A Rail line model with distributed parameters of track circuit

Models of continuous jointlesstrack circuits with an adaptive receiver are presented, where the power supply is connected to the beginning or middle of the rail circuit, and also to the locomotive receiver. The aim of the work is to develop models of rail lines, which take into account the actual current distribution along the track line and which may be used to research adaptive jointlesstrack circuits. The electric schemes of the jointlesstrack circuits are given, equations, connecting currents and voltages at the ends of the rail line, coefficient of four-pole rail lines, algorithms for calculating track circuits. In conclusion, that the track circuit can operate at an insulation resistance four times lower than the permissible value, where the permissible insulation resistance is Ri = 1om*km. New approaches and tools for analyzing and synthesizing solutions are considered, with considering account real operating conditions and disturbing factors.


Introduction
The analysis of the operation of tonal jointless track circuits is devoted to [1-6, [10][11][12] and others.The issues of automation of the process of their design and reliability are considered in [7-9, [16][17][18][19][20]. On the problems of expertise and safety testing of railway automation and telemechanics systems are considered [18][19][20]. At the same time, there are practically no publications on the intellectualization of the solution of problems of the analysis and optimization of the parameters of track circuits in various operating modes.In connection with this actual seems to development of a hybrid expert system for analyzing the operation of a jointless tonal track circuit.
where ꞇ 1 = 1/ ℎ 2 + ( ) ℎ 2 ; ꞇ 2 = 1/ ℎ 2 + ( ) ℎ 2 ; ꞇ 3 = 1/ ℎ 2 + ( ℎ ) ℎ 2 ; ꞇ 4 = 1/ ℎ 1 + ( ) ℎ 1 ; In figure 2 shows the rail line of the beginning , the middle and the end with shunts , , , respectively. The impact on the rail line of adjacent track circuits is taken into account by means of the resistances of the beginning and the end . (instead of and in figure 1). Instead of the second shunt, the resistance of which in figure 1 is designated ℎ2 , on figure 2 includes an equivalent ER receiver with a resistance . Through means of resistances 1 and 1 (instead of in figure 1) the influence of rail lines is taken into account located behind the and shunts, respectively. On each of the rail lines , and , different insulation resistance and rail can be set, therefore, instead of the propagation constant γ, the designations , and are provided, and instead of the wave impedance -designations , and . The dependences between the voltages and currents of the equivalent generator eG and the equivalent receiver ER are shown by equation (7). These equations are obtained from equation (1) with the replacement of the notation in figure1 to the designations in figure2: where = ꞇ 1 ( ℎ 2 + ℎ 2 + ( ) ℎ 2 ) + ꞇ 2 ( ℎ 2 + ℎ 2 ); (8) = ꞇ 3 ꞇ 4 ℎ + ꞇ 5 ℎ , On figure 3 shows the algorithm of the program for calculating a rail line with distributed parameters with an adaptive receiver powered from the end. Block-schemes of the algorithm have the following purpose: Taking into account the proposed algorithm, programs were developed, which are an integral part of the track circuit model.

Result and discussion
The model of a rail line with distributed parameters makes it possible to carry out studies of the ATC (adaptive track circuit) taking into account the real current distribution along the rail line. The disadvantage of the presented model is that cannot be used for jointlesstrack circuits powered from the middle. For the research of jointlesstrack circuits with two receivers at the ends of the rail line, a universal model is proposed.

Universal model rail line of the jointless track circuit with adaptive receiver
A typical running jointlesstrack circuit has one track generator and one or two track receivers. On the figure 4 shows the replacement scheme of the track circuit, which allows you to calculate and research a track circuit with an adaptive receiver, both with power from the end and from the middle. On the scheme shows: start rail line, two rail lines middle * and , rail line of end , equivalent generator, an equivalent receiver of the beginning of with resistances * and an equivalent receiver of the end of with resistances , train shunts , * , and , input resistances 1 , 1 , , * , * and . The rail lines of the and of both schemes completely coincide, and the rail lines * and on Fig.4 are a mirror image of the right side, i.e.rail lines and . By changing the values of insulation resistances, rails, shunts and their coordinates, as well as the parameters of equivalent receivers and a generator can be imitated any train situations and jointlesstrack circuit parameters. The dependences between the voltages and currents of the equivalent generator of the and the equivalent receiver of the for the circuit in figure 4 can be written by analogy with equations (7-11) for the circuit in figure 2 (in the notation of the diagram in figure4): where = ꞇ 1 ( ℎ 2 + ( ) ℎ 2 ) + ꞇ 2 ℎ 2 ; = ( ℎ 1 ℎ 2 + ꞇ 3 ℎ 2 ; (17) = ( 1 )(ꞇ 1 (ꞇ 4 ( ) + ꞇ 5 ) + ꞇ 2 ꞇ 4 ; ꞇ 4 = ℎ 2 + ( * ) ℎ 2 + * ℎ + * ℎ ; (21) * = ( + * )/( * + * ).

Conclusion
The proposed models of the rail lines make it possible to carry out studies of rail circuits with an adaptive receiver in conditions of significant longitudinal asymmetry of insulation resistance under the intense influence of atmospheric influences. For the analysis of jointless track circuits with an adaptive receiver have to consider of condition (the presence of shunts, the value of the insulation resistance of each radar line, the dynamics and range of variation of this resistance, etc.) several jointless track circuits at the same time. Their mutual influence on each other. In conditions, when monitoring condition of each jointless tone track circuit depends on the state of the rail lines of other sections, model needs to be investigated, which would represent a collection of rail lines. The research of such track circuits differs significantly from the study of track circuits with relay action receivers.