10th

International Conference on Contact Mechanics

CM2015, Colorado Springs, Colorado, USA

Study on Importance of Wheel-Rail Contact Modeling in Wheel Wear

Simulation

Gongquan Tao, Zefeng Wen, Xin Zhao, Xuesong Jin

State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

*E-mail: zfwen@home.swjtu.edu.cn

ABSTRACT

This paper focuses on comparing three non-elliptic contact models, namely Kik-Piotrowski, STRIPES and

ANALYN, and the difference of wheel wear evaluated based on the three contact models. The three

non-elliptic contact models are compared in terms of normal contact solution and tangential contact

solution which is obtained by modifying Kalker’s simplified theory. In order to investigate the influence of

contact models on wheel wear, a wheel wear prediction model, including multi-body model of railway

vehicle, local contact analysis and wheel wear model based on USFD wear function, is developed. The

wear distributions over wheel profile under different operating conditions are analyzed. The results show

that the wear result based on elliptic approach has a relatively good agreement with CONTACT, which is a

surprising result. In all simulation cases, STRIPES and ANALYN predict nearly the same wheel wear and

both of them underestimate the wheel wear.

1. INTRODUCTION

The railway, as an eco-friendly and energy- efficient

mode of transportation, has attracted more and more

attentions in recent years. To meet the higher and

higher requirements of the modern railway,

especially of for the high speed and the heavy haul,

wear of the wheel-rail contact pair has to be

understood better in theory and well controlled in

practice. It has been well recognized by train

operators that a reliable prediction of wheel wear can

help to optimize the maintenance plan of wheelsets,

and the design of vehicles such as that of the

wheel/rail profiles and the suspension.

Complexity or uncertainty of the prediction of wheel

wear may come from simulation of the vehicle-track

dynamics, modeling of the wheel-rail rolling contact,

determination of the wear rate and other technic

details such as the smoothing and updating of the

profile after each cycle. The contact solutions

required in wear prediction include the size and

shape of the wheel-rail contact patch, normal and

tangential contact stresses, and the stick-slip

distinction in the contact patch. Sufficient accuracy is

required in the obtained results because errors can be

constantly accumulated in simulation, besides which

and the contact model embedded has to be should be

low in computational costs because the wheel-rail

rolling contact needs to be solved at every time step.

Rolling contact models developed with the boundary

element method, like Kalker’s CONTACT [1], or

with the finite element (FE) method are not suitable

due to their high computational costs, being

especially true for FE models. Analytical solution of

rolling contact, instead, is a more feasible choice, at

least for the current computational power. Today,

analytical solutions for non-elliptic contact derived

with the virtual penetration method have been

proposed by Linder [2], Kik-Piotrowski [3-4],

Ayasse-Chollet [5], Alonso-Giménez [6-7] and so on,

and that derived from the concept of approximate

surface deformation has also been proposed by

Sichani-Enblom-Berg [8]. In these models, tangential

problem for the non-elliptic contact is usually solved

with the modified FASTSIM of Kalker [9].

Sichani et al. [10] investigated the precision and

accuracy of non-elliptic contact models, including

Linder method [2], Kik-Piotrowski method [3-4] and

Ayasse-Chollet method (STRIPES) [5], these models

were implemented and compared in terms of contact

patch, as well as contact pressure and traction

distributions, and the CONTACT software was taken

as a reference. Besides, Sichani et al. [11]

investigated the difference between the new method,

named ANALYN [8], developed by themselves

recently and the approximate model of

Kik-Piotrowski and the results were evaluated using

CONTACT code. The research indicates ANALYN

to be more accurate in terms of contact patch and

stress distribution as well as creep force estimation.

Enblom and Berg [12] investigated the effect of the

elastic deformation contribution to the sliding

velocity on wheel wear. The rigid and elastic

methods employed in FASTSIM and CONTACT

code were compared, and it was indicated that a

reasonable agreement in wheel wear volume for pure

slip with large spin but a significant difference for

partial slip. Moreover, the influence of non-elliptic

contact modelling (STRIPES) on wheel wear rate

and profile shape also investigated by Enblom and

Berg [13].

The focus of this paper focuses on is to investigation

of the calculation accuracy and efficiency of

non-elliptic contact models, including

Kik-Piotrowski method [3-4], Ayasse-Chollet

method (STRIPES) [5] and Sichani-Enblom-Berg

method (ANALYN) [8], and the importance of

wheel-rail contact modeling in wheel wear

simulation. For comparison of normal solutions, i.e.,

of the shape and size of contact patch and the

pressure distribution, methods of those non-elliptic

models mentioned above and Hertz method are

chosen. Kalker’s CONTACT is taken as a reference.

Based on the normal solutions, Kalker’s simplify

theory (program FASTSIM) and the modified

FASTSIM for non-elliptic contact are employed to

solve the tangential contact problem. The obtained

tangent solutions such as the stick-slip distinction,

micro-slip distribution and the creep force are

compared with each other and with those of

CONTACT. Afterwards, the USFD wear function

[14] proposed by the University of Sheffield is

employed to calculate the wear, in which the local

wear rate is assumed to be determined by the energy

dissipation. It should be noted that the elastic

deformation that has a significant contribution to the

micro-slip distribution is considered in the present

work.

2. DESCRIPTION OF NON-ELLIPTIC

CONTACT

Hertz’s theory is widely used in railway dynamics

simulations for wheel-rail contact. However, the

Hertz solution is limited by some hypothesis, the

curvature within contact patch should be constant,

and the contact patch is assumed as an elliptic with

an elliptic contact pressure distribution. For

evaluation of the tangential properties FASTSIM

algorithm based on Kalker’s simplified theory is the

prevailing approach. However, the assumptions

adopted in Hertz’s theory are rarely meet, especially

for worn wheel and rail profiles.

To improve the contact modelling, several more or

less approximate alternative procedures have been

proposed in the past. The Kik-Piotrowski method [3],

STRIPES [5] and ANALYN [8] are investigated in

this paper.

2.1 Non-elliptic Contact Models

The Kik-Piotrowski method

Kik and Piotrowski [3] proposed a non-elliptic

contact model based on the concept of virtual

penetration (VP). The elastic deformation of both

contact bodies is neglected,, and based on the

assumption that the contact bodies can penetrate into

each other. In reality, the penetration does not occur

between the contacting bodies, while the deformation

occurs and the contact area is generated. On the basis

of some similarity of shapes of the contact area and

interpenetration region, the contact zone is

determined by the following assumption: the surfaces

of the bodies are virtually penetrated and the

resulting interpenetration region is taken as the area

of contact. Therefore, the interpenetration region will

be larger than the real contact area, and the

interpenetration region encloses real contact area. So

the rigid approach between the two bodies should be

reduced by a scaling factor, a constant number ε =

0.55 was adopted by Kik and Piotrowski. Besides, a

shape correction strategy is applied to the contact

patch, in which the shape ratio and area of the

contact patch remain the same as the interpenetration

area. As the same as the common assumption for the

methods based on the virtual penetration, the normal

pressure distribution in the direction of rolling is

assumed as the semi-elliptical. The Kik-Piotrowski

method is described in detail in ref. [3] and [4].

The Ayasse-Chollet method

The non-elliptic contact method developed by

Ayasse and Chollet (STRIPES) [5] also relies on the

interpenetration approach. In the STRIPES method, it

is possible to consider non-Hertzian conditions in

lateral direction, which means the lateral curvatures

within the contact area are not constant, while the

longitudinal curvatures remain constant as in the

Hertzian assumptions.

The correction strategy in STRIPES is different from

Kik-Piotrowski method, Ayasse and Chollet

proposed that the contact patch in the geometric

problem as well as in the Hertz problem should have

the same characteristics, in the other words, the shape

ratio of the geometric ellipse and the contact ellipse

should be the same, and the semi-axes of the

geometric ellipse and the contact ellipse also should

be the same. To meet these, curvatures and rigid

approach in geometric problem should be corrected.

In ref. [5], three correction strategies were proposed:

(1) compensating the longitudinal curvature only and

smoothing of lateral curvature; (2) compensating

lateral curvature; (3) compensating both longitudinal

and lateral curvature. In this article, the last one is

used, both relative curvatures Ai and Bi in each

longitudinal stripes are supposed to be corrected. The

detailed descriptions of STRIPES method can be

seen in ref. [5] and [15].

The Sichani-Enblom-Berg method

Unlike the VP-based methods, Sichani, Enblom and

Berg [8] developed a novel method (ANALYN) to

solve the normal contact problem in the wheel-rail

interface. The surfaces deformation of wheel and rail

is estimated using the separation between them,

instead of being neglected, and there is no correction

of relative curvatures or rigid approach, it is named

the approximate surface deformation (ASD) method.

In order to estimate the contact patch, for the

VP-based methods, the intersection of the curve

z=g(y) with a horizontal line, z=εδ0, identifies the two

ends of the contact patch width, so the width of the

evaluated patch dependents on the value of

interpenetration. While for the ANALYN method,

z=g(y) is intersected by the curve, z=δ0-β(y)g(y), for

the width estimation. The different methods used to

evaluate the contact patch width are illustrated in

-10 -5 0 5 10 15-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

ASD method width

CONTACT width

Z [

mm

]

Y [mm]

VP-based method width

g(y)

0-(y)g(y)

0

Fig. 1. Contact patch width estimation by different methods [8]

Figure 1. The detailed descriptions of ANALYN

method can be seen in ref. [8].

The common assumption for the VP-based methods

and ASD method is the semi-elliptical normal stress

distribution in the direction of rolling, while it is

non-elliptical in the lateral direction.

2.2 The Solution of Tangential Contact Problem

The FASTSIM algorithm, based on Kalker’s

simplified theory [9], is the most widely used for

solving the tangential wheel-rail contact problem,

because of its perfect efficiency and accuracy.

Moreover, it can obtain not only the creep force but

also the tractions and the micro-slip distribution.

However, the original FASTSIM is developed for

elliptic contact patches, in order to adapt FASTSIM

to non-elliptic patches the flexibility parameters

should be re-calculated.

Piotrowski and Kik [4] proposed an equivalent

ellipse method to calculate the flexibility parameters.

An equivalent ellipse is defined for each separate

contact region by setting the ellipse area equal to the

non-elliptic contact area and ellipse semi-axes ratio

equal to length-to-width ratio of the patch.

A local ellipse method is used by Ayasse and Chollet

[5] to calculate the flexibility parameters. The contact

patch should be divided into several independent

longitudinal stripes, then, a virtual local ellipse can

be assigned to each strip, the flexibility parameters

can be calculated using the local ellipses. The local

ellipses are determined by employing relative

curvatures at the center of each strip in Hertz solution.

ANALYN has the same form as STRIPES for the

tangential solution.

It should be noted the contact patch is assumed to be

planar, and the spin value is constant across the patch

and calculated using the contact angle at the

geometry contact point in Kik-Piotrowski method,

however, in STRIPES and ANALYN, each strip has

a different contact angle,,which causes different spin

value.

3. RESULTS AND DISCUSSION OF

WHEEL-RAIL CONTACT

In order to compare the difference among the

Kik-Piotrowski method [3], STRIPES [5] and

ANALYN [8], Kalker’s program CONTACT [1]

is used as a reference. In addition, the results are

also compared with Hertz solution. The tangential

contact of the non-elliptic models is then solved by

using the FASTSIM algorithm [9], which is

modified to be available for the non-elliptic

patches.

The non-elliptic patch is formed by the contact

between a wheel with standard profile LM and a

rail of standard profile CHN60 with the inclination

of 1:40. Both wheel and rail are assumed to have

the same material properties with ν = 0.28 and E =

206 GPa. The back-to-back distance of wheelset is

1353 mm with a mean rolling circle radius of 420

mm, and the gauge is 1435 mm. The axle load is

14 ton. Several contact cases with different

wheelset displacements are investigated. The

contact patch, contact pressure, and micro-slip

distribution and traction distributions are

compared.

3.1 The results of normal contact

Taking a wheelset lateral displacement of Δy = 3

mm as an example, which is a typical example of a

non-elliptic tread contact, the lateral relative

curvature within contact area is not a constant, As

shown in Figure 2,it is composed of a piecewise

function, and is not continuity.

Figure 3 shows the contact patch and maximum

pressure predicted by the three non-elliptic contact

models and they are compared with the results of

CONTACT and Hertz solution. From Fig.3 it can

be seen that all three non-elliptic methods predict a

non-elliptic patch with relatively good agreement

with the CONTACT results. The ANALYN patch

is closer to the CONTACT patch. However,

Kik-Piotrowski method overestimates the patch

and STRIPES underestimate (taking CONTACT

results as a reference). Furthermore, the contact

patch predicted by STRIPES and ANALYN is not

smooth around the break point of curvature. Figure

3(b) shows the maximum contact pressure along

lateral direction. From the results it can be found

that the pressure of STRIPES and ANALYN is

similar to CONTACT, and the peak occurs at the

geometry contact point. The maximum value of

STRIPES and ANALYN is little larger than that of

CONTACT. Among these methods,

Kik-Piotrowski method predicts lower pressure

levels because its evaluated contact area is larger

than the other methods. Considering other contact

cases, it seems that the STRIPES and ANALYN

method results in more accurate patches and

pressure.

-5 -4 -3 -2 -1 0 1 2 3 40

1

2

3

4

5

6

Rel

ativ

e cu

rvat

ure

B [

m-1

]

Y [mm]

Fig. 2. The lateral relative curvature within the contact patch for

wheelset lateral displacement of Δy = 3 mm

Table 1 and 2 list the contact area and maximum

pressure with the wheelset lateral displacements of

Δy = 0, 3, 5, 8 mm. The results indicated that

Hertz solution generally underestimated the

contact area, but Kik-Piotrowski method has the

opposite rules. And the STRIPES and ANALYN

are closer to CONTACT. As to the maximum

pressure, the results are just reversed, Hertz

solution predicts a larger contact pressure,

Kik-Piotrowski method underestimates, the

STRIPES and ANALYN have a good agreement

with CONTACT.

-5 -4 -3 -2 -1 0 1 2 3 4-8

-6

-4

-2

0

2

4

6

8

X [

mm

]

Y [mm]

Contact

Hertz

Kik

Ayasse

Sichani

(a)

-5 -4 -3 -2 -1 0 1 2 3 40

300

600

900

1200

1500

1800

Pre

ssu

re [

MP

a]

Y [mm]

Contact

Hertz

Kik

Ayasse

Sichani

(b)

Fig. 3. Contact patch and maximum pressure distribution along

lateral direction with wheelset lateral displacement of Δy = 3 mm.

Comparison with CONTACT and Hertz solution results, the lateral

axis is positive towards the field side. (a) Contact patch, (b)

maximum pressure

3.2 The Results of Tangential Contact

During the tangential contact solution procedure,

Hertz method and the three non-elliptic contact

models are based on Kalker’s simplified theory

FASTSIM algorithm [9] or a version adapted for

non-elliptic patches, while the CONTACT

software is based on Kalker’s complete theory [1].

As the same with the normal contact solution, the

wheelset lateral displacement of Δy = 3 mm is also

taken as an example.

Figure 4 shows the longitudinal stress and total

creep distribution along the contact patch

centerline estimated by the three non-elliptic

contact models, and they are compared with the

CONTACT and Hertz+FASTSIM results. It

should be kept in mind that the normal pressure in

FASTSIM has a parabolic distribution rather than

semi-elliptic. The contact patch is partial slip (see

Figure 5) at this contact case.The FASTSIM-based

approach for calculation of tractions results in

almost the same tangential stress distribution along

the rolling direction. This is because the tangential

stress increases linearly in the adhesion area until

it saturates and follows a parabolic traction bound

curve in the slip area when FASTSIM is used. It

also indicates a larger slope in the patch. However,

the stress is non-linear in the adhesion area for

CONTACT solution. The characteristic of

tractions obtained in this paper is similar to

Enblom’s [12]. Figure 4(b) shows the total creep

magnitude distribution along the contact patch

centerline for partial slip, and the elastic

deformation contribution to the creep is taken into

account. In this case the total creep achieved by

the FASTSIM-based approach is generally larger

than CONTACT, and the total creep distribution

calculated by Hertz+FASTSIM, Ayasse+

FASTSIM and Sichani+FASTSIM is almost the

same and the value is also larger than other

approaches.

The stick-slip distribution within the contact patch

predicted by different models is illustrated in

Figure 5. In the pictures, the blank area stands for

adhesion region and arrows area is micro-slip

region, and the direction of arrows indicates the

slip direction of the particles within micro-slip

region, and the length of the arrows means the

relative magnitude of the creep. As shown in Fig.5,

the contact patch is partial slip, only the trail area

of the contact patch is in micro-slip state. The

stick-slip distribution and the slip direction of the

particles within micro-slip region between all

methods almost have no difference.

-8 -6 -4 -2 0 2 4 6 80

50

100

150

200

250

300

Lo

ng

itu

din

al s

tres

s [M

Pa]

X [mm]

CONTACT

Hertz+FASTSIM

Kik+FASTSIM

Ayasse+FASTSIM

Sichani+FASTSIM

(a)

-8 -6 -4 -2 0 2 4 6 8

0.0

0.2

0.4

0.6

0.8

1.0

To

tal

cree

p [

%]

X [mm]

CONTACT

Hertz+FASTSIM

Kik+FASTSIM

Ayasse+FASTSIM

Sichani+FASTSIM

(b)

Fig. 4. Longitudinal stress and total creep distribution along the

contact patch centerline with wheelset lateral displacement of Δy =

3 mm. The creepages are obtained dependent on the results of the

relationship of contact geometry (the yaw angle of wheelset is

unconsidered) and ξx = -0.07%, ξy = 0, ξη= -0.195 [1/m]. (a)

Longitudinal stress, (b) total creep

Table 1. Contact area comparison between different models (mm2)

Wheelset displacement (mm) CONTACT Hertz Kik Ayasse Sichini

0 67.2 60.5 75.1 63.8 58.9

3 75.1 60.4 85.9 68.2 72.4

5 103.9 102.6 109.9 100.6 100.0

8 41.5 26.5 62.6 31.8 48.4

Table 2. Maximum pressure comparison between different models (MPa)

Wheelset displacement (mm) CONTACT Hertz Kik Ayasse Sichini

0 1689 1697 1399 1754 1696

3 1580 1697 1233 1753 1694

5 1007 989 924 989 989

8 3296 3738 1675 3779 3732

-8 -6 -4 -2 0 2 4 6 8-6

-4

-2

0

2

4

CONTACT

Y [

mm

]

X [mm]

-8 -6 -4 -2 0 2 4 6 8-6

-4

-2

0

2

4

Hertz+FASTSIM

Y [

mm

]X [mm]

(a) (b)

-8 -6 -4 -2 0 2 4 6 8-6

-4

-2

0

2

4

Kik+FASTSIM

Y [

mm

]

X [mm]

-8 -6 -4 -2 0 2 4 6 8-6

-4

-2

0

2

4

Ayasse+FASTSIM

Y [

mm

]

X [mm]

-8 -6 -4 -2 0 2 4 6 8-6

-4

-2

0

2

4

Sichani+FASTSIM

Y [

mm

]

X [mm]

(c) (d) (e)

Fig. 5. Stick-slip distribution for Δy = 3 mm predicted by (a) CONTACT, (b) Hertz+FASTSIM, (c) Kik+FASTSIM, (d) STRIPES+

FASTSIM, (e) ANALYN+FASTSIM, with ξx = -0.07%, ξy = 0, ξη= -0.195 [1/m]

4. WHEEL WEAR PREDICTION MODEL

Wheel wear prediction is a very complicated

process and it is an across-disciplines. A general

architecture of the wheel wear prediction model is

shown in Fig. 6, and is consisted of four main

modules: (1) multi-body simulation of railway

vehicle-track dynamics; (2) local contact model; (3)

wear calculation; (4) smoothing and updating of

the wheel profile.

The wheel wear prediction starts from the vehicle

and track dynamic simulation which is done using

commercial software SIMPACK. At each

integration step of the vehicle-track dynamic

simulation, global contact parameters (position

and dimensions of the various active contacts,

normal force, wheelset lateral displacement, yaw

angle and creepages) are output and used to

perform the local contact analysis, the tractions

and creep distribution within contact patch are

achieved. Then the wear function developed by

USFD [14], related the energy dissipated in the

wheel-rail contact patch with the amount of worn

material to be removed from the contact surface, is

used to evaluate wheel wear. At last the wear

distribution and worn profile are smoothed, then

the worn profile is input into the next wear step.

The local contact model is described in the Section

2, so only the multi-body model of vehicle-track

and wear model are introduced in this section.

Fig. 6. General architecture of the wheel wear prediction model

4.1 Multi-Body Model of Railway Vehicle

The B-type metro train (see Fig. 7(a)) running on

Beijing Changping metro line is modeled in this

paper, which composed of four powered coaches

in the middle and two trailer coaches at external,

but only a trailer coach has been performed in

present research activity. The vehicle model

consists of a coach and two bogies with two

wheelsets, the axle-box is also considered in this

model. The vehicle model developed in this paper

is provided with two stages of suspensions (see

Fig. 7(b)). The primary suspensions are made up

of coaxial spring and nonlinear vertical damper,

which link the axle boxes with the bogie frame.

Because the maximum oprational speed of this

vehicle is 120 km/h, for the running stability

against the hunting at high speed in straight track

requires primary suspensions have higher

longitudinal stiffness, a longitudinal linking arm is

equipped which connects the axle box with the

frame and provides a higher longitudinal stiffness.

The secondary suspension stage, connecting the

bogie frame with the car body, comprises the

following elements: two air-springs for

longitudinal, lateral and vertical stiffness; a

nonlinear traction rod, to transmit the traction or

braking efforts; nonlinear lateral bump stops;

nonlinear lateral dampers. All the linking elements

of primary and secondary suspensions are modeled

as viscoelastic force elements, taking into account

all the mechanical nonlinearities (vertical dampers

of primary suspensions, traction rod, lateral bump

stops and lateral dampers of secondary

suspensions). The resultant whole SIMPACK

multibody model includes 15 rigid bodies: 1 coach,

2 bogie frames, 4 wheelsets and 8 axle boxes.

The flexibility of the track is neglected in present

model, the rail profile is 60 kg/m in China

(CHN60), the gauge is 1435 mm, wheel nominal

rolling radius is 420 mm, wheelset back-to-back

distance is 1353 mm. The FASTSIM based on

Kalker’s simplified theory [9] is used to solve the

wheel and rail contact. The coefficient of friction

is set to 0.3 and track irregularity of AAR6 is

considered.

P,yw, ψ, j

Normal contact solution

New profiles

Wheel wear calculation Accumulated wear depth

USFD wear function

Local contact model

Hertz, Kik, Ayasse,

Sichani, CONTACT

P3j, a, b

Tangential contact solution

FASTSIM, CONTACT

Ptj, γj

Lo

cal co

nta

ct mo

del

Multi-body model (SIMPACK)

(a)

(b)

Fig. 7. The photos of B-type metro train. (a) the train, (b) the

feature of the bogie

4.2 Wear Model

The wear function developed by USFD [14],

considering the energy dissipated in the wheel-rail

contact patch with worn material, is used to

evaluate wheel wear. The analytical expression for

wear rate Kw (μg/m·mm2), which expresses the

weight of lost material (μg) per distance rolled (m)

per contact area (mm2), is given by the following

equation:

5.3 10.4

55.0 10.4 77.2

61.9 4778.7 77.2

w w

w w

w w

I I

K I

I I

(1)

where Iw (N/mm2) is the local frictional power in

contact patch, which can be evaluated by the

means of the wear index：

( , )=p( , ) γ( , )wI x y x y x y (2)

where p(x,y) and γ(x,y) are the tractions and local

creep in each point (x,y) of the contact patch grid.

After estimating the wear rate, the wear

distribution δp(t)( x,y) in each point (x,y) of the

contact patch grid can be calculated as

( ) ( , ) wp t

Kx y x

(3)

where ρ is the material density of wheel material

(expressed in kg/m3) and Δx is the width of

meshes of contact patch.

Then, all the wear contributions within contact

patch is summed in the longitudinal direction, the

wear distribution at one across section is achieved:

( )

( ) ( )( )

( ) ( , )a y

tot

p t p ta y

y x y dx

(4)

At last, the wear distribution during the dynamic

simulation is summed, as

( )

1( ) ( )

2

end

p tstart

Ttot

dT

W y y vdtR

(5)

where R is the nominal rolling radius and v is the

vehicle speed.

5. THE RESULTS OF WHEEL WEAR

PREDICTION

From the analysis of wheel-rail contact solution

based on different models, it is obvious concluded

that the different methods may show somewhat

significant differences at contact solution,

especially at normal contact. To investigate the

influence of wheel-rail contact modelling on wheel

wear calculation, the accumulated wheel wear for

a few type cases has been simulated (Table 3). In

the wheel wear simulation, all these contact

models are taken as a post-processing rather than

online solution.

The curve passing cases includs the entrance and

exit transition curves and a circinal arc curves.

Equal amount of right-hand and left-hand curves

as well as forward-backward symmetry is

assumed.

Table 3. The wheel wear simulation cases

Case Radius (m) Cant (mm) Speed (km·h-1)

Tangent ∞ 0 90

R400 400 120 60

R600 600 120 80

R1000 1000 76 80

The normalized wear depth for the four simulation

cases are presented in Figure 9, in the diagrams the

lateral coordinate is taken positive towards the field

side (Figure 8).

-60 -40 -20 0 20 40 60-10

0

10

20

30

Ver

tica

l p

osi

tio

n [

mm

]

Lateral position [mm]

Wheel profile LM

Fig. 8. Wheel profile coordinates

For the tangential case (Figure 9(a)) the wear

spread predicted based on different local contact

model is almost the same and mainly distributed

between -20~10 mm. However, the peak depth has

significant difference. CONTACT predicts the

biggest peak depth, but STRIPES and ANALYN

underestimated wheel wear relative to CONTACT.

The ratio of peak depth of CONTACT,

Hertz+FASTSIM, Kik+FASTSIM, STRIPES+

FASTSIM and ANALYN+FASTSIM is

1:0.87:0.81: 0.30:0.27 (taken CONTACT as a

reference). That is to say, the wear depth evaluated

based on STRIPES and ANALYN is more than

three times lower than CONTACT. Both wear

distribution and peak depth of Kik+FASTSIM are

similar to CONTACT, and elliptic approach also

has a good prediction.

-40 -30 -20 -10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

No

rmal

ized

wea

r d

epth

Lateral position [mm]

CONTACT

Hertz

Kik

Ayasse

Sichani

(a)

-40 -30 -20 -10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed w

ear

dep

th

Lateral position [mm]

CONTACT

Hertz

Kik

Ayasse

Sichani

(b)

-40 -30 -20 -10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

No

rmal

ized

wea

r d

epth

Lateral position [mm]

CONTACT

Hertz

Kik

Ayasse

Sichani

(c)

-40 -30 -20 -10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

-35 -33 -31 -29 -27 -250.0

0.2

0.4

0.6

0.8

1.0

No

rmal

ized

wea

r d

epth

Lateral position [mm]

CONTACT

Hertz

Kik

Ayasse

Sichani

(d)

Fig. 9. Normalized wear depth and distribution predicted by the

USFD wear function based on different local contact models. (a)

Tangential case, (b) R1000 case, (c) R600 case, (d) R400 case

For curving cases (Figure 9(b), (c) and (d)) the

differences between different models are relative

small, especially for the wear towards the flange

root running as outer wheel. STRIPES and

ANALYN predict almost the same wear

distribution. In a word, the wear predicts based on

elliptic approach has a good agreement with

CONTACT either the outer wheel or the inner

wheel. That is a surprising result. Kik-Piotrowski

method also has a good prediction, but STRIPES

and ANALYN underestimate the wear.

6. COMPARISON OF COMPUTATIONAL

COST

In dynamics simulation of railway vehicles and

wheel and rail wear simulation, the contact

problem in the wheel-rail interfaces should be

solved every millisecond. So it is especial

importance to utilize a fast and less

computationally expensive method with higher

accuracy. The CPU time taken by five contact

models are compared and tabulated in Table 4. In

the present research, a total of 1851 contact cases

are considered, including normal and tangential

contact solution. It should be kept in mind that the

tangential solution of the Hertz method and the

three non-elliptic contact models are based on

FASTSIM, and the contact patch is divided into

40*40 elements both in FASTSIM and

CONTACT. It should also be noted that

CONTACT is a Fortran code, while the other

methods are implemented in e Matlab environment.

All the calculations are performed with the same

computer with 3.1 GHz processor.

Table 4. CPU time taken by different contact models

Hertz Kik Ayasse Sichani CONTACT

Time (s) 4.0 25.3 108.4 185.8 15772.5

Ratio 1.0 6.3 27.1 46.5 3943

* The ratio is taken Hertz method as reference.

The results show that the more complex model, the

more time will cost. Hertz+FASTSIM is the fastest

method, and it costs about 4 seconds to calculate

a total of 1851 contact cases, while the CONTACT

is very time consuming and taken about 4.38 hours

to do the same work. Therfore, the CONTACT is

unsuitable to evaluate wheel wear. From the

previous research it can be found that the

STRIPES and ANALYN predict nearly the same

wheel wear, but STRIPES is about 1.71 times

faster than ANALYN.

7. CONCLUSIONS

The main work of this research activity is to compare

wheel-rail contact models and its effect on wheel

wear simulation. The contact models based on virtual

penetration, like Kik-Piotrowski method and

STRIPES, and approximate surface deformation

method ANALYN are compared. To evaluate these

models, both normal and tangential contact problem

are performed through several contact cases. The

CONTACT software based on Kalker’s complete

theory is taken as reference, moreover, the Hertz

solution is also performed. In terms of wheel wear

prediction all these contact models are taken as a

post-processing rather than online solution, and the

USFD wear function is used to calculate wheel wear.

Based on the obtained results, the following

conclusions are drawn.

(1) The contact patch and pressure distribution

predict by both STRIPES and ANALYN have a

relatively good agreement with CONTACT, however,

Kik-Piotrowski method generally overestimates the

contact patch and underestimates the pressure and the

Hertz solution is generally opposite with Kik-

Piotrowski method.

(2) In the tangential case, the wheel wear predicts

based on Kik-Piotrowski method has a relatively

good agreement with CONTACT. In the curving

cases, the differences between different models are

relative small, especially for the wear towards the

flange root running as outer wheel. The wear predicts

based on elliptic approach has a good agreement with

CONTACT either the outer wheel or the inner wheel,

this is a surprising result. In all simulation cases,

STRIPES and ANALYN evaluate nearly the same

wheel wear and both of them underestimate the

wheel wear.

(3) The computational cost between these contact

models has a significant difference. The ratio of time

cost between Hertz, Kik-Piotrowski, STRIPES,

ANALYN methods and CONTACT is

1:6.3:27.1:46.5: 3934. The CONTACT is the most

time consuming method and unsuitable for wheel

wear.

8. ACKNOWLEDGMENTS

The present work is supported by the National

Natural Science Foundation of China (Nos.

U1134202, 51275427 and 51275430).

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