Train Simulator

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TRAIN SIMULATOR S. Colombi S" 'i "

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Abstract. This paper de scribes a realtime digital train simulator which was reali ze d to develop real braking devices . The main origin a lities of thi s simulator consists in the solutions introduced in order to allow a true simulation of the reality at re asonable price . In particular, in the modellin g, we simplified th e coupling s tatic characteristics. Thi s made it poss ible an analytic solution of th e motion and couplin g equations and there for e a redu c tion of the computin g power requirements . On the other hand , to limit the hardware cost, we adopted a multiprocessor architecture wh ere the simulation processors work in pipelin e. Keywords. Contro l e n g ineering computer applications , Modelling , Nonlinear eq uations, Numerical method s, Convergence of num e rical me thods , Multiproce sso r architecture, Parall e l processing.

tank, a command tank and a tripl e valve. An engine driver 's cock pe rmit s to va ry th e air press ure inside the main co nduit in o rd e r to control the brakin g force. Thr o ugh pr ess ur e sensor analog outputs, th e digital train s imulator can monitor pr ess ur es PbO to Pb n in s id e brake cylinders. U nd e r conditions impo se d by the u se r ( train typ e, trip configuration, ... ), th e simulator determines in real time the dynamic behaviour of th e train (translatory speeds, periph e ral speeds, drawhook efforts , ... ) in res pon se to pres s ures PbO to P bn and manipulator po s iti o n changes. It also tr ansmits to th e brakin g in s tallation binar y signals in orde r to control th e a nti -s lip sys te m (signals Sg 1 to Sg n) and th e sw itc hing to rapid brake (signals sRO to SR n)' Thi s ty pe of sys te m is a very powerful tool to develop braking dev ic e s. In this paper , different asp ects of th e di gi ta l train simulator will be described. First, we d ea l with the mod e llin g iss ue and th e ma nne r various physical ph e nomen o ns are simulated. Then, we describe the implemen tation in a rea l time environm e nt of th e s imulation and supervIsion algorithms . At la s t. so me tri a l results are pre se nted.

lNTRODucnON In order to complete th ei r braking installation , Oerlikon-BUhrl e Ltd ha s mandated the Laboratoire d'Electronique Industrielle (LEI) of the Swiss Federal Institute of Technolo gy in Lausanne to develop a realtim e digital train simulator. Figure 1 shows th e structure of the whole system for a train composed of one loco motive and n wagons.

n! I

IJ RA"I 'JG \:\ " T,\I.LATION

n "' \

; C== ' R

Fig. 1.

J"---.....

." ~

',-C==

Structure of the installation .

MODELLING Locomotive

The braking in s ta llation is co mposed of real braking equipments that come from a 50 wagons train. It includes primarily the main air conduit and for the locomotive and each wagon there exist a brake cylinder , an auxiliary air

The locomotive is represented by a second order model (chassis and casing , axles) based on the variables represented in Fig. 2 and clarified in appendix 1.

155

156

S. Cololllhi normal running skidding or slipping

normal running

20=

o

skidding or slipping

(4)

(GObw t olO + Zb}J O) / 4

Zj

Z}JO Fig. 2.

Main variables occuring in locomotive modelling.

The dynamic behaviour of the axles (we don't simulate each axle separately) can be described by the equation

It should be noted that the braking effort Z b 0 and the adherence effort Z).I 0 act like frictions and therefore their sign must be changed when the ve hicle moves back. This is true even for the total traction resistance effort GobwtotO where the vehicle speed dependence is taken into account in the factor WtotO' This factor include s diverse sources of traction resistances air resistance, friction between wheel and rail (which determines the wrenching torque when Vo=O), bending influence, falling and rising gradient, tunnel s . Different type s of pneumatic brakes are considered : block brakes, disk brakes, .... The pressure inside the brak e cylinder is used to calculate the m ec ha ni ca l braking effort Zbo'

(I)

i-th wagon with 2

C

= aro vpo

10

(2)

The electrical traction and braking force of the locomotive (Zj effort) can be varied with a manipulator (see Fig . I ). At this stage, we simulate the locomotiv e eng ine characteristics and the graduator be haviour (SBB, 1963) where we take into account the possible wrong manipulations . Adherence characteristics between wheel and rail (Z).IO effort) are taken into account by decrea sing the absolute value of the adherence effort when skidding or s lipping occurs (Weber, 1965 ).

Each wagon is represented by a third order model (chassis and casing, axles, coupling) . In fact, the coupling between the locomotive and the first wagon is taken into account in the first wagon and the coupling be tween the i-th wagon and the (i+ I )-th wagon is taken into account in the (i+l )- th wagon. The wagon modelling is based on the variables represented In Fig. 3 and clarified in appendix I.

~Z

, ,

t,x, !

2

!

r----; ! i

V, -----..

G,

The chassis and cas in g motion can be described by the following equation (3)

with cvo= ___a_ -

Z}Ji

1000 SaGo Fig . 3 .

10 1 + - --=-----

normal running

skidding or slipping

Main variables modelling.

occuring

The dynamic behaviour of the desc ribed by the equation

In

axles

wagons

can

be

Traill Sillllll al()r

V pi = - sign(V J C vpi (ZJli + ZbJ

(5)

with

l:ji

di s placement bet wee n wagons t- x i . As an example, Fig . 4 shows two pos s ible characteristics Zist (t- x i) for goods and passe ngers wagons.

(6) The chassis and cas ing m o tion can be expressed by the following equation

(7) wi th rb)

(a)

Fig. 4.

Ji 1+ - - 2 1000 Gjf i

Characteristics Zist (t-X i) for goods (a) and pa sse nge rs ( b) wagons .

n or mal runnin g SIMULATION skiddin g

General

s tru c tur e

Figure 5 s hows th e block diagram of an nwago n train and Fig.6 s h ows th e ge ne ral s imul a tion s tructure for a wagon ( i-th wagon). A ppendix 1 clarify th e used sy mbol s .

n ormal running sk idding

(8) The coupling betwee n the i-th wagon and th e ( i+ 1)-wagon can be d esc ribed by the foll ow in g equations

(9) ( 10 )

( I 1) ( I 2) w ith

C

x

1 2a

=-

( 13 )

The ge neral si mul a ti o n s tru ct ur e of th e locomoti ve is very si mil ar of th e wago n one and it wo n ' t be described in detail. The main differencies are : e lec tri ca l tr ac ti on a nd brakin g force s imulation , s lippin g si mulation , n o co uplin g. To describe th e wagon ge n era l s imulati o n str uct ure we assume, in o rd e r to s implify th e ex planations, a uniqu e sa mplin g period T for th e reso lution of each e quati o n . This t S usually neve r the case in a rea l tim e programming co ntex t. The value of a var iab le x at time kT and (k+ I )T wi II th en be no ted as x(k) respectively x( k + I ). Assuming th at th e train s tate (va riabl es state) is known a t th e sa mpling in s tan t k, th e ca lc ulati o n o f th e i -th wagon s ta te at th e samp lin g in sta nt k+1 is pe rformed as follows

Th e static component Zi st [equation (12)J of th e e ffort Zi is a nonlinear fun c tion of the V,

v1 wagon I

Z2 y 0

wago n i

Z, _I

y

0

com m and d es k

Fig. 5 .

Block diagram of an n-w ago n train.

wagon n

S. ( :,,1,,111 i>i

Calculations sequence

("-'-'-'- ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - ' - "

i i i i i i i i i i .

i i i i i i i i i i i i

i

Pbi

i

!i VI

V ]- 1

y

To explain the calculation sequence at the level of the whole train , we refer to Fig. 5 which clarifies the inter ac tions between the locomoti ve and the fir s t wagon as well as bet wee n the n wagons. Assuming that the speeds Y j(k) (i=O,I, .. . ,n) and th e efforts Zj( k) (i= 1,2, ... ,n) are known, the calculations sequence is the following (the arrows in bracket s show the information flow direction ) calculation of Y o( k+ I ) passage of Y o(k+ I ) (----7) calculation of the tran s lato ry speed Y o( k+ 1) passage of Y o( k+ 1) (----7) repeat for i= I to n calculation o f th e tran s lator y speed Yj (k+l ) and of th e effort Zj(k+l) p assage of Yj(k + 1) (----7)

o i.._._._._._._._._._._._._._._._._._._._._._._._._ ..i

Fig. 6.

Gen era l wagon.

s imul a tion

s tru c tur e

of

a

Braking force block Ca lcu late th e braking effo rt Zbj( k) usi ng the pressure in sid e th e brake cylinder Pbj (k ) and th e peripheral speed Ypj(k) Adherence bloc k Calculate th e adherence effort sk iddin g s peed Y g j( k) and co nditions CAj(k).

Z~j(k)

the

us ing the adherence

Skidding bl oc k Desc ribe th e dynamic be ha vio ur of th e axle. Us in g th e effo rt s Zbj(k) and Z~j(k) and th e tran slatory speed Yj(k), calculate th e effec tiv e braking effort Zb~j(k) (w hich mu st be pa ssed to th e coupling and m o ti on bl ock), th e sk iddin g speed Y gj( k ), th e bin ary si gnal sgj(k) and th e new peripheral speed Ypj(k+ I) .

end re petition passage of th e e ffort s Zj (k+ 1) (f-); i= I to n. Numerical differential

in

real tim e

of

the

The wagon m o ti o n equation (7) a nd the coupling equations (9) to (12) hav e to be so lved with th e sa me sa mplin g period. Th e wagon motion is no t too c riti ca l. On th e o th e r hand , the natural frequency of th e coupling oscillations may be quite hi g h and it can be s hown that an ex tr e m e ly small sampling peri od would have been used. This would dramatically redu ce the simulation capabilities of one processor. Th erefo re, we h ave to find a new so luti o n m e th od of th e wago n and coupling diffre nti a l e quati o n s that would allow a tru e simulati o n of the rea lity with a n in creased sa mpling pe riod. Th e basic id ea is th e following: thr o u g h a of th e coup ling s tatic s implifi ca ti on c hara c ter is tic s , make it possible to analytically so lv e the moti o n a nd co upling e quations . Figure 7 sh ows th e performed simplifi ca tion s.

Coup ling and m o ti on block Describe th e dynamic be h av io ur of the wago n (c ha ss is) and th e coupling. Using the tran s latory speed sY j_l(k) and Yj_l(k+l) of th e preceding wago n , th e s p eed Yj(k) of the wagon it se lf. th e displacement tI x j(k) w i th respec t to th e preceding wagon, the brakin g eff o rt Zj + I ( k ) on th e rea r dr aw ho o k , th e effec ti ve braking effo rt Zb~j(k) and th e tot a l

Z ,::1 \

l:::.x

tr ac tion r es i s tanc e w IOlj (k), thi s block calculates th e new tr a ns lat o ry speed Yj ( k+ I) , the binary sig na l sR j (k+ I ) as well as th e ne w trac tion effort Zj(k+ I ) on th e fr o nt drawh ook. Traction resis ta nc e bl oc k Us in g the loco mo ti ve position Y o( k ), ca lculate th e i-th wago n positi o n Yj (k ). This a llow s th e d e te rminati o n of th e total tr ac tion re s istance wtolj(k) as we ll as th e adherence co ndition s CAj(k).

so lution e qu a ti o ns

(a )

Fig. 7.

I

(b l

Simplifi e d characteristics Zjsl(tlXj) for goods (a) and passengers (b) wagon s.

The real coupling static characteristics for goods and pa sse n ge r s wagons h ave bee n repr ese nted b y 3 s tr a ig ht -lin es. Each line define a region

!:"j ')

(a, b, or c) for L',xi where an analytic solution w ill be possible .

d ampin g and the same total s tatic energy of th e real couplings.

Equation (2) become

We still have to solve the equ a tion s (1), (5) (ax les ) and (3) (Iocomoti ve motion) . The se differential equations are nonline ar. Different numerical methods are available. In our case, we have to use a method requirin g the knowl e dge of only one point of th e so lution c urve. In fact, for th e equation s (1), (3) a nd (5), the evaluation of the nonline ar functions is not poss ible between two sa mpling in s ta nt s. Thi s limits our choice to the Euler method and to th e sam plin g system m e thods. For com putin g tim e reaso ns, our final choice beared it on th e E ul e r method w hich is equivalent to the sa mplin g sys te m me thod wi th first order approximation.

(14 )

The factors Yi, Pi and the term t.Xi (14) and (11) d epe nds on (reg ion a,b, or c). Defi nin g

the

10

equa ti o ns

value

of L', x i

( 15 ) a nd making the following hypoth es is th e factor ~ i in equation (8) is cons idered as a constant without regard to th e axle s tat e (normal running o r skiddin g). W i is considered as a constant betwee n tw o sa mpling in s tants relatives to eq ua ti o ns (7) a nd (9). Vi-I a nd Zi+l are considered as lin ea rl y varying betwee n th e sampling in s tants k and k+1.

Yi t.Xi + Wi i s co n s idere d as a cons ta nt betwee n th e sa mpl ing instants k and k+1.

Sampling tim e c hoi ce About the coupling and wago n differential equa ti o n s, th e new so luti o n method used enab les us to ob tain a correct simul ati o n w ith a reaso nab le sa mpling period. The same samp lin g period was eq uall y used to solve th e locomoti ve motion equati o n (3). As for ax les eq uati o ns ( 1) a nd (5), th ey were so lved wi th a sa mplin g peri od allowing an exact description of the fa stes t possible phenomenon, i.e. a w hee lse t lockin g du e to a rud e braking (e m erge n cy brakin g) with po o r adherence con diti o n s. It s hould be noted that th e various sam pling periods have been determin e d in num e ri cal s imulati o n using critical trial s s imul a te d w ith ex trem e ly small sampling periods (reference sim ulati ons).

. Zi+J,k = Zi + i, k+ J we ob ta in th e final equati ons * i Xi,k+J = Eixi,k+ hi Vi.J ,k + hi V i-1,k+ l +

SIMULATION AND SUPER VISION ALGORITHMS IMPLEM ENTATION ( 16 \

where

x.

-1

= [t.x i] Vi

(18 )

1

Ei' hi, hi and h zi

are calculated usi ng the matri x

exponential

function

As

values

for

the

method

(Schmidt,

of Yi, Pi and

~Xi'

In order to ob ta in a n op tim a l use of th e processor in a rea ltim e programming contexl , th e ca lc ul a tion s of th e blocks of Fig. 6 ha ve to be performed w ith diffe ren t sa m p lin g periods (depe ndin g o n th e rapidit y of the si m ul a ted tran s ie nt ph e nom e no n). Tw o ty pe s of rea ltim e programming ca n be co nside red (SUhl e r, 1988) : th e sy nchr o nous pr og rammin g a nd th e asynchronous pro gr a mming . In o ur pa rti c ular case, we mad e u se of the sync hr o n o u s programming for seve ral reasons. First, th e ca lculation sequence is very s tri ct a nd seco nd , the probl e m it se lf ha s n o t any para ll e li s m. Figure 8 sho ws the hardw are orga ni za tion.

1980) . the se

coefficients depend on the region where L', x i is found (Fig . 7), The parameters of the co uplin g e quiv a lent characteristics (Yi, Pi ' ~Xi) a re determined in order to obtain a good oscillation

For th e si mul ati o n part , economical reaso ns lead u s to a multiprocessor so lution with high performance mi c ropro cesso rs (N S32000 family), With o ne control proces so r ( P e tri ) a nd 5 si mulation proc esso rs (Psim J to P simS ), we can simul a te a tra in of up to 50 wagons. The co ntrol

s. Co lollliJi

160

PC

I

!

P clrl

I I I

RAM

Psim1

P s im2

RAM

RO M

I/O

ROM

S UPERVIS ION

p s1 015

I I I

I I I I I I RAM

ROM

Fig. 8.

RAM

RA ,j

ROM

Hardware

RO,!

organization .

processor contro ls th e timin g (w hi c h gives th e basic samp lin g p e riod) as well as th e input/output (a nalog and dig ita l input /o utput , visualization color screen, video synchroni zation output) whereas the simulation processors share the train simulation task. The double direction links (speeds and efforts) between wagons (see Fig. 5) impose a sequential solution of th e wagon eq uations. Thus, the simul ation task distribution needs a pipeline organization of the processors where the synchronization is mad e by passing variables (Z and V). For the s upervI sIOn part , we made use of an IBM personal computer. The supervision system allows the user to dialogue with the train si mulator. Sever al functionalities are provided : starting a nd stopping, fai lure diagnosis, data acquisition, trip and train configuration ed ition, calibration a nd mainte nance works, .... Fig. 9.

Res ults of an ant i-skid devices test.

TRIAL RESULTS Figure 9 s how s the res ult s obtained on the visualization screen during a test of the antiskid devices . We have visuali zed the locomoti ve speed (V o ), the drawhook (b uffer) effort of the locomotive (Z I> as well as the braking efforts of the 1st, 8th and 15th wagon (Zbl, Zb 8 and ZblS) during a braking on tracks contaminated over a di s tan ce of 400 m. On the screen, we can c learly see the effect of the anti-skid devices, the interval of time in which the individual carriage passes over the critical section and the influence of the length of the main brake pipe (braking delays).

CONCLUSIONS The a bove described realtim e di g it al train simulator has been installed at Oerlikon-Biihrle Ltd an d works in a re markable manner. The w h o le system (including th e braking in stallati o n) is a very powerful tool to de ve lop braking devices . It is possible to quick ly carry out numerous te s ts un der a multitude of different co nditions without any risk for people and the material. This constitutes evident ly an inexpensive solution. The originali ti es introduced at the modelling level as well as at the hardware architecture allowed us to develop at reasonable price a simu l ator allowing a true sim ul ation of the reality. This is

IGI

effective braking effort at wheel

confirmed by the fact that the UIC (International Union of Railways) has approved its use to homologate new brake systems. The realization of this simulator has required about 7,5 engineer-years and has been possible thanks to the collaboration of several members of the Industrial Electronic Laboratory : Prof. H. BUhler, S. Colombi (modelling); H. Nguyen (hardware architecture); S. Colombi, S . Conod, B. Filipuci and Ph . Panchaud (software engineering).

G ~

REFERENCES J BUhler, H. (1988). Conception de systemes automatigues. Presses Poly techniques Romandes, Lausanne. Chap. 6, pp. 161-169. Henschel (1960). Henschel-Lokomotiv-Taschenbuch. VDI-Verlag, DUsseldorf. SBB

(1963). Elektrischen Lokomotiven 11201 u.f. Report SBB R 430.3, Bern.

Nr.

Schmidt, G. (1980). Simulationstechnik. R.Oldenbourg Verlag MUnchen, Wien. Webei', H.H. (1965). Untersuchung und Erkennt-nisse Uber das Adh~isionsverhalten elektrischer Lokomotiven. Schweizerische Bauzeitung, tome 83, Nr. 48, 877-899.

APPENDICES 1) Significance of the used symbols

Constants for unit transformations

a

=

36, [km/h] m/s

b = 9,SJ[N/kg]

Variables Symbols concerning the locomotive or the i-th wagon are respectively designated by an (0) or (i) index. A symbol with the same significance for the locomotive and for the wagons will be reported only once without index (e.g. Vo. Vi -> V).

Zj Zb L1.< ZbJlo

electrical braking or traction effort at wheel [N] pneumatic braking effort at wheel [N] adherence effort at wheel IN] effective adherence or braking effort at wheel [Nl

[N]

electrical traction or braking effort [N] at wheel in normal running traction (braking) effort on the front drawhook (buffer) static component of the effort Zj dynamic component of the effort instantaneous translatory speed [km/h) instantaneous peripheral speed [km/h) instantaneous skidding speed between wheel and rail [km/h) [t] vehicle weight factor taking account of the increase [ 1) of the rotating mass inertia total rotating mass moment of [Nms 2 ) inertia reduced at axle

r

wheel spoke

r

damping

constant

[m)

[~/h]

pressure inside brake cylinder [bar] displacement between i-th and (i-l)th wagons [m) vehicle position on the trip [m] adehrence conditions [I) total traction resistance [kg/t] binary signal indicating a skidding speed greater than a given value [1) binary signal to rapid brake switching [1)