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3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Edición Especial Special Issue Abril 2020

EXTENDED KALMAN FILTER FOR ESTIMATION OF

CONTACT FORCES AT WHEEL-RAIL INTERFACE

Khakoo Mal

PhD Scholar, Department of Electronic Engineering,

Mehran University of Engineering and Technology, Jamshoro, (Pakistan).

E-mail: 17phdiict05@students.muet.edu.pk ORCID: https://orcid.org/0000-0002-5754-0441

Imtiaz Hussain

Associate Professor, Electrical Engineering.

DHA Sua University. Karachi, (Pakistan).

E-mail: imtiaz.hussain@dsu.edu.pk ORCID: https://orcid.org/0000-0002-7947-9178

Bhawani Shankar Chowdhry

Professor Emeritus.

Mehran University of Engineering and Technology. Jamshroo, (Pakistan).

E-mail: bhawani.chowdhry@faculty.muet.edu.pk ORCID: https://orcid.org/0000-0002-4340-9602

Tayab Din Memon

Associate Professor, Department of Electronics.

Mehran University of Engineering and Technology. Jamshoro, (Pakistan).

E-mail: tayabdin82@gmail.com ORCID: https://orcid.org/0000-0001-8122-5647

Recepción:

20/01/2020

Aceptación:

15/04/2020

Publicación:

30/04/2020

Citación sugerida Suggested citation

Mal , K., Hussain, I., Chowdhry, B. S., y Memon, T. D. (2020). Extended Kalman lter for estimation

of contact forces at wheel-rail interface. 3C Tecnología. Glosas de innovación aplicadas a la pyme. Edición

Especial, Abril 2020, 279-301. http://doi.org/10.17993/3ctecno.2020.specialissue5.279-301

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3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Edición Especial Special Issue Abril 2020

ABSTRACT

The wheel-track interface is the most signicant part in the railway dynamics because the

forces produced at wheel-track interface governs the dynamic behavior of entire vehicle.

This contact force is complex and highly non-linear function of creep and aected with

other railway vehicle parameters. The real knowledge of creep force is necessary for reliable

and safe railway vehicle operation. This paper proposed model-based estimation technique

to estimate non-linear wheelset dynamics. In this paper, non-linear railway wheelset is

modeled and estimated using Extended Kalman Filter (EKF). Both wheelset model and

EKF are developed and simulated in Simulink/MATLAB.

KEYWORDS

Railway dynamics, Wheel-rail interface, Model-based estimation, Extended Kalman Filter.

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3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Edición Especial Special Issue Abril 2020

1. INTRODUCTION

The main element of any study of rolling stock behavior is the wheel-track interaction

patch (Simon, 2006). All the forces which help and direct the railway vehicle transmit via

this narrow area of contact and knowing of the nature of these forces is most important for

any investigation of the generic railway vehicle behavior (Melnik & Koziak, 2017).

The Wheel-track condition information can be detected in real time to provide traction

and braking control schemes for re-adhesion. For example, in Charles, Goodall and Dixon

(2008) an indirect technique based on Kalman Filter (KF) is proposed for the estimation

of low adhesion with wheel-track prole by using conicity and wheel-rail contact forces.

A method using Kalman lter has also been introduced in Mei, Yu and Wilson (2008)

and Hussain and Mei (2009) to identify the slip after evaluating the torsional frequencies

in the axle of wheelset. Two indirect monitoring schemes using a bank of Kalman lters

are proposed for (i) wheel slip detection and, (ii) real time contact condition and adhesion

estimation in Hussain and Mei (2010, 2011). In Hussain, Mei and Ritchings (2013) and

Ward, Goodall and Dixon (2011), the development of techniques based on Kalman-Bucy

lter proposed for the estimation of wheel-track interface conditions in real time to predict

the track and wheel wear, the development of rolling contact fatigue and any regions of

adhesion variations or low adhesion.

However, due to nonlinear nature of wheel-rail dynamic behavior, Kalman-Bucy lter

is dicult to use for entire operating conditions. A method using Heuristic non-linear

contact model and Kalker’s linear theory is proposed in Anyakwo, Pislaru and Ball (2012)

for modeling and simulation of dynamic behavior of wheel-track interaction in order to

discover the shape of interaction patch and for obtaining the tangential interaction forces

generated in wheel-rail interaction area. On the basis of measurement of traction motor’s

parameters, (i) creep forces can be predicted by means of Kalman lter between roller and

wheel (Zhao, Liang & Iwnicki, 2012) and (ii) slip-slide is detected and estimated by using

Extended Kalman Filter (EKF) (Zhao & Liang, 2013).

A system based on two dierent processing methods, i.e., model-based approach using

Kalman-Bucy lter and non-model based using direct data analysis, is presented for on-

board indirect detection of low adhesion condition in Hubbard et al. (2013a, 2013b).

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However, the technique using yaw acceleration as a normalization method provides only a

rough estimate and introduces a huge delay to obtain an estimate. A model-based technique

using Unscented Kalman Filter (UKF) is proposed by Zhao et al. (2014) for estimation

of creep, creep forces as well as friction coecient from the behavior of traction motor.

However estimators seem unreliable in some critical track conditions, hence still work is

needed to monitor these wheel-rail parameters more eectively in real time.

A system based on the principles of synergetic control theory is proposed in Radionov

and Mushenko (2015) to estimate adhesion moment in wheel-track contact point. Two-

dimensional inverse wagon model based on acceleration is developed in Sun, Cole and

Spiryagin (2015) for evaluation and monitoring of wheel-rail contact dynamics forces. The

results at higher speed are agreeable, however improvement in the model is further needed

to reduce the error at all expected speeds. Another technique using multi-rate EKF state

identication is presented in Wang et al. (2016) for detection of slip velocity by merging

the multi-rate technique and Extended Kalman lter technique to identify the load torque

of traction motor. On the basis of tting non-linear model, EKF can also be applied to

identify the wheel-track interaction forces and moments that takes into account the interface

nonlinearities (Strano & Terzo, 2018).

After reviewing the literature on condition monitoring of railway wheelset dynamics, it

is observed that the problem to analyze wheelset conditions and update them to desired

situation still needs to be improved in order to accomplish the expectation of railway vehicle

to be really high speed, high comfort, more safer and economical means of transport across

the world.

In this paper, Extended Kalman lter is designed for non-linear railway wheelset model

to estimate lateral velocity and yaw rate of wheelset as well as creep and creep force.

Polach formulae for creep force and friction coecient are used in modeling of non-

linear wheelset. Both modeling of non-linear wheelset and designing of EKF are done in

Simulink/MATLAB.

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2. MODELING OF NON-LINEAR WHEELSET

The motion of a railway vehicle is directed by interaction forces produced at wheel-

track contact, which change non linearly with respect to creepage and are aected by the

unpredictable variations in the adhesion conditions (Hussain, 2012). A single solid-axle

wheelset shown in Figure 1 is taken for modeling and estimation of wheel-rail conditions.

Figure 1. Railway wheelset [captured by author during eld visit].

The creepages (the relative speed of the wheel to rail) of right and left wheels of wheels in

longitudinal direction are expressed in following equations.

(1)

(2)

The main objective of this paper is to develop a state of art technique to detect the changes

in wheel-rail contact conditions. The term

in equations (1) and (2) does not involve

lateral and yaw dynamics, hence can be excluded in simplied longitudinal creep equations

because only yaw and lateral dynamics are sucient for detecting these changes. Further

, so the simplied creep equations used in above model become as:

(3)

(4)

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The creepages in lateral direction are expressed as:

(5)

While in equations (6) total creep of the wheels is depicted.

(6)

As the wheel-rail contact forces govern railway vehicle’s dynamics are creep forces and

are the function of creeps. The adhesion coecient is the ratio of tangential force that

is creep force to normal force and hence is also a function of creep. Figure 2 illustrates a

classic nonlinear change of the adhesion coecient with respect to creepage for all track

conditions i.e. dry, wet, poor and worst conditions.

Figure 2. Creep v/s Adhesion Coefcient for all conditions of wheel-rail interface.

Following equations illustrate creep forces and adhesion coecient.

(7)

i = Right and left wheels, j = longitudinal and lateral directions

F

i

is the total creep force and can be calculated by Polach formula (Polach, 2005).

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(8)

Where U is friction coecient, is gradient of the tangential stress in area of adhesion, k

A

is reduction factor in the area of adhesion and is the reduction factor in slip. Both U and

are illustrated as:

(9)

Where u

0

is maximum friction coecient at zero creep velocity, A is ratio of friction coecient

at innity creep velocity to u

0

and B is coecient of exponential friction decrease.

=

(10)

While a and b are half-axes of contact ellipse and c is coecient of contact shear stiness

in N/m

3

.

(11)

The equations of motion of railway wheelset at any point of creep curve of Figure 2 are

expressed as (Hussain and Mei, 2009):

(12)

(13)

(14)

(15)

(16)

(17)

Where

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F

C

is centripetal force component and can be neglected when vehicle does not run in curves

and C

S

is material damping of shaft which is normally very small. Hence both terms are

not considered in this research.

In Table 1 detailed information of all parameters used in simulated wheelset model is given.

Table 1. Parameters used in modeling on non-linear wheelset.

No. Symbol Parameter Value Unit

1 γ

xR

Right wheel creep in longitudinal direction calculated ratio

2 γ

xL

Left wheel creep in longitudinal direction calculated ratio

3 γ

yR

Right wheel creep in lateral direction calculated ratio

4 γ

yL

Left wheel creep in lateral direction calculated ratio

5 γ

R

Total creep of right wheel calculated ratio

6 γ

L

Total creep of left wheel calculated ratio

7 r

0

Wheel radius 0.5 (constant) m

8 L

g

Half gauge of track 0.75 (constant) m

9 λ

w

Wheel conicity 0.15 (constant) rad

10 ɷ

L

Angular velocity of left wheel calculated rad/sec

11 ɷ

R

Angular velocity of right wheel calculated rad/sec

12 v Vehicle’s forward velocity calculated m/sec

13 y Lateral displacement Output m

14 y

t

Track disturbance in lateral direction input m

15 Ψ Yaw angle output rad

16 F

xR

Right wheel creep force in longitudinal direction calculated Newton

17 F

xL

Left wheel creep force in longitudinal direction calculated Newton

18 F

yR

Right wheel creep force in lateral direction calculated Newton

19 F

yL

Left wheel creep force in lateral direction calculated Newton

20 F

R

Total creep force of right wheel calculated Newton

21 F

L

Total creep force of left wheel calculated Newton

22 µ Adhesion coefcient between track and wheel calculated ratio

23 N Normal load on wheel constant Newton

24 M

v

Vehicle mass 15000 (constant) Kg

25 I

w

Yaw moment of inertia of wheelset 700 (constant) Kgm

2

26 K

w

Yaw stiffness 5x10

6

(constant) N//rad

27 m

w

Wheel weight with induction motor 1250 (constant) Kg

28 v

0

Vehicle’s forward velocity at initial input m/sec

29 ɷ

0

Angular velocity of wheelset at initial input Rad/sec

30 T

m

Torque of traction motor input Nm

31 T

s

Torsional torque calculated Nm

32 T

R

Traction torque on right wheel calculated Nm