as the bogie
model, simulated in SIMPACK is shown in Fig. 6.
The parameters of interest are listed in Appendix A.
3 Methodology
3.1 Track deterioration model
Öberg (2006)’s review of 21 track deterioration
models concerning ballasted tracks showed few track
deterioration models dealt with several mechanisms
of track deterioration. Smith et al. (2015) used a track
deterioration model that considers four mechanisms
(TS, TCF, AW, and RCF) to determine track access
charges; this same track deterioration model was used
to evaluate the track friendliness of different vehicles
(Bruni et al., 2016). We use these four mechanisms in
our work.
Fig. 3 Selected vibration modes of the flexible wheelset together with the corresponding frequencies
Fig. 4 Topology of the wheelset-track model
(Explanations of the variables are listed in Appendix A)
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3.1.1 Track settlement (TS)
TS consists of ballast settlement, sub-ballast
settlement, and subgrade settlement, of which the
ballast settlement plays the most important role in
track degradation (Shenton, 1984; Chrismer and Selig,
1993). Many models have been used to predict TS
(Elkhoury et al. 2018). The basis of the introduced TS
model here is the ballast settlement model defined by
the Technische Universität München (TUM), Ger-
many. Referring to Smith et al. (2015), a simplified
model is used in our work.
The TUM model is defined by
1.21
sln ln ,TAp NBp N (2)
where Ts is the TS index (mm), N is the number of
axle passes, ΔN is the number of axles passes 10 000
after tamping, p is the ballast pressure (N/mm2), and A
and B are constants.
The simplified model can be represented by
*1.21
slg ,TAQ N (3)
where Q is the maximum vertical force at the wheel-
set, and A* is a constant. In this paper, A*=1.
3.1.2 Track component fatigue (TCF)
TCF refers to internal fatigue of components
such as rails, sleepers, fasteners, ballast, and other
mechanisms as well as abrasive wear and RCF of rails
(referred to as surface fatigue of rails) (Öberg and
Andersson, 2009). TCF is affected by repeated loads
in which the vertical and lateral track forces have the
greatest impact. The TCF index introduced here was
developed by UIC/ORE based on extensive full-scale
tests during the 1980s, and is expressed as a function
of vertical and lateral track forces, as shown in
Eq. (4):
221.5
cf tot qst
1
(),
ii
N
i
TQY

(4)
where Tcf is the TCF index, toti
Q is the total vertical
force including quasi-static and dynamic forces, and
qsti
Y is the quasi-static lateral force.
Fig. 5 Geometry of the wheel flat (a) and eight simulated
wheel flats (b)
(b)
Radius variation (mm)
(a)
R
B
o
A
L
f
B
dd
f
x
f
ω
A
Ψ
(b)
Fig. 6 Locomotive wagon (a) and bogie (b)
(a)
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
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3.1.3 Abrasive wear (AW)
The wear amount is taken as a function of ma-
terial properties, contact pressures, creepages, sliding
velocities, and environmental conditions. Currently,
there are many Tγ-based models that can be used to
calculate the material loss of railway wheels (Pearce
and Sherratt, 1991; Zobory, 1997; Braghin et al., 2006;
Enblom, 2009; Pombo et al., 2011; Tao et al., 2017;
Peng et al., 2019; Ye et al., 2020d), such as the British
Rail Research (BRR) model, Zobory model, Univer-
sity of Sheffield (USFD) model. In these models, the
first step is to calculate the product of the tangential
force (T) and the creepage (γ) in the WR contact patch,
i.e. Tγ, which is given by
,
xx yy
TFvFvM
 (5)
where Fx and Fy are longitudinal and lateral creep
forces, vx and vy are longitudinal and lateral creepages,
respectively, M is the moment, and φ is the spin.
3.1.4 Rolling contact fatigue (RCF)
Rolling contact creates both elastic and plastic
deformations in the contact area, alternating stress
that leads to fatigue damage with a correspondingly
high number of cycles. In the rail vehicle sector,
damage caused in this way is referred to as RCF.
According to Burstow (2003) and Smith et al. (2016),
the RCF damage index on the rail surface is also
calculated based on the Tγ value, as shown in Fig. 7.
1. Below 15 J/m (or N), the energy is insufficient
to initiate the RCF cracks.
2. Above 15 J/m, the damge increases to a
maximum of 1×105/axle at a Tγ value of 65 J/m.
3. As Tγ increases from 65 to 175 J/m, the level of
energy is such that the dominant form of surface
damage is the wear (rather than the crack initiation).
4. Tγ values greater than 175 J/m result in wear
but no RCF initiation.
5. The unit of the RCF damage index is
105/axle.
3.2 Kriging surrogate model (KSM)
KSM consists of a global regression model and a
random correlation function. It is assumed that the
response value corresponding to the sample point
group x=[x(1), x(2), …, x(n)] is Y=[y1, y2, …, yn], Y is
the response vector, and n is the length of the vector.
The relationship between the input variable and its
response then is expressed as (Ye and Sun, 2020; Ye
et al., 2020d):
T
() () (),yZ
xfx x (6)
where ( )yx is the response, fT(x) is the regression
model founded by the known function that depends
on x, β is an undetermined coefficient, and Z(x) is a
random Gaussian distribution with a mean of zero and
variance of σ2. The covariance matrix of Z(x) for an
m-variable design space can be expressed as (Ye and
Sun, 2020)
() ( ) 2 () ( )
2
() ( ) () ( )
1
Cov[ ( ), ( )] ( , , ),
(, , ) exp ,
ij ij
m
ij i j
ll l
l
ZZ R
Rxx
 
xx xx
xx
(7)
where x(i) and x(j) are two sample points in the sample
space, and 1i, jn; R(θ, x(i), x(j)) represents the spatial
correlation between the sample points x(i) and x(j);

()
i
j
ll
x
x represents the absolute distance between
the lth components of x(i) and x(j); θl is the lth com-
ponent of θ which indicates how active a variable is in
the surrogate model. Larger values of θl can be in-
terpreted as high-level of activity while smaller val-
ues of θl indicate that the variable can be ignored in
the surrogate model (1l2 in this paper). Therefore,
a correlation matrix between the sample points and
their response values can be obtained as (Ye and Sun,
2020)
Fig. 7 Rail RCF damage function
RCF damage index, RCF (×105/axle)
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(1) (1) (1) (2 ) (1) ( )
(2) (1) (2) (2) (2) ( )
() (1) () (2) () ()
(, , ) (, , ) (, , )
(, , ) (, , ) (, , ).
(, , ) (, , ) (, , )
n
n
nn nn
RR R
RR R
RR R







xx xx xx
xx xx xx
R
xx xx xx
 
 
 
(8)
Therefore, the value of θ needs to be determined
first, calculated by maximizing the likelihood esti-
mate of the response value as
2
TT1 T
2
1ˆ
ln ln ln
2
1ˆˆ
()().
ˆ
n
 
 
R
Yf RYf
(9)
The estimate of θ depends on the estimated un-
determined coefficient matrix ˆ
and the estimated
variance 2
ˆ.
ˆ
and 2
ˆ
can be calculated using the
generalized least square method, given as
T1 1 T1
ˆ()(),
 
FRF FRY (10)
2TT1T
1ˆˆ
ˆ()(),
n
 YF RYF
(11)
where F=[f(x(1)), f(x(2)), …, f(x(n))]T. For the final
determined value of θ please see Section 4.2.
Finally, after determining the input information
of the unknown point x*, the corresponding response
value can be predicted by the KSM using
TT1***
ˆˆ
ˆ() () () ( ),y
 xFx rxRYF
(12)
where r(x*)=[R(θ, x*, x(1)), R(θ, x*, x(2)), …, R(θ, x*,
x(n))] is the correlation function vector of the sample
point to be tested and each known sample point. The
mean squared error (MSE), which is again dependent
on r, is used to measure the uncertainty of the pre-
dicted value:
T12
22T1
T1
*(1 )
ˆˆ
() 1 .s

 


1
1
Rr
xrRr
Rr (13)
The square root of Eq. (13) (RMSE) is used to
measure the accuracy of the established model over
the design space. The uniform experimental design
sampling principle (Xin et al., 2017) is used to select
the sample points in our work.
3.3 Technique route
The technique route of this method is shown in
Fig. 8. The simulation steps are summarized as
follows:
Step 1: Select sample: the corresponding wheel
flat lengths and the vehicle speeds are selected
according to the uniform experimental design
sampling principle.
Step 2: The wheel flat curve is constructed and
imported into the MBS model.
Step 3: Run the short-term simulation in
SIMPACK and generate wheel-rail vertical force,
wheel-rail lateral force, wear number, etc.
Step 4: Calculate the total loss of each of the four
mechanisms (TS, TCF, AW, and RCF).
Step 5: Four quantification indicators (see
Section 4.1) are introduced to quantify the influence
of wheel flats on track deterioration.
Step 6: A KSM-based quantification model is
built.
4 Simulation results
MBS results are required for the damage calcu-
lation using the deterioration mechanisms mentioned
in Section 3.1. To study the severity of track deteri-
oration with the change of vehicle speed and wheel
flat length, we did simulations of seven different
vehicle speeds v (30 km/h, 40 km/h, …, 90 km/h), and
under each speed, the wheel flat length L goes from 0
to 40 mm in an increment of 5 mm (0 mm, 5 mm, …,
40 mm, Fig. 6c), with a total of 63 simulations. The
wheel flat is created on the right wheel of the first
wheelset with the help of the untrueness modeling
capability of the SIMPACK.
It should be noted that the calculation time step
needs to be discreetly chosen, especially for such
shock signals arising from wheel flats. Like other
computerized calculation tools, SIMPACK is limited
to the numerical methods’ precision and inherent
errors. Whilst the calculation time step is reduced, the
‘resolution’ of the simulation results is enhanced, and
the overall time to perform the simulation is extended.
Considering both the precision and computational
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
791
effort, 0.05 ms is used in this work referring to Bernal
et al. (2019).
4.1 Quantification indicators
This work was done to study the effect of trains
with wheel flats on track deterioration relative to
normal trains. Four relative quantification indicators
are used to evaluate the effects of wheel flats on TS,
TCF, AW, and RCF (qTS, qTCF, qAW, and qRCF).
Among them, qTS is defined by
1.21
sf sf
TS
so so
,
TQ
qTQ




(14)
where Tsf is the TS caused by the train with a wheel
flat; Tso is the TS caused by a normal train with a
speed of 30 km/h; Qsf is the WR vertical peak force
caused by the train with a wheel flat; Qso is the WR
vertical peak force caused by the normal train with a
speed of 30 km/h.
According to Eq. (14), it can be known that in
simulation, the most important indicator for solving
the TS is the WR vertical peak force Q. The WR
vertical peak force, however, could be affected by
track irregularities. Also, the vehicle-track system has
many nonlinear factors including characteristics
of yaw dampers and suspensions, as well as the
geometric contact characteristics of wheels and rails.
Therefore, the peaks of the WR vertical peak forces
generally during each wheel rotation period, usually
are unequal, as shown in Fig. 9a. Based on these
considerations, we used the average of the peak as the
WR vertical peak force Qsf, calculated by
12
sf ,
k
A
AA
Qk

(15)
where Ai (i=1, 2, …, k) represents the WR vertical
peak force at the ith wheel rotation, and k represents
the number of wheel rotations.
qTCF can be calculated by
cff
TCF
cfo
,
T
qT
(16)
where Tcff is the TCF caused by the train with a wheel
flat; Tcfo is the TCF caused by the normal train with a
speed of 30 km/h.
qAW is calculated by
f
AW
o
,
T
qT
(17)
where Tγf is the AW caused by the train with a wheel
Fig. 8 Technique route of the quantification model
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
792
flat; Tγo is the AW caused by the normal train with a
speed of 30 km/h, as shown in Fig. 9b.
As mentioned in Section 3.1.4, when the Tγ
value is below 15 J/m, the energy is insufficient to
initiate the RCF cracks, which means that RCF
cracking may not happen on wheels if the wear
number is below 15 J/m. This situation may occur in
normal trains or trains with small wheel flats.
Therefore, the relative quantitative indicator for RCF
is itself.
RCF CF.qR (18)
4.2 Simulation results
Appendix B lists the original simulated results,
including Q, Tcf, Tγ, and Rcf. Based on these original
data, the quantification indexes qTS, qTCF, qAW, and
qRCF can be calculated by Eqs. (14), (16), (17), and
(18), respectively. In the construction of the KSM
model, the length of wheel flat (Lf) and vehicle speed
(v) are set as the inputs of KSM, while qTS, qTCF, qAW,
and qRCF are set as the output responses, respectively,
i.e. x=[Lf, v], and y(x)=qTS, y(x)=qTCF, y(x)=qAW or
y(x)=qRCF in Eq. (6). Then, the values of θ (Eq. (9))
and R (Eq. (7)) of the surrogate model can be derived.
Finally, the established KSM concerning qTS, qTCF,
qAW, and qRCF is shown in Fig. 10, in which the cal-
culated values of θ are [1.25, 1.25], [0.625, 1.25],
[1.25, 1.25], and [2.5, 1.7678], respectively. To en-
sure the correctness of the KSM, the accuracy of the
KSM should be verified first. Fig. 11 displays the
absolute value of RMSE value derived from Eq. (13).
These four figures reveal that the errors on the edges
and corners of the design space are larger than that in
the central part, as shown in Fig. 11. However, these
errors can be negligible, which means that these KSM
models are accurate enough.
qTS (Fig. 10a) shows an increase with the in-
crease of vehicle speed and wheel flat length. When
the vehicle speed is increased to 90 km/h and the
wheel flat length is increased to 40 mm, the TS caused
by the vehicle is about 35 times of the TS caused by
the vehicle when the vehicle speed is 30 km/h and the
wheel flat length is 0 mm. In terms of qTCF (Fig. 10b)
and qAW (Fig. 10c), like the qTS, they also show a
consistent increase with the increase of vehicle speed
and wheel flat length. When the vehicle speed is in-
creased to 90 km/h and the wheel flat length is in-
creased to 40 mm, the TCF and AW caused by the
vehicle are higher than 250 and 400 times, respec-
tively, relative to that caused by the train with a speed
of 30 km/h and a wheel flat length of 0 mm. This
rising trend will become more pronounced as the
vehicle speed and the length of wheel flat increase.
The qRCF (Fig. 10d) at low speeds (v<75 km/h) in-
creases gradually as the wheel flat length increases; at
high speeds (v>75 km/h), it first increases sharply and
then decreases gradually, reaching a maximum value
of about 10 when the wheel flat length is close to
35 mm.
Based on the above phenomena, we reach two
conclusions:
1. The wheel flat has a serious impact on track
deterioration. In general, qTS, qTCF, and qAW increase
with the increase of the wheel flat length and vehicle
speed, and this increasing trend becomes more acute
with the increase of the wheel flat length and vehicle
speed. At low speeds, qRCF increases as the wheel flat
length increases; at high speeds, it first increases and
then decreases. The reason for this phenomenon is
that the value of Tγ increases with the increase of the
wheel flat length and vehicle speed. When the
increase of the wheel flat length and vehicle speed
(a)
Fig. 9 Vertical force (a) and wear number (b) of the whee
l
with a wheel flat when the vehicle speed is 30 km/h
(simulated result), where S represents the distance
(b)
Wear number (J/m)
0 5 10 15 20 25 30 35 40 45 50
S (m)
Lf=10 mm
Lf=0 mm (no wheel flat)
0
100
200
300
400
500
A2
A1Ak
Vertical wheel-rail force (kN)
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
793
RMSE RMSE
40
20
040 60
80
0
10
20
30
RMSE
5
10
15
20
25
40
20
040 60
80
RMSE
0
0.02
0.04
0.06
0.08
0.02
0.03
0.04
0.05
0.01
0.06
0.07
(a)
(b)
(c)
(d)
Fig. 11 RMSE results over the design space: (a) qTS, (b)
qTCF, (c) qAW, and (d) qRCF
0
10
20
30
40
10
5
15
20
30
25
40
20
040 60
80
Quantifica tion factor
50
0
100
150
250
200
040 60
80
40
20
Quantification factor
-100
0
100
200
300
Quantif ication factor
040 60
80
40
20
-200
0
200
400
600
100
0
50
150
200
250
300
350
400
Quantif ication facto r
040 60
80
40
20
-5
0
5
10
15
2
0
3
4
5
1
6
7
8
9
10
(a)
(b)
(c)
(d)
Fig. 10 KSM results concerning: (a) qTS, (b) qTCF, (c) qAW,
and (d) qRCF
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
794
causes Tγ to be greater than 65 J/m, due to the
relationship in Fig. 7, qRCF will not continue to
increase. Specifically, when 65 J/m<Tγ<175 J/m, the
main form of surface damage caused by energy levels
is wear rather than crack initiation so that qRCF
decreases when wheel flat length and vehicle speed
increase to a certain extent.
2. The influence of the wheel flat on qTCF and
qAW is the most obvious, indicating that TCF and AW
are the most sensitive to wheel flats. When the vehicle
speed is increased to 90 km/h and the wheel flat
length is increased to 40 mm, the TCF and AW
caused by the vehicle are higher than 250 and 400
times, respectively, relative to that caused by the train
with a speed of 30 km/h and a wheel flat length of
0 mm. Followed by TS, when the vehicle speed is
increased to 90 km/h and the wheel flat length is
increased to 40 mm, the TS caused by the vehicle is
about 35 times of the TS caused by the normal vehicle
with a speed of 30 km/h. Besides, the value of qRCF is
0 when the vehicle speed is 30 km/h and the wheel flat
length is 0 mm, and it increases to around 10 when the
vehicle speed approaches 90 km/h and the wheel flat
length is close to 35 mm.
5 Conclusions and discussion
Deterioration of rail tracks is an inevitable phe-
nomenon of the railway infrastructure affected by
traffic and climate and is one of the main concerns for
train operators and infrastructure sectors. Under-
standing and quantifying the underlying engineering
characteristics of rail track deterioration are critical
aspects of improving train safety, advancing mainte-
nance strategies, and optimizing track access charg-
ing. Today, however, current quantitative methods do
not consider the anomalous interaction between roll-
ing stock and infrastructure, which could be caused
by RSFs. Taking the wheel flat, which is a common
RSF, as an example, this work used four quantifica-
tion indicators to evaluate the track deterioration
based on the KSM.
To date, track deterioration mechanisms are
mainly classified into four categories: TS, TCF, AW,
and RCF. In this work, four indicators are introduced
to quantify the severity of these four damage mecha-
nisms, namely qTS, qTCF, qAW, and qRCF, respectively.
These four indicators can not only help us understand
the influence of abnormal RSFs on track deterioration,
but also provide a reference for the track charging
models of infrastructure companies.
1. Based on a locomotive/track coupled dynam-
ics model, our results show that the wheel flat has a
significant influence on track deterioration. More
specifically, TS, TCF, and AW increase sharply with
the increase of the wheel flat length and the vehicle
speed, and this increasing trend becomes more acute
with the increase of the wheel flat length and the
vehicle speed. At low speeds, RCF increases gradu-
ally as the wheel flat length increases; at high speeds,
it increases sharply at first and then decreases gradu-
ally. The influence of the wheel flat on TCF and AW
is the most obvious, followed by TS and RCF.
2. RSFs have a significant influence on track
deterioration.
There are two points worth mentioning here.
1. This study can be integrated into the bottom-
up-model based track charging model for estimating
the damage and marginal cost of a vehicle on rail
infrastructure. However, such a track charging model
consists of two stages: (I) engineering simulation
methods that estimate the track deterioration caused
by vehicles; (II) econometric methods that estimate
the relationship between the actual maintenance costs
and the different deterioration mechanisms (Smith et
al., 2017). Our work has limits because we investi-
gated only the engineering simulation step.
2. Since the actual wheel flat is usually 3D, when
the train is running on a curve, the wheel may be
moved laterally, causing the contact length of the
wheel flat and the actual length of the wheel flat to be
different. When the train is running on a small-radius
curve, it may even cause the WR contact to not occur
in the flat. Therefore, this paper only analyzed the
case of the train running on a straight line and did not
analyze the case of the curve. Further investigation of
running on the curve is needed.
The engineering applicability of this work re-
quires further investigation and more comprehensive
research, including more vehicle models and more
rolling stock failures, should be continued.
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
795
Replication of results
The unlisted data about the locomotive are confidential
and the authors have no rights to provide it. However, the
original simulated data are listed in Appendix B. Readers
interested in the MATLAB code are encouraged to contact the
corresponding author by e-mail.
Contributors
Yun-guang YE: conceptualization, formal analysis,
funding acquisition, investigation, methodology, validation,
visualization, writing-original draft, writing-review & editing.
Da-chuan SHI: conceptualization, formal analysis, investiga-
tion, methodology, writing-review & editing. Sara
POVEDA-REYES: formal analysis, funding acquisition,
project administration, writing-review & editing. Markus
HECHT: funding acquisition, project administration, resources,
software, and supervision.
Conflict of interest
Yun-guang YE, Da-chuan SHI, Sara POVEDA-REYES,
and Markus HECHT declare that they have no conflict of
interest.
Open access
This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits
use, duplication, adaptation, distribution and reproduction in
any medium or format, as long as you give appropriate credit to
the original author(s) and the source, provide a link to the
Creative Commons license and indicate if changes were made.
References
Andreas S, Allan Z, Joseph P, et al., 2012. Development of the
Future Rail Freight System to Reduce the Occurrences
and Impact of Derailment. D-RAIL Project Report, Eu-
ropean Commission.
Appel P, Hecht M, 2017. Möglichkeiten zur Lärmminderung
des Schienengüterverkehrs in Deutschland. Lärmbekä-
mpfung, 12(2):47-56 (in German).
Baeza L, Fayos J, Roda A, et al., 2008. High frequency railway
vehicle-track dynamics through flexible rotating wheel-
sets. Vehicle System Dynamics, 46(7):647-659.
https://doi.org/10.1080/00423110701656148
Belotti V, Crenna F, Michelini RC, et al., 2006. Wheel-flat
diagnostic tool via wavelet transform. Mechanical Sys-
tems and Signal Processing, 20(8):1953-1966.
https://doi.org/10.1016/j.ymssp.2005.12.012
Bernal E, Spiryagin M, Cole C, 2019. Wheel flat detectability
for Y25 railway freight wagon using vehicle component
acceleration signals. Vehicle System Dynamics, in press.
https://doi.org/10.1080/00423114.2019.1657155
Bosso N, Gugliotta A, Zampieri N, 2018. Wheel flat detection
algorithm for onboard diagnostic. Measurement, 123:
193-202.
https://doi.org/10.1016/j.measurement.2018.03.072
Braghin F, Lewis R, Dwyer-Joyce RS, et al., 2006. A mathe-
matical model to predict railway wheel profile evolution
due to wear. Wear, 261(11-12):1253-1264.
https://doi.org/10.1016/j.wear.2006.03.025
Bruni S, Alfi S, Gialleonardo ED, et al., 2016. Analysis of
Passive and Mechatronic Steering Bogie Solutions for
Freight Locomotives–Section 2.3 (Dynafreight-
Shift2Rail Poject). Report No. DYF-TSK2, 3-D-POL-
037-01, European Commission.
Burstow M, 2003. Whole Life Rail Model Application and
Development for RSSB–Development of an RCF Dam-
age Parameter. RSSB Report, AEATR-ES-2003-832 Is-
sue 1, Rail Safety & Standards Boards, London, UK.
Chaar N, Berg M, 2006. Simulation of vehicle–track interac-
tion with flexible wheelsets, moving track models and
field tests. Vehicle System Dynamics, 44(S1):921-931.
https://doi.org/10.1080/00423110600907667
Chowdhury R, Adhikari S, 2012. Fuzzy parametric uncertainty
analysis of linear dynamical systems: a surrogate mod-
eling approach. Mechanical Systems and Signal Pro-
cessing, 32:5-17.
https://doi.org/10.1016/j.ymssp.2012.05.002
Chrismer S, Selig ET, 1993. Computer model for ballast
maintenance planning. Proceedings of 5th International
Heavy Haul Railway Conference, p.223-227.
Elkhoury N, Hitihamillage L, Moridpour S, et al., 2018. Deg-
radation prediction of rail tracks: a review of the existing
literature. The Open Transportation Journal, 12(1):88-
104.
https://doi.org/10.2174/1874447801812010088
Enblom R, 2009. Deterioration mechanisms in the wheel–rail
interface with focus on wear prediction: a literature re-
view. Vehicle System Dynamics, 47(6):661-700.
https://doi.org/10.1080/00423110802331559
Falomi S, Malvezzi M, Meli E, 2011. Multibody modeling of
railway vehicles: innovative algorithms for the detection
of wheel–rail contact points. Wea r , 271(1-2):453-461.
https://doi.org/10.1016/j.wear.2010.10.039
Halama R, Fajkoš R, Matušek P, et al., 2011. Contact defects
initiation in railroad wheels–experience, experiments and
modelling. Wear , 271(1-2):174-185.
https://doi.org/10.1016/j.wear.2010.10.053
Han J, Zhong SQ, Xiao XB, et al., 2018. High-speed wheel/rail
contact determining method with rotating flexible
wheelset and validation under wheel polygon excitation.
Vehicle System Dynamics, 56(8):1233-1249.
https://doi.org/10.1080/00423114.2017.1408920
Hecht M, Leiste M, Jobstfinke D, et al., 2018. Roadmap zur
Digitalisierung der Wagentechnischen Untersuchung.
Technical Report, Technische Universität Berlin,
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
796
Germany (in German).
Higgins C, Liu X, 2018. Modeling of track geometry degra-
dation and decisions on safety and maintenance: a liter-
ature review and possible future research directions.
Proceedings of the Institution of Mechanical Engineers,
Part F: Journal of Rail and Rapid Transit, 232(5):1385-
1397.
https://doi.org/10.1177/0954409717721870
Liang B, Iwnicki SD, Zhao Y, et al., 2013. Railway wheel-flat
and rail surface defect modelling and analysis by time–
frequency techniques. Vehicle System Dynamics, 51(9):
1403-1421.
https://doi.org/10.1080/00423114.2013.804192
Lyon D, 1972. The calculation of track forces due to dipped
rail joints, wheel flats and rail welds. Proceedings of the
2nd ORE Colloquium on Technical Computer Programs.
Mitusch K, Hecht M, 2017. Lärm des Schienengüterverkehrs-
wie weiter nach Einführung der Verbundbremssohle.
ZEVrail, 141(8):294-300 (in German).
Öberg J, 2006. Track Deterioration of Ballasted Tracks: Mar-
ginal Cost Models for Different Railway Vehicles.
TRITA-AVE Report No. 88, Division of Rail Vehicles,
Royal Institute of Technology, Stockholm, Sweden.
Öberg J, Andersson E, 2009. Determining the deterioration
cost for railway tracks. Proceedings of the Institution of
Mechanical Engineers, Part F: Journal of Rail and Rapid
Transit, 223(2):121-129.
https://doi.org/10.1243/09544097jrrt222
Odolinski K, Nilsson JE, 2017. Estimating the marginal
maintenance cost of rail infrastructure usage in Sweden;
does more data make a difference? Economics of Trans-
portation, 10:8-17.
https://doi.org/10.1016/j.ecotra.2017.05.001
Pearce TG, Sherratt ND, 1991. Prediction of wheel profile wear.
Wear , 144(1-2):343-351.
https://doi.org/10.1016/0043-1648(91)90025-p
Peng B, Iwnicki S, Shackleton P, et al., 2019. Comparison of
wear models for simulation of railway wheel polygoni-
zation. Wear , 436-437:203010.
https://doi.org/10.1016/j.wear.2019.203010
Pombo J, Ambrósio J, Pereira M, et al., 2011. Development of
a wear prediction tool for steel railway wheels using three
alternative wear functions. Wea r, 271(1-2):238-245.
https://doi.org/10.1016/j.wear.2010.10.072
Regazzi D, Alfi S, Bruni S, et al., 2019. Cost-driven and
eliability-driven analysis of wagon condition data
(INNOWAG Project). European Commission.
https://cordis.europa.eu/project/rcn/206229/factsheet/en
Shenton MJ, 1984. Ballast deformation and track deterioration.
Proceedings of a Conference on Track Technology,
p.253-265.
Smith A, Iwnicki S, Kaushal A, et al., 2017. Estimating the
relative cost of track damage mechanisms: combining
economic and engineering approaches. Proceedings of
the Institution of Mechanical Engineers, Part F: Journal
of Rail and Rapid Transit, 231(5):620-636.
https://doi.org/10.1177/0954409717698850
Smith ASJ, Kaushal A, Odolinski K, et al., 2015. Estimating
the damage and marginal cost of different vehicle types
on rail infrastructure: combining economic and engi-
neering approaches. The Stephenson Conference: Re-
search for Railways, p.21-23.
Smith ASJ, Odolinski K, Saeed HN, et al., 2016. Estimating
the Marginal Cost of Different Vehicle Types on Rail In-
frastructure. Working Papers in Transport Economics,
KTH Royal Institute of Technology, Sweden.
https://ideas.repec.org/p/hhs/ctswps/2016_026.html
Smith RA, 2003. The wheel–rail interface—some recent ac-
cidents. Fatigue & Fracture of Engineering Materials &
Structures, 26(10):901-907.
https://doi.org/10.1046/j.1460-2695.2003.00701.x
Soleimanmeigouni I, Ahmadi A, Kumar U, 2018. Track ge-
ometry degradation and maintenance modelling: a review.
Proceedings of the Institution of Mechanical Engineers,
Part F: Journal of Rail and Rapid Transit, 232(1):73-102.
https://doi.org/10.1177/0954409716657849
Tao GQ, Du X, Zhang HJ, et al., 2017. Development and
validation of a model for predicting wheel wear in
high-speed trains. Journal of Zhejiang University-
SCIENCE A (Applied Physics & Engineering), 18(8):
603-616.
https://doi.org/10.1631/jzus.a1600693
Tao GQ, Ren DX, Wang LF, et al., 2018. Online prediction
model for wheel wear considering track flexibility.
Multibody System Dynamics, 44(3):313-334.
https://doi.org/10.1007/s11044-018-09633-5
Wheat P, Smith ASJ, 2008. Assessing the marginal infra-
structure maintenance wear and tear costs for Britain’s
railway network. Journal of Transport Economics and
Policy (JTEP), 42(2):189-224.
Wu XW, Rakheja S, Ahmed AKW, et al., 2018. Influence of a
flexible wheelset on the dynamic responses of a
high-speed railway car due to a wheel flat. Proceedings of
the Institution of Mechanical Engineers, Part F: Journal
of Rail and Rapid Transit, 232(4):1033-1048.
https://doi.org/10.1177/0954409717708895
Xin CF, Lu Q, Ai CF, et al., 2017. Optimization of hard modi-
fied asphalt formula for gussasphalt based on uniform
experimental design. Construction and Building Materi-
als, 136:556-564.
https://doi.org/10.1016/j.conbuildmat.2017.01.068
Ye YG, Sun Y, 2020. Reducing wheel wear from the perspec-
tive of rail track layout optimization. Proceedings of the
Institution of Mechanical Engineers, Part K: Journal of
Multi-body Dynamics, in press.
https://doi.org/10.1177/1464419320956831
Ye YG, Shi DC, Krause P, et al., 2020a. A data-driven method
for estimating wheel flat length. Vehicle System Dynamics,
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
797
58(9):1329-1347.
https://doi.org/10.1080/00423114.2019.1620956
Ye YG, Sun Y, Dongfang SP, et al., 2020b. Optimizing wheel
profiles and suspensions for railway vehicles operating on
specific lines to reduce wheel wear: a case study. Multi-
body System Dynamics, in press.
https://doi.org/10.1007/s11044-020-09722-4
Ye YG, Shi DC, Sun Y, et al., 2020c. Rotary-scaling fine-
tuning (RSFT) method for optimizing railway wheel
profiles and its application to a locomotive. Railway En-
gineering Science, 28(2):160-183.
Ye YG, Shi DC, Krause P, et al., 2020d. Wheel flat can cause or
exacerbate wheel polygonization. Vehicle System Dy-
namics, 58(10):1575-1604.
https://doi.org/10.1080/00423114.2019.1636098
Zobory I, 1997. Prediction of wheel/rail profile wear. Veh i cl e
System Dynamics, 28(2-3):221-259.
https://doi.org/10.1080/00423119708969355
中文概要
题目量化铁路车辆机械故障对轨道退化的影响
目的了解和量化铁路车辆机械故障对铁路基础设施退
化的影响有利于提高列车安全性,合理制定维护
策略,以及优化轨道收费模型。本研究为欧洲
Shift2Rail-Assets4rail 项目的一部分(报告以非公
开的形式被递交),旨在量化铁路车辆机械故障
对轨道退化的影响,为调整现有的轨道收费模型
提供合理的建议。
创新点:1. 分析一个常见的铁路车辆机械故障(擦伤)对
四个用于轨道收费模型的量化指标的影响;2.
入金代理模型方法以减少仿真次数。
方法1. 建立一个带有擦伤的机车多体动力学模型,并
考虑车轮和轨道的柔性;2. 引入金代理模型以量
化车辆速度和擦伤尺寸对四种损坏机制(轨道沉
轨道构件疲劳钢轨磨耗和钢轨滚动接触疲
劳)的影响。
结论1. 轨道沉降、轨道构件疲劳和钢轨磨耗随着擦伤
尺寸和车速的增加而急剧增加,并且这种增加趋
势随着擦伤尺寸和车速的增加而变得更加尖锐。
2. 在低速时,滚动接触疲劳随着擦伤尺寸的增加
而逐渐增加;在高速时,它首先急剧增加,然后
逐渐减小。3. 擦伤对轨道构件疲劳和钢轨磨耗的
影响最为显著,其次是轨道沉降和滚动接触
疲劳。
关键词:铁路车辆故障;轨道退化;量化;轨道收费;
擦伤
Appendix A
Table A1 Primary parameters of the locomotive
/
track model
Parameter Value
Vehicle frame mass (kg) 61 882
Bogie frame mass (kg) 4698.5
Wheelset mass (including axlebox) (kg) 3562
Motor mass (kg) 3068
Sleeper mass (kg) 330
Carbody roll moment of inertia
(kg·m2)
95 970
Carbody pitch moment of inertia
(kg·m2)
1 539 990
Carbody yaw moment of inertia
(kg·m2)
1 536 740
Bogie frame roll moment of
inertia (kg·m2)
2260
Bogie frame pitch moment of
inertia (kg·m2)
8480
Bogie frame yaw moment of
inertia (kg·m2)
10 360
Wheelset roll moment of inertia
(kg·m2)
2064
Wheelset pitch moment of inertia
(kg·m2)
573
Wheelset yaw moment of inertia (kg·m2)2064
Motor roll moment of inertia (kg·m2) 320
Motor pitch moment of inertia (kg·m2) 350
Motor yaw moment of inertia (kg·m2) 320
Distance between center pivots (m) 8.9
Wheel base (m) 2.8
Wheel rolling circle diameter (mm) 1250
Gauge distance (mm) 1435
Primary suspension stiffness
(each axlebox) (kN/m)
36 000, 4830,
2910
Secondary suspension stiffness
(each spring) (kN/m)
2265, 2265,
5570
Contact stiffness, kc (kN/m) Non-linear
Fastener stiffness, kfy, kfz (kN/m) 1700, 280 000
Ballast stiffness, kby, kbz (kN/m) 20 000, 75 000
Contact damping, cc (kN·s/m) 10
Fastener damping, cfy, cfz (kN·s/m) 5.5, 63
Ballast damping, cby, cbz (kN·s/m) 49, 94
Friction coefficient between
wheels and rails
0.35
Poisson’s ratio 0.28
Wheel profile S1002
Rail profile UIC60e2
Wheel-rail contact algorithm Hertzian contact+
FASTSIM
Ye et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2020 21(10):783-798
798
Appendix B
Table B1 Simulated results concerning Q, Ts, Tcf, Tγ, and Rcf
Velocity
(km/h)
Q (kN)
Lf=0 mm Lf=5 mm Lf=10 mm Lf=15 mm Lf=20 mm Lf=25 mm Lf=30 mm Lf=35 mm Lf=40 mm
30 138.772 204.644 364.763 543.094 745.865 905.407 1054.545 1211.643 1354.305
40 147.408 228.927 409.859 621.881 859.481 1064.443 1291.836 1524.398 1755.420
50 157.675 249.777 437.228 663.460 935.775 1164.950 1420.208 1691.860 1953.971
60 166.295 263.598 485.110 726.141 1019.990 1263.348 1543.853 1819.356 2096.783
70 176.524 283.405 543.348 796.832 1116.920 1369.828 1657.456 1963.951 2284.305
80 184.785 309.817 566.773 836.709 1171.126 1451.327 1767.410 2101.838 2417.527
90 217.001 315.049 591.014 867.626 1226.383 1518.982 1850.138 2209.940 2573.360
Velocity
(km/h)
Ts
Lf=0 mm Lf=5 mm Lf=10 mm Lf=15 mm Lf=20 mm Lf=25 mm Lf=30 mm Lf=35 mm Lf=40 mm
30 2 312 281 3 699 699 7 445 412 12 051 863 17 691 918 22 368 506 26 900 741 31 822 841 36 410 982
40 2 487 516 4 237 303 8 573 204 14 198 479 21 003 025 27 206 566 34 388 771 42 015 022 49 837 530
50 2 698 661 4 708 626 9 270 690 15 355 061 23 279 469 30 345 009 38 565 720 47 662 454 56 737 024
60 2 878 188 5 025 690 10 512 903 17 127 384 25 838 098 33 473 291 42 664 706 52 042 248 61 792 427
70 3 093 769 5 486 168 12 058 706 19 165 037 28 837 802 36 916 582 46 492 242 57 087 854 68 540 600
80 3 269 807 6 110 741 12 690 557 20 331 556 30 539 796 39 590 530 50 249 714 61 972 728 73 406 530
90 3 971 679 6 235 827 13 350 234 21 244 100 32 291 870 41 834 445 53 109 540 65 850 009 79 170 086
Velocity
(km/h)
Tcf
Lf=0 mm Lf=5 mm Lf=10 mm Lf=15 mm Lf=20 mm Lf=25 mm Lf=30 mm Lf=35 mm Lf=40 mm
30 7.550×10
16
9.326×10
1
6
1.759×10
1
73.581×10
1
77.227×10
1
71.158×10
1
8
1.708×10
1
8
2.458×10
1
8
3.310×10
1
8
40 8.113×10
16
1.021×10
1
7 2.103×10
1
74.731×10
1
71.009×10
1
8
1.736×10
1
8
2.896×10
1
8
4.537×10
1
8
6.696×10
1
8
50 8.664×10
16
1.159×10
1
7 2.390×10
1
75.478×10
1
71.245×10
1
8
2.191×10
1
8
3.726×10
1
8
6.023×10
1
8
8.999×10
1
8
60 9.383×10
16
1.268×10
1
7 2.919×10
1
76.761×10
1
71.551×10
1
8
2.717×10
1
8
4.676×10
1
8
7.364×10
1
8
1.096×10
1
9
70 1.044×10
1
7 1.440×10
1
7 3.704×10
1
78.494×10
1
71.971×10
1
8
3.386×10
1
8
5.695×10
1
8
9.130×10
1
8
1.397×10
1
9
80 1.225×10
1
7 1.759×10
1
7 4.275×10
1
79.901×10
1
72.285×10
1
8
4.032×10
1
8
6.902×10
1
8
1.118×10
1
9
1.658×10
1
9
90 1.557×10
1
7 2.002×10
1
7 4.791×10
1
71.085×10
1
8
2.567×10
1
8
4.534×10
1
8
7.785×10
1
8
1.279×10
1
9
1.969×10
1
9
Velocity
(km/h)
Tγ (N or J/m)
Lf=0 mm Lf=5 mm Lf=10 mm Lf=15 mm Lf=20 mm Lf=25 mm Lf=30 mm Lf=35 mm Lf=40 mm
30 8.000 13.081 33.409 86.876 166.700 255.295 353.385 472.513 599.063
40 10.223 16.563 44.613 111.808 208.900 312.986 451.807 632.564 805.492
50 12.565 21.548 59.440 133.973 257.471 388.604 558.205 762.245 1015.930
60 15.998 28.597 81.567 173.495 325.282 476.062 718.515 1018.48 1437.830
70 19.264 35.711 106.310 218.346 404.299 644.176 1018.350 1492.250 2168.330
80 20.723 41.936 127.814 268.715 543.879 899.166 1415.950 2065.450 2799.730
90 21.029 49.129 159.960 332.594 707.707 1178.000 1891.720 2513.870 3272.990
Velocity
(km/h)
Rcf (×105/axle)
Lf=0 mm Lf=5 mm Lf=10 mm Lf=15 mm Lf=20 mm Lf=25 mm Lf=30 mm Lf=35 mm Lf=40 mm
30 0 0 0.092 0.537 0.991 1.371 1.889 2.228 2.342
40 0 0 0.151 0.684 1.061 1.670 2.219 2.786 3.112
50 0 0 0.219 0.739 1.249 2.022 2.740 3.307 3.685
60 0 0 0.324 1.029 1.720 2.388 3.512 4.504 4.764
70 0 0 0.409 1.333 2.050 3.712 5.638 6.302 6.714
80 0 0 0.521 1.647 3.017 5.833 8.048 8.778 8.507
90 0 0 0.765 1.993 4.581 7.843 9.623 10.172 9.561
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