WHEEL AND RAIL PROFILE \VEAR PROCESSl

PERJODjCA POLYTECE~ICA SER. TRAt ... ·SP. ENC. \.'OL. 26, NO. 1-2, PP. 3-17 (1998)

or~

DETERMINISTIC AND STOCHASTIC SIMULATION OF

WHEEL AND RAIL PROFILE \VEAR PROCESSl

Andras SZABO and Istvan ZOBORY Department of Railway Vehicles Technical University of Budapest

H-1521 Budapest, Hungary Received: ='iovember 13, 1996

Abstract

in the paper the formerly eiaborated sim,llation method for determining the wear propa- gation on the wheel-tread and flange is extended for the case of cO!7lbined wheel/rail wear processes. In the simulation D1ethod the straight and cur\"ed track sections arc treated distinctly taken into consideration it non-linear vehicle model moving on the track sections belonging to a specified network. The material remow.l is considered to be proportional to the dissipated energy and the specific TIonnal :raction distribution on the actual COTI1I110n

contact patches .. Also the frequency of contact is involved into the analysi~ chara.cterising actual railway operation. As a result of the simulation procedure both the magnitude of the l'ail wear and its distribution aiong the track (right and left rail distinctly), as well as the wheel wear (right and left wheels distinctly) can be determined for the considered railway' system, In the analysis also the stochastic lateral rail irregularities are taken into consideration. it will be ;:hawn how it is possible to extend the comDined wheel/rail sim- ulation prOCedure for the case of semi-.\larkovian stochastic operation conditions of the vehicles on a topo!ogicctlly specified railway net'Nork,

Keywords: n:hicle-track dynamics. combined wheel and rail WCct^r simulation.

1. Introduction

In the combined rail/wheel wear simtdation method the straight and curved track sections are treated disti netly. The material removal is considered to be proportional to the energy dissipated on the actual common contact patches of the rail and wheel. As an important parameter, also the contact frequency is involved into the numerical analysis of the railway operation process considered. :\s a result of the simulation procedure both the mag- nitude of the rail profile wear for the track sections of different curvature, (right rail and left rail distinctly), and the wheel wear (right wheels and left wheels distinctly) ca.n be determined for the railway operation process

lThis research was supported by the ~ational Scientific Research Fund (OTKA) Grant

~o. T 017169,

4 A. SZABO a!:d r ZOBOR''!''

considered. In the analysis also the stochastic lateral rail irregularities are taken into consideration based on the spectral density functions evaluated from track misalignment and gauge measurements.

2. Dynamical IVlodel

The lumped-parameter track-vehicle model consists of the vehicle body, the bogies, the wheel-sets and the discrete masses representing the track inertia.

The sprung structural connections between the rigid bodies mentioned are modelled by piece-wise linear characteristics, vlhile the dampers supposed

to be parallel to the former ones are definitely linear (see Fig. 1). The used wheel and rail profiles can be practically arbitrary.

The track can be composed of specified st raighl (cnd curved sections coming one after another in an arbitrary order. The transition curves of ar- bitrari!y prescribed curvature functions can be included between the straight.

and circular sections.

I!> The track can be laterally 'imperfect': i.e. a stochastic lateral irregu-

larity can be taken into consideration.

@ The vertical wheel loads are constants on the straight sections. while in curved sections the quasi-static compensation of the centrifugal forces and the super-elevation are carried out.

@ The wheel-rail contact on the wheel tread is treated as a creep-depen- dent force transfer spot, the creep coefficients are treated by Kalker's linear theory.

€) The longitudinal and lateral contact forces, as well as the spin mo- ment are bounded by the values based on a constant sliding friction coefficient.

i!\ The fianging is considered as a conditional, laterally elast ic and dam- pedlinear connection between the wheel-set and the mass representing the rail inertia.

ill In the model, a specified constant torque is acting on each wheel-set, which represents the resultant traction resistances and the eventually acting tractive or braking torques.

® It is always assumed that no braking torque is exerted by frictional tread braking.

The vehicle-track model in question takes into consideration track section-wise constant travelling velocities and torques on each wheel-set.

It is reasonable to use a constant average travelling velocity along the whole railway line examined, and also an average torque to act on the \vheel-sets on the basis of a preliminary 'speed distance covered' analysis.

HAIL PHOFILE WEAH PHOCESS

---

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Y I

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--'- _Jp?"

1 ^----' Yp?} ^{I -}

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~wv---f~"WkJ~

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;~b I YrAj I Fig. 1. Dynamical model of the vehicle-track system

3. Wear Hypothesis

The most frequently used wear hypothesis was formulated in terms of the proportionality between the specific energy dissipated over the contact sur- face and the specific mass removal for the unit of the distance covered [3].

Formula

am ( .

as == k^t Fx/Jx

+

^FyL'y

+

^{1\15 V.,;)}

is valid for the rolling contact of the wheel and the rail realized on the wheel tread, while for the sliding contact of the flange and the rail head formula

6 A.. SZ/;,Blc) and 1. ZOB02Y

am _

^bF, 6.v^s

as -

^{J J U}

is valid. Coefficients k_t a.nd k j can take different values for the wheel and reLil materials, which fact should be taken into consideration in the simulation procedure. In the present paper coefficients kt and kf are considered as known constants. I\evertheless the latest results of measurements show that the coefficients in question can depend on the total dist2.nce cO\'ered by tbe i'ehide

It is t.o be mentioned that the material removal in every discrete step of simulation ba.sed on formula

::'lm =

--c.,s am

is distributed among thc: profile partition elements covered by the contact p,.,tch. The of the distribution mentioned is based on the weighting factors reflecting the relative portion of normal force acting all the partition elements. i.e. for thei-th partition element intersecting the contact patch norrmd force is to be di\'ided by total normal force F

=

acting on the ',':hole c:ont3ct patch. It can be seen that the material remm'al is carried out by combining the dissipated energy based we::tr hypothesis and the wear hypothesis b2scd on the normal force of contact [1],

4. Model of Operation

It is obvio'ls t.hat the irliensity of wear of surfcLces undergoing roliing contact is proportiolleli to the frequency of contact. This fact emphasises that the inlen5ity of wheel wear is proportional to the distance covered by the wheel, while the intensity of raii wear is proportional to the number of \\'heel- sets pasosed through the track cross section considered. In the real raih';a~'

operation many kinds of vehicles should be reckoned with. In accordance

\\"ith our \\'ear simulation procedure vehicles of different geometriccJ and mechanical parameters can be considered and after a sequential computation of rail wear conditions the expected rail wear propagation can be determined by weighted averaging of the results of the individual computations. In each computation step cL specified number of axle passages should be taken into consideration.

5. Simulation of vVorn Profiles

The fundamental idea of the wear simulation is to consider the actual wheel profile and railhead profile as the basis of the contact geometrical, dynamical

RA1L PROFILE V/EAR PROCESS T

and energetical (dissipation) operations. The energetical operations result in the wear load distributions along the wheel meridian profile and the railhead profile. The 'stabilized' wear-load distribution both for the wheel profile and the rail profile is determined on the basis of a sufficiently long distance covered on straight or curved track sections. The discrelization principle applied in the simulation procedure implies the extension of the validity of the wpar load distributions mentioned above. In case of \\'heel wear simulation the stabilized wear load distribution is considered as valid for an extended (~ 1000 km) distance covered. In case of rail wear simulation the stabilized wear load distribution with respect to the passage of a single wheel-set is considered as valid for the passages many (~ 40000) wheel-sets.

The profile alteration, i.e. the reduction in rolling radii and reduc- tion in railhead height ordinates is carried out by using the wear load distributions mentioned above and appropriate physical and mathematical smoothing procedures to balance the errors caused by the used discretiza- tion method. In this way, a discrete step of profile alteration due to \vear is done both for the wheel and the rail examined. The resulting new wheel and rail profiles take over the role of the initial profiles, and a subsequent discrete step can be done, etc. In the course of the whole simulation the mentioned smoothing procedures should be sequentially applied. The phys- ical smoothing procedure is built up on the basis of continuous evaluation of the geometrical compatibility of the contacting rail and wheel profiles. The mathematical smoothing is based on the Cl spline method, i.e. a smoothly connected piece-wise second order parabola system is used.

The described simulation method results in the \vorn wheel and rail profile sequences reflecting the combined wear propagation process uncler the considered operation conditions.

6. Simulation Results

The simulation procedure was carried out by using real vehicle and track data. The considered vehicle was a four-axle rapid train carriage of tradi- tional construction, see Fig. 2.

The considered track was the southern ramp of the 'Gotthard Line' between Airolo and Bodio. The top view of the line topology is visualized in Fig. 3. The distribution of the evaluated track curvatures can be seen in

Fig.

4.

\Vith the simulation some special conditions were chosen to represent the wear propagation process in question. The computation results are shown in Figs. 5-10.

In Fig. 5 the wear propagation on the left and right wheels can be seen up to mileage performance 21800 km. In the course of the simulation the mass removal from the wheels was carried out after each 872 km distance

A. SZABO <lr:d r. ZOBORY

Fig. 2. Passenger carriage for rapid train operation

--...

R 28C .. 3 i O. G3UgC: 1435 mfr!

···~

.••• 'ODlO

Fig. 3. The considered railway line: The southern ramp of 'Gotthard line' between Airolo awl Bodio

Fig.

4.

Distribution of curvatures

RAIL PROFILE WEAR PROCESS 9

covered. The worn profiles indicated in Fig. 5 represent profile states ^In steps of 4360 km.

In Figs. 6-10 the wear propagation and wear load distributions dia- grams are plotted for the left and right rail heads. The total number of axle passages were of 10⁶ order of magnitude.

The above mentioned characteristic diagrams can be seen for the straight sections in Fig. 6. for the curved sections of radius +1400 m in Fig. '1, for the curved sections of radius -1400 m in Fig. 8, for the curved sections of radius +500 m in Fig. 9 and for the curved sections of radius -.500 m in Fig. 10. The positive signs identify the left curves while the negative signs identify the right curves.

7. Stochasticity of Wear Propagation of the VVheel and Rail Profiles

The simulation procedure should be modified if the non-conform character of the w heel profiles is taken into consideration. On the railway line under consideration several types of railway vehicles are in operation and each vehicle has its OW:1 wheel profiles in a certain state of wear.

Due to the mentioned fact the material removal should be carried out by using a modified weighting of the wear-load functions in accordance with the actual statistical manifold of the \"\;heel profiles passing through the track cross section selected for examination. In formulae:

nvp

w£ = I:w;jPj, j=l

~Pj

=

^{1, i =} 1, 2, ... , jV,

j:;:;;1

where ^Wij is the conditional wear load on the rail profile in the i-th profile partition element caused by the j-th class of wheel profiles passing through the track cross section considered, Pj is the probability of the passage of a wheel profile belonging to the j-th class, while N is the number of partition elements on the rail head.

With the knowledge of wear load distributions ^Wi i = 1,2, ... , N the rail profile of the track cross section can be modified as it has been introduced for the deterministic case [7].

There are four possible operational cases to be distinguished with the rail wear profile process:

a.) The wheel profile manifold and the probability distribution of the pro- file classes are stabilized (many vehicles, methodical profile renewal).

b.) The wheel profile manifold changes, the probability distribution is stationary (few vehicles, rigid operation sched uling).

10 A. SZABO and I. ZOBORY

Fig. Q. Wheel profile wear propagation

c.) The probability distributions change, the profile manifold is station- ary (many vehicles in operation on an extended network, fluctuating operation conditions on the line considered).

d.) Both the profile manifold and its probabiiity distribution change (few vehicles in operation on a small net\\·ork, fluctuating operation condi- tions on the line considered).

The simulation procedure formulated for a single railway line can be extended for a complete railway network [4],[5]. The stochastic operation conditions of the trains along the branches of the graph representing the network in question can be treated in the framework of semi-Markovian

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model based on the transition probability matrix and the matrix of the conditional probability distribution functions characterizing the probability measure of the number of passages on the lines in the examined network.

Though the stochasticity of the wheel and rail wear process has ap- peared due to the presence of stochastic track irregularities representing excitation sources for the lateral motion process of the vehicle moving along the track and the material removal due to wear takes over this stochastic- ity, the essential stochastic character of the com bined wheel and recil wear process is caused by the stochasticity of the operational process. In former papers [4],[5] the tools of simulation have been elaborated in the framework of the mentioned semi-:\hrkovian model.

The stochastic simulation of the wheel and rail wear processes lead to the realisation functions of the wheel and rail profiles in a natural way.

The sequential repetition of the simulation of the motion and wheel and rail profile wear processes the realisation manifold consisting of the v;orn profiles can be determined. These two profile manifolds are the representations of the two characteristic stochastic wear processes, describing the wheel and rail profile alteration in the course of operation. The parameter space of the stochastic processes in question is the lateral position co-ordinate. The marginal distributions and the statistical parameters (expectation, variance etc.) can be determined to each lateral position. With knowledge of the mentioned statistical quantities a very impressive, detailed wear characteri- sation can be carried out. For the case of the wheel profile wear the diagrams in [5] can be referred to.

8. Concluding Remarks

® The dynamics and tribology based simulation model is apt to give predictions about the wheel and rail wear propagation caused by the regular operation of specified vehicles on a specified line.

€I In the simulation model disctretization technique is used. To achieve reasonable accuracy and computation time consumption the selection of the discretized lengths of distance covered and the number of axle passages in a discrete computation step are of basic importance.

€I The simulation model was tested by using the data of the 'Gotthard' line and a rapid train carriage. The computation results show that the wear load of the rail head on straight track sections is negligible in comparison with those realized in curved sections of 1400, 500 and 300 m radii.

® The wear coefficients belonging to the rail should be determined on the basis of extended rail profile measurements reflecting the variation with time of the profiles under known loading conditions, i.e. by taking into account the axle loads and the total number of axle passages.

RAlL PROFILE WEAR PROCESS 17

~ The combined wheel and rail profile wear simulation can be extended to the case of taking into account specified statistical wheel profile and rail proTIIe manifolds. In this case the whole combined wear process becomes a stochastic phenomenon.

e;; Taking into consideration the parameter spectrum of the vehicles and the random character of the railway operation on a network the ex- pected wheel and rail wear propagation can also be predicted.

'!iJ The latter predictions can be the basis of a computer based complex

rail and wheel management system to be elaborated in the future.

References

[1] FmES. R. H. D,wILA. C. G.: Analytical .vlethods for Wheel and Rail iVear Pre- diction. The Dynamics of Vehicles on Roads and on Tracks. Proceedings 9th lA VSD Symposium, 1985 Swets &: Zeitlinger B.V. - Lisse. pp. 112-125.

[2J CHl.iDZIKIEWICZ. A.: Progress Wear of Wheel in Simulation Research. Procecdzngs of the 2nd "'[ini Conference on Vehicle System Dynamics, Identification and Anomalies.

Held at the TU of Budapest, 1990, pp. 209-230.

[3J KALKER, J. J.: IYear, Vol. 150 (1991) pp. 355-365.

[4] SZABO, A. - ZOBORY, I.: On Stochastic Simulation of the Wheel-Profile Wear Process of a Railway Vehicle Operating on a Specified Network. Proceedings of the 4th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, held at the TU of Budapest, 7-9 )i'overnber. 1994, pp. 246-259.

[5] SZABO, A. - ZOBORY. I.: Simulation-based Prediction of Wheel Profile Wear under Long Term Stochastic Operation Conditions. Proceedings of the 3rd International Con- ference on Railways Bogies and Running Gears, held in Budapest, 18-20 September, 1995. pp. 231-244.

[6] KRETTEK, O. - SZABO, A. BEKEFI. E. ZOBORY, I.: On Identification of Wear Coefficient Used in the Dissipated Energy Based Wear Hypot hesis. Proceedings of the 2nd .vfini Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Budapest, 29<31 July, 1996, pp. 260-265.

[7J SZABO. A. ZOBORY, i.: On Combined Simulation of Rail/Wheel Profile Wear .. Pro- ceedings of the 2nd Afini Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Budapest. 29-31 July, 1996, pp. 196-206.