CALCULATION OF BASIC INDICATORS OF RUNNING SAFETY ON THE EXAMPLE OF A FREIGHT WAGON WITH THE Y25 BOGIE

Resume Freight wagons are among the most widely used means of transporting goods by land. Such a number of wagons and transported material and amount of material need to meet requirements in terms of safety and reliability. A wagon bogie is a key element in the wagon running safety point of view. The Y25 bogie is a most used bogie for freight wagons in the region of the central and west Europe. As this bogie was developed several decades ago, it is interesting to evaluate its running properties according to current standards. The presented research brings results of calculation of chosen basic indicators in terms of running safety. The calculations of the freight wagon with the Y25 bogie was performed by means of a multibody model. Simulation computations were carried out for an empty and loaded wagon, which has been running in curves with various radii and at several running speeds.

The French technical solution of railway freight wagons of the Y type comes from a realization of the primary suspension system by means of a couple of double coil springs, which are placed on a axlebox sides. One of the double coil spring (nearer to a bogie centre) is supplemented with the friction damper (a SNCF Lenoir patent) [10]. Friction force is generated between an axlebox and a guidance. More detailed description of this friction damper can be found below (section 2).
As a railway wagon is subjected to complicated dynamic influences during the operation, dynamic properties of a railway wagon have to be evaluated and investigated in terms of running safety. From the point of view of railway wagons themselves, the main demands are placed on their quality of running and derailment safety [11][12][13]. The running safety is affected by number of factors, among them are track irregularities, running speed, track geometry, technical conditions of a wagon, the load of wagons and others [14][15][16][17].

The Y25 bogie
The French national railways initiated the development of the Y25 bogie in 1960. The goal was

Introduction
Recently, large amount of goods is transported by railways. There are relatively many types of freight wagons for transportation of various kinds of goods, e.g. hopper wagons, tank wagons, wagons for transportation of steel coils, intermodal transport, cars transport and others [1][2][3]. The most of them are equipped by a twoaxle bogie. As regards wagons used in the Central and West Europe, there are wagons with the Y25 bogie. Its development dates back to the sixties of the previous century. The objective of this work was to approach some specific features of this bogie and to calculate the basic indicators related to the running safety [4][5][6]. They must meet the given criteria for safety operation of freight wagons, as well as an entire train set [7][8][9].
From the historical point of view, the two main lines of development of freight wagons can be recognized. The European line is typical, that these bogies use a primary suspension system and do not have installed the secondary suspension system. The main advantage of these bogies is lower unsprung mass. Usually, the suspension system contains coil springs. On the other hand, the American development line of bogies is characterized that these bogies have higher unsprung mass due to missing the primary suspension system and they are equipped only with the B260 D I Ž O e t a l .
If one considers that the force F L acts in the Lenoir link, the force of one friction couple F F is given as following: where F V is the force in a coil spring, f is a friction coefficient and φ is an angle of a Lenoir link inclination. However, one axlebox includes two friction couples, therefore, the total force for one axlebox is doubled [23][24]. The friction forces in the friction damper are described by the Coulomb friction law. However, this formulation often leads to numerical problems during the simulation computations due to a discontinuous course of the force. Hence, the force is modelled as a continuous function.

Computer simulation of a freight wagon
A computational model of a freight wagon and simulations of its running on a track have been performed by a multibody software. A complex multibody model is described by differential-algebraic equations (DAE) [25][26][27][28].
During the modelling of a freight wagon in a multibody software, it is necessary to pay attention to proper locations of individual components of a wagon [29][30]. Components are located in these positions to design a bogie, which would occupate less space and which would have lower weight in comparison to the one used at the time, the Type 931. The efforts resulted in the Y25 bogie. It has the wheelbase of 1800 mm and the wheels' radius of 920 mm. Its suspension consists of duplex coil springs with a bilinear characteristics and they are combined with friction dampers, typical just for this bogie. The body of a wagon is connected with the bogie by means of a central pivot and with a couple of side bearers. The central pivot includes a special pad of a relatively high stiffness. Yaw oscillation of the bogie is eliminated by suspended side bearers. The bogie is usually designed for maximal running speed of 100 km/h at the maximal axle load of 22.5 t (or 25 t) or for the maximal running speed of 120 km/h at the maximal axle load of 20 t [7,[18][19].
The structure of the bogie is typical by the two longitudinal girders and one central lateral girder supplemented by ending lateral supports. Increasing demands on the noise level, total weight of wagons, running safety and others led to a modified Y25 bogie design, which does not use ending supports. Therefore, one can meet recently two basic bogie frame designs. An example of the Y25 bogie is shown in Figure 1.
A vertical load of the bogie is absorbed by vertical coil springs. The friction damper works on the principle of the Lenoir link. The Lenoir link ensures a generation of a friction forces between friction surfaces of an axlebox and a guidance. In this type of a bogie, the values of these forces depend on operational load of a freight wagon, thus on the load of the system (fully loaded, partially loaded) [20][21][22].
A scheme of the friction damper is shown in Figure  2. The friction damper is composed of an axlebox and a guidance.

Evaluation of a freight wagon dynamics
In this work, the quantities of a freight wagon are evaluated in terms of the running safety, which wagon was analysed in the loaded as well as in empty state at.
The calculation part of the work has consisted of performing the simulation computations in a commercial multibody software. Parameters of the freight wagon have been defined, as it is described in the previous section. Two loading conditions have been modelled, i.e. the empty wagon and the loaded wagon. The entire investigation process of the wanted outputs indicators has been running based on simulations computations. Parameters of the running conditions are described below.

Derailment quotient Y/Q
The ratio Y/Q is called the derailment safety and it is one of the running safety criteria. The derailment safety was evaluated for the freight wagon running in a curve with various radii and at various running to each other and they are interconnected by springdamper modelling elements. The centre pivots distance of bogies is 15.7 m.
Parameters of individual components of the Y25 bogie, entering to simulations, are listed in Tables 1  and 2.
The body of the wagon has been created by the two rigid bodies connected by torsion spring with defined a torsion stiffness and by rotational joint (with a longitudinal axis of rotation). Parameters are introduced in Table 3.

Evaluation of the rail vehicles' dynamics
The UIC 518 standard was the first UIC standard describing the running tests of the rail vehicles, which was gradually supplemented [31][32]. This standard has become the basic for European standard 14 363 and other standards and some of its requirements are included in TSI standards. Measurement and evaluation of the vertical wheel forces Q and lateral wheel forces Y are the part of commissioning of new vehicles, according to UIC 518 standard, EN 14 363 standard and TSI [31][32].
Regarding the evaluation of tests of rail vehicles for commissioning, three main areas are defined: • running safety, • track load, • running characteristics and vehicle vibrations.
The running safety is evaluated by several parameters. Quantities, which evaluate forces between a wheel and a rail, can be divided, according to EN 14 363, as follows [31]:    radius. Further, it is obvious that this ratio indirectly depends on the wagon weight, i.e. in the case of an empty wagon running in a curve it is higher than in the case of the loaded wagon in a curve of the same radius.
Comparing the Y/Q values for considered conditions one can conclude that the most unfavourable case in terms of safety is when the empty wagon runs in a curve with a small radius.

Sum of lateral forces ∑Y
Values of the lateral forces in the wheel/rail contact must be within certain limits.
The results for the limited value for a wheelset depends on an axleload and it is given as following: where Q [N] is the maximal force on an axle, α is a coefficient and for freight wagons α = 0.85 [-].
An empty freight wagon has a considered axleload of 36.35 kN and for it, the following limit value is valid: The limit value for the loaded freight wagon by the same manner (the axleload of 220.24 kN) has also been calculated according to the formulation: . .  Table 4. The values presented in Table 4 indicate that the highest percentage difference of the derailment quotient for a comparison of the loaded wagon and the empty wagon is for the curve of 400 m and the running speeds of 11 m/s (39.6 km/h). This percentage is of 48.28 %. Other comparisons bring the percentage of 2.59 % for the curve of 200 and the running speed of 11 m/s (39.6 km/h) and finally of 3.37 % for the curve of 60 m, but the running speed has been of 6 m/s (21.9 km/h).
Graphs in Figure 4 show waveforms of the derailment safety for an outer wheel of the first wheelset for an empty wagon for running in a curve of 400 m at the speed of 11 m/s. Figure 5 shows a graph of the derailment ratio of an outer wheel of an empty wagon in a curve of 60 m at the speed of 6 m/s and a graph of the derailment ratio of a loaded wagon in a curve of 200 m at the speed of 11 m/s. Negative values of the derailment ratio are caused by an orientation of lateral wheel forces in a global coordinate system.
From values of the derailment ratio (Table 5) one can conclude that the biggest risk of derailment of a wagon during running in a curve occurs on the outer wheel of the first wheelset (in the wagon running direction). This ratio increases with a smaller curve which operational characteristics will be reached on tracks with a real geometry. It relates to development of other realistic models of railway wagons, which will help to reveal positive properties in terms of operational safety. On the other hand, they will be helpful for indication of negative effects without a risk of damage of a final wagon design directly during the operation [43][44][45][46][47][48].

Conclusion
The article presented evaluation of some parameters of a freight wagon equipped by the Y25 bogie, according to the selected criteria. The research was performed by means of a multibody model and by simulation calculations. The reference freight wagon was tested Similar to the assessment of the running safety, several simulation calculations were performed to evaluate the sum of lateral forces for various running regimes. The sum of lateral forces was assessed for the first wheelset in the running direction. These sums were compared to the limited value according to Equations (3) and (4). The results are listed in Table 4. The determined limited values of the sum of lateral forces were not exceeded.
The railway transportation of goods is being and in the future will be needed. It has specifics, which predetermine it for longer distances [35][36]. It is connected with the development of newer and more effective wagons and their structural units [37][38][39][40][41][42]. Therefore, the future research in this field will be focused on investigation of a wagon under various operational conditions. It will be important to know that the calculated values did not exceed the limited values.

Acknowledgement
This research was supported by the Cultural and Educational Grant Agency of the Ministry of Education of the Slovak Republic in the project No. KEGA 023ZU-4/2020: "Development of advanced virtual models for studying and investigation of transport means operation characteristics".
at various conditions and that for the loaded state corresponding to the maximal axleload of 22.5 t as well as for the empty wagon. The wagon was run in various curves and at various speeds. The wagon properties were assessed based on some criteria introduced on the UIC 518 standard (or EN 14 363).
The derailment safety was evaluated for a wheel with the most unfavourable properties. It is the wheel of the first wheelset in the running direction (an outer wheel). Similarly, the first wheelset has the most unfavourable properties in terms of the sum of lateral forces. Evaluation of results of both criteria has shown