具有裂纹-碰摩耦合故障转子-轴承系统的动力学研究

以非线性动力学和转子动力学理论为基础，分析了带有碰摩和裂纹耦合故障的弹性转子系统的复杂运动，在考虑轴承油膜力的同时构造了含有裂纹和碰摩故障转子系统的动力学模型。针对短轴承油膜力和碰摩-裂纹转子系统的强非线性特点，采用Runge-Kutta法对该系统由碰摩和裂纹耦合故障导致的非线性动力学行为进行了数值仿真研究，发现该类碰摩转子系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象，该研究结果为转子-轴承系统故障诊断、动态设计和安全运行提供理论参考。     

考虑密封的悬臂转子系统的裂纹故障分析

以双盘悬臂立式转子-轴承系统为研究对象，建立了系统运动微分方程，并用数值方法分析了在非线性密封力和非线性油膜力作用下的裂纹转子的动力学特性。分析表明，在一定深度裂纹下，转子系统响应随不同角频率比表现出复杂的非线性现象，出现了周期k运动、拟周期运动和混沌运动等多种运动形式。在一定角速度时，工作在远离临界角速度区的转子系统对裂纹非常敏感，而工作在近临界角速度区的转子系统对裂纹不是特别敏感，但是裂纹对它的运动状态影响较大。该研究结果为该类转子-轴承系统的安全运行与故障诊断提供了一定的理论参考。     

不平衡量对非线性多转子系统动力特性的影响

用近代非线性动力学理论分析了弹性支承有间隙和摩擦的非线性刚性多转子系统的复杂运动．建立了支座有间隙和有摩擦的弹性支承的力学模型．导出了这类多转子系统的运动微分方程组．用数值方法得到系统在某些参数区域内的轴心轨迹图，Poincare映射图和分岔图等．以转子不平衡量为控制参数讨论了进出混沌区的不同路径和系统各种形式的拟周期，倍周期和混沌运动．分析结果为定性地改善转子系统的稳定运行状态提供了理论依据．     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

磁浮轴承-转子系统非线性动态特性分析

考虑非线性电磁力对刚性Jeffcott转子系统的影响，采用Hopf分岔理论及CPNF法对系统平衡点解和周期解进行研究，数值仿真得到系统Jacobi矩阵特征值、轴心轨迹图和Poincare映射图。转子运动呈现Hopf分岔、倍周期分岔及拟周期运动等复杂的非线性动力学特征，其结果可为磁浮轴承-转子系统设计和运行状态控制提供理论依据。     

叶片振动影响下双盘转子-轴承系统的稳定性与分岔

研究叶片与转子-轴承系统的耦合非线性振动,建立了一个带叶片的双盘转子-轴承系统的非线性动力学模型,其中包含一个弹性转轴、两个滑动轴承、两个刚性圆盘和两组弹性叶片.为了分析叶片的惯性影响,将其简化为单摆模型.采用4阶Runge-Kutta法进行了数值模拟,并利用分岔图、三维谱图、轴心轨迹和Poincaré映射图等方法分析了系统的非线性动力学特性.研究发现,随着转速的变化,系统响应演化出了倍周期运动、概周期运动、混沌运动和倍周期分岔等典型的非线性动力学行为.在与忽略了叶片振动的转子系统对比后发现,叶片振动使转子发生混沌运动的转速区域增大.在某些参数条件下,采用不同的叶片刚度,叶片振动可能引起转子系统产生混沌运动.     

受电磁激励的连续转子-轴承系统非线性振动与分岔

研究了受横向不平衡电磁激励的转子．轴承系统的非线性振动响应。首先将转子．轴承系统简化为带有质量不平衡并受横向激励的连续梁,由于短轴承的油膜力和电磁力的共同激励,系统振动具有强非线性特性。用Galerkin方法把偏微分控制方程离散为常微分方程组,采用四阶Runge—Kutta法对该系统进行数值仿真研究。其次比较了转轴分别在电磁力、油膜力单独作用和两种力共同作用下的振动特性,研究表明电磁力和油膜力对转子系统的非线性振动和分岔有着不同的贡献：油膜力的存在抑制了拟周期运动的发生,延长了稳定运行区域;电磁力拉长了拟周期发生的区域,降低了转子系统发生突发性破坏的风险。最后给出了系统响应随转速、电磁参数、油膜粘度等控制参数变化的分岔图,表明：系统在两个方向的运动随控制参数的变化趋势基本相同,经历了周期、倍周期、拟周期等非线性运动交替出现的过程;且油膜粘度的增大有利于转子系统的安全运行。     

弹性支承有间隙的复合转子系统的混沌特性

用近代非线性动力学理论分析了支承有间隙的调整对对称刚性复合转子系统的复杂运动,用数值方法得到系统在某些参数区域内的轴心轨迹图、Poincare映射图和分岔图,讨论了转速变化时出现的周期、倍周期、拟周期和混沌运动,分析结果为定性地改善转子系统的稳定运动状态提供了理论依据。     

转子—轴承系统发生动静件碰摩时的混沌路径

分析了一个由油膜轴承支承的转子系统在发生动静件碰摩时的振动特性。转子转速与不平衡量被用来作为控制参数以研究进入和离开混沌区域的各种路径以及系统的各种形式的周期、拟周期与混沌运动。结果证明碰摩转子系统在进入和离开混沌区域时可经由倍周期分岔、阵发性和拟周期路径，以及一种由周期运动直接到混沌状态的突发路径。     

轴承-转子系统在基础运动作用时的非线性分析

轴承-转子系统的非线性特性及其在基础运动作用时的响应,是离心机设备设计阶段必须考虑的。本文使用简化的多自由度转子模型进行模拟分析,运动方程考虑了非线性的油膜润滑轴承模型。应用自适应时间步长的Runge-Kutta-Felburg法求解微分运动方程组,将人造的正弦波加速度作为基础运动输入系统,使用Poincaré图、分岔图和瀑布图分别考察了垂直放置转子在有无基础运动作用时的动力学性质。快速傅里叶变换在频域内揭示了转动频率与基础振动频率之间的组合共振现象。计算的结果不仅给出了泵转子自身的非线性性质,也展示了泵转子在基础运动作用时的组合共振。     

裂纹转子在支承松动时的振动特性研究

以具有支承松动的Jeffcott裂纹转子为研究对象，分析了支承松动和轴上横向裂纹对转子系统刚度的影响，建立了转子系统振动的微分方程，并用数值方法分析了其振动特性。分析表明，转子在裂纹和支承松动这两种非线性因素的作用下，表现出复杂的非线性行为。     

Nonlinear dynamic responses of high-speed railway vehicles under combined self-excitation and forced excitation considering the influence of unsteady aerodynamic loads

The dynamic characteristics of a railway vehicle system under unsteady aerodynamic loads are examined in this study. A dynamic analysis model of the railway vehicle considering the influences of aerodynamic loads was established. The model not only considers the forced excitation effect of unsteady aerodynamic loads but also accounts for the effect of unsteady aerodynamic loads on the change of the wheel–rail contact normal forces as well as changes of the wheelset creep coefficients and creep forces/moments. Therefore, this model also considers the influences of unsteady aerodynamic loads on the self-excited vibration characteristics of the vehicle system. The time-history curves, phase trajectory diagrams, Poincaré sections, and Lyapunov exponents of the vehicle system running on a smooth straight track under unsteady aerodynamic loads were determined. The results show that when the critical speed is exceeded, the vehicle system usually performs quasi-periodic motion under unsteady aerodynamic loads, which is significantly different from the periodic motion under steady aerodynamic loads. In different cases, the amplitude and phase of motion are significantly different. The amplitude of the motions can be increased by more than 159%, and the difference of phase can be up to 173°. (The phase is almost reversed.) The dynamic responses of the vehicle system under unsteady aerodynamic loads contain abundant frequency components, including the frequency of the self-excited vibration, the frequency of the forced excitation, and combinations of their integer multiples. The vibration forms corresponding to the main harmonic components under unsteady and steady aerodynamic loads were compared, and the self-excited vibration component of the vehicle system under unsteady aerodynamic loads was identified. The variations in the critical speed with various parameter combinations were computed. The variation range of the critical velocity can reach 73%.

     

基于Lyapunov指数谱的航空发动机故障诊断研究

提出了基于Lyapunov指数谱和Lyapunov指数谱熵的航空发动机状态识别和故障诊断新方法。基于实测的某型航空发动机振动时间序列求解了系统不同工作状态和故障状态的Lya-punov指数谱;基于Lyapunov指数谱,对该型航空发动机进行了状态识别和故障诊断;为给出对Lyapunov指数谱及其对状态识别和故障诊断的整体表述,定义了Lyapunov指数谱熵,并基于该谱熵对该型航空发动机进行了状态识别和故障诊断。研究结果表明该型航空发动机振动时间序列在不同状态下具有不同的Lyapunov指数谱及其谱熵,即可以Lyapunov指数谱及其谱熵作为识别其状态的特征量,为航空发动机的故障诊断和状态监控提供了新的可靠的方法。     

Vibration characteristics of a hydraulic generator unit rotor system with parallel misalignment and rub-impact

The object of this research aims at the hydraulic generator unit rotor system. According to fault problems of the generator rotor local rubbing caused by the parallel misalignment and mass eccentricity, a dynamic model for the rotor system coupled with misalignment and rub-impact is established. The dynamic behaviors of this system are investigated using numerical integral method, as the parallel misalignment, mass eccentricity and bearing stiffness vary. The nonlinear dynamic responses of the generator rotor and turbine rotor with coupling faults are analyzed by means of bifurcation diagrams, Poincaré maps, axis orbits, time histories and amplitude spectrum diagrams. Various nonlinear phenomena in the system, such as periodic, three-periodic and quasi-periodic motions, are studied with the change of the parallel misalignment. The results reveal that vibration characteristics of the rotor system with coupling faults are extremely complex and there are some low frequencies with large amplitude in the 0.3–0.4× components. As the increase in mass eccentricity, the interval of nonperiodic motions will be continuously moved forward. It suggests that the reduction in mass eccentricity or increase in bearing stiffness could preclude nonlinear vibration. These might provide some important theory references for safety operating and exact identification of the faults in rotating machinery.     

Torus doublings and chaotic amplitude modulations in a two degree-of-freedom resonantly forced mechanical system

This work studies the response of a weakly non-linear vibratory system with two degrees-of-freedom when the system is excited near resonance. The two linear modes are in 1:3 internal resonance. The asymptotic method of averaging and direct numerical integration are used to obtain the response of the system. Over a range of excitation frequencies and modal damping, the averaged equations in slow time are found to possess limit cycle solutions. These solutions undergo period doubling bifurcations to chaotic solutions. The averaging theory then implies the existence of amplitude modulated motions, the exact nature of modulations not being well defined. Numerical simulation of the original vibratory two degree-of-freedom system shows that the system does undergo amplitude modulated motions. For sufficiently large damping, only periodic modulations arise in the form of a 2-torus. For lower damping, the 2-torus can undergo doubling and ultimate destruction to result in a chaotic attractor. Poincare sections of steady state solutions are used to characterize the various types of amplitude modulated motions.     

The “resultant bifurcation diagram” method and its application to bifurcation behaviors of a symmetric railway bogie system

The concept of symmetric bifurcation for a symmetric wheel-rail system is defined. After that, the time response of the system can be achieved by the numerical integration method, and an unfixed and dynamic Poincaré section and its symmetric section for the symmetric wheel-rail system are established. Then the ??resultant bifurcation diagram?? method is constructed. The method is used to study the symmetric/asymmetric bifurcation behaviors and chaotic motions of a two-axle railway bogie running on an ideal straight and perfect track, and a variety of characteristics and dynamic processes can be obtained in the results. It is indicated that, for the possible sub-critical Hopf bifurcation in the railway bogie system, the stable stationary solutions and the stable periodic solutions coexist. When the speed is in the speed range of Hopf bifurcation point and saddle-node bifurcation point, the coexistence of multiple solutions can cause the oscillating amplitude change for different kinds of disturbance. Furthermore, it is found that there are symmetric motions for lower speeds, and then the system passes to the asymmetric ones for wide ranges of the speed, and returns again to the symmetric motions with narrow speed ranges. The rule of symmetry breaking in the system is through a blue sky catastrophe in the beginning.     

翼型颤振压电俘能器的输出特性研究

压电俘能器能够为自然界中低功率的微机电系统持续供能. 为了模拟机翼的沉浮?俯仰二自由度运动和有效俘获气动弹性振动能量, 本文提出一种新颖的翼型颤振压电俘能器. 基于非定常气动力模型, 推导翼型颤振压电俘能器流?固?电耦合场的数学模型. 建立有限元模型, 模拟机翼的沉浮?俯仰二自由度运动, 获得机翼附近的涡旋脱落和流场特性. 搭建风洞实验系统, 制作压电俘能器样机. 利用实验验证理论和仿真模型的正确性, 仿真分析压电俘能器结构参数对其气动弹性振动响应和俘获性能的影响. 结果表明: 理论分析、仿真模拟和实验研究获得的输出电压具有较好的一致性, 验证建立数学和仿真模型的正确性. 仿真分析获得机翼附近的压力场变化云图, 表明交替的压力差驱动机翼发生二自由度沉浮?俯仰运动. 当风速超过颤振起始速度时, 压电俘能器发生颤振, 并表现为极限环振荡. 当偏心距为0.3和风速为16 m/s时, 可获得最大输出电压为17.88 V和输出功率为1.278 mW. 功率密度为7.99 mW/cm3, 相比较于其他压电俘能器, 能实现优越的俘获性能. 研究结果对设计更高效的翼型颤振压电俘能器提供重要的指导意义.      

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.