A computational efficient general wheel-rail contact detection method

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/225873449

A computational efficient general wheel-rail contact detection method ARTICLE in JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY · DECEMBER 2004 Impact Factor: 0.84 · DOI: 10.1007/BF02916162

CITATIONS

READS

12

129

2 AUTHORS: João Pombo Heriot-Watt University 49 PUBLICATIONS 513 CITATIONS SEE PROFILE

Jorge A.C. Ambrósio University of Lisbon 208 PUBLICATIONS 2,508 CITATIONS SEE PROFILE

Available from: Jorge A.C. Ambrósio Retrieved on: 03 February 2016

Journal of Mechameal Setence and Technology, Vol 19, No 1, (Spectat Edzt,on) pp 411~ 421, 2005 411

A Computational Efficient General Wheel-Rail Contact Detection Method Jo~o Pombo IDMEC Instituto Superior T~emco, Av Rovtsco Pats 1, 1049-001 Lisboa, Portugal

Jorge Ambr6sio* I D M E C Inst~tuto Superior T~cmco, A v. Rovtsco Pats 1, 1049-00t Lisboa, Portugal

The development and lmplementatmn of an approprmte methodology for the accurate geometric description of track models is proposed in the framework of multibody dynamics and it includes the representatmn of the track spatial geometry and its lrregularmes The wheel and rail surfaces are parametenzed to represent any wheel and rad profiles obtained from direct measmements or design requnements A fully generic methodology to determine, onhnc during the dynamm smmlatlon, the coordinates of the contact points, even when the most general three dlmensmnal inotmn of the wheelset w~th ~espect to the lads is proposed This methodology Is apphed to study specific issues m railway dynamics such as the flange contact problem and [cad and lag contact configuratmns A formulation for the descrIptmn of the normal contact forces, which result from the wheel rail interactmn, is also presented The tangentml creep forces and moments that develop m the wheel rail contact aiea are evaluated using Kalker hnear theory, Heuristm force method, Polach formulatmn The methodology is implemented in a general muttibody code The dtscussmn is supported through the application of the methodology to the radway vehmle ML95, used by the L~sbon metro company Key Words : Railway Dynamics, Multlbody Dynamics, Contact Mechanics, Rail-Wheel Contact

1. Introduction In ratlway vehmle dynamms, the wheel-rad mteracnon plays a crucial role since the railway vehicle is guided by the forces generated by such contact The problems to consider when studying the wheel-rail contact ate (a) The contact geometry, i e, the problem of determining the location of the contact point on the profiled surfaces usmg geometric contact * Correg!~ondm~ Author. E-mail jpombo@dem 1st uIl pt I'EL +351-21-8417680,FAX +351-21-8417915 1DMEC lnsntuto Super,or Tgcmr Av Rovlsco Pals 1, 1049 001 Llsboa, Portugal {Manuscript Received November 29, 2004,Revised December 15, 2004)

constraints (b) The contact klnematms, 1 e, the problem of defining the creepages at the point of contact (c) The contact mechanics, 1 e, the problem of determining the tangentlal creep forces and the spin creep moment Several authors (Kalker, 1990, Polach, i999; K,k, 1996) studied the contact forces between the wheel and the ratl making available several computer routines for the calculations of the tangentlat forces at the contact point given the normal force and the relative vetoclttes between the contacting bodms (Kalker, 1990, Polach, 1999) The problem here is reduced to provide descrlptmns of the surfaces in contact and of the kinematics of the bodies

Copyright (C) 2005 NuriMedia Co., Ltd.

412

JoOo Pombo and Jorge AmbrOs~o

The track centerhne geometry may be described by different types of parametric curves such as cubic, Ak~ma or shape preserwng sphnes The track description adopted uses Frenet frames that prowde the appropriate referennal at every point and the defimtion of the cant angle vaHatmn along the rmlway A pre processor ~s used to define the nominal geometry of both left and r~ght rails based o11 the lnterpolatmn of a &sc~ete number of points, which aie representauve of their space curves (Pombo, 2003a, b) For the complete representation of the track geometry, both

stabihty is concerned

2. Parameterization of Railway Track A pre processor program defines the track model as two parametenzed curves that represent ~he nominal geometry of the left and right rails space curves Paramemc track descriptions using different types of sphnes are available (Pombo, 2003c) The mformahon is orgamzed m two databases where ai! quantittes, necessary to define the rails

rails are considered separate geometNc entrees

curves, are functmn of the arc length of each raft,

For ettic~eney, a pre-processor generates a table

measured from theu origin The methodology ts summarized as

w~th all track posmon data and othe~ quantities reqmred for the multxbody code as functmn of the left and r~ght ra~t lengths During a dynamic smmlatmn the program interpolates hneaily both ra~ls databases to obtain the reformation necessaxy to find the wheel/rad Interactmn The coordinates of the contact points are evaluated during the dynamic analysts by introducing surface parameters that describe the geometry of the tad and wheel contact surfaces, each described by two su[face parameters (Pombo, 2003b) The methodology allows the existence of two or more points

(a) The geometry of the track centerline is parametenzed u3mg a p~ecew~se cubic mterpolation scheme (b) The track cant angle ~s parametenzed as functmn of the track length (c) The track centerhne ts also parametenzed as functmn of the track length (Pombo, 2003c) (d) The track ~rregular~t~es, measured exper~mentally, are parametertzed as coImnumn functions of the track length

of s~multaneous contact between the wheel and the rail in the wheel tread or flange The normal contact forces that develop m the wheel-rail interface are calculated usmg the Hertz contact force model w~th hysteresis damping to account for the d~sstpat~en of engrgy during contact (Lankaram, 1994) The creepages, or normahzed relative velocmes at the contact point, are used w~th the normal contact force to determine the creep forces and the spin creep moment Three d~fferent methodologies are implemented In order to calculate these tangential contact forces These are the Kalker linear theory (Kalker, 1979, 1990), the Heuristic nonlinear creep force model (Shen, 1983) and the Polach formulation (Polach, 1999) The melhodolog~es proposed here are implemented m a general multibody code that ~s used

I tnpulOal~toParame'et~the zaTfa~ Ir~putDatatoPara,n~la~ze Ih~"'t~ck 1~CenIerllne ~_~y ~#~hl PEecew~sg I zCugm{ LI~, nlet#~llg[!I ~ _ ~ ~lrr~g~larliles } ~

for the dynamic analys~s of rail graded vehicles FinaLly, the compute~ code is apphed to the study of a railway vehmle in what ~ts dynamics and

Copyright (C) 2005 NuriMedia Co., Ltd.

Lef[an~Righl~all~S~, . ~eeCorves

('a,am~tar.ze,~ as ~,,c~.~,, of I ~ A.r I e~lhs I

Fig, 1 Flowchart of the railway pLe~processor

A Ccmzp.tatio,~a! E/]ficient Ge~teral Wheel Rai/('o~ttact Detection Medlod (e) Define a set of control points that are reo presentative

of the left and

right

profile coordinate system !~R,., z~,R,., SR, >' ), shown

rails space

curves.

413

in Figure 3, translates along a raiI space curve and rotates about its origin. The location of the

(f) Paramelerize the rails space curves as a function of the a~c lengths. Account I'ur the track cant angle and rail mclinalion. (g) Create a database lbr each rail, stored with a small track lengtk step. A schematic represent:tlion of t-he methodology used in the railway pre processor is presented in Fignre 1. The interested reader is referred to lhe work of P o m b o and Ambrosio (2003a,b).

3. W h e e l

and R a i l S u r f a c e s

I

The definition of the wheel and rail needs to satisfy three main requirements. First, the sttrfaces have to be defined in a global coordinate system. Second, 1he parametric equations must be able to

~T

represent any spatial configuration of the wheelsets and rails. Third. tim representation of any

/

.....

.... 11.,

-"-I

wheel and rail profiles, obtained by measurements or design requirements, must be possible.

Let two sets of independent stir(ace parameters be used to define the geometry of each of the wheel and rail in conlact be ,q,',, and u,., for the rail surface geolnetry, and ,I/-Z.

the rad and to the wheel respectively whereas the subscript (.)~,s are referred to the wheelseL In order to account for any possible scenarios, such as a variation in the gauge or rcJ.ative dis~ placements a n d / o r rotations of the rails due to the track irregularities, it is necessary to def'ir~e the surf;ice of each rail independently, as depicted by r i s u r e 3. where ,;ubsci'ipts; (.}L~ and (.}/~, are referred to tile left ai~d right rails respectively. Let a profile coordinate system be defined on each rail to idemit}.' the position and orientation of any cross section along ~he rail space curve and Y be a point of contact with the w h e e l The right

Copyright (C) 2005 NuriMedia Co., Ltd.

Fig. 3

ParametJiza|Jon o1" the rail .,urfaee

Jo5o Pombo and Jorge Ambr6sio

414

profile coordinate system along the space curve can be defined in such a way that the contact point P lies in its (zlR~, ffR~) plane. The location

A-] LeRwheel

of the origin and the orientation of the right rail profile coordinate system, defined respectively by the vector rer and the transformation matrix As~, are uniquely determined using the surface parameter Sr (Berzeri, 2000). The location of the contact point P on the rail surface is re =r~,-+A~rs~,-

(2)

where s~', is the position vector that defines the location of the contact point P on the proFig. 4

file coordinate system. The transformation matrix Aer is a function of the unit vectors that define the moving reference frame associated to the right rail space curve. In railway applications, the function f,- that defines the rail profile is a function of the surface parameter u , using a piecewise cubic interpolation schcmc (De Boor, 1978). Hence, to obtain f,(u~), the user only has to define a set of control points that are representative of the rail profile geometry, as shown in Figure 3.

rotation of the wheel profile coordinate system (@, z]w, ~'~0) with respect to the wheelset coordinate system (~ws, z]ws, ~ws), and the lateral position of the contact point in the wheel profile coordinate system. The location of the origin and the orientation of the wheelset frame are defined by vector r~s and matrix A,,~. The global position of an arbitrary point on the wheel is r ~ r ~ +A~o, ( h ~ + AL~s~.~

The detection of the location of the contact points between two parametric surfaces requires the definition of the normal vector to the rail surface n,-s at the point of contact

n.~- A~n~

(3)

where n~,.~={0, cos 7R~, sin 7R~} r is the unit vector normal to the rail surface, defined in the profile coordinate system. This vector is obtained

dfr(Ue,.) d~JR~-

/

(4)

The surface of revolution of each wheel is generated by a complete rotation, about the wheel axis, of the two dimensional curve that defines the wheel profile (Shabana, 2001). Figure 4 shows the left wheel with arbitrary surface profile assembled in a wheelset. The surface geometry of the wheel is described using the two surface parameters Sw and u~, that represent the

(5)

where hL~o={0 1/2H 0) ~ is the local position vector that defines the location of the profile coordinate system with respect to the wheelset relerence frame, being f l the lateral distance to the ,.'Q :p wheel profile origin, sLw and sR~ are the local position vectors that define the location of the contact points Q on the wheel surfaces with respect to the profiles coordinate systems, i.e.

through the contact angle 7Rrs, shown in Figure 3. The contact angle is

tg

Parametrization of the wheel surface

s?=(0

z/

r

(6)

To use the multibody contact model to solve thc problem of wheel rail contact it is necessary to devise a strategy to determine the location of the contact points between two parametric surfaces. This tbrmulation requires that the parametric sin'faces are convex. Therefore, the wheel profile is represented by two independent functions f t and f ~ that parameterize the wheel tread and flange, respectively. The search for the location of the contact points requires the definition of two tangent vectors to the wheel surfacc, r and twz,

Copyright (C) 2005 NuriMedia Co., Ltd.

415

A Computational Efficient General Wheel Rai[ Contact Detectiwt Methoct

~l, II

Tread Nodal = """

= ',

1q'

rlanpge Nodal 0=

-.,,i

l."

i.(,3ze\:

where /2 is the friction coefficient. The new resuLtant creep force F~, is used to calculate the tangential lbrces a s Fig. 9

Copyright (C) 2005 NuriMedia Co., Ltd.

[he ML95 trainse!

418

Joao Pombo and Jorge Ambrdsio

trainset is an electrical three-car unit composed

The trailer vehicle carbody is supported by four

of two powered end vehicles with driving cabs, and a intermediate vehicle, represented in Figure 10. Each ML95 trailer vehicle is composed of one

airsprings, and with each one there is a vertical "Chevron" bumpstop assembled in series. In parallel with the airsprings, four vertical hydraulic dampers and four vertical liftstops devices, shown in Figure 12, are mounted. The connection be-

carbody where the passengers travel, supported by two bogies through the secondary suspension,

tween the carbody and each bogie is done by a

which is set to minimize the vibrations induced

shaft, which guarantees an appropriate and stable

by the track on the passenger compartment. The

rotation of the bogie with respect to the carbody,

bogies arc the subsystems that, through the wheelsets, are in contact with the track and include

The mechanical elements that assure the connec-

the primary suspension, which is the main responsible for the steering capabilities and stability behavior. Each trailer bogie of the ML95 consists of one frame, two wheelsets, four axleboxes and the mechanical elements that compose the primary suspension. The bogie frame is supported by the axleboxes through eight metal-rubber springs of the "Chevron" type, The vertical displacements of the primary suspension are limited by bumpstops and liftstops, shown in Figure I1.

9

....~

~'~' i,:~,

9i, .~..

~i,

'i'.

,~' ~

,/ ,':; ~&i , ~,

tion between each bogie and the carbody are mounted between a center plate and the bogie frame, as shown in Figure 13, The transmission of traction and braking efforts between each bogie and the carbody is done by traction rods. The lateral stabilization of the carbody needs two transversal hydraulic dampers, between the center plate and bogie fi'ame. The characteristics of the ML95 trainset are shown in Table 1. The model of the railway vehicle leads to representation of the multibody model shown in Figure 14. The mass and inertia properties of system components have been supplied by the manufacturer company. For bodies with no data

Trailer Motor Fig, 10 Schematic representation of the ML95

Table 1 Main characteristics of the ML95 vehicle Traffic velocity range Minimum curve radius on track Track gauge Wheel rolling radius new Bogie wheelbase Bogie center distance Wheelset weight Bogie weight Weight of the carbody Floor height Vehicle height Vehicle width Vehicle length

Bum

Lil

Fig. 11 Primary suspension of the trailer bogie

~ l y

~

40 60 Km/h 60 m 1.435 m 0.43 m 2.1 m 1I+I m 1109 Kg 4200 Kg 11160 Kg 1.155 m 3+523 m 2.789 m 15.30 m

Airac, ring

t r a n r a -v~ e. . . . . . ' r ,a . . .a. . . . . . ~: c e, .,o n, : t e~j Transversal

bumpstop~ I

9

,- ""

".

Pivot shaft

support

rn

Fig. 12 Secondary suspension of the trailer bogie

Copyright (C) 2005 NuriMedia Co., Ltd.

Fig. 13 Bogie carbody connection of the vehicle

A Computational Efficient General Wheel Rail Contact Detection Method available, the mass and inertia properties are estimated based on their geometry. The location and type of kinematic joints is also obtained with the manuf;tcturers information. The first simulation scenario ttsed to apply the methodology developed corresponds to a straight track with no irregularities in which a vehicle

419

vehicle9 At sufficiently high speeds, 70 m/s for instance, the laleral oscillations increa,