国产高速动车组失稳类型的数学证明及其奇异性分析应用研究

The stability of the EMU is an important issue in vehicle dynamics research, and also the basis of the operation safety. The numerical method is commonly applied to study, but using analytic or semi-analysis approach to study the principles is relatively few. Aiming at the different bifurcation behavior of two typical domestic multiple units of type CRH2 (or CRH380A) and type CRH3 (or CRH380B) when loss of stability, it is proved and studied in this project, with using combined methods of theory proof, numerical simulation and experimental test. Firstly, the field and roller rig tests for the two multiple units are to be conducted to obtain the lateral acceleration of the instable bogie. Secondly, the lateral dynamics models for the two high speed bogies are to be established with mainly considering the nonlinear elements of the vehicle. Then the Hopf norm form theory in nonlinear dynamics is to be utilized to prove the different Hopf bifurcation behavior of the two bogies, meanwhile the numerical approach is also to be applied to get the simulation results which are used to validate the reliability of the course of proof combined with the test and simulation results. Afterwards, the proof process is to be generalized to investigate the influence of vehicle parametric variation on the bifurcation types and get the critical parameters, which is also validated by the simulation results. Finally, the universal unfolding of the vehicle Hopf norm form is solved to investigate the influence of unfolding parameters on bifurcation type and to obtain all of the parameter perturbations behaviors which the vehicle potentially contains. This project is to carry out a theory basis for finding the principles of vehicle instability and offer an analytic method to study the influence of the multi-parameters’ perturbation on bifurcation type.

动车组运动稳定性是车辆动力学研究的一个重要课题，也是车辆运行安全性的基础。一般以数值方法为手段，而采用分析或半解析法进行机理研究的相对较少。本课题拟采用理论证明、数值仿真和试验测试结合的方法，对我国典型动车组CRH2（或CRH380A）与CRH3（或CRH380B）横向失稳时的不同分岔行为进行数学证明及应用研究。具体包括：对两类动车组进行线路或台架试验，获得其在失稳时横向加速度数据；建立两种转向架的横向动力学模型，重点考虑非线性元件；采用Hopf规范型理论对两转向架不同Hopf分岔类型进行证明，结合试验与数值结果，验证证明过程的可靠性；对关键参数进行变参研究，找出影响车辆分岔行为敏感的参数；应用奇异性理论求出Hopf规范型的普适开折，分析开折参数对分岔类型的影响，以揭示车辆可能包含的所有扰动影响。本课题旨在对寻求车辆失稳的根本原因奠定理论基础以及车辆多参数扰动的分岔研究提供一种分析方法。

本项目采用理论研究、数值模拟和实验相结合的方法，对CRH2与CRH3两类高速动车组失稳后存在不同的分岔现象进行了数学证明与参数设计优化研究。首先，在合作单位西南交大参与人员协助下，对两类高速动车组的线路运行试验以及台架试验进行了测试，根据GB5599评定要求获取了转向架横向振动加速度数据，并进行了数据处理。然后建立了整车动力学仿真模型，以及两类转向架横向动力学方程，用数值求解仿真了失稳现象，与测试结果对比一致。接着运用非线性动力学中的规范型理论，对两类转向架的Hopf规范型进行了推导，计算了第一李雅普诺夫指数，该指数大于0则对应发生亚临界分岔，小于0则发生超临界分岔，对应分岔方程中抛物线的系数。结果表明，CRH2转向架的第一李雅普诺夫指数大于0，CRH3转向架的第一李雅普诺夫指数小于0，则证明了两类转向架发生不同分岔现象的原因。再根据该指数的计算流程，对车辆关键参数进行了变参，找出了对该指数影响敏感的参数，如一系横向定位刚度，抗蛇行减振器阻尼均能改变两转向架的分岔类型。接着运用奇异性理论分析了CRH3转向架的普适开折分岔图，得出了Hopf分岔附近的全局分岔特性，并分析了部分不对称的扰动参数如施加曲线半径，二系横向减振器阻尼等对分岔结果的影响。最后，运用非线性动力学中理论与分析方法，设计了一种相对定频的隔振器；分析了磁浮车-道岔梁-控制耦合系统的悬浮间隙分岔现象；分析了公铁两用车的运动稳定性并求解了其不同编组模式下的临界速度。