Theoretical Calculation And Simulation Analysis Of Rail Impedance Of Ballastless Track Tircuit

Ballastless track technology and jointless track circuit are two key technologies used in high-speed railway construction in China.Compared with ballastless track,ballastless track is laid with monolithic track bed instead of granular gravel in ballastless track,which avoids the phenomenon of ballast splashing during high-speed train operation,and has become the main form of high-speed railway track structure.The track circuit is laid on the ballastless track bed,and the ballastless track board contains transverse and longitudinal staggered reinforcement network,which affects the transmission characteristics of the track circuit,thus making the problem of the compatibility between the ballastless track and the jointless track circuit more prominent.As one of the primary parameters of track circuit,rail impedance directly affects the transmission performance of track circuit.Accurate calculation of rail impedance of ballastless track circuit is of great significance to ensure the safe operation of high-speed train.Therefore,this paper uses Carson theory and electromagnetic field finite element method to calculate the rail impedance of ballastless track circuit,and analyzes the variation law of rail impedance with the surrounding environment,earth,current,frequency and other factors,so as to provide theoretical basis and reference model for transmission performance analysis and optimal design of ballastless track circuit.Firstly,the rail impedance of ballastless track is calculated based on Carson’s theoretical formula.Rail impedance includes rail self impedance and mutual impedance,and self impedance consists of internal impedance and external impedance.Considering the skin effect and ferromagnetic characteristics of rail,the internal impedance of rail is calculated by Carson formula,Rolle mean theorem and maclaurian approximate formula.The theoretical calculation formula in wide frequency range is derived and simulated by finite element method.Without considering the reinforcement mesh,the rail is equivalent to a double conductor overhead system.Considering the influence of ground loop impedance,Carson formula is used to calculate the rail external impedance and rail mutual impedance,and the theoretical calculation formula of rail external impedance and rail mutual impedance is obtained.The correctness of the formula is verified by finite element method.Secondly,considering the reinforcement mesh,based on the electromagnetic field finite element method,a three-dimensional electromagnetic field simulation model of ballastless track with reinforcement mesh is established to calculate the incremental influence of reinforcement mesh on the rail impedance of ballastless track.In order to solve the problems of large number of mesh generation and convergence difficulty when calculating rail impedance increment directly using 3D model,the 3D model of ballastless track is simplified according to the modeling principle of 3D model,the principle of track centrosymmetry and the uniform distribution characteristics of steel mesh,and the simplified minimum element model is obtained,The model simplification method is used to verify the correctness of the model simplification method.The simulation results of the minimum element model are compared with the measured data to verify the correctness of using the minimum element model to calculate the incremental impedance of steel mesh to rail.Finally,the internal impedance of rail and the external and mutual impedance without steel mesh are calculated by theoretical calculation formula,and the incremental influence of steel mesh on the rail impedance of ballastless track is simulated by the minimum element model of ballastless track.Based on the theoretical calculation formula and simulation model,the variation law of rail impedance with current frequency,current amplitude,track height,earth conductivity(resistivity)and soil depth is analyzed,which provides theoretical basis and reference for ballastless track optimization design and traction network system modeling.