Research On Railway Vehicle Lateral Stability Based On Equivalent Circuit Model

The mathematical model of vehicle dynamics system is a multi-DOF second order differential equations which contains many strong nonlinear factors such as dry friction,piecewise linear and power function,in the equations,the parameters are coupled with each other.Its solution and analysis are very complex in mathematics,and calculation requires huge amount of calculation and time using numerical.Considering the similarity in mathematics between the characteristics of analog integrating circuit and the state equation of vehicle system,the thesis designs and implements an analog circuit model which has the same mathematical expression whith vehicle dynamics system,and considers the piecewise linearity,dry friction and other nonlinear factors on the basis of this circuit model,used to analyze vehicle system stability.The thesis discusses and research the application of circuit model to calculate the dynamic equations with nonlinear factors.Provide a research tool and method to realize fast calculation with real-time adjustable parameters,in order to quickly reveal the laws contained in the dynamic system with nonlinear factors.The thesis mainly includes the following aspects of work and content:(1)According to the mathematical similarity between mechanical system dynamic state equation and analog integrated circuit equation,the relationship between them is derived.On this basis,using Matlab GUI designed a interactive program,which can import the data in Excel file format and output result after calculation.The program has the functions of calculating state equation coefficient matrix,the resistance matrix of the equivalent circuit,linear critical velocity and variable time-domain waveform.It can simplify the calculation in the process of realizing the equivalent circuit and make the design of the equivalent circuit convenient and fast.(2)The author studies the design and implementation of nonlinear characteristics such as symmetric piecewise linearity,asymmetric piecewise linearity,power term,Maxwell viscosity and dry friction by using the saturation and amplification characteristics of operational amplifiers.It provides a basis for analyzing nonlinear dynamic systems by directly adding nonlinear factors into the linear equivalent circuit.(3)Taking the 2-DOF elastic single wheelset model as the research object,The author analyzes and proves that the lateral instability is due to the self-excited vibration of the coupling between the lateral motion of the wheelset and the shaking motion by using the transfer function,and deduces the crawl vibration motion frequency formula,its verified by the Routh Hurwitz criterion.Furthermore,the equivalent circuit of the elastic wheelset model is established by using the designed program,and proved its correctness with the MATLAB.On this basis,nonlinear factors such as symmetric and asymmetric piecewise linear flange force and axle box dry friction are added,and the influence of nonlinear factors on the system is analyzed.(4)A mathematical model for lateral stability of 6-DOF of two axle bogie and 23 DOF vehicle is established.The program is used to realize the transformation of state equation and calculate its critical velocity.Further,the resistance matrix in the equivalent circuit is calculated by program,the equivalent circuit are completed in Multisim 14.0 software.The results are compared with MATLAB simulation,which further shows the correctness and rationality of applying the equivalent circuit to study the lateral stability of railway vehicles.Based on the linear equivalent circuit model,considering the piecewise linear characteristics of symmetric/asymmetric rims and the dry friction of axle box,the analysis is carried out.The research shows that the equivalent circuit has the advantages of fast running speed,simple parameter adjustment and more efficient implementation in the analysis of nonlinear systems.(5)A 6-DOF PCB model of the lateral dynamics system is designed and implemented.The model is designed according to the modular design.Through the adjustment of the input signal and resistances,the results verify that the application of the equivalent circuit model in the study of linear and nonlinear systems has the advantages of fast operation speed and real-time adjustable parameters,and can quickly reveal the operation laws contained in the dynamics system with nonlinear factors,It provides a reference tool and method for the analysis and research of mechanical dynamic systems.The research shows that the method of studying vehicle system dynamics through the similarity between analog integrating circuit and mechanical system is completely feasible.In particular,analog integrating circuit doesn’t need programming,and the implementation is relatively simple.It has better advantages in terms of real-time adjustment of running speed and parameters.However,due to the accuracy of the components or signal interference in the analog circuit,the calculation accuracy is relatively lower than the numerical calculation.The error can be controlled within 5% using appropriate accuracy components.Therefore,this method is more suitable for finding the operation law in a large range in the research,and the field of teaching applications or engineering without programming requirements.