Study On Stability And Bifurcation Types Of Railway Vehicles

With the continuous speed up of Chinese railways these decades, now we step into high speed railway era, and this makes vehicle stability problem more conspicuous and propose a higher request and correspongding technical speicification. Domestic EMU CRH2 or its derived series CRH380A and EMU CRH3 or its derived series CRH380B behave as tremendous different bifurcation phenoemenon when the vehicles lose stability. China railway has established overall policy that is introduction, digestion, absorption, innovation. Under these guidelines, proving the reseaon for the different stability behavior and revealing the basic priciples of vehicle parametric design between Japanese style EMU and Euro style EMU, are very important to during the’sinnovation’stages. The traditional numerical approach is mature. It can offers a way to solve this vehicle stability problem. But it can only find out the result what it is rather than proving why it is. Therefore, it is necessary to prove and study this problem with using some basic mathematical methods. The analysis process involves today’s cutting edge of dynamics problems in engineering, such as nonsmooth dynamics, the number and distribution of limit cycle, et al. Besides, this analysis method is somehow weak and local. The comprehensive and rigorous method involves the unsolved 16th Hilbert problem. This thesis mainly includes:(1) The building up of mathematic model of bogie lateral motion. The nonlinearities such as equivalent conicity, suspension elements, flange contacts are considered. Particularly, the modeling of the nonsmooth elements such as equivalent conicity, yaw damper, flange contact force are highlighted. Meanthile, the piecewise lineaer and fitting smooth characteristic for yaw damper are compered.(2) Sovle the lateral motion bifurcation diagram of two high speed bogies with numerical methods. The continuation method is chosed through the comparision of shooting method, continuation method, time forward and reversed integration method to solve the instability behavior for CRH2 and CRH3 bogie. That is, small and large ampilitude instability occur in CHR2 and CRH3 bogie, which respectively corresponds to subcritical and supercritical Hopf bifurcation.(3) The two analytical methods Hopf norm form and Poincare section for Hopf bifurcation are derived. Besides, Hopf norm form method is chosed after comperison to prove why two kinds of simple wheelsets models perform different bifurcation types. The solution process uses both symbolic and numerical computation softwares which are maple and matlab, to program. Furthermore, this procedure is popularized to the high dimensional bogie model to prove why the two high speed vehicles described earlier perform as subcritical and supercritical bifurcations.(4) Based on the proving course, the key parameters variation of two bogies is investigated with using Hopf norm form. The influence of paramters on bifurcation type is studied to find out the critical parameter value which changes bifurcation type. This can provide theoretical base for vehicle paremetric design in engineering. At last, a critical case which is neither subcritical nor supercritical Hopf bifurcation is discussed.(5) The whole problem of vehicle stability and bifurcation involved the latter part of 16th Hilbert problem is proposed. Specifically, the number and the distribution of the limit cycle correspond, respectively, to the number of times of vehicle bifurcation and the vibration amplitude when instability occurs.(6) The rigorously defined Hopf bifurcation point for the whole CRH380B vehicle is analyzed. By comparing with the common reseach the influence of parameters on VE, which is defined according to engineering application, it yields different results. Furthermore, the mothed for raising VE is proposed. Then the low frequence swaying phenomenon for CRH380B running on Beijing-Shanghai high speed line is preliminarily investigated. At last, the problem of simulation algorithmic error and vehicle stachastic stability theory that arised from engineering application need to be further studied.