转子有碰摩和支承松动故障时的非线性特性研究

以具有支承松动的Jeffcott转子为研究对象，并考虑到转子系统转子和定子间的碰摩现象，分析了支承松动和碰摩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非线性动力学特性。数值分析表明，转子在碰摩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。     

油膜支承转子系统动静件碰摩特征分析

以支承在油膜轴承上的Jeffcott转子为对象，分析了油膜力对碰摩转子动力学行为的影响。通过与刚支情形对比，发现油膜力是耦合作用于碰摩转子系统，有时能够抑制振动，有时却加剧振动。因此实际转子碰摩故障诊断过程中，必须在充分考虑支承情况的基础上建立合理的非线性动力学模型，才能为实际转子系统的碰摩故障分析提供必要的理论依据。     

开闭裂纹转子的弯扭耦合振动研究

以水平放置的Jeffcott裂纹转子为研究对象，建立了开闭裂纹转子弯扭耦合振动的非线性运动微分方程，并用数值方法分析了纯弯曲振动与弯扭耦合振动情况下转子的动力响应。结果表明：弯扭耦合振动是由转子质量的偏心和转子自重的共同作用而产生的，当质量偏心很小时可以不考虑扭转振动的影响，当偏心较大时，扭转对弯曲振动的影响主要体现在高转速部分，且由于裂纹开闭的作用，使扭转的耦合作用存在一个范围，随裂纹深度的增加，扭振影响的转速下限就会越低，但当裂纹较深、转速较快时，扭转对弯曲振动在作用范围内有明显的影响，使频谱图和轴心轨迹都发生较大的变化，且对转速的变化极为敏感，因此在故障诊断时必须对扭转的耦合作用高度重视。     

带裂纹的转子——支承系统的振动特性

本文在[1]的基础上,提出一种更为精确的振动轴横向裂纹的力学模型,建立了含有多个不同方位、不同尺寸横向裂纹的转子横向振动方程式.修正了Newmark 数值积分方法,对建立的非线性微分方程组进行直接积分,得出了一些十分有意义的结论,很好地解释了国外一些有关论文之间的矛盾,并为裂纹振动监测提供了可能性....     

弹性支承滑动轴承不平衡转子系统非线性动力稳定性和分岔的研究

研究弹性支承滑动轴承不平衡转子系统的稳定性及分岔特性。建立了弹性支承-滑动轴承-转子非线性动力系统的力学模型，在油膜力非线性的情况下，应用数值模拟，采用打靶法计算了刚性转子系统的周期解，并与龙格-库塔法计算的结果进行了对比，依据Floquet理论，分析了周期解的稳定性，再结合龙格-库塔法、Poineare映射法作出了系统运动分岔图。最后，讨论了轴的柔性对转子系统运动稳定性的影响。     

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．     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

转子—非线性支承系统振动响应的优化计算

本文用一种新的优化方案计算装有非线性弹性支承－挤压油膜阻尼器的转子系统的振动响应。首先根据转子系统的结构特点，建立其无量纲形式的非线性运动微分方程；然后由微分方程构造－控制目标函数，最后对此目标函数进行优化计算，求得转子系统的振动响应。     

基于随动坐标系的开裂纹转子系统转动阻尼对振动稳定性影响的研究

区分固定阻尼和转动阻尼的情况下,建立了基于Lagrange方程的随动坐标系下开裂纹转子的运动方程。在此基础上采用了基于Routh-Hurwitz判据的根轨迹法,做出了裂纹转子非线性振动的坎贝尔图、衰变率图、根轨迹图;以此为依据分别研究了无阻尼开裂纹转子、具有一定比例的粘滞阻尼开裂纹转子运动稳定性。从而得出粘滞阻尼、粘滞阻尼中不同转动阻尼所占的比例以及对系统稳定性的影响,为裂纹转子故障诊断和不稳定振动控制提供了理论依据。     

裂纹转子的振动响应研究

本文研究了裂纹转子的振动响应。文章首先通过应力强度因子积分得到含裂纹轴单元的刚度矩阵；建立了裂纹转子的运动微分方程。进而研究了裂纹转子的振动响应，得出了裂纹转子的振动响应随裂纹位置和深度的变化关系。为工程上早期诊断微小裂纹提供了理论根据。     

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。     

Grazing Bifurcation in the Response of Cracked Jeffcott Rotor

A cracked rotor is modeled by a piecewise linear system due to thebreath of crack in a rotating shaft. The differential equations ofmotion for the nonsmooth system are derived and solved with thenumerical integration method. From the simulation results, it isobserved that a grazing bifurcation exists in the response. Thegrazing bifurcation can give rise to jumps between periodic motions,quasi-periodic motions from the periodic ones, chaos, and intermittentchaos.     

Non-linear global dynamics of an axially moving plate

In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes.     

Robust control for MIMO hybrid dynamical system of underwater vehicles by composite adaptive fuzzy estimation of uncertainties

An organization structure of global oscillation with respect to a cracked rotor system with oil-film force is investigated in this paper. We profit from GPU cluster parallel computing to present a number of high-quality phase diagrams, and exhibit global dynamic characteristics of the system. An interesting scenario, “eye” of chaos, is discovered in this cracked rotor system, emerging as the accumulation limit of forward and reverse period-doubling bifurcation cascades. In this system, it is a common phenomenon that the vibration response of the rotor presents three typical characteristics in parameter space with the rotation speed increasing. Moreover, these phase diagrams assist us to identify multi-attractor coexisting that makes the dynamics behavior of this system become more enrich and complex. These results we represent get us better to understand the nonlinear response of the cracked rotor system and are beneficial to control and diagnose the crack.     

Impact phenomena of rotor-casing dynamical systems

Rubbing and impacting between a rotor and adjacent motion-constraining structures is a serious malfunction in rotating machinery. A shaver rotor-casing system with clearance and mass imbalance is modelled with two second-order ordinary differential equations and inelastic impact conditions. The dynamics is investigated analytically, as well as by numerical simulation. A Lyapunov exponent technique is developed to characterize the topologically different behavior as the parameters are varied. The dry friction coefficient and the eccentricity of the rotor imbalance were chosen to be the two variable parameters, the effect of which on the system dynamics is illustrated through phase plots, bifurcation diagrams, as well as Poincaré maps. The results demonstrate the existence of both rubbing and impacting behavior. Depending on values of the parameters, rubbing motion in both the clockwise and counter-clockwise directions may occur. Within the impact regime, the impact behavior could be periodic, quasi-periodic or chaotic, as confirmed by the calculation of Lyapunov exponents.     

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

The modal interaction which leads to Hamiltonian Hopf bifurcation is studied for a nonlinear rotating bladed-disk system. The model, which is discussed in the paper, is a Jeffcott rotor carrying a number of planar blades which bend in the plane of the motion. The rigid rotating disk is supported on nonlinear bearings. It is supposed that this dynamical system is a Hamiltonian system which is perturbed by small dissipative and nonlinear forces. Krein’s theorem is employed for obtaining a stability criterion. The nonlinear eigenvalue equations on the stability boundary are turned into ordinary differential equations (ODEs) by differentiating them over the rotating speed. By solving these ODEs, the eigenmodes and the eigenvalues on the stability boundary are obtained. The bifurcation analysis is performed by applying multiple scales method around the boundary. The rotor nonlinear behavior and damping effects are studied for different conditions on the rotating speed and nonlinearity type by the bifurcation equation. It is shown that the damping distribution between the blades and bearings may shift the unstable mode. Depending on the nonlinearity type, subcritical and supercritical Hopf bifurcation are possible.     

Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum

Lubrication oil in a rotor system guarantees the rotating components working smoothly and protects the system from being damaged due to friction. A volume of lubrication oil, however, sometimes leaks into the inner cavity of shaft and drums of rotor system and forms an oil-block during rotating operation. The oil-block usually induces abnormal vibration of the rotating machine, which is often observed in practical cases, such as in aero-engine. The work in this paper studies the nonsynchronous vibration (NSV) induced by an oil-block in a rotating drum of a Jeffcott rotor system, which consists of a shaft, a drum and two supporting isotropic bearings. The additional effect due to an oil-block rotating on the inner wall of the drum is included into rotor system differential equations considering the Coriolis acceleration and friction interaction between the oil-block and the drum. Numerical simulations are carried out under two rotating speeds conditions: a lower one and a higher one than the first critical rotor speed, which are defined as rigid rotor case and flexible rotor case. Numerical results states the transverse vibrations by bifurcation diagrams, shaft center trajectories, frequency spectra and Poincare diagrams, which reveal multi-periodic, quasi-periodic and other complex motions due to the existing of oil-block. The internal friction coefficient and mass of the oil-block are found to have a significant effect on the generation and development of NSV. As the oil-block case is very common in practice, the investigation of NSV caused by oil-block in rotor system would benefit the understanding of complex phenomena and contribute to fault detection and diagnosis of rotating machine.     

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。     

Non-linear dynamic analysis of a HSFD mounted gear-bearing system

An investigation is carried out on the systematic analysis of the dynamic behavior of the hybrid squeeze-film damper (HSFD) mounted a gear-bearing system with strongly non-linear oil-film force and gear meshing force in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, damping coefficient and the dimensionless rotating speed ratio as control parameters. The non-dimensional equations of the gear-bearing system are solved using the fourth order Runge-Kutta method. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, bifurcation diagrams, maximum Lyapunov exponents and fractal dimension of the gear-bearing system. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotating speed and highly non-linear regimes.