To the efficiency of locomotives of electric tractions on a hilly section of the railway

. The results of the substantiation of the average kinematic parameters of the movement of freight trains and the energy efficiency indicators of the transportation work of locomotives of electric traction without stops and with stops on a virtual hilly section of the railway are presented. The stated goal of the research was realized through the theory of locomotive traction through a graphical method of integrating the differential equation of train motion, based on the finite increment method, with subsequent calculation of the numerical values of the specified parameters and indicators. Research results obtained in the form of tabular data, graphical dependencies and equations regression to determine the efficiency indicators of locomotives of electric traction on virtual and real hilly sections of railway, which are recommended on the practice work of specialists in the operation workshop of locomotive depots of the Uzbek railways


Introduction
Currently, railway transport is the largest, natural monopoly in Uzbekistan and occupies a leading position in ensuring and implementing a given volume of national economic transportation of goods and passengers of different structure, type, view and content.
The effective operation of the locomotives fleet of railways, taking into account their infrastructure, has a significant impact on the entire transport complex and plays an important role in the development of the country's economy.
Thus, a certain range of tasks is outlined to improve methods for solving and selecting optimal control of the movement of locomotives, taking into account the development and implementation of a set of programs aimed at achieving one of the most pressing goals for railway transport -saving fuel and energy resources for traction of trains through the most efficient operation operating locomotive fleet.

Objects and methods of research
An analysis of scientific research by foreign scientists [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], carried out by the author of this article, indicates that these works do not consider the issues of energy efficiency of locomotives of electric traction in real conditions of organizing freight traffic on sections of Uzbek railways and do not use methods of traction theory trains.
This determines the conduct of scientific research work to substantiate the parameters of the main indicators of the use of locomotives depending on the operating modes of their power plants and systems, taking into account different conditions for organizing the transportation process, for example, in relation to hilly sections of railways, based on the theoretical foundations of locomotive traction.
Based on the above, the purpose of this study is formulated, which is to theoretically substantiate the parameters of the main indicators of energy efficiency of the transportation operation of mainline (train) freight electric locomotives of the 3VL80 S series on a virtual hilly section of the railway, where the operating conditions and railway transportation of goods are assumed to be similar to real ones.
To implement the formulated research goal, the author uses the graphic-analytical way [16] to perform traction calculations based on the integration of the differential equation of train motion using the finite increment method [17], of the initial data [18] about of the 3VL80 S freight electric locomotive under study and a virtual hilly section of the railway, the object and subject of research.
The graphical method (way) for solving the differential equation of train motion is based on the geometric relationship between the specific accelerating (decelerating) forces in each accepted speed range, the train's travel time and the distance it travels.
The reference point of the specified graphic-analytical method adopted by the author of this article is the diagram of the specific resultant force acting on the train and the straightened track profile of a given section of the railway.
A diagram of the specific resultant forces of a train depending on its speed, taking into account the parameters of the track profile of a given railway section, is constructed in certain, strictly verified scales of construction.Otherwise, the graphical construction will not have any logical and physical meaning, and the resulting velocity graphs V(S) will not be correct.
The method for performing traction calculations is that the permissible value of the train speed in a given section is divided into successive quite small speed intervals ΔV, at each of which the average speed value is found in the form Vav = (V1 + V2)/2, then according to the diagram specific resultant forces for a given value Vav, the average value fav(Vav) is determined, and from it the corresponding path interval ΔS and time interval Δt are calculated.
A fragment of the graphical method for integrating the differential equation of train motion, taking into account changes in train traffic conditions depending on the steepness of the slope of the track profile element, is shown in fig. 1.
At the beginning, on the site -this is the first element of the track profile, where station B is located, the pole of construction is the origin of coordinates (point 0).Straight lines 1-1, 2-2, 3-3, 4-4 pass through point 0, to which perpendiculars -chords -are alternately restored with a right triangle for each selected, accepted speed interval ΔV not exceeding 10 km/h, that is ΔV ≤ 10 km/h.
If the train enters a rise with a steepness of +i, ‰, then the origin of coordinates of the characteristics of the accelerating forces fav is shifted to the left by i, ‰ (point 01), thereby subtracting the movement resistance from this rise from the value of fav at the site (i = 0), equal to value i.On the contrary, if the train enters the descent -i, the origin of coordinates of the fav characteristic is shifted to the right by the amount i, ‰ (point 02), thereby adding the component of the train's gravity force to the specific accelerating force on the platform.When switching to the idle mode (coasting), instead of the characteristic of the specific resultant forces, the curve of the specific main resistance to the movement of the train on the coasting w0id(V) is used.In the same way, segments of the curve time t(S) are constructed, only for their construction a straight parallel line is used to the left of the 0V axis at a distance of 30 mm, onto which the value of the average speed Vav of the train is plotted.The second point is always taken to be point 0 -the origin of coordinates.
The object of the study is freight trains with unequal mass and a constant number of train axles, three-section mainline (train) freight electric locomotives of the 3VL80 S series and a straightened track profile of a virtual hilly section of the railway.
The subject of the study is the parameters of the main indicators of transportation work and energy efficiency of the studied 3VL80 S electric locomotives in quantitative and monetary terms on the accepted (given) virtual section of the railway.

Results and their discussion
Parameters of energy efficiency indicators for of three-section mainline (train) freight electric locomotives 3VL80 S series on a virtual hilly section of the railway when moving without stops and with stops at an intermediate point (station) in quantitative and monetary terms, taking into account different conditions for organizing the transportation work of these locomotives, are given in table 1.Index (sign) asterisk * is the cost of funds (cost of electrical energy) taking into account value added tax (VAT).
The dynamics of the averaged values of the kinematic parameters of the movement of freight trains and the parameters of the energy indicators of the transportation work of the studied freight electric locomotives 3VL80 S series depending on the mass of the freight train for two (both) types of railway transportation of goods are shown, respectively, in fig. 1 (values of movement speed V, km/h are halved) and fig. 2.   The averaged values mentioned above were calculated (defined) as arithmetic mean values for two types of movement in we accepted the range of changes in mass of trains (from Q1 = 2500 t to Q3 = 3500 t) of a freight train.
Evaluation and analysis of the efficiency of the transportation work of three-section mainline (train) freight electric locomotives 3VL80 S series on a given, virtual, hilly section of the railway were carried out by comparing the numerical values of the above-mentioned kinematic and energy parameters with similar values of a schedule (unified) freight train.
Comparative analysis of the research results [19][20][21] and the data in table 1 regarding freight train with a unified mass of the train Q2 = 3000 t and a constant number of m = 200 axles in the train showed the following (values for traffic conditions with stops at an intermediate station are given in parentheses).
1.The average total travel time of the train is 0.517 hours (0.62 hours), a decrease in the mass of the train by ∆Q = 500 tons leads to a decrease in the total travel time of the train by 2.43 (4.03) percent, and with an increase in the mass of the train by ∆Q = 500 t there is an increase in this time by 3.88 (4.03) percent.
2. Technical speed of the train with a similar change of the mass of the composition tends to increase and decrease within the same limits, and, on average, it is equal to 88.75 (74.11) km/h.3. The average time for a train to accelerate -decelerate is 0.0341 hours, reducing the mass of the train by ∆Q = 500 tons leads to a decrease in the time for deceleration and acceleration, respectively, by 3.55 percent and 7.07 percent.With an increase in train mass by ∆Q = 500 t, the train's acceleration and deceleration time increases, respectively, by 6.6 percent and 4.72 percent.
5. An increase in the mass of the train by ∆Q = 500t contributes to an increase in the total energy consumption by 7.62 (7.08) percent, however, the specific power consumption decreases by 7.76 (8.2) percent, and a decrease in the weight of the train by ∆Q = 500 t ensures a decrease in total and an increase in specific energy consumption, respectively, by 11.21 (10.79) and 6.52 (7.08) percent.
6. Reducing the mass of the train by ∆Q = 500 t leads to a decrease in the total and unit cost by an average of 11.21 (10.78) percent, and with an increase in the mass of the train by ∆Q = 500 t, these indicators increase by an average of 7.62 (7.08) percent.
7. Reducing the mass of the train by ∆Q = 500 t leads to an increase and decrease in the use of traction modes [18,21], as well as idling and braking [18,21], respectively, by 0.8 (0.2) percent, and with an increase in the mass of the composition by ∆Q = 500 t, on the contrary, these indicators decrease and increase by 1.53 (0.7) percent.
8. The train running time in idle and braking modes, as well as in mode traction, varies, respectively, from 0.168 hours (0.223 hours) to 0.192 hours (0.240 hours) and from 0.334 hours (0.368 hours) to 0.3243 (0.405 hours).When the mass of the train increases by ∆Q = 500 t, the train's running time in idling and braking modes, as well as in mode traction, increases, respectively, by 0.015 hours (0.005 hours) and 0.005 hours (0.02 hours).The running time of the train in idling and braking mode increases, and in mode traction it decreases, respectively, by 0.008 hours (0.008 hours) and 0.004 hours (0.017 hours) with a decrease in the mass of the train by ∆Q = 500 tons.
Using the standard Microsoft Office Excel series program, regression equations (analytical expressions) were obtained to calculate the parameters of the main indicators of the transportation work of 3VL80 S electric locomotives on a virtual hilly section of the railway track for any i -th mass Q of a freight train (in parentheses -traffic conditions with a stop at an intermediate station).In formulas (1) -(10), a sufficient value for the reliability of the approximation is R 2 = 1.0 (the necessary condition for reliability is R 2 ≥ 0.8), and the signs (indices) are an asterisk * for movement with stops of at an intermediate station and two asterisks * * -taking into account value added tax (VAT), and the value Qi = 1, 2, 3 is a factor (indicator) of the traction calculation option.
Technical speed of the train Vt, km/h Vt = -0,555Q 2 -0,555Q + 92,45 ∕ Vт * = 0,12Q 2 -3,47Q + 80,49 Total train travel time tt tr, min tttr = 0,225Q 2 -0,075Q + 29,86 ∕ tx * = 1,5Q + 34,2 Train travel time in mode traction ttr, min ttr = 0,025Q Analysis of the above regression equations shows that the dynamics of the above parameters, depending on the change in the mass of the freight train, is described by a polynomial of the second degree, with the exception of the total travel time of the train with a stops at an intermediate station (linear dependence) with one hundred percent accuracy of their calculation.
In the course of the research, various conditions for organizing the movement of freight trains with different masses of trains were studied, the analysis of the results of which allows us to formulate the following intermediate conclusions: -when organizing railway transportation of goods of different structure, type, view and content, the uniform movement of a freight train is exclusively dominant, and slow and accelerated types of movement, that is, movement with a changing and inconsistent speed, are encountered (present) only in cases of braking (stopping), starting and accelerating train.
-the consumption of electrical energy spent on moving freight trains by 3VL80 S electric locomotives varies depending on the operating time of the power plants (systems) under current, that is by mode traction, a decrease in which will lead to a decrease in the mechanical works of the mentioned electric locomotives, and as a result, will ensure a reduction in consumption (consumption) of electrical energy; -the amount (value) of electrical energy consumption spent on decelerationacceleration, at each stop of a freight train at an intermediate station or separate point, ranges from 129.21 kW-h / stop (Q1 = 2500 t) to 141.01 kW-h / stop (Q3 = 3500 t), and on average this amount is 136.22 kW-h / stop.
-an increase in the volume of transportation work by 3VL80 S electric locomotives helps to increase the efficiency of using these electric locomotives under operating conditions, regardless of the type (structure, type, view and content) of the cargo transported and the type of movement of freight trains.

Conclusion
Analysis of the results of the conducted studies identified the following general conclusions.
1.The kinematic parameters of the movement of freight trains and the parameters of the energy efficiency indicators of the studied 3VL80S electric locomotives are obtained in the form of tabular data and graphical dependencies.
2. Regression equations were obtained to determine the main indicators of the transportation work of the studied of locomotives of electric traction on virtual and, identical to them, real hilly sections of the railway track.
3. The results of the study are quite adequately consistent with research data [1, 21-23 and others] and can be implemented in the practice of work locomotive depots of the Uzbek railways on hilly sections with the second type of track profile when assessing the efficiency of the transportation work of the studied of locomotives electric traction in real conditions for organizing railway transportation of goods of different structure and content.
4. These results are recommended to specialists of the locomotive complex of «Uzbekistan Railways» JSC, whose production and professional activities directly relate to the energy sector of electric railways and are associated with the movement of freight trains on railway sections with a hilly track profile, organized by locomotives of electric traction.

Fig. 1 .
Fig. 1.Illustration of graphical construction of a train speed curve depending on changes in the slope of a track profile element.Source: «Compiled by the author».
Source: «Compiled by the author».

Fig. 2 .
Fig. 2. Average parameters of energy efficiency indicators of electric locomotives 3VL80 S series on a virtual hilly section of the railway.Source: «Compiled by the author».

Table 1 .
Indicators of transportation work of 3VL80 S electric locomotives on a virtual hilly section of the railway track Averaged kinematic motion parameters of freight train on a virtual hilly section of the railway.