CAJ | 학술논문

为研究弹性约束轮对系统随机可靠性，建立考虑轨道不平顺与结构自身参数随机因素作用的随机动力学模型。运用拟不可积Hamilton系统随机平均法，将该模型表示为一维扩散的平均伊藤随机微分方程，利用奇异性边界理论分析系统随机全局稳定性，获得发生首次穿越可靠性破坏条件。建立可靠性函数满足的后向Kolmogorov方程及首次穿越时间概率密度函数满足的广义Pontryagin方程，结合初始条件、边界条件给出首次穿越问题提法。结果表明，系统失稳后车辆系统并非立即不能满足运营要求发生脱轨等行为，但能量达到系统储存极限时，系统可靠性能随时间推移会逐渐降低，且可靠性最终会被破坏并发生首次穿越脱轨失效，若系统继续增加能量，发生脱轨时刻会提前，脱轨可能性增大；故在工程应用中应对车辆横向振动能量进行监测与控制，使其维持在脱轨能量或失稳能量以下，并使系统耗能能力始终大于系统增加的能量，以保障轨道车辆安全运行，尤其高速列车更重要。
위연구탄성약속륜대계통수궤가고성，건립고필궤도불평순여결구자신삼수수궤인소작용적수궤동역학모형。운용의불가적Hamilton계통수궤평균법，장해모형표시위일유확산적평균이등수궤미분방정，이용기이성변계이론분석계통수궤전국은정성，획득발생수차천월가고성파배조건。건립가고성함수만족적후향Kolmogorov방정급수차천월시간개솔밀도함수만족적엄의Pontryagin방정，결합초시조건、변계조건급출수차천월문제제법。결과표명，계통실은후차량계통병비립즉불능만족운영요구발생탈궤등행위，단능량체도계통저존겁한시，계통가고성능수시간추이회축점강저，차가고성최종회피파배병발생수차천월탈궤실효，약계통계속증가능량，발생탈궤시각회제전，탈궤가능성증대；고재공정응용중응대차량횡향진동능량진행감측여공제，사기유지재탈궤능량혹실은능량이하，병사계통모능능력시종대우계통증가적능량，이보장궤도차량안전운행，우기고속열차경중요。
In order to study stochastic reliability of an elastically constrained wheelset system,its stochastic dynamic model was established considering track random irregularity and structural random parameters.Using Hamilton system and the stochastic averaging method,the model was expressed as an averaged ito stochastic differential equation of a one-dimensional diffusion process.The stochastic global stability of the system was analyzed using the theory of singular boundary to get the failure condition of stability with the first-passage occurring.The backward Kolmogorov equation satisfied by the stability function and the generalized Pontryagin equation satisfied by the first-passage time probability density function were derived,combining with the initial conditions and boundary conditions to present the problem of the first-passage.The numerical simulation was performed.The results showed that after the vehicle system is unstable the derailment does not appear at once;but when the energy reaches the storage limit of the system,the system relizbility drops gradually with time,at last the reliability is destroyed and the failure of first-passing derailment appears;if the system energy increases continuously,the time instant to derail will be earlier the possibility to derail rises;so in engineering application,the vehicle's transverse vibration energy should be monitored and controlled to keep it below the level of the derailment energy in the energy for losing stability and to make the energy dissipation ability of the system always be larger than the increased energy,on order to ensure the safe operation of rail vehicles,especially,high speed trains.