EMS型低速磁浮列车/轨道系统的动力相互作用问题研究
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摘要
车轨耦合振动问题影响系统造价和车辆运行的舒适度,是EMS型低速磁浮车商业化进程中必须解决的问题。本文参考轨道交通领域的最新研究成果,将磁浮系统和轨道简化成不同的形式,按由简到繁的原则,从悬浮系统和磁浮轨道两方面着手,研究系统的稳定性和非线性动力学、结构动力学特性,目的在于从理论上探讨车轨耦合振动现象出现的原因,寻找抑制车轨耦合振动的方法,为悬浮控制器和轨道结构设计提供参考。
本文首先研究了刚性轨道条件下位置和速度控制时滞对悬浮系统稳定性的影响,得到了控制参数与系统固有频率和时滞临界值间的关系,指出系统存在多个固有频率。基于特征根法给出了时滞系统的稳定性条件,得到系统在临界分岔点的Hopf分岔方向和稳定性。接着考虑轨道的几何不平顺,将其简化成已知简谐激励,基于中心流形约化和Poincaré规范型理论,运用多尺度法研究了扰动频率与系统固有频率比为1:1、1:3、3:1和不成整数比的情况下磁浮系统的非线性响应,研究了响应的奇异性、分岔、浑沌等动力学行为,研究表明控制时滞可以作为控制复杂动力学行为的开关。给出了控制参数的调节趋势,以抑制系统的动态响应。
为了使理论模型进一步接近真实系统,将轨枕简化成均布的弹性支撑,将磁浮系统简化为移动的均布力,建立了平直双层砼梁轨道的解析模型,采用模态叠加法得到了轨道响应的闭环解。分析指出轨道系统的第一固有频率远小于第二固有频率,在车轨耦合振动中起主要作用。数值仿真得到了轨枕刚度和其它结构参数与固有频率的关系。讨论了轨道变形和负载运行速度的关系。
文中还将磁浮列车简化成一列匀速通过轨道的均布力,在研究轨道响应闭环解的过程中发现了共振和消逝现象,推导出了共振和消逝速度。指出当列车运行于共振速度时,轨道变形会随着通过车辆数的增加而增加,这种情况应该极力避免。而当列车运行于消逝速度时,轨道变形较小。本文还给出了最佳的车长-桥跨长度之比,使得系统的结构共振现象最微弱。
在文章的最后,我们基于前面的分析,建立了统一的磁浮车-弹性轨道的数学模型,运用数值仿真的方法分析了线性系统的特征根变化情况,讨论了控制时滞对车轨耦合振动的影响,最后通过试验验证了文中部分理论结论的正确性。
Vehicle-guideway interaction vibration greatly influences the system price and ride comfort. It is an important problem that must be settled in the commercial process of the EMS low speed maglev transportation system. From simplicity to complexity, this dissertation simplifies the maglev system and levitation guideway into different formats, studies system stability and response of nonlinear dynamics and structure dynamics by respectively analyzing maglev system and levitation guideway based on the recent results of the track transportation system. It aims at exploiting the rules of vehicle-guideway interaction theoretically and finding the methods to suppress the oscillation, and helps to design the levitation controller and guideway structure.
The effect of the time delay in position and speed feedback signal to the stability of the maglev system with rigid guideway is considered. The relationship between control parameters and system natural frequency, critical time delay are obtained. It shows that the maglev system have several natural frequencies. The stability conditions of the system are obtained based on characteristic root method. The Hopf bifurcation direction and stability of the system at the critical point are also investigated. Then the elasticity of the guideway is considered, its deflection is simplified as known cosine wave.Center manifold reduction and Poincarénormal form theory are employed in this paper. The nonlinear oscillation with the proportion between disturbance and natural frequency to be of 1:1, 1:3, 3:1 and none of the above are investigated based on the method of Multiple Scale. Singularity, bifurcation and chaos etc. are found in the system response. It is shown that time delay can control the existence of the complicated dynamic behavior. The trend of the control parameters to weaken the dynamic response is given too.
To approach the real system more, the sleeper is simplified as evenly distributed elastic foundation. The analytical model of smooth and straight concrete guideway is constructed. Simplifying the maglev vehicle to an evenly distributed force, the closed form solution of the guideway is deduced based on mode superposition method. It is pointed out that beacuse the first natural frequency is much smaller than the second one, it bears the primary function in vehicle guideway interaction. The relationship between natural frequency and structure parameters are acquired. Guideway deflection influenced by the running speed of the load is also discussed.
The maglev train is simplified as a series of evenly distributed force. Resonant and cancellation phonomenon are found when we analyze the closed form solutions of the guideway. The resonant and cancellation speed are deduced. They indicate that the displacement of the guideway will increase when the maglev train runs at resonant speed and decrease when it runs at cancellation speed. The resonant speed should be avoided. The investigation about the ratio of span to the length of the vehicle shows that the smaller the ratio is, the larger the dynamic impact of the guideway will become. Properly selecting the ratio can suppress the vehicle-guideway structure interaction.
At last, the vehicle-guideway dynamic model is built. We use numerical simulation method to analyze the variation of characteristic roots of the linearized system. The effect of the control delay to the vehicle-guideway interaction is also discussed. Finally, a few conclusions presented in the article are testified by the experiments.
本文首先研究了刚性轨道条件下位置和速度控制时滞对悬浮系统稳定性的影响,得到了控制参数与系统固有频率和时滞临界值间的关系,指出系统存在多个固有频率。基于特征根法给出了时滞系统的稳定性条件,得到系统在临界分岔点的Hopf分岔方向和稳定性。接着考虑轨道的几何不平顺,将其简化成已知简谐激励,基于中心流形约化和Poincaré规范型理论,运用多尺度法研究了扰动频率与系统固有频率比为1:1、1:3、3:1和不成整数比的情况下磁浮系统的非线性响应,研究了响应的奇异性、分岔、浑沌等动力学行为,研究表明控制时滞可以作为控制复杂动力学行为的开关。给出了控制参数的调节趋势,以抑制系统的动态响应。
为了使理论模型进一步接近真实系统,将轨枕简化成均布的弹性支撑,将磁浮系统简化为移动的均布力,建立了平直双层砼梁轨道的解析模型,采用模态叠加法得到了轨道响应的闭环解。分析指出轨道系统的第一固有频率远小于第二固有频率,在车轨耦合振动中起主要作用。数值仿真得到了轨枕刚度和其它结构参数与固有频率的关系。讨论了轨道变形和负载运行速度的关系。
文中还将磁浮列车简化成一列匀速通过轨道的均布力,在研究轨道响应闭环解的过程中发现了共振和消逝现象,推导出了共振和消逝速度。指出当列车运行于共振速度时,轨道变形会随着通过车辆数的增加而增加,这种情况应该极力避免。而当列车运行于消逝速度时,轨道变形较小。本文还给出了最佳的车长-桥跨长度之比,使得系统的结构共振现象最微弱。
在文章的最后,我们基于前面的分析,建立了统一的磁浮车-弹性轨道的数学模型,运用数值仿真的方法分析了线性系统的特征根变化情况,讨论了控制时滞对车轨耦合振动的影响,最后通过试验验证了文中部分理论结论的正确性。
Vehicle-guideway interaction vibration greatly influences the system price and ride comfort. It is an important problem that must be settled in the commercial process of the EMS low speed maglev transportation system. From simplicity to complexity, this dissertation simplifies the maglev system and levitation guideway into different formats, studies system stability and response of nonlinear dynamics and structure dynamics by respectively analyzing maglev system and levitation guideway based on the recent results of the track transportation system. It aims at exploiting the rules of vehicle-guideway interaction theoretically and finding the methods to suppress the oscillation, and helps to design the levitation controller and guideway structure.
The effect of the time delay in position and speed feedback signal to the stability of the maglev system with rigid guideway is considered. The relationship between control parameters and system natural frequency, critical time delay are obtained. It shows that the maglev system have several natural frequencies. The stability conditions of the system are obtained based on characteristic root method. The Hopf bifurcation direction and stability of the system at the critical point are also investigated. Then the elasticity of the guideway is considered, its deflection is simplified as known cosine wave.Center manifold reduction and Poincarénormal form theory are employed in this paper. The nonlinear oscillation with the proportion between disturbance and natural frequency to be of 1:1, 1:3, 3:1 and none of the above are investigated based on the method of Multiple Scale. Singularity, bifurcation and chaos etc. are found in the system response. It is shown that time delay can control the existence of the complicated dynamic behavior. The trend of the control parameters to weaken the dynamic response is given too.
To approach the real system more, the sleeper is simplified as evenly distributed elastic foundation. The analytical model of smooth and straight concrete guideway is constructed. Simplifying the maglev vehicle to an evenly distributed force, the closed form solution of the guideway is deduced based on mode superposition method. It is pointed out that beacuse the first natural frequency is much smaller than the second one, it bears the primary function in vehicle guideway interaction. The relationship between natural frequency and structure parameters are acquired. Guideway deflection influenced by the running speed of the load is also discussed.
The maglev train is simplified as a series of evenly distributed force. Resonant and cancellation phonomenon are found when we analyze the closed form solutions of the guideway. The resonant and cancellation speed are deduced. They indicate that the displacement of the guideway will increase when the maglev train runs at resonant speed and decrease when it runs at cancellation speed. The resonant speed should be avoided. The investigation about the ratio of span to the length of the vehicle shows that the smaller the ratio is, the larger the dynamic impact of the guideway will become. Properly selecting the ratio can suppress the vehicle-guideway structure interaction.
At last, the vehicle-guideway dynamic model is built. We use numerical simulation method to analyze the variation of characteristic roots of the linearized system. The effect of the control delay to the vehicle-guideway interaction is also discussed. Finally, a few conclusions presented in the article are testified by the experiments.
引文
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