Parametric analysis of wheel wear in high-speed vehicles

Abstract

In order to reduce the wheel profile wear of high-speed trains and extend the service life of wheels, a dynamic model for a high-speed vehicle was set up, in which the wheelset was regarded as flexible body, and the actual measured track irregularities and line conditions were considered. The wear depth of the wheel profile was calculated by the well-known Archard wear law. Through this model, the influence of the wheel profile, primary suspension stiffness, track gage, and rail cant on the wear of wheel profile were studied through multiple iterative calculations. Numerical simulation results show that the type XP55 wheel profile has the smallest cumulative wear depth, and the type LM wheel profile has the largest wear depth. To reduce the wear of the wheel profile, the equivalent conicity of the wheel should not be too large or too small. On the other hand, a small primary vertical stiffness, a track gage around 1,435-1,438 mm, and a rail cant around 1:35-1:40 are beneficial for dynamic performance improvement and wheel wear alleviation.

J. Mod. Transport. (2014) 22(2):7683 DOI 10.1007/s40534-014-0053-z

Parametric analysis of wheel wear in high-speed vehicles

Na Wu Jing Zeng

Received: 9 December 2013 / Revised: 29 April 2014 / Accepted: 30 April 2014 / Published online: 23 May 2014 The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract In order to reduce the wheel prole wear of high-speed trains and extend the service life of wheels, a dynamic model for a high-speed vehicle was set up, in which the wheelset was regarded as exible body, and the actual measured track irregularities and line conditions were considered. The wear depth of the wheel prole was calculated by the well-known Archard wear law. Through this model, the inuence of the wheel prole, primary suspension stiffness, track gage, and rail cant on the wear of wheel prole were studied through multiple iterative calculations. Numerical simulation results show that the type XP55 wheel prole has the smallest cumulative wear depth, and the type LM wheel prole has the largest wear depth. To reduce the wear of the wheel prole, the equivalent conicity of the wheel should not be too large or too small. On the other hand, a small primary vertical stiffness, a track gage around 1,4351,438 mm, and a rail cant around 1:351:40 are benecial for dynamic performance improvement and wheel wear alleviation.

Keywords Parametric analysis Wheel prole wear

Flexible wheelset High-speed railway Vehicle dynamic

model Finite element method

1 Introduction

With the rapid development of high-speed railways, study on wheel prole wear has become increasingly important

[1, 2]. Wheel and rail wear is a fundamental problem in railways; the change of prole shape affects the dynamic characteristics of railway vehicles such as stability and passenger comfort and, in the worst case, can cause derailment [3]. Therefore, it is very important to establish a reliable vehicle dynamic model and wheel/rail wear model to analyze the inuence of vehicle parameters on the wear of the wheel prole. However, it is difcult to predict wheel and rail wear simultaneously using state-of-the-art numerical techniques [4]; so we focus on predicting the wear of railway wheels in this work.

To date, many papers on wheel/rail wear prediction have been published. The existing research work of wheel prole wear prediction mainly focus on three aspects: 1) to establish a prediction model based on the vehicle dynamics model, wheelrail rolling contact model, and wheel material wear model; 2) to conrm the maximum limit value while updating wheel proles; and 3) to analyze the inuence of vehicle track parameters on the wear.

For the wheel prole wear prediction model and maximum limit value as the interval for the wheel prole updating in the repeated dynamic analysis of the vehicle, some scholars carried out studies in different ways. Fries et al. [5] compared four existing wear models, predicting the wear of a freight wagon wheel prole when travel ing in straight lines. The results showed that there was no signicant difference between the four wear models. Pearce et al. [6] proposed a wear model for a simple wheel prole by calculating the global contact forces and creep-age acting on the contact patch. The amount of material removed was calculated through a wear index (later called the Derby wear index), and the wear process was analyzed on a combined straight line and S-curve route. They established that a distance of 1,100 km could be traveled before the wear surface needed upgrading. Li et al. [7]

N. Wu (&) J. Zeng

State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, Chinae-mail: [email protected]

J. Zenge-mail: [email protected]

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Parametric analysis of wheel wear in high-speed vehicles 77

adopted SIMPACK software to simulate vehicle dynamics. They analyzed the wheelrail contact with the non-Hertzia multi-point and conformal contact model based on CONTACT, and the wear depth of 0.1 mm is considered as the interval for the wheel prole updating in the repeated dynamic analysis of the vehicle. Jendel et al. [8] developed total simulation conditions using discrete and grouped different curve radii, and analyzed the wheelrail contact problem using the Hertz theory, Fastsim method, and the Archard model for wear calculations. The update of the wheel prole wear was established when the maximum wear value reached 0.1 mm or the operation distance reached 1,500 or 2,500 km.

The wheelrail wear is inuenced by many factors, and governed by a complex mechanism. Some researchers addressed this problem by analyzing the effect of vehicle and track parameters on the wheel wear. Luo et al. [9] analyzed the inuence of the vehicle parameters on the wheel prole wear with a frictional work model. Ignesti et al. [10] developed a mathematical model for wheelrail wear evaluation in complex railway lines and compared the performance provided by different wheel proles in terms of resistance to wear and running stability. Pombo [11] used a computational tool to simulate the dynamic performance of an integrated railway system and predict the wear evolution of wheel proles, taking into account the inuence of track condition. Agostinacchio et al. [12] evaluated the inuence of the geometrical and mechanical parameters of the superstructure on the dynamic response of the railway. Fergusson et al. [13] presented an analysis of wheel wear as a function of the relationship between the lateral and longitudinal primary suspension stiffness and the coefcient of friction at the center plate between the wagon body and the bolster. Li et al. [14] studied the relationship between the rail cant and wheelrail rolling contact behavior. The results showed that the rail cant had a great inuence on the wheelrail rolling contact behavior. Wang et al. [15] analyzed the rolling contact geometrical parameters and creepage of the JM3 wheelset and 60 kg/m rail track in static rolling contact under different structural parameters of the track such as rail cant and rail gage. Chen et al. [16] simulated and analyzed the inuence on wheel/ rail wear caused by vehicle speed, rail cant, super-elevation on curve, and rail lubrication.

Most of the above studies regarded wheel as a rigid body when carrying out the wheel wear prediction. However, when the vehicle passed through a small radius curve, the inuence of wheel proles on the wheelrail normal force, the contact patch size, position of the contact point, adhesion area, and the distribution of the slide area were different for a exible wheelset and a rigid wheelset. Chang et al. [17] studied the wheelrail wear by establishing a three-dimensional dynamic nite element model.

Baeza et al. [18] built a model that coupled rotating exible wheelset and a exible track model for simulating vehicle track interaction at high frequencies when investigating growth in rail roughness. Due to the increase of the vehicle speed and the presence of roughness, contact geometry perturbations induce a variation of forces in the vertical and tangential direction, and the torsional vibration of the wheelset axle may, therefore, be excited at high frequency. These vibrations directly affect the contact dynamic action of wheel/rail, and then inuence on the wheel prole wear. Therefore, in the prediction of wheel prole wear, wheelset should be considered as exible body.

In addition, when analyzing the impact of rail and vehicle parameters on wheel prole wear, the above studies completed the wheel prole wear prediction by a single iteration. However, wheel prole deformation caused by wear will change the tendency of these parameters inuence on the wheel prole wear. Therefore, when analyzing the inuence of the rail and vehicle parameters on the wheel prole wear, wheel prole should be updated many times in calculation.

In the present work, in order to reduce wear of the wheel prole and extend the service life of wheels, a dynamic model for a high-speed vehicle was set up, in which the wheelset was regarded as exible body, and the actual measured track irregularities and line conditions were considered. The wear depth of the wheel prole was calculated by the well-known Archard wear law [19]. Through this model, the inuence of the wheel prole, primary suspension stiffness, track gage, and rail cant on the wear of the wheel prole were studied through multiple iterative calculations.

2 Model descriptions

2.1 Vehicle dynamic model

The rigid-exible coupling dynamic model of a high-speed vehicle was established, and the vehicle system included a car-body, two bogie frames, four wheelsets, and eight axle boxes. To take into account the effect of wheelrail high-frequency vibration on the wear, the wheelset was considered to be exible, and the other bodies assumed to be rigid. The nonlinearities caused by wheelrail interaction and suspension parameters were considered in the model. The vehicle system dynamic equations can be expressed in the following form:

M

x F x; _

P x; _

x

x; t

; 1 where x denotes the displacement vector, M indicates the system mass matrix, F is the nonlinear suspension forces, and P is an item related to the nonlinear wheel/rail forces and track inputs.

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78 N. Wu, J. Zeng

The wheelset nite element model was set up using ANSYS software, in which one axle, two wheels, and three brake discs were included. The eight-node hexahedral 3D solid element mesh division was adopted for the modeling, and the whole unit had 70,592 elements with 83,616 nodes. The wheelset nite element model is shown in Fig. 1.

Using the Guyan reduction method and maintaining the overall shape of the structure, a freedom set with a uniform distribution was selected. Through modal analysis using the nite element model and without imposing any constraints, the rst 30 modes were obtained and imported to the SIMPACK dynamic analysis software. The rigid-exible coupling dynamic model of the vehicle system was then built. The mode shapes of the exible wheelset are shown in Fig. 2. The exible wheelset had many mode shapes which might affect the wear of the wheel prole, and thus the exibility of the wheelset could not be ignored.

2.2 Wear model

Archards wear model is a function of the sliding distance, normal force, and hardness of the material. The wear volume of the material worn away is proportional to the product of the sliding distance and the normal force, and

Fig. 1 Wheelset nite element model

(a)

(d)

(b)

(e)

(c)

Fig. 2 Mode shapes of the exible wheelset. a First vertical and horizontal bending modes (77 Hz). b Second vertical and horizontal bending modes (133 Hz). c Third vertical and horizontal bending modes (575 Hz). d First umbrella mode (225 Hz). e Second umbrella mode (282 Hz)

123 J. Mod. Transport. (2014) 22(2):7683

Parametric analysis of wheel wear in high-speed vehicles 79

q

2

P (Pa)

0.8H

dx; y D x

n /y

2 g /x

; 4

zx; y

k4 300-400

3NkD x 2p abH

1

x a

r

n uy

2 g ux

2

q

2

2

y b

;

5

k1 1-10

k2 30-40

k3 1-10

0.2 0.7 v

Fig. 3 Coefcient k

Nd

H ; 2 where Vwear is the wear volume matrix, d the sliding distance vector, N the normal force matrix, H is the hardness of the worn material, and k is the wear coefcient.

The wear coefcient k can be determined by laboratory tests or by performing extensive eld measurements. It is generally a function of the sliding velocity, contact pressure, temperature, and contact environment. The wear coefcient used in the present calculation is described in the wear chart from Ref. [7]. It can be expressed in Fig. 3, in which the horizontal and vertical axes are the sliding velocity and contact pressure, respectively. This gure has been derived under dry contact conditions. The tread contact occurs in region k2, and the ange contact occurs in the regions k1, k2, k3, and k4. In this study, k is taken as the middle value in each region.

The wheelrail contact model was set up using the simplied Kalkers algorithm Fastsim in which the wheel/ rail contact ellipse is divided into many elements. In each element, the normal contact pressure P, sliding distance d, and wear depth z are expressed, respectively, by Eqs. (3) (5):

Px; y

where x denotes the longitudinal direction of the contact plane; y is the transversal direction of the contact plane, and the element center point (x, y) are the Cartesian coordinates of the contact patch; n, g, and / denote the longitudinal creepage, lateral creepage, and spin creepage, respectively; a and b denotes the long axis and short axis of contact patch, respectively.

2.3 Process of wear prediction

The vehicle parameters, wheelrail initial prole, mode shapes of wheelset, track random inputs, and track line conditions were taken into account in the vehicle system dynamic model. The contact patch location, size, creepage, and normal stress distribution were then calculated. Subsequently, the amount of wear for the wheel was calculated using the wear model. Finally, the wheel wear distribution was obtained, and the wheel prole was updated using the smoothing method of cubic spline interpolation. The wheelrail contact patch was divided into 50 9 50 elements. The wear model predicted the change in the wear of the wheel prole through multiple iterations. The integrated simulation process for wheel wear is shown in Fig. 4.

To accelerate the wear prediction, the following hypotheses for calculating wheel wear were developed:

(1) During one integrated simulation of wear prediction, the prole of the wheel remained unchanged, and the tread was updated when the wear depth was 0.1 mm or the vehicle had traveled through 1,500 km according to previous studies [4, 8]. On the basis of the eld analysis of the measured data for a high-speed vehicle, a running distance of 1,000 km was taken as the step length for updating the wheel prole in this study.

(2) The vehicle structure was symmetrical, and the left and right rails on the curved track were arranged

inversely proportional to the hardness of the worn material. It can be described by Eq. (2):

Vwear k

1

r

3N 2p ab

x a

2

2

y b

; 3

Vehicle parameters

Initial wheel profile

Rigid-flexible coupling vehicle model

Dynamic simulation

FASTSIM

Wear calculation and profile updating

New wheel profile

Flexible wheelset

Track condition

Fig. 4 Integrated simulation process

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80 N. Wu, J. Zeng

Table 1 Typical scenarios

Track radius (m) Vehicle speed (km/h) Percentage (%)

2,200 160 4

2,800 180 4

4,000 200 4

Straight 200 88

0.5

symmetrically. The vehicle always traveled forward and backward on the line, thus the wheel wear for wheelsets one and four was the same, and for wheelsets two and three was also the same.(3) The track excitation was random, and the impact of rail wear on wheel wear was not considered.

For the wheel wear calculation, the vehicle was assumed to pass through a prescribed track consisting of three curved tracks and one straight track [20], which is shown in Table 1.

3 Parametric analysis of wheel wear

It is essential to acquire a better understanding on how the operation conditions inuence wear evolution of the wheel prole. Therefore, the following analysis focuses on vehicle/track parameters inuence of wheel prole on wear.

3.1 Inuence of wheel prole on wear

The wear depth and distribution of four types of wheel proles (LM, LMA, XP55, and S1002) were compared on the prescribed line conditions for the same operating mileage. Figure 5 illustrates the equivalent conicities of the

0.6

Equivalent conicity

LMA S1002 XP55 LM

0.4

0.3

0.2

0.1

0.0 0 2 4 6 8 10

Wheelset lateral displacement (mm)

Fig. 5 Equivalent conicities for different types of wheel proles

(a)

6

(b)

16

XP55 LMA LM S1002

XP55 LMA LM S1002

5

14

12

Wear depth (m)

Wear depth ( m)

4

10

3

8

2

6

4

1

2

0

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

y (mm)

y (mm)

(c)

(d)

12

12

10

10

8

XP55 LMA LM S1002

XP55 LMA LM S1002

Wear depth (m)

Wear depth (m)

8

6

6

4

4

2

2

0

y (mm)

y (mm)

Fig. 6 Wear comparison for different types of wheel proles. a Wear stage 1. b Wear stage 2. c Wear stage 3. d Wear stage 4

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Parametric analysis of wheel wear in high-speed vehicles 81

Table 2 Wear distribution zone for different wheel proles (mm)

Wear stage Wheel proles

XP55 LMA LM S1002

1 -47?18 -44? 26 -52? 16 -46?29

2 -44?24 -43?24 -45?26 -51?24

3 -44?26 -45?26 -44?25 -47?27

4 -51?26 -45?32 -43?31 -51?31

four wheel proles, and Fig. 6 shows the wear depth changes for the four wheel proles. Figure 6 includes four wear stages for the wheel wear prediction, labeled (a), (b),(c), and (d), respectively, and each stage covered a distance of 1,000 km. After each stage, the wheel prole was updated to enable the calculations for the next stage. In the gures, the abscissa y is the horizontal axis of the wheel prole, and the origin is at the wheel nominal rolling circle position.

As known, the wear depth initially increased rapidly and then slowed with the increase in running mileage, and the wear range slowly broadened.

Table 2 shows the distribution of different types of wheel proles for the four wear stages. In stage 1, because the type LM prole had the largest equivalent conicity, the wheel wear was close to the ange; the S1002 prole had

the smallest equivalent conicity, and the wheel wear was near the outside of the wheel. For the later wear stages, the wear volume for LM was the greatest and the wear ranges the widest; and the wear volume for XP55 the smallest. Therefore, the selection of an appropriate wheel prole and equivalent conicity is very important for the actual wheel wear. If the equivalent conicity was too large, then the large contact angle would cause the spin creep to increase. At the same time, the wheel rail contact point was closer to the ange, and the wheel wear would be more serious. On the other hand, if the difference in the rolling radii between the left and right wheels increased, then the deviation from the center position of the wheelset caused greater longitudinal creep and increased the wear depth. If the equivalent conicity was too small, then the lateral motion of the wheelset would be greater to widen the wear range because of the weak centering ability. Therefore, a too large or too small equivalent conicity will intensify the wheel wear.

3.2 Inuence of primary vertical stiffness on wear

To compare the inuence of primary vertical stiffness on the wear depth and range, the primary vertical stiffness with values 0.8, 1.0, 1.2, and 1.4 MN/m was adopted for the calculation. Figure 7 shows that the primary vertical stiffness has little inuence on the wear range. In the wear

(a)

(b)

5

25

0.81.01.21.4

4

20

Wear depth (m)

0.81.01.21.4

Wear depth ( m)

3

15

2

10

1

5

0

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

y (mm)

y (mm)

(c)

(d)

8

8

7

7

0.81.01.21.4

6

Wear depth (m)

6

Wear depth (m)

5

5

0.81.01.21.4

4

4

3

3

2

2

1

1

0

y (mm)

y (mm)

Fig. 7 Wear comparison for different primary vertical stiffnesses. a Wear stage 1. b Wear stage 2. c Wear stage 3. d Wear stage 4

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82 N. Wu, J. Zeng

(a)

(b)

5

18

1432 1435 1438 1441

1432 1435 1438 1441

4

15

Wear depth (m)

Wear depth (m)

12

3

9

2

6

1

3

0

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

y (mm)

y (mm)

(c)

(d)

24

18

1432 1435 1438 1441

15

1432 1435 1438 1441

20

Wear depth (m)

Wear depth (m)

16

12

12

9

6

8

3

4

0

y (mm)

y (mm)

Fig. 8 Wear comparison for different track gages. a Wear stage 1. b Wear stage 2. c Wear stage 3. d Wear stage 4

(a)

(b)

8

1:25 1:30 1:35 1:40

10

1:25 1:30 1:35 1:40

Wear wepth (m)

6

8

Wear wepth (m)

6

4

4

2

2

0

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

0 -60 -40 -20 0 20 40 -60 -40 -20 0 20 40

y (mm)

y (mm)

(c)

(d)

16

14

14

12

1:25 1:30 1:35 1:40

10

1:25 1:30 1:35 1:40

Wear wepth (m)

12

Wear wepth (m)

10

8

8

6

6

4

4

2

2

0

y (mm)

y (mm)

Fig. 9 Wear comparison for different rail cants. a Wear stage 1. b Wear stage 2. c Wear stage 3. d Wear stage 4

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Parametric analysis of wheel wear in high-speed vehicles 83

stage 3, the primary vertical stiffness has little effect on the wear depth; in the further wear stages, the stiffness1.0 MN/m will cause greater wear than the others, and the stiffness 0.8 MN/m has the least wear. With the increasing of running mileage, the wear depths increase rapidly in the early stages and slowly in the later stages.

3.3 Inuence of track gage on wear

The computed track gages were 1,432, 1,435, 1,438, and 1,441 mm, and their inuences on the wear depth and distribution of the wheel proles were compared in Fig. 8. We can see that wear depth reduces and wear range gradually moves away from the ange with the increase in track gage in the rst stage. In the later stages, track gages 1,435 and 1,438 mm have the least wheel wear depth. Thus, slightly widening the track gage is advantageous for reducing wheel wear.

3.4 Inuence of rail cant on wear

Rail cants of 1:25, 1:30, 1:35, and 1:40 were selected for the wheel wear calculation. As shown in Fig. 9, the wear depth was small when the rail cant angles were 1:35 and 1:40, and the wear distribution was near the ange. Thus, the rail cant should be between 1:35 to 1:40 to reduce wheel wear.

4 Conclusions

To study wheel prole wear, a vehicle dynamic model and a wheel prole wear model were established. The inuence of wheel prole, primary vertical stiffness, track gage, and rail cants on wheel prole wear was investigated through numerical simulations, and the following conclusions were reached:

(1) The shape of the wheel prole has a signicant inuence on wheel wear depth and range. Among the four types of wheel proles, the type XP55 wheel had the smallest cumulative wear depth, and LM had the largest wear. To reduce the wear of the wheel prole, an appropriate wheel equivalent conicity needs to be designed, and must not be too large or too small.

(2) Using a small primary vertical stiffness can have a better dynamic performance and reduce wheel wear.

(3) The track gage should be between 1,435 and 1,438 mm, a too large or too small gage will aggravate the wheel wear, and rail cant should be between 1:35 to 1:40.

Acknowledgments The authors would like to acknowledge the support of the National Natural Science Foundation of China (No. 51005189) and the National Key Technology R&D Program of China (2009BAG12A01).

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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