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Research Papers

# Wheel–Rail Impact at Crossings: Relating Dynamic Frictional Contact to DegradationOPEN ACCESS

[+] Author and Article Information
Zilong Wei

Section of Railway Engineering,
Faculty of Civil Engineering and Geosciences,
Delft University of Technology,
Stevinweg 1,
Delft 2628 CN, The Netherlands
e-mail: Z.Wei@tudelft.nl

Chen Shen

Section of Railway Engineering,
Faculty of Civil Engineering and Geosciences,
Delft University of Technology,
Stevinweg 1,
Delft 2628 CN, The Netherlands
e-mail: C.Shen-2@tudelft.nl

Zili Li

Section of Railway Engineering,
Faculty of Civil Engineering and Geosciences,
Delft University of Technology,
Stevinweg 1,
Delft 2628 CN, The Netherlands
e-mail: Z.Li@tudelft.nl

Rolf Dollevoet

Section of Railway Engineering,
Faculty of Civil Engineering and Geosciences,
Delft University of Technology,
Stevinweg 1,
Delft 2628 CN, The Netherlands
e-mail: R.P.B.J.Dollevoet@tudelft.nl

1Corresponding author.

Contributed by Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 18, 2016; final manuscript received January 19, 2017; published online February 8, 2017. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 12(4), 041016 (Feb 08, 2017) (11 pages) Paper No: CND-16-1082; doi: 10.1115/1.4035823 History: Received February 18, 2016; Revised January 19, 2017

## Abstract

Irregularities in the geometry and flexibility of railway crossings cause large impact forces, leading to rapid degradation of crossings. Precise stress and strain analysis is essential for understanding the behavior of dynamic frictional contact and the related failures at crossings. In this research, the wear and plastic deformation because of wheel–rail impact at railway crossings was investigated using the finite-element (FE) method. The simulated dynamic response was verified through comparisons with in situ axle box acceleration (ABA) measurements. Our focus was on the contact solution, taking account not only of the dynamic contact force but also the adhesion–slip regions, shear traction, and microslip. The contact solution was then used to calculate the plastic deformation and frictional work. The results suggest that the normal and tangential contact forces on the wing rail and crossing nose are out-of-sync during the impact, and that the maximum values of both the plastic deformation and frictional work at the crossing nose occur during two-point contact stage rather than, as widely believed, at the moment of maximum normal contact force. These findings could contribute to the analysis of nonproportional loading in the materials and lead to a deeper understanding of the damage mechanisms. The model provides a tool for both damage analysis and structure optimization of crossings.

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## Introduction

Switches and crossings (S&C, turnouts) intersecting different tracks at the same level are fundamental components of track systems. Because of irregularities in the geometry and flexibility of S&C, such as the gap between the closure rail and the crossing nose as well as the variation in the sleeper spans, high dynamic forces can be exerted as vehicles pass. The resulting degradation of S&C happens much faster than that of plain tracks, increasing maintenance costs and disrupting the operation of railway networks. For example, 7195 crossings served the Dutch railway network in the year 2012 [1]; of these, about 400 crossings were replaced, and 100 of these replacements were urgently required [2]. Figure 1 shows two examples of crossing degradation. The crossing in Fig. 1(a) required urgent replacement because of two severe cracks: one 220–280 mm from the tip of the crossing nose, and the other longer, forming at 170–330 mm from the tip of the crossing nose. The crossing in Fig. 1(b) deformed significantly because of cumulative plastic deformation and wear over long-term usage. The crossing was later maintained by welding and grinding.

Measures have been developed and applied to decrease the dynamic force and the resulting damage at S&C, e.g., movable point frog which is widely used on high-speed lines. However, rigid crossings are still common on conventional railway lines, and it is difficult to significantly decrease crossing damage using the current design, construction, and maintenance methods. A better understanding is therefore needed for the characteristics of wheel–rail frictional contact at crossings, especially that corresponding to impact.

The multibody dynamics (MBD) method is often used for the analysis of dynamic wheel–rail interactions at crossing panels. In this method, the vehicle and crossing components are modeled as combinations of rigid or flexible bodies, springs, and dampers. To account for the variations in geometry and flexibility of the crossing panel, Andersson and Dahlberg [3] developed a simplified numerical model in which the vehicle is modeled using the MBD method, and the rails and sleepers are treated as beams. Regarding the contact between wheels and rails, only the normal solution was taken into account using nonlinear Hertz spring, whereas the tangential solution was neglected. This approach was improved by Kassa and Nielsen [4] by including the missing degrees-of-freedom of both vehicle and crossing panel, e.g., the lateral translation as well as the yaw and pitch rotation of a vehicle. This allowed the vehicle to move in a diverging route. The tangential solution of the wheel–rail interaction was considered using fastsim. Similar methods were also developed in other studies [512]. In these approaches, the solution of the wheel–rail contact is restricted by the linear elasticity and half-space assumption, which makes these methods incapable of treating nonlinear material behavior such as plastic deformation and strain rate dependency. In addition, because frictional contact and structural vibration are solved independently, the influence of the dynamic wheel–rail interaction on the evolution of frictional contact, for example, by the inertia effect or wave propagation, may not be properly taken into account.

With the rapid development of computational power, the finite-element (FE) method attracts more attentions as an alternative approach for the study of dynamic wheel–rail interactions. Li et al. [13] successfully simulated wheel–rail impact using the FE method in a study of short wavelength defects on straight tracks. However, the interaction between the wheelset and the crossing is more complicated by the complex contact geometry and structure of the crossing panel. The dynamic behavior of wheels passing through a crossing was studied by Wiest et al. [14] in which the plastic deformation of the crossing nose because of cyclic loading was investigated. In their model, the gap between the closure rail and crossing nose was neglected. Instead, the geometric irregularity was modeled by inclining the crossing nose with an angle. However, this simplification is unable to yield accurate dynamic responses and precise contact solutions. A more sophisticated FE model of a wheel passing through a crossing was presented by Pletz et al. [15]. Their model included a wheel with constant loading on the axle and a section of crossing panel suspended on a Winkler foundation. The focus of their work was on the normal contact, whereas the analysis on the tangential problem, which is essential for an insightful understanding of the frictional contact behavior, such as tangential force and surface shear traction, is incomplete. Besides, further verification is required for the normal solution, because the simulated dynamic contact force produces different outcomes to both other numerical approaches and in situ measurements (see Fig. 9 in Ref. [16]). Recently, in situ axle box acceleration (ABA) measurements have been shown to be capable of detecting short wavelength irregularities in straight tracks [1719] by identifying certain characteristic responses. The complex geometry of crossings can be regarded as a kind of irregularity, and ABA measurement should be able to capture the characteristic dynamic responses of wheel–rail impact at crossings.

In this paper, a contact model capable of simulating wheel–rail impact at crossing panels was developed using the FE method. Precise contact solutions during the impact were obtained and used for the analysis of crossing nose degradation. The structure of this paper is as follows: The modeling of the wheelset and the crossing panel and the calculating procedure are described in Sec. 2. In Sec. 3, the simulated dynamic response is verified using in situ ABA measurements. In Sec. 4, the evolution of frictional contact during the impact is examined. Special attention is paid to the reliable contact solution, including not only dynamic contact force but also particularly the distribution of adhesion–slip regions, shear traction, and microslip. In Sec. 5, the contact solution is then used to calculate the degradation of the crossing caused by plastic deformation and wear. The results are discussed in Sec. 6, and the main conclusions are drawn in Sec. 7.

## Modeling of Wheelset and Crossing Panel

The crossing used in this study is a right-hand constructed turnout of the 54E1-1:9 type with a nominal rail profile of UIC54 and a crossing angle of 1:9. An overview of the crossing is given in Fig. 2. The length of the crossing model was 17.8 m, which is equal to 30 sleeper spans and which has proved to be reasonable for the wheel–rail impact [20]. The rails and sleepers were modeled with solid elements, while the rail pads and ballast were modeled as linear springs and viscous dampers. The modeling of the rail pads and ballast is shown in Fig. 3. A rail pad consists of a uniform grid of 3 × 4 discretely distributed spring–damper pairs, divided into three rows (along the longitudinal direction x in Fig. 1) and four columns (along the lateral direction y in Fig. 1). The ballast under each sleeper consists of a uniform grid of 3 × 9 discretely distributed spring–damper pairs, divided into three rows and nine columns. The parameters of the rail pad and ballast were obtained from in situ hammer test on the Dutch railway [21]. The stiffness and damping were 1560 MN/m and 67.5 kNs/m for a standard rail pad, with the corresponding values for each spring–damper pair being 130 MN/m (1560/12) and 5.6 kNs/m (67.5/12). The stiffness and damping of the ballast were 90 MN/m and 64 kNs/m for a standard concrete sleeper, with the corresponding values for each spring–damper pair being 3.3 MN/m (90/27) and 2.4 kNs/m (64/27).

One wheelset of a Dutch ICR type locomotive was modeled using solid elements, whereas both the car body and the bogie were simplified as a lumped mass and supported on the wheelset axle by linear springs and viscous dampers. The wheel profile was UIC S1002, the axle load was 16 ton, and the stiffness and damping of the primary suspension were 1150 kN/m and 2500 Ns/m, respectively.

A three-dimensional Cartesian coordinate was adopted, with the axes $x$, $y$, and $z$ oriented in the longitudinal, lateral, and vertical directions. The origin $o$ was at the intersection of the three planes: the $xy$ plane across the rail foot, the $xz$ plane across the centerline of the through track, and the $yz$ plane across the tip of the crossing nose. In the FE model, the motion of the wheelset is defined as follows:

• Longitudinal translation and rolling rotation about the$y$ axis: They are prescribed by specifying the driving torque and the initial angular velocity on the wheelset and specifying the initial translational velocity on both the car body and wheelset.

• Lateral translation and yaw rotation about the$z$ axis: No constraints are imposed on them. The wheelset follows the through route guided by the wheel–rail contact, and the resulted lateral displacement and yaw angle can happen yet with small values (e.g., the lateral displacement is smaller than 1 mm in Ref. [22]).

If the divergent motion of the wheelset is simulated in further work, the lateral displacement and yaw angle become large. Consequently, the mutual influence between these motions and the dynamic contact solutions will be significant. In such a case, the mutual influence can be obtained from MBD simulations or in situ measurements and then be specified in the FE model.

• Vertical translation and roll rotation about the$x$ axis: They are a part of the dynamic response of wheel–rail interaction, so that the values can neither be specified at the initial stage nor be fixed.

To account for the plastic deformation of the wheelset and the rail, a bilinear elastoplastic material model was employed. The wheelset is made of 35CrMo steel, with the density, Young's modulus, yield strength, and Poisson's ratio being 7800 kg/m3, 210 GPa, 835 MPa, and 0.29, respectively. The rail is made of Hadfield steel, with the density, Young's modulus, yield strength, and Poisson's ratio being 7800 kg/m3, 190 GPa, 1000 MPa, and 0.3, respectively [23]. The friction between the wheelset and the rail was defined using Coulomb's friction law, and the friction coefficient μ was set to 0.5 for dry and clean wheel–rail contact surfaces.

The commercial code aysys/ls-dyna was used in this study. In the FE model, all continua, i.e., wheelset, rails, and sleepers, were meshed with eight-node solid elements, with a minimum element size of $0.6×0.6$ mm in the contact patch, see the inset in Fig. 3. The capacity of the proposed FE model in analyzing the dynamic wheel–rail interaction is demonstrated in Ref. [24], where the contact solutions in terms of adhesion–slip state, contact stresses, and microslip coincide well with the Hertz theory and Kalker's computer program contact. For more generalized contact problems, the FE solutions are validated with Spence's semi-analytical method for frictional compression, Cattaneo's analytical method for frictional shift, and Kalker's contact for frictional rolling [25]. The FE model should be able to produce reliable contact solutions during wheel–rail interaction at crossings.

The dynamic response and contact solution of the FE model are obtained with a combination of a static analysis using an implicit integration method and a dynamic analysis using an explicit integration method. The static analysis is used to calculate the static equilibrium under gravity assuming that the wheelset stands still on the crossing. This step is necessary to avoid the unrealistic vibration that may be caused by in-equilibrium state of the system. The nodal displacements calculated from the static analysis define the initial state of the dynamic analysis when stress initialization is performed in the explicit integration method. Thereafter, initial translational and angular velocities as well as driving torque are applied on the wheelset and car body to simulate the passage of the wheelset on the crossing.

The initial kinematic and dynamic solutions were obtained in a global three-dimensional Cartesian coordinate system. To determine the detailed contact solution in the contact patch, e.g., shear traction, microslip, and frictional work, a local coordinate system is required. A fortran program was developed for deriving the coordinate transformation and for calculation of the adhesion–slip regions, microslip, and frictional work in the contact patches.

In the explicit analysis, the kinematic and dynamic results (e.g., nodal displacement and force) are calculated in the global coordinate system oxyz. These nodal results are then projected to local Cartesian coordinate o′αβγ using Eqs. (1) and (2) of Ref. [26]. In the local coordinate o′αβγ, the origin o′ is invariably located at the contact patch center and moves with it, with the axes α, β, and γ oriented in the rolling, transversal, and normal directions, as shown in Fig. 4. Thereafter, the contact solutions can be obtained in each local coordinate system. A node is located in the contact patch if

Display Formula

(1)$|Fn_N|≥εN$

In addition, the node is located in the adhesion region if Display Formula

(2)$μ|Fn_N|−|Fn_T|≥εT$

where $Fn_N$ is the normal nodal force along the normal direction γ; $Fn_T$ is the tangential nodal force in the tangent plane o′αβ; and $εN$, and $εT$ are the tolerances. Here, $εN$ is set to be 0.15% of the maximum normal nodal force on the rail surface, while $εT$ is set to be 0.4% of the maximum tangential force on the rail surface.

The frictional work at a node of the rail surface $Wf$ is calculated as [27] Display Formula

(3)$Wf=∫0tτs dt=∑i=1nτisiΔt$

where $τ$ and $s$ are the surface shear traction and microslip, and $Δt$ is the output time step. Here, $Δt$ is set to $4×10−5 s$, at which the wheelset translates 0.84 mm along the longitudinal direction x with the speed of 21 m/s.

## Verification of the Simulated Dynamic Response Using ABA Measurement

In situ ABA measurement was employed to verify the simulated dynamic response of the wheel–rail interaction at the crossing panel. An accelerometer was mounted on the axle box in the vertical direction, and a Global Positioning System locator was used to record the location of the acceleration signal and the train speed. The ABA signal was recorded at a sampling frequency of 25.6 kHz and was further low-pass filtered with the frequency of 1 kHz. The crossing was in good condition during the measurement. To confirm the replicability and reliability, the measurement was taken twice using the same train on the same crossing panel. In both measurements, the train passed through the crossing panel with approximately 21 m/s in the facing-through direction (see Fig. 2).

Figure 5 shows the time history of the ABA signals. To obtain an insight into the characteristic time and frequency response of wheel–rail impact at crossings, wavelet transform analysis was used to extract the characteristic waveform from the measured and simulated ABA signals. In wavelet analysis, the signal processing is independent of the window size, making it suitable for investigating the transient processes of brief events. Figure 6(a) compares the wavelet power spectrum between the measured and simulated ABA, where the scale shows the amount of energy concentrated at a certain location (the horizontal axis) and frequency (the vertical axis). Figure 6(b) shows the global wavelet spectra, defined as the wavelet spectrum averaged over the location at each frequency [28].

As can be seen from Fig. 6, the measured and simulated signals were in good agreement in terms of the major frequency contents, wavelet power, and impact position. The FE model captured the three major frequency characteristics, which arose around 35, 90, and 250 Hz (marked with white rectangles). The frequencies around 90 and 250 Hz were in the region where the wheelset jumped from the wing rail to the crossing nose (also see Fig. 8), and were therefore related to the impact of the wheelset on the crossing nose. The 35 Hz frequency appeared before the impact region and was distributed along a longer distance, and at first glance seems irrelevant to the impact. However, the wavelet power, depicted by the color, is higher around the impact region than elsewhere, suggesting that this frequency was also further excited by the impact.

Field observations (e.g., Fig. 2 in Ref. [12] and Fig. 2(c) in Ref. [14]) have shown that degradation will develop and accumulate at the location of the impact, exacerbating the impact, and extending and accelerating the degradation. It is thus highly likely that in degraded conditions, the energy concentration can occur at a frequency higher than 250 Hz.

Because of randomness in the train–track system, the moving trajectory of the wheelset was different at each measurement. Therefore, each measured signal was somewhat different, as shown in Fig. 6. For the same reason, it was difficult to achieve a precise match between the measurements and the simulation. Nevertheless, the major characteristics could be captured. It can be concluded that the FE model is able to represent the main dynamic characteristics of wheel–rail impact at crossing panel.

## Evolution of Frictional Rolling Contact

The evolution of the frictional rolling contact as the wheelset passed through the crossing panel was investigated, and the adhesion–slip regions, pressure, surface shear traction, and microslip on the local surface of the wheel were determined. In the simulation, the wheelset passed through the crossing panel at 21 m/s in the facing-through direction. The wheelset is driven by a constant torque prescribed on the axle, which is expected to generate a longitudinal traction force equal to 30% of the static normal load when the inertia of the wheelset is ignored. During dynamic wheel–rail interaction, the ratio of the tangential contact force to the normal contact force varies with time along the track, and its variation can be exacerbated by the geometric discontinuity of crossings.

Figure 7 shows the time series of the normal contact force. As can be seen, the force on the stock rail fluctuated around the static load (84.3 kN), and the amplitude of the fluctuation reached a maximum of 24.9% during the transition. The force on the closure/wing rail fluctuated with a similar amplitude until the wheel jumped from the wing rail to the crossing nose. During the jump, the normal contact force on the wing rail dropped while the force on the crossing nose rose sharply, reaching its maximum value of 167.1 kN within 2 ms. This is approximately double the static load. Thereafter, the normal contact force decreased, returning to the static load.

To gain an insight into the evolution of the frictional contact during the transition, four instants (see Fig. 7) were selected and a detailed analysis of the contact solutions was made at these instants. Figure 8 shows the contact status at each instant. The location of the contact patch when the wheelset was on the closure rail is given in Fig. 8(a), where the contact was between the wheel tread and the rail top. Because the longitudinal axis of the wing rail was no longer aligned with the rolling direction of the wheelset (see Fig. 2), the contact patch moved toward the field side of the wheel tread from $t1$ to $t2$, as shown in Fig. 8(b).

Because the lateral–vertical sectional profile of the crossing nose widened along the longitudinal direction, the flange root of the wheel started to make contact with the crossing nose as the wheel rolled further from $t2$ to $t3$. Hence, the situation of two-point contact occurred, an example of which is shown in Fig. 8(c). Thereafter, the wheel gradually lost its contact with the wing rail and was supported solely by the crossing nose. Figure 8(d) shows the moment when the normal contact force on the crossing nose reached its maximum value. Note that the longitudinal coordinates $x$ of the two contact patches at $t3$ (Fig. 8(c)) were different, being 240.46 mm on the wing rail and 248.39 mm on the crossing nose, respectively. This was attributed to the complex geometry of the crossing nose, in particular the rise in its height along the rolling direction (see Fig. 1(b)). As a result, the center of the contact patch on the crossing nose shifted forward in the rolling direction.

Table 1 summarizes the contact solution at the four instants, and Fig. 9 presents the evolution of the adhesion–slip regions during the transition. As shown in Fig. 9(a), the contact patch approximated the shape of an ellipse at $t1$. When the wheelset arrived at the wing rail, the contact patch rotated slightly clockwise (see Fig. 9(b)) and becomes longer and narrower because of the misalignment between the rolling direction of the wheelset and the longitudinal axis of the wing rail. The size of the contact patch dropped by 6% from $t1$ to $t2$, whereas the adhesion region increased from 51% to 69%.

As soon as the wheelset got contact with the crossing nose, the contact patch on the crossing nose grew whereas that on the wing rail shrank. At $t3$, the two contact patches were of equal width, but significantly different lengths (Fig. 9(c)). This reflected the different radii of the wheel and rail profiles at their respective contact patches. The lateral radius of the wheel flange root is smaller than that of the wheel tread, whereas the lateral radius of the crossing nose was smaller than that of the wing rail. The two contact patches on the crossing nose shown in Figs. 9(c) and 9(d) appeared similar. The length and width, which were influenced by the widening of the crossing nose in the rolling direction, increased by 11% and 25% from $t3$ to $t4$, respectively. The sectional profile of the crossing nose would eventually evolve into the normal UIC54 type, and the distribution of adhesion–slip regions would be again analogous to that at $t1$.

Figure 10 shows the field of the surface shear traction during the transition. The maximum value of the shear traction was at the junctions between the adhesion and slip regions. At $t1$, the shear traction vectors are pointed in approximately the moving direction of the wheelset. The small lateral components observed in Fig. 10(a) can be attributed to geometric spin arising from the contact angle between the rolling axis of the wheelset and the local areas of the contact patch (see Fig. 8(a)). As soon as the wheelset arrived at the wing rail, the rolling direction of the wheelset was no longer aligned with the longitudinal axis of the wing rail, and the contact patch moved from the tread toward the field side of the wheel. As a result, lateral creepage arose, and the lateral components of the shear traction at $t2$ become larger (see Fig. 10(b)).

During the two-point contact, the shear traction vectors on the wing rail turned further clockwise (Fig. 10(c)) to almost the lateral direction by $t3$. The change in direction can be explained by the distribution of the frictional force during the two-point contact, as shown in Fig. 11(a). The longitudinal contact force on the wing rail decreased quickly to zero once the two-point contact occurred, whereas the decrease in the lateral contact force on the wing rail started later. The lateral contact force on the wing rail therefore remained, and the lateral shear traction on the wing rail in Fig. 10(c) becomes dominant. The lateral contact force on the wing rail took longer to disappear, because the lateral creepage raised as a result of the misalignment between the longitudinal axis of the wing rail and the rolling direction of the wheel, as mentioned above.

Between $t3$ and $t4$, the contact force on the wing rail quickly decreased to zero, and the crossing nose turned to solely take over the wheel load. The lateral contact force on the crossing nose consisted of three constituents. The first was the lateral component of the wheel load, which pointed toward the wheel flange. The other two were lateral creep forces pointing to the field side of the wheel. One of these was from geometric spin, and its value was determined by the contact angle; the other was attributed to the misalignment between the trajectory of the contact patch and the moving direction of the wheel (see Fig. 11(b)). In the current case, the latter constituent was dominant. In practice, such a high lateral creep force combined with the impact loading could cause the large plastic flow and cracks shown in Fig. 1(a). At $t4$, both two-point contact and the misalignment of the wing rail disappeared, as did their contribution to the lateral shear traction. However, the misalignment caused by the widening of the crossing nose still persisted. In brief, the lateral shear traction in Fig. 10(d) was mainly because of the misalignment, and to a lesser extent to the contact angle.

As shown in Fig. 11(a), the variations in the normal, longitudinal, and lateral contact forces were out-of-sync. On the one hand, both the normal and lateral forces on the crossing nose rose from $t3$ to $t4$, whereas the longitudinal force decreased. On the other hand, the decrease in the normal and lateral forces on the wing rail took more time than that of the longitudinal force. The normal, longitudinal, and lateral forces all reached their maxima between 0.25 and 0.27 m, whereas the crossing nose was still much narrower than the UIC54 profile (Figs. 8(c) and 8(d)) and had a lower bearing capacity. It is reasonable to expect this region to be vulnerable to damage (see Fig. 1). The out-of-sync dynamic forces exert the nonproportional loading in the materials and may significantly influence the initiation and growth of rolling contact fatigue (RCF) [29]. These out-of-sync peak forces arise from the combination of the geometry and structure of the crossing panel, the misalignment of the wing rail and crossing nose, and the change in the contact angle. It is possible to optimize the geometry and structure of the crossing panel so as to minimize the forces during the impact, which will not only improve the ride quality of vehicles but will also decrease the contact stresses and related damages.

Figure 12 shows the distribution of shear traction along the local longitudinal axis. Note that, because of the complex contact geometry, the maximum pressure and shear traction at each instant may not locate at the same local longitudinal axis. For illustration purposes, the local lateral coordinates of the axes as well as the traction bound, which is the pressure multiplied by the friction coefficient, are given. As can be seen, the peaks in the shear traction at all the selected instants occurred in the rear half of the contact patches. The pressure on the closure rail reached a maximum of 1317.6 MP at $t1$ and increased by 33% at $t2$, followed by a decrease as soon as the two-point contact occurred, whereas the maximum surface shear traction decreased by 11% from $t1$ to $t3$. The maximum stresses were significantly higher on the crossing nose than on the closure/wing rail. A 75% increase in the pressure and a 39% increase in the surface shear traction were observed from $t1$ to $t4$.

Figure 13 shows the field of microslip during the transition. There was no microslip in the adhesion regions. The microslip in the slip regions was in an opposite direction to that of the surface shear traction, and the maximum microslip occurred around the trailing edge of the contact patch. The magnitudes of the microslip, indicated by color, increased progressively during the transition, with the maximum value increasing by 84% from $t1$ to $t4$. It can be seen from Figs. 13(c) and 13(d) that the distributions of the microslip at $t3$ and $t4$ were not as regular as those in the earlier instants. This is because dynamic interactions between solids, especially during impact, inherently contain high-frequency vibrations and waves. The vibrations and waves cause loading and unloading at local areas of the contact patch, resulting in a local change in the magnitude of microslip. The effect of this loading and unloading on the distribution of microslip becomes significant at $t3$ and $t4$ because of the impact.

As shown in Figs. 10 and 13, both shear traction and microslip grew in magnitude during the impact, with a 39% increase in the maximum shear traction and an 84% increase in the maximum microslip from $t1$ to $t4$. The combination of high microslip with high shear traction can produce high frictional power, speeding up the degradation of crossings.

## Degradation of the Crossing Nose During the Impact

In this section, the degradation of the crossing nose by plastic deformation and wear during the impact is discussed, and the relationship between the trajectory of the contact patch and the degradation of the crossing nose is analyzed.

The von Mises yield criterion was employed to calculate the plastic deformation. Figure 14(a) shows the distribution of the maximum von Mises stress along the longitudinal axis of the crossing nose. As can be seen, there was no plastic deformation in the initial stage of the two-point contact because of the small loads. As the load in the material exceeded the yield strength, plastic deformation grew quickly. Here, plastic deformation of the crossing nose is distributed in the range of 230–330 mm from the tip of the crossing nose. The maximum von Mises stress of 1279 MPa occurred during two-point contact. After this, the value of von Mises stress decreased monotonically. At $t4$, the value was 1265 MPa, a drop of 1.1% from the maximum value.

Figure 14(b) shows the trajectories of the maximum von Mises stress as well as the center of the contact patch. In general, the two trajectories were close to each other. The difference between the two trajectories can be mainly attributed to the complex contact geometry and the nonproportional loading conditions. Because the crossing nose widened along the longitudinal direction, the trajectory of the contact patch misaligned with the rolling direction of the wheelset, leading to large lateral creep forces. The lateral coordinate of the maximum von Mises stress increased with the movement of the wheel until the crossing nose profile evolved into the standard UIC54 type.

It is often assumed that wear is proportional to frictional work [30,31]. Figure 15(a) shows the distribution of the maximum frictional work along the longitudinal axis of the crossing nose. As can be seen, the maximum frictional work grew rapidly while the wheel was in touch with the crossing nose, reaching a peak of 2.85 × 104 J/m2 shortly after $t3$. The maximum frictional work and plastic deformation occurred at approximately the same time. At $t4$, when the normal contact force reached its peak, the frictional work dropped to 2.21 × 104 J/m2, or 22.5% of the maximum value. Thereafter, the maximum frictional work fluctuated downward, eventually stabilizing at around 0.56 × 104 J/m2.

Figure 15(b) compares the trajectories of the maximum frictional work and the center of the contact patch during the impact. The maximum frictional work occurred around the center of the contact patch with some fluctuations. Similar fluctuations can be observed in Fig. 14(b), but are more frequent in Fig. 15(b). Because frictional work is the product of shear traction and microslip [27] and reflects their nonsmoothness (see Figs. 10 and 13), the distribution of frictional work is not as smooth as that for plastic deformation.

## Discussion

In Sec. 5, it was noted that the maximum values for both plastic deformation and frictional work appeared during two-point contact rather than at the moment of maximum normal contact force. The degradation of the crossing can therefore be attributed to the combined effect of the normal, longitudinal, and lateral contact forces. Their nonproportionality should be taken into account [29]. This highlights the necessity for detailed analysis of stress and strain during the impact, to develop an insightful understanding of the initiation and growth of crossing degradation.

In this research, we have demonstrated the capacity of the FE model to analyze the plastic deformation and frictional work of the crossing nose. Regarding degradation such as RCF, the contact solution obtained from the FE model can also provide accurate input for damage prediction [3235].

The analysis of crossing degradation presented in Sec. 5 is based on a single wheelset passage, and the effect of material hardening under cyclic loading was not considered. In future work, the performance of crossing panel in terms of RCF resistance under cyclic loading will be studied. This will be done by simulating multiple wheel passages and then estimating the crossing degradation over a long term.

###### Application of Anomaly Detection at Crossings.

The present work has established a correlation between measured and simulated ABA signals. The FE model can be further employed to reproduce the ABA signal in the presence of track structural anomalies and to extract the signature waveform of ABA signal, which should allow anomalies at the crossing panel to be detected.

###### Motion of Vehicles.

In this study, the motion of the vehicle was in the through route. For other scenarios, for example, the motion in the diverging direction, the trajectory of the wheelset would be more complex. Although the FE method is capable of modeling a bogie or a whole vehicle in the way similar to the MBD method, the computational procedure would be extremely time-consuming. In further work, the trajectories of the wheelset will be investigated using in situ measurement [36] or vehicle dynamics simulation [37] to represent realistic movement of the wheelset.

## Conclusions

In this research, wheel–rail impact at crossing panel was investigated using the FE method. The model was first verified by comparing the simulated axle box acceleration with in situ measurements in terms of the major frequency contents, wavelet power, and impact position. Special attention was paid to reliable contact solutions that help extend our understanding of crossing degradation. The contact solution took account not only of the dynamic contact force but also the distribution of adhesion–slip regions, pressure, surface shear traction, and microslip. The contact solution was then used to calculate the plastic deformation and frictional work of the crossing nose during one wheelset passage. The following conclusions are drawn:

1. (1)The variations of the normal contact force and the tangential force on both the wing rail and the crossing nose are out-of-sync during the impact. This can lead to nonproportional loading in the materials and should be taken into account in damage analysis.
2. (2)The longitudinal axis of the wing rail is misaligned with the wheelset rolling direction. The widening of the crossing nose also causes misalignment between the wheelset rolling direction and the trajectory of the contact patch. The misalignment causes large lateral creepage, often resulting in severe plastic flow and wear.
3. (3)At the two-point contact stage, the decrease in the lateral contact force on the wing rail is slower than that of the longitudinal contact force, and the vectors of shear traction and microslip on the wing rail therefore point almost toward the lateral direction. After the two-point contact, the longitudinal contact force on the crossing nose begins to decrease, whereas the increase in the lateral contact force speeds up.
4. (4)By optimizing the geometry and the structural design of the crossing panel, it is possible to minimize the forces and therefore the degradation. The relationship between the plastic deformation, the frictional work, the geometry, and the structure can be used for the optimization and performance prediction.
5. (5)The locations of the maximum values along the crossing nose do not coincide with the moving trajectory of the contact patch because of the complex contact geometry and the nonproportional loading condition.
6. (6)Under the assumption of nominal contact geometry and facing-through motion of vehicles with the loading conditions studied, the maximum values of both the effective plastic deformation and the frictional work of the crossing nose occur during the two-point contact transition from the wing rail to the crossing nose rather than, as widely believed, at the moment of maximum normal contact force. For other scenarios such as degraded contact profiles and divergent motion of vehicles, more experimental and numerical works are required in further study, in an effort to obtain a more comprehensive understanding of the behavior of dynamic wheel–rail interaction and the related failures at crossings.

## Acknowledgements

The authors would like to thank the China Scholarship Council (CSC) for financial support for the first author. This research was supported by the Dutch Technology Foundation STW, which is part of The Netherlands Organisation for Scientific Research (NWO) and is partly funded by the Ministry of Economic Affairs.

## References

ProRail, 2015, “ Jaarverslag ProRail 2015,” Technical Report, p. 127.
Shevtsov, I. Y. , 2013, “ Rolling Contact Fatigue Problems at Railway Turnouts—Experience of ProRail,” Meeting Materials: Materials Under Combined Durability Conditions, Lochristi, Belgium, p. 20.
Andersson, C. , and Dahlberg, T. , 1998, “ Wheel/Rail Impacts at a Railway Turnout Crossing,” Proc. Inst. Mech. Eng., Part F, 212(2), pp. 123–134.
Kassa, E. , and Nielsen, J. C. , 2009, “ Dynamic Train–Turnout Interaction in an Extended Frequency Range Using a Detailed Model of Track Dynamics,” J. Sound Vib., 320(4), pp. 893–914.
Alfi, S. , and Bruni, S. , 2009, “ Mathematical Modelling of Train–Turnout Interaction,” Veh. Syst. Dyn., 47(5), pp. 551–574.
Bruni, S. , Anastasopoulos, I. , Alfi, S. , Van Leuven, A. , and Gazetas, G. , 2009, “ Effects of Train Impacts on Urban Turnouts: Modelling and Validation Through Measurements,” J. Sound Vib., 324(3), pp. 666–689.
Johansson, A. , Pålsson, B. , Ekh, M. , Nielsen, J. C. , Ander, M. K. , Brouzoulis, J. , and Kassa, E. , 2011, “ Simulation of Wheel–Rail Contact and Damage in Switches and Crossings,” Wear, 271(1), pp. 472–481.
Pålsson, B. A. , and Nielsen, J. C. , 2012, “ Wheel–Rail Interaction and Damage in Switches and Crossings,” Veh. Syst. Dyn., 50(1), pp. 43–58.
Sun, Y. Q. , Cole, C. , and McClanachan, M. , 2010, “ The Calculation of Wheel Impact Force Due to the Interaction Between Vehicle and a Turnout,” Proc. Inst. Mech. Eng., Part F, 224(5), pp. 391–403.
Lagos, R. F. , Alonso, A. , Vinolas, J. , and Pérez, X. , 2012, “ Rail Vehicle Passing Through a Turnout: Analysis of Different Turnout Designs and Wheel Profiles,” Proc. Inst. Mech. Eng., Part F, 226(6), pp. 587–602.
Nicklisch, D. , Kassa, E. , Nielsen, J. , Ekh, M. , and Iwnicki, S. , 2010, “ Geometry and Stiffness Optimization for Switches and Crossings, and Simulation of Material Degradation,” Proc. Inst. Mech. Eng., Part F, 224(4), pp. 279–292.
Markine, V. L. , Steenbergen, M. J. M. M. , and Shevtsov, I. Y. , 2011, “ Combatting RCF on Switch Points by Tuning Elastic Track Properties,” Wear, 271(1–2), pp. 158–167.
Li, Z. , Zhao, X. , Esveld, C. , Dollevoet, R. , and Molodova, M. , 2008, “ An Investigation Into the Causes of Squats—Correlation Analysis and Numerical Modeling,” Wear, 265(9), pp. 1349–1355.
Wiest, M. , Daves, W. , Fischer, F. , and Ossberger, H. , 2008, “ Deformation and Damage of a Crossing Nose Due to Wheel Passages,” Wear, 265(9), pp. 1431–1438.
Pletz, M. , Daves, W. , Yao, W. , and Ossberger, H. , 2014, “ Rolling Contact Fatigue of Three Crossing Nose Materials—Multiscale FE Approach,” Wear, 314(1), pp. 69–77.
Pletz, M. , Daves, W. , and Ossberger, H. , 2012, “ A Wheel Set/Crossing Model Regarding Impact, Sliding and Deformation-Explicit Finite Element Approach,” Wear, 294–295, pp. 446–456.
Westeon, P. , Ling, C. , Roberts, C. , Goodman, C. , Li, P. , and Goodall, R. , 2007, “ Monitoring Vertical Track Irregularity From In-Service Railway Vehicles,” Proc. Inst. Mech. Eng., Part F, 221(1), pp. 75–88.
Lee, J. S. , Choi, S. , Kim, S.-S. , Park, C. , and Kim, Y. G. , 2012, “ A Mixed Filtering Approach for Track Condition Monitoring Using Accelerometers on the Axle Box and Bogie,” IEEE Trans. Instrum. Meas., 61(3), pp. 749–758.
Molodova, M. , Li, Z. , Núñez, A. , and Dollevoet, R. , 2014, “ Automatic Detection of Squats in Railway Infrastructure,” IEEE Trans. Intell. Transp., 15(5), pp. 1980–1990.
Molodova, M. , Li, Z. , and Dollevoet, R. , 2011, “ Axle Box Acceleration: Measurement and Simulation for Detection of Short Track Defects,” Wear, 271(1), pp. 349–356.
Oregui, M. , Li, Z. , and Dollevoet, R. , 2015, “ An Investigation Into the Modeling of Railway Fastening,” Int. J. Mech. Sci., 92, pp. 1–11.
Ren, Z. , Sun, S. , and Zhai, W. , 2005, “ Study on Lateral Dynamic Characteristics of Vehicle/Turnout System,” Veh. Syst. Dyn., 43(4), pp. 285–303.
Guo, S. , Sun, D. , Zhang, F. , Feng, X. , and Qian, L. , 2013, “ Damage of a Hadfield Steel Crossing Due to Wheel Rolling Impact Passages,” Wear, 305(1–2), pp. 267–273.
Zhao, X. , and Li, Z. , 2011, “ The Solution of Frictional Wheel–Rail Rolling Contact With a 3D Transient Finite Element Model: Validation and Error Analysis,” Wear, 271(1), pp. 444–452.
Wei, Z. , Li, Z. , Qian, Z. , Chen, R. , and Dollevoet, R. , 2016, “ 3D FE Modelling and Validation of Frictional Contact With Partial Slip in Compression–Shift–Rolling Evolution,” Int. J. Rail Transp., 4(1), pp. 20–36.
Chang, L. , Dollevoet, R. , and Hanssen, R. , 2014, “ Railway Infrastructure Monitoring Using Satellite Radar Data,” Int. J. Railway Technol., 3(2), pp. 79–91.
Zhao, X. , Wen, Z. , Zhu, M. , and Jin, X. , 2014, “ A Study on High-Speed Rolling Contact Between a Wheel and a Contaminated Rail,” Veh. Syst. Dyn., 52(10), pp. 1270–1287.
Torrence, C. , and Compo, G. P. , 1998, “ A Practical Guide to Wavelet Analysis,” Bull. Am. Meteorol. Soc., 79(1), pp. 61–78.
Liu, Y. , Liu, L. , and Mahadevan, S. , 2007, “ Analysis of Subsurface Crack Propagation Under Rolling Contact Loading in Railroad Wheels Using FEM,” Eng. Fract. Mech., 74(17), pp. 2659–2674.
Archard, J. , 1953, “ Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp. 981–988.
Rodkiewicz, C. , and Wang, Y. , 1994, “ A Dry Wear Model Based on Energy Considerations,” Tribol. Int., 27(3), pp. 145–151.
Dirks, B. , and Enblom, R. , 2011, “ Prediction Model for Wheel Profile Wear and Rolling Contact Fatigue,” Wear, 271(1), pp. 210–217.
Bogdański, S. , and Lewicki, P. , 2008, “ 3D Model of Liquid Entrapment Mechanism for Rolling Contact Fatigue Cracks in Rails,” Wear, 265(9), pp. 1356–1362.
Santamaria, J. , Vadillo, E. , and Oyarzabal, O. , 2009, “ Wheel–Rail Wear Index Prediction Considering Multiple Contact Patches,” Wear, 267(5), pp. 1100–1104.
Fletcher, D. , Smith, L. , and Kapoor, A. , 2009, “ Rail Rolling Contact Fatigue Dependence on Friction, Predicted Using Fracture Mechanics With a Three-Dimensional Boundary Element Model,” Eng. Fract. Mech., 76(17), pp. 2612–2625.
Anderson, R. , and Bevly, D. M. , 2010, “ Using GPS With a Model-Based Estimator to Estimate Critical Vehicle States,” Veh. Syst. Dyn., 48(12), pp. 1413–1438.
Zhai, W. , Xia, H. , Cai, C. , Gao, M. , Li, X. , Guo, X. , Zhang, N. , and Wang, K. , 2013, “ High-Speed Train–Track–Bridge Dynamic Interactions—Part I: Theoretical Model and Numerical Simulation,” Int. J. Rail Transp., 1(1–2), pp. 3–24.
View article in PDF format.

## References

ProRail, 2015, “ Jaarverslag ProRail 2015,” Technical Report, p. 127.
Shevtsov, I. Y. , 2013, “ Rolling Contact Fatigue Problems at Railway Turnouts—Experience of ProRail,” Meeting Materials: Materials Under Combined Durability Conditions, Lochristi, Belgium, p. 20.
Andersson, C. , and Dahlberg, T. , 1998, “ Wheel/Rail Impacts at a Railway Turnout Crossing,” Proc. Inst. Mech. Eng., Part F, 212(2), pp. 123–134.
Kassa, E. , and Nielsen, J. C. , 2009, “ Dynamic Train–Turnout Interaction in an Extended Frequency Range Using a Detailed Model of Track Dynamics,” J. Sound Vib., 320(4), pp. 893–914.
Alfi, S. , and Bruni, S. , 2009, “ Mathematical Modelling of Train–Turnout Interaction,” Veh. Syst. Dyn., 47(5), pp. 551–574.
Bruni, S. , Anastasopoulos, I. , Alfi, S. , Van Leuven, A. , and Gazetas, G. , 2009, “ Effects of Train Impacts on Urban Turnouts: Modelling and Validation Through Measurements,” J. Sound Vib., 324(3), pp. 666–689.
Johansson, A. , Pålsson, B. , Ekh, M. , Nielsen, J. C. , Ander, M. K. , Brouzoulis, J. , and Kassa, E. , 2011, “ Simulation of Wheel–Rail Contact and Damage in Switches and Crossings,” Wear, 271(1), pp. 472–481.
Pålsson, B. A. , and Nielsen, J. C. , 2012, “ Wheel–Rail Interaction and Damage in Switches and Crossings,” Veh. Syst. Dyn., 50(1), pp. 43–58.
Sun, Y. Q. , Cole, C. , and McClanachan, M. , 2010, “ The Calculation of Wheel Impact Force Due to the Interaction Between Vehicle and a Turnout,” Proc. Inst. Mech. Eng., Part F, 224(5), pp. 391–403.
Lagos, R. F. , Alonso, A. , Vinolas, J. , and Pérez, X. , 2012, “ Rail Vehicle Passing Through a Turnout: Analysis of Different Turnout Designs and Wheel Profiles,” Proc. Inst. Mech. Eng., Part F, 226(6), pp. 587–602.
Nicklisch, D. , Kassa, E. , Nielsen, J. , Ekh, M. , and Iwnicki, S. , 2010, “ Geometry and Stiffness Optimization for Switches and Crossings, and Simulation of Material Degradation,” Proc. Inst. Mech. Eng., Part F, 224(4), pp. 279–292.
Markine, V. L. , Steenbergen, M. J. M. M. , and Shevtsov, I. Y. , 2011, “ Combatting RCF on Switch Points by Tuning Elastic Track Properties,” Wear, 271(1–2), pp. 158–167.
Li, Z. , Zhao, X. , Esveld, C. , Dollevoet, R. , and Molodova, M. , 2008, “ An Investigation Into the Causes of Squats—Correlation Analysis and Numerical Modeling,” Wear, 265(9), pp. 1349–1355.
Wiest, M. , Daves, W. , Fischer, F. , and Ossberger, H. , 2008, “ Deformation and Damage of a Crossing Nose Due to Wheel Passages,” Wear, 265(9), pp. 1431–1438.
Pletz, M. , Daves, W. , Yao, W. , and Ossberger, H. , 2014, “ Rolling Contact Fatigue of Three Crossing Nose Materials—Multiscale FE Approach,” Wear, 314(1), pp. 69–77.
Pletz, M. , Daves, W. , and Ossberger, H. , 2012, “ A Wheel Set/Crossing Model Regarding Impact, Sliding and Deformation-Explicit Finite Element Approach,” Wear, 294–295, pp. 446–456.
Westeon, P. , Ling, C. , Roberts, C. , Goodman, C. , Li, P. , and Goodall, R. , 2007, “ Monitoring Vertical Track Irregularity From In-Service Railway Vehicles,” Proc. Inst. Mech. Eng., Part F, 221(1), pp. 75–88.
Lee, J. S. , Choi, S. , Kim, S.-S. , Park, C. , and Kim, Y. G. , 2012, “ A Mixed Filtering Approach for Track Condition Monitoring Using Accelerometers on the Axle Box and Bogie,” IEEE Trans. Instrum. Meas., 61(3), pp. 749–758.
Molodova, M. , Li, Z. , Núñez, A. , and Dollevoet, R. , 2014, “ Automatic Detection of Squats in Railway Infrastructure,” IEEE Trans. Intell. Transp., 15(5), pp. 1980–1990.
Molodova, M. , Li, Z. , and Dollevoet, R. , 2011, “ Axle Box Acceleration: Measurement and Simulation for Detection of Short Track Defects,” Wear, 271(1), pp. 349–356.
Oregui, M. , Li, Z. , and Dollevoet, R. , 2015, “ An Investigation Into the Modeling of Railway Fastening,” Int. J. Mech. Sci., 92, pp. 1–11.
Ren, Z. , Sun, S. , and Zhai, W. , 2005, “ Study on Lateral Dynamic Characteristics of Vehicle/Turnout System,” Veh. Syst. Dyn., 43(4), pp. 285–303.
Guo, S. , Sun, D. , Zhang, F. , Feng, X. , and Qian, L. , 2013, “ Damage of a Hadfield Steel Crossing Due to Wheel Rolling Impact Passages,” Wear, 305(1–2), pp. 267–273.
Zhao, X. , and Li, Z. , 2011, “ The Solution of Frictional Wheel–Rail Rolling Contact With a 3D Transient Finite Element Model: Validation and Error Analysis,” Wear, 271(1), pp. 444–452.
Wei, Z. , Li, Z. , Qian, Z. , Chen, R. , and Dollevoet, R. , 2016, “ 3D FE Modelling and Validation of Frictional Contact With Partial Slip in Compression–Shift–Rolling Evolution,” Int. J. Rail Transp., 4(1), pp. 20–36.
Chang, L. , Dollevoet, R. , and Hanssen, R. , 2014, “ Railway Infrastructure Monitoring Using Satellite Radar Data,” Int. J. Railway Technol., 3(2), pp. 79–91.
Zhao, X. , Wen, Z. , Zhu, M. , and Jin, X. , 2014, “ A Study on High-Speed Rolling Contact Between a Wheel and a Contaminated Rail,” Veh. Syst. Dyn., 52(10), pp. 1270–1287.
Torrence, C. , and Compo, G. P. , 1998, “ A Practical Guide to Wavelet Analysis,” Bull. Am. Meteorol. Soc., 79(1), pp. 61–78.
Liu, Y. , Liu, L. , and Mahadevan, S. , 2007, “ Analysis of Subsurface Crack Propagation Under Rolling Contact Loading in Railroad Wheels Using FEM,” Eng. Fract. Mech., 74(17), pp. 2659–2674.
Archard, J. , 1953, “ Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp. 981–988.
Rodkiewicz, C. , and Wang, Y. , 1994, “ A Dry Wear Model Based on Energy Considerations,” Tribol. Int., 27(3), pp. 145–151.
Dirks, B. , and Enblom, R. , 2011, “ Prediction Model for Wheel Profile Wear and Rolling Contact Fatigue,” Wear, 271(1), pp. 210–217.
Bogdański, S. , and Lewicki, P. , 2008, “ 3D Model of Liquid Entrapment Mechanism for Rolling Contact Fatigue Cracks in Rails,” Wear, 265(9), pp. 1356–1362.
Santamaria, J. , Vadillo, E. , and Oyarzabal, O. , 2009, “ Wheel–Rail Wear Index Prediction Considering Multiple Contact Patches,” Wear, 267(5), pp. 1100–1104.
Fletcher, D. , Smith, L. , and Kapoor, A. , 2009, “ Rail Rolling Contact Fatigue Dependence on Friction, Predicted Using Fracture Mechanics With a Three-Dimensional Boundary Element Model,” Eng. Fract. Mech., 76(17), pp. 2612–2625.
Anderson, R. , and Bevly, D. M. , 2010, “ Using GPS With a Model-Based Estimator to Estimate Critical Vehicle States,” Veh. Syst. Dyn., 48(12), pp. 1413–1438.
Zhai, W. , Xia, H. , Cai, C. , Gao, M. , Li, X. , Guo, X. , Zhang, N. , and Wang, K. , 2013, “ High-Speed Train–Track–Bridge Dynamic Interactions—Part I: Theoretical Model and Numerical Simulation,” Int. J. Rail Transp., 1(1–2), pp. 3–24.

## Figures

Fig. 4

Coordinate transformation

Fig. 6

Wavelet analysis of the ABA signals: (a) wavelet power spectrum of measured and simulated ABA. The rectangles indicate the major frequency contents, and the main difference between measurements. The impact happens at approximately 0.25 m from the tip of the crossing nose. (b) Global wavelet power spectra of measured and simulated ABA. The major frequency characteristics are around 35, 90, and 250 Hz.

Fig. 5

Time history of ABA: (a) measured signal from a global view and (b) comparison of ABA signals at the impact

Fig. 1

Degradation of the crossing nose: (a) cracks and plastic flow. The ruler at the bottom of the figure indicates the distance to the tip of crossing nose and (b) degradation because of cumulative plastic deformation and wear. The lower plot compares the nominal and measured longitudinal–vertical profile. The two crossings are of identical types.

Fig. 3

Schematic diagram of wheel–rail interaction with the close-ups of mesh

Fig. 2

The FE model of a right-hand crossing panel

Fig. 12

Distribution of surface shear traction along local longitudinal axis

Fig. 13

Field of microslip on the wheel

Fig. 7

Time history of normal contact force in facing-through motion. The starting point (0 ms) is at 700 mm ahead of the nose tip.

Fig. 8

Contact status during the transition with the center of the contact patch shown as

Fig. 9

Fig. 10

Field of surface shear traction on the wheel

Fig. 11

(a) Time series of contact forces during the transition and (b) trajectory and contact angle of the center of the contact patch

Fig. 15

Maximum frictional work of the crossing nose: (a) along the longitudinal direction and (b) trajectories for () the maximum frictional work and () the center of the contact patch

Fig. 14

Plastic deformation of the crossing nose: (a) maximum von Mises stress along the longitudinal direction and (b) trajectories for () the maximum von Mises stress and () the center of the contact patch

## Tables

Table 1 Contact solution during the transition

## Discussions

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