Cieślakowski S.J. Determination of safe track brake locations in gravitational marshalling systems.

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DETERMINATION OF SAFE TRACK BRAKE

LOCATIONS IN GRAVITATIONAL

MAR-SHALLING SYSTEMS

Cieślakowski J.

Radom K. Pulaski Technical University, Faculty of Transport Ul. Malczewskiego 29, Radom, Poland

Abstract: Shunting yards, large maneuver, plant and shipyard yards constitute principal centres

of logistical infrastructure. Gravitational marshalling systems are key points of this infrastructure. A high number of carriage accidents in such yards is due to, among other factors, wrong situation of certain components of the logistical infrastructure. Safe distance between space brakes and the first hump change of gradient is calculated in this paper.

1. Introduction

Specific infrastructure is a necessary condition for functioning of a logistical system. The infrastructure should enable efficient and smooth implementation of all logistical func-tions. From the macroeconomic viewpoint, logistical infrastructure consists of [3]:

 all transportation routes, including industrial transport, that is, pipelines,

 transport centres, particularly sea, river and air ports, container terminals, transfer and

marshalling railway yards, combined transport terminals,

 storage and warehousing buildings and structures with their facilities to handle cargo and fulfill basic functions, e.g. assembly, disassembly and packaging, as well as stor-age areas, loading and unloading fronts, ramps, etc,

 element of centre-based logistical infrastructure, such as distribution, logistical

ser-vices centres, warehousing and transport districts,

 information processing and transmission equipment and facilities, including neces-sary software.

Infrastructure allows for implementation of principal logistical processes and, at the same time, influences their course and, even more importantly, the volume of costs.

Infrastructure of logistical processes should be considered as a technical and organiza-tional system where maximum cost reduction while maintaining efficiency and reliability of logistical processes should be the fundamental criterion of optimization [3]. An

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addi-tional consideration is that safety of the logistical processes ought to be assured. Railway centres are divided into principal and auxiliary. The former group includes marshalling and large maneouvre yards. Auxiliary centres include the other maneouvre yards and in-termediate stations.

PKP (Polish National Railways) maintain the following marshalling yards: Warszawa Praga, Skarżysko Kamienna, Łódź Olechów, Tarnowskie Góry, Kraków Prokocim, Zajączkowi Tczewskie, Zabrzeg Czarnolesie, Szczecin Port Centralny, Poznań Franowo, Wrocław Brochów. Large PKP maneouvre yards include, inter alia: Lublin Tatary, Kielce Herbskie, Toruń, Łazy, Rybnik Towarowy. Marshalling yards, Large PKP maneouvre yards, large company and port yards are fitted with gravitational marshalling systems that enable most effective carriage marshalling. The following belong among the large com-pany and port yards: Huta Sendzimira, Gdynia Port.

This paper aims at determining safe location of space brake in gravitational marshalling systems.

2.

Current literature of the issue

The literature [1, 5, 6] assumes that, at one space braking position, the space brake should be situated 120-175 m away from the hump ridge, that is, 115-170 m from the first change of gradient of the marshalling hump. The authors cite results of simulation tests. The resis-tance of slow-moving carriage, 4,7 N/kN, does not obtain at PKP at the moment.

The paper [4] sets the minimum distance between the start of track brake and the shalling hump top at 109.6 m, or 104.6 m from the first change of gradient of the mar-shalling hump. The resistance of slow-moving carriage, 6.9 N/kN, assumed for the pur-poses of calculation, does not occur at PKP at present. The calculations involved an arbi-trary assumption of the difference between passage times of a slow and fast-moving car-riage from the hump peak to the brake start of t = 2s. The brake’s response time 1s, as-sumed in the calculations, does not obtain with the new automated systems.

The issue of design and function of track brakes was discussed in [7]. Safe location of space brakes was not taken into consideration, however.

3. Formulation of the problem

Safety of rail carriages is most vulnerable when they are marshaled in gravitational mar-shalling systems, inter alia, at space brakes. At present, there is no method to determine a location of the brake that would be safe to wagons.

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Therefore, the function F needs to be developed that transforms the configuration of a gravitational marshalling system K, marshalling technology TE, and selected carriage parameters P into a safe distance L of a space rail brake from the first change of gradient of marshalling hump:

F : (K, TE, P)  L (1)

4. Test method and results

Safety status of a carriage can be represented as a situation where:

x < X (2) where:

x – status of carriage, X - limitation. The first limitation is:

V < Vmax (3)

where:

V – speed of carriage,

Vmax – permissible speed of carriage entering space brake.

The second limitation is:

t > tmin (4)

where:

t – time interval between the preceding and the following carriage,

tmin - minimum time interval between carriages necessary to set space brake.

Speed of carriage VL at the start of space brake removed at a distance L from the first

hump change of gradient can be calculated using the formula [1]:

V

2 g

i(

w

)

L

V

_Ł

o

p

2 o









[m/s] (5) where:

Vo – speed of carriage pushing [m/s],

g - modified acceleration of gravity [m/s2_],

i – average hump inclination towards space brake, wp – unit air carriage resistance,

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wŁ - unit curve carriage resistance.

In view of the brake’s design, a brake will be safe on a brake when:

VL < 8,5 m/s (6)

The time tL when a wagon covers the distance L since the start of space brake can be

calcu-lated using the formula:

_V _V ₂_g ₍_i _w _w _w ₎_L L 2 Ł o p 2 o o L t        [s] (7)

The time a carriage travels tL+13,8 from the first hump change of gradient to the moment it

leaves a space brake equals:

_V _V ₂_g ₍_i _w _w _w ₎₍_L ₂₈_,₂₅₎ ) 25 , 28 L ( 2 Ł o p 2 o o tL 28,25           _[s] (8)

Wagons can safely pass through space brakes if the following condition is met [2]:

trz > ttch (9)

where:

trz - the actual time between the preceding carriage leaves the space brake and the next

carriage enters the brake [s],

ttch – technological time necessary to set the brake [s].

These times can be calculated on the basis of the following equations:

trz = To + tL  tL+28,25 [s] (10)

ttch = ts + tr + tp [s] (11)

where:

To - the time between the moment the preceding carriage begins to roll down to the

mo-ment the next carriage begins to roll down [s], ts – control time (1,1s),

tp – time of brake lifting (0,83 s),

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tr = 0,179 + 0,079 log2 n [s] (12)

where:

n – the number of possible situations (4).

5. Discussion

For two consecutive carriages, with the first one being 2-axle, at draft pushing speed Vo =

1,4 m/s, To = 7,14 s. The functions: L ) w w w i ( g 2 V f₁ _o2   _p _o _Ł (13) and ) 25 , 28 L ( ) w w w i ( g 2 V f₂  _o2   _p _o  _Ł  (14)

can be represented with the aid of Maclaurin’s formula. This will facilitate subsequent cal-culations.

After inserting the transformed functions f1 and f2 into the inequality (9), the following

re-sults:

0 )

42 ,

105 L

)(

13 ,

81 L

(

)

04 ,

468 L

)(

54 ,

5 L

(

33 ,

33

_







(15) The inequality (15) is satisfied when: 81,13 m < L < 468,04 m, while the inequality (6) is satisfied when: L< 166,17 m. This means that the safe location of track brake is: 81,13 m < L < 166,17 m.

6. Conclusion

Tests indicate that the start of a space brake can be situated at a distance 81.13 m < L < 166.17 m. The design of directional track head determines the closest location of a space brake of around 120 m from the first change of gradient of marshalling hump.

Otherwise, when consecutive carriages, where the first is a 2-axle wagon, are pushed at a speed of Vo=1,4 m/s, they catch up with each other at the brake, which results in a

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10,000. The issue is important as about 40% of carriage drafts rolling down one after an-other pass through space brakes.

Vertical position of a space brake can be calculated by means of the dependence:

Ho = L  i (16)

Vertical position of a destination brake Hd can be calculated using a formula developed by

this author:

Hd = 1,25 Ho (17)

Horizontal position of a destination brake Ldcan be calculated using a formula developed

by this author:

Ld = 2  L + 70 (18)

References

1. Cieślakowski St.J.: Stacje kolejowe (Railway stations). WKŁ, Warsaw, 1992. 2. Cieślakowski St.J.: Kształtowanie bezpieczeństwa wagonów kolejowych w

systemach rozrządzania grawitacyjnego (Managing safety of rail carriages in gravitational marshalling systems). Research paper 2005/47/P. Radom Technical University, Radom 2004.

3. Gołembska E., Szymczak M.: Logistyka międzynarodowa (International logistics). Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań 2000.

4. Kozak T.: Racjonalne układy torów w rejonie górki rozrządowej ze szczególnym uwzględnieniem 32 i 48 torów kierunkowych (Rational track arrangement in the area of marshalling hump, particularly including 32 and 48 directional tracks). COBiRTK, Warsaw 1967.

5. Sutarzewicz D.: Warunki jakim powinny odpowiadać w planie i profilu układy torów górek rozrządowych przystosowanych do mechanizacji i automatyzacji (Conditions to be met by lay-outs and profiles of marshalling hump track arrangements as they are adapted to mechanization and automation) Automatyka Kolejowa, 6,1983. 6. Sutarzewicz D.: Układy torów stacji rozrządowych (marshalling hump track

arrangements). Drogi Kolejowe, 12, 1984.

7. Węgierski J.: Układy torowe stacji (Station track arrangements). WKŁ, Warsaw 1974.