Stochastic Analysis Method Of The Train-Track System Under Crosswind

The train-track coupling system is a dynamic system with strong randomness.Randomness of excitation such as track irregularity and wind causes the strong randomness of system response.Traditional deterministic analysis of single sample or several discrete samples is difficult to accurately reflect the stochastic characterization of train-track system.Therefore,seeking an efficient and accurate stochastic analysis method to study the stochastic vibration response of train-track system under crosswind can more reasonably evaluate the dynamic performance of trains.The main research work and conclusions are as follows:(1)According to the finite element method,a spatial nonlinear model of train-track coupling system considering wheel-rail separation is established by using the principle of total potential energy with stationary value in elastic system dynamics and the rule of ’ Set-in-right-position ’ for formulating system matrix.The multidimensional hypercube point set is generateded by gp set method of Number Theoretical Method,and the representative point set is obtained by screening and stretching transformation.Combined with the generated representative point set,stochastic track irregularity samples and fluctuating wind time-history samples as excitation sources of the system are obtained based on the stochastic harmonic function method and the harmonic superposition method.Then,the deterministic response of the train-track system is obtained by solving the dynamic equation of the train-track system using the cross-iteration algorithm of the separation system and the gradual integration method.(2)According to the concerned system response and its derivative term,the generalized probability density evolution equation of the system is established,and the bilateral difference method of TVD format is used to solve the probability information of the concerned response.The calculation results obtained by PDEM method are compared with those by MCM method,which further verifies the feasibility,accuracy and efficiency of the probability density evolution method for the stochastic vibration analysis of train-track system under dual stochastic factors.(3)The reliability analysis method of train-track system under crosswind is established.Taking the probability of 95% as an example,the influence of average wind speed on train operation safety is analyzed.The operation safety indexes include wheel load reduction rate,tilting coefficient,derailment coefficient,wheel lifting amount and wheel-rail relative transverse displacement.The example shows that with the increase of the average wind speed,the train operation index increases.When the train speed is 300 km/h and the average wind speed is 25 m/s,the wheel lift exceeds the limit,and the train operation safety is difficult to guarantee.