转子-机匣局部碰摩的分叉与混沌行为分析

研究了转子-机匣系统发生碰摩时的分叉与混沌行为,分析了转子机匣频率比与刚度比、偏心质量等参数对系统分叉与混沌特性的影响.当转子机匣系统发生碰摩时除了通过倍周期、阵发性和拟周期分叉进入混沌外,还发现了孪生叉形分叉现象,呈现出非常丰富的动力学行为.     

一类非线性油膜轴承—转子系统的碰摩数值分析

本文结合非线性油膜力模型和碰摩速度跃迁公式,建立了描述非线性油膜轴承-转子系统碰摩的刚性约束非光滑模型。通过数值模拟,得到了该系统随转动角频率及油膜特性参数变化发生碰摩的分岔特性,并揭示出转子系统的碰摩与油膜振荡的1/2亚谐共振有密切关系。     

航空发动机整机耦合动力学模型及振动分析

面向航空发动机整机振动, 建立了航空发动机转子-滚动轴承-机匣耦合动力学模型. 该模型具有如下特点: (1)考虑转子、滚动轴承及机匣之间的耦合作用; (2)考虑了实际航空发动机的弹性支承及挤压油膜阻尼效应; (3)将转子考虑为等截面自由欧拉梁模型, 运用模态截断法进行分析; (4)考虑了滚动轴承间隙、非线性赫兹接触力以及变柔性VC(Varyingcompliance)振动; (5)考虑了转子与机匣之间的碰摩故障. 运用数值积分方法研究了航空发动机的整机振动规律, 包括: 滚动轴承VC振动分析、弹性支承刚度对耦合系统临界转速的影响、转轴模态截断阶数NM对系统响应的影响分析、挤压油膜阻尼器参数对系统响应的影响分析、突加不平衡的瞬态响应分析以及转静碰摩故障特性分析等.      

迷宫密封转子系统非线性动力稳定性的研究

研究迷宫密封对转子系统动力稳定性的影响，迷宫密封的气动力采用Muszynska非线性力模型，计算了单盘Jeffcott转子非线性动力学特性。对Jacobi矩阵的分析表明，在密封力的影响下，转子达到一定转速后开始失稳，发生Hopf分岔，进入周期涡动状态，涡动幅度随转速的提高而增大，提高到一定程度，密封和转子发生碰摩，采用Runge-Kutta法数值模拟了转子的轴心轨迹。最后分析了迷宫密封的物理和结构参数对系统运动特性的影响。     

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。     

碰摩转子系统的非光滑分析

通过建立转子系统碰摩的Ｐｏｉｎｃａｒｅ映射,将对非光滑碰摩系统的研究转化为对Ｐｏｉｎｃａｒｅ映射的分析,文中主要对转子碰摩当中一类特殊的运动形式－单点碰摩下的擦边现象者了详细研究。从序列的极限理论出发分析了该映射的周期不动点的稳定性及其吸引域,得到了转子系统在接近擦边运动时解随系统参数变化的分岔情形。     

磁摩转子系统中的碰擦分岔现象

对于旋转机械中的常见故障这一－－转子与定子碰摩，应用非线性动力学理论分析了一个简单碰摩转子系统的碰擦分岔现象。通过对运动微分方程的数值积分。研究了转速比变化时系统具有的各种形式的分岔。结果表明：系统的运动具有周期与混沌运动交替、周期递增现象，倍周期分岔，以及随控制参数的减小运动从的周期轨道分岔为混沌吸引了。系统的这非线性特征对于准确地诊断这一故障具有重要意义。     

转子与定子碰摩的非线性动力学研究

转子与定子碰摩的动力学行为及其与系统参数关系对旋转机械设计和安全运行至关重要. 转子/定子碰摩系统是一类多参数控制的高维非光滑强非线性系统, 其动力学行为非常复杂. 本文主要从动力学与控制的角度对过去半个世纪有关转子与定子碰摩的研究成果进行归纳和总结, 其目的在于帮助读者尽可能全面系统地了解该问题的研究现状, 提炼尚待解决的问题, 以求推动转子与定子碰摩研究的进一步深入, 并为解决实际问题提供帮助. 本文将首先从碰摩局部模型和碰摩系统模型两个方面对已有的转子/定子碰摩系统的建模进行了简单的划分和归类. 其次, 以典型碰摩非线性响应为主线, 分别介绍了有关同频碰摩响应、谐波周期碰摩响应、准周期局部碰摩响应、干摩擦自激反向全周涡动响应、碰摩的全局响应行为以及碰摩响应的分岔与混沌方面的研究成果. 接下来讨论了在主被动抑制碰摩振动方面取得的结果. 最后, 给出结论并提出有待进一步研究的问题.     

非线性碰摩力对碰摩转子分叉与混沌行为的影响

研究了具有非线性碰摩力的转子局部碰摩的分叉与混沌运动,利用计算机仿真对某发动机转子的碰摩故障进行了数值模拟,讨论了转子系统参数的变化对转子混池运动状态的影响,并与碰摩实验结果进行了比较,发现了具有非线性碰摩力的转子局部碰摩转子系统的各种多周期运动和混沌运动及其演变过程。     

考虑定子质量和碰摩面刚度的转子/定子系统碰摩响应的全局动力学特性研究

对考虑定子质量和碰撞面刚度的四自由度转子/定子模型的全局响应特性进行了研究。首先,通过解析方法确定了无碰摩响应的边界,然后,求解了同频全周碰摩解并进行了稳定性分析得到了同频全周碰摩响应的区域。在此基础上,利用非线性动力学分析的数值方法,确定了准周期局部碰摩与反向涡动失稳的边界,由此得出了参数平面内的不同碰摩响应的稳定区域图。进而研究了定子与转子质量比和碰撞面刚度对碰摩全局响应特性的影响,得到了不同碰摩响应共存及随系统参数变化的典型全局响应分岔图。     

Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.     

Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull

Electromagnetic and mechanical forces are main reasons resulting in vibrations in hydraulic generating set. The non-symmetric air-gap between the rotor and stator creates an attraction force called unbalanced magnetic pull (UMP). The UMP can produce large oscillations which will be dangerous to the machines. In this paper, the nonlinear dynamic characteristics of a rotor-bearing system with rub-impact for hydraulic generating set under the UMP are studied. The rubbing model is established based on the classic impact theory. Through the numerical calculation, the excitation current, mass eccentricity, stiffness of shaft and radial stiffness of stator are used as control parameters to investigate their effect on the system, by means of bifurcation diagrams, Poincaré maps, trajectories and frequency spectrums. Various nonlinear phenomena including periodic, quasi-periodic and chaotic motions are observed. The results reveal that the UMP has significant influence in the response of the rotor system that the continuous increase in the excitation current induces the alternation of quasi-periodic and chaotic motions, the co-occurrence of oil whip and rub in a wide excitation range aggravates the vibration and leads to the instability of the system. In addition, the large eccentricity and radial stiffness of stator, as well as the small stiffness of shaft may lead to the occurrence of full annular rubbing while increasing the stiffness of the shaft can play an important role of suppressing the chaotic motion, reducing the vibration and improving stability of the system.     

Analysis of a new three-dimensional chaotic system

In this paper, a new three-dimensional autonomous chaotic system is presented. There are three control parameters and three different nonlinear terms in the governed equations. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation. The nonlinear characteristic of the new three-dimensional autonomous system versus the control parameters is illustrated by bifurcation diagram, Lyapunov-exponent spectrum, phase portraits, etc.     

Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos.     

Response analysis of a dual-disc rotor system with multi-unbalances–multi-fixed-point rubbing faults

Rotor unbalance and rub-impact are major concerns in rotating machinery. In order to study the dynamic characteristics of these machinery faults, a dual-disc rotor system capable of describing the mechanical vibration resulting from multi-unbalances and multi-fixed-point rub-impact faults is formulated using Euler beam element. The Lankarani–Nikravesh model is used to describe the nonlinear impact forces between discs and casing convex points, and the Coulomb model is applied to simulate the frictional characteristics. To predict the moment of rub-impact happening, a linear interpolation method is carried out in the numerical simulation. The coupling equations are numerically solved using a combination of the linear interpolation method and the Runge–Kutta method. Then, the dynamic behaviours of the rotor system are analysed by the bifurcation diagram, whirl orbit, Poincaré map and spectrum plot. The effects of rotating speed, phase difference of unbalances, convex point of casing and initial clearance on the responses are investigated in detail. The numerical results reveal that a variety of motion types are found, such as periodic, multi-periodic and quasi-periodic motions. Moreover, the energy transfer between the compressor disc and the turbine disc occurs in the multi-fixed-point rubbing faults. Compared with the parameters of the turbine disc, those of the compressor disc can affect the motion of the rotor system more significantly. That is, the responses exhibit simple 1T-periodic motion in the wide range of rotating speed under the conditions of sharp convex point and larger initial clearance. These forms of dynamic characteristics can be effectively used to diagnose the fixed-point rub-impact faults.     

磁场中轴向运动条形板强非线性超谐共振及混沌运动

针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究。应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解,得到超谐波共振下系统的分岔响应方程。根据奇异性理论对非线性动力学系统的普适开折进行分析,求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图。通过数值算例,分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图,以及反映不同运动行为区域的动力学响应图形,讨论分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,可通过相应参数的改变实现对系统复杂动力学行为的控制。     

Dynamical behavior analysis and bifurcation mechanism of a new 3-D nonlinear periodic switching system

This paper presents a new periodic switching chaotic system, which is topologically non-equivalent to the original sole chaotic systems. Of particular interest is that the periodic switching chaotic system can generate stable solution in a very wide parameter domain and has rich dynamic phenomena. The existence of a stable limit cycle with a suitable choice of the parameters is investigated. The complex dynamical evolutions of the switching system composed of the Rössler system and the Chua’s circuit are discussed, which is switched by equal period. Then the possible bifurcation behaviors of the system at the switching boundary are obtained. The mechanism of the different behaviors of the system is investigated. It is pointed out that the trajectories of the system have obvious switching points, which are decided by the periodic signal. Meanwhile, the system may be led to chaos via a period-doubling bifurcation, resulting in the switching collisions between the trajectories and the non-smooth boundary points. The complicated dynamics are studied by virtue of theoretical analysis and numerical simulation. Furthermore, the control methods of this periodic switching system are discussed. The results we have obtained clearly show that the nonlinear switching system includes different waveforms and frequencies and it deserves more detailed research.     

非自治时滞反馈控制系统的周期解分岔和混沌

研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理,研究对应的线性平衡态失稳的临界边界,将时滞非线性控制方程化为泛函微分方程,给出由Hopf分岔产生的周期解的解析形式．通过分析周期解的稳定性得到周期解的失稳区域,使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路：倍周期分岔和环面破裂．其结果表明,时滞在控制系统中可以作为控制和产生系统的复杂运动的控制“开关”．     

Dynamical properties and simulation of a new Lorenz-like chaotic system

This paper formulates a new three-dimensional chaotic system that originates from the Lorenz system, which is different from the known Lorenz system, Rössler system, Chen system, and includes Lü systems as its special case. By using the center manifold theorem, the stability character of its non-hyperbolic equilibria is obtained. The Hopf bifurcation and the degenerate pitchfork bifurcation, the local character of stable manifold and unstable manifold, are also in detail shown when the parameters of this system vary in the space of parameters. Corresponding bifurcation cases are illustrated by numerical simulations, too. The existence or non-existence of homoclinic and heteroclinic orbits of this system is also studied by both rigorous theoretical analysis and numerical simulation.