轴向槽气体轴承—非线性转子系统的分岔和混沌

轴向槽动压气体轴承具有高精度、低摩擦、低噪声和高稳定性的特点,广泛应用于精密仪器、医疗器械、飞机仪表舱等设备。由于轴向槽动压气体轴承支承的转子系统是典型的非线性动力系统,所以必须采用非线性分析的方法来研究系统的动力学行为。因此,运用非线性动力学理论研究三轴向槽动压气体轴承-转子系统的非线性行为。建立与时间相关的轴向槽可压缩气体润滑的压力分布模型,运用微分变换法求解可压缩气体润滑的Reynolds方程,得到轴向槽动压气体轴承的非线性气膜力。建立具有陀螺效应的转子系统模型,基于改进的Wilson-θ法求解系统动力学方程,得到系统的非线性不平衡响应。运用分岔图、轨迹图、Poincare映射、时间序列和频谱图分析不平衡响应的分岔和混沌。数值分析结果表明:非线性气膜力对转子系统的稳定性影响很大,系统展现出丰富的非线性行为,如周期解、倍周期解、拟周期解、周期四亚谐运动和混沌运动等。所做研究为工程中轴向槽动压气体轴承-转子系统的设计提供了理论指导。     

微气体轴承-转子系统动力特性研究

针对微气体轴承,基于1阶速度滑移边界,推导得到修正Reynolds方程,然后采用双向隐式算法(ADI)求解动态Reynolds方程,得到轴承非线性气膜力,并结合刚性转子运动方程,计算转子系统不平衡响应,得到了转子轴心轨迹、时间历程、功率谱和Poincare图等,分析了微气体轴承-转子系统的动力特性。分析表明,随着转子转速的升高,转子系统运动表现出倍周期和概周期等复杂的动力特性。     

基于Wilson-θ法的柔性转子系统的动力学分析

根据转子动力学理论建立了对称柔性转子-轴承系统的力学模型及非线性动力学方程;运用Wilson-θ法,并结合预估-校正机理和Newton-Raphson法,提出了一种有效的求解动力学系统不平衡响应的方法。以柔性转子转轴的刚度为控制参数,运用该方法求解了转子系统的不平衡周期响应,并结合Floquet分岔理论和Poincaré映射,分析了系统周期运动的稳定性及其分岔行为。数值结果揭示了系统具有周期运动、三周期运动、准周期运动、五周期运动、跳跃等复杂丰富的非线性动力学现象。     

含外圈故障的高速列车轴承转子系统非线性动力学行为分析

针对高速动车组列车的轴箱轴承,建立一种含外圈故障的滚动轴承非线性动力学模型,并分析轴承在正常状态和故障状态下模型的非线性动力学行为。该轴承为高速列车圆锥滚子轴承,模型考虑了轴承间隙、滚子和滚道之间的非线性赫兹接触力、由于转子质量偏心引起的不平衡力等因素。对模型进行数值求解,通过对比仿真和实际求得的变刚度频率外圈故障特征频率验证了模型的正确性。得到系统复杂的非线性动力学响应,分析转子速度、故障尺寸等因素对系统稳定性的影响,随着转子速度和故障尺寸的增大,系统会逐渐偏离稳定的运动状态,更早地进入混沌。通过频谱图、相平面图、分岔图以及Poincare映射图进行系统分岔和混沌特性分析,发现了通往混沌的拟周期运动、阵发性和倍周期分岔途径。分析结果对研究列车轴箱轴承故障的产生机理和演化规律具有一定的价值。     

轴向槽气体润滑轴承-转子系统非线性行为

基于非线性理论,分析了气体动压轴承-转子非线性动力系统的不平衡响应.建立了与时间相关的非线性气体动压轴承的压力分布模型和气体动压轴承-刚性Jeffcott转子系统的动力学模型.运用微分变换法求解了动压气体润滑的Reynolds方程,得到了非线性气膜压力分布.运用分岔图、轨迹图、Poincaré映射图及频谱图研究了三轴向槽有限宽气体轴承支承的非线性转子系统的不平衡响应.数值结果表明,系统的非线性行为包括周期运动、周期二运动、周期四运动、周期八运动及混沌运动等.     

非线性转子-轴承系统的动力学特性及稳定性

研究非线性转子—轴承系统的动力学特性及稳定性。采用改进的自由界面模态综合技术给出一种自由度降阶方法，该方法将非线性油膜力及非线性自由度保留在物理空间，以增加非线性分析的精度，使降阶系统仍具有局部非线性特征。基于打靶法及将延续算法和打靶法相结合的轨迹预测追踪算法，研究系统非线性不平衡响应，结合Floquet理论分析非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。     

轴承-转子系统不平衡周期响应的稳定性和分岔

研究了轴承-转子系统的非线性动力响应及分岔,建立了滑动轴承支承的对称单圆盘柔性转子系统的运动微分方程,针对转子系统具有的局部非线性特征,将Newton-Raphson方法和Wilson-è法相结合,形成了一种求解转子系统不平衡周期响应的迭代方法.运用该方法使得非线性响应的迭代求解仅在非线性自由度上进行,并运用Floquet稳定性理论分析了转子系统周期响应的稳定性和分岔形式.以转速作为分岔参数,对轴承-转子系统进行计算分析.数值结果表明,系统主要发生倍周期分岔和准周期分岔,具有各种周期解共存、跳跃现象,随着转速的不断增加,系统周期解将发生倒分岔和再分岔.     

考虑接触效应的拉杆转子非线性动力学特性分析

本文建立了两盘拉杆式转子轴承系统动力学模型,模型受不平衡力和非线性油膜力激励,拉杆转子轮盘之间接触刚度由接触理论计算得到,采用4阶龙格库塔法进行求解,并使用分岔图和Poincare映射对比分析了不同的转速下,拉杆转子与单盘整体转子的非线性动特性的差异。通过研究得到以下结论:随着转速变化,相比于单盘整体式转子,考虑盘间接触效应的影响会使系统非线性动力学行为更加复杂,在中高转速范围内拉杆转子系统响应状态在周期运动与准周期运动或混沌运动状态之间出现多次反复,拉杆转子系统初次发生分岔的转速值变大,响应的幅值减小,在低转速范围内,盘间接触状态对系统状态影响较小,系统不受转速变化影响。     

轴向槽气体轴承-转子非线性系统的动力学行为

针对轴向槽气体轴承支承的转子非线性动力系统,研究了系统动力学行为的不平衡响应和分岔。采用矢量拟合近似求解的方法,建立了轴向槽气体轴承的有理函数模型,通过耦合转子运动模型,提出了一种轴向槽气体轴承-转子非线性系统动力学模型,在对其动力学行为求解过程中避免了对动态气膜力的反复求解,减少了计算时间。运用轴颈和圆盘中心的轨迹图、频谱图、Poincaré映射和分岔图分析了轴向槽气体轴承-转子系统的非线性不平衡响应和分岔行为。以转速为分岔参数研究了非线性系统从倍周期运动通向混沌的道路,以质量偏心为分岔参数研究了非线性系统的倍周期运动的倒分岔行为。数值结果表明轴向槽气体轴承-转子非线性系统存在复杂的动力学现象及分岔行为。     

基于增量谐波平衡法的支承松动故障特性研究

针对含支承松动的Jeffcott转子系统,考虑系统一端支承松动以及转子不平衡的外扰激励,建立带阶跃变化刚度的系统振动微分方程。采用增量谐波平衡法对非线性方程进行求解,结合迭代算法获得系统振动周期解。运用Floquet理论判定周期解的稳定性。最后,通过实例仿真,得出系统响应的时域波形、幅值谱图、相图和Poincare截面图,分析带支承松动故障的转子系统复杂的运动特性,验证了增量谐波平衡法求解非线性系统的有效性,并为支承松动故障诊断提供理论依据。     

A novel nonlinear model of rotor/bearing/seal system and numerical analysis

A novel nonlinear model of rotor/bearing/seal system based on the Hamilton principle is proposed for steam turbine systems in power plants. The Musznyska model and unsteady bearing oil-film force model were applied to describe the nonlinear steam excitation force and oil-film force. The Runge-Kutta method was used to solve the motion equation of the rotor/seal/bearing system. The dynamic characteristics of the rotor/bearing/seal system were analyzed with bifurcation diagrams, time-history diagrams, trajectory diagrams, Poincare maps and frequency spectrums. The numerical analysis indicates that the seal force and the oil-film force influence the nonlinear dynamic characteristics of the rotor system. With the increase of rotation speed, the rotor system exhibits rich forms of periodic, double-periodic, multi-periodic, quasi-periodic and chaotic motion. The combined impact of steam excitation force and bearing oil-film force may cause a severe vibration which seriously affects the safety and stability of the rotor. The presented model provides a theoretic foundation for further research on the ultra-supercritical steam turbines.     

质量慢变转子-滚动轴承系统的支承松动故障分析

根据转子动力学、非线性动力学及Hertz理论,建立了带有一端支座松动故障的滚动轴承—质量慢变转子系统的非线性动力学模型。通过数值积分和Poincare映射方法对其非线性动力学行为进行了数值仿真研究,给出了系统响应随转子转动频率变化的分岔图和一些典型的轴心轨迹图及Poincare截面图,分析了转动频率对转子系统动力学行为的影响。结论表明,转子系统在滚动轴承、支承松动和质量慢变的同时作用下具有复杂的动力学行为,转子系统的起始松动频率为0.6倍的固有频率,转子的周期运动均为多周期运动,转子圆盘和松动质量的运动特性均不稳定等。     

圆柱滚子轴承刚性转子系统周期运动分岔

推导了考虑径向力、力矩联合作用的滚子轴承的非线性轴承力和力矩,建立了圆柱滚子轴承刚性转子系统的四自由度动力学方程,利用求解非线性非自治动力系统周期解的延拓打靶算法进行计算,根据Floquet乘子判断周期运动的分岔.以某滚子轴承刚性转子系统为例,研究了该类转子系统在径向间隙-转速、阻尼-转速、力矩-转速参数域内周期运动的分岔及失稳规律.结果发现:随径向间隙、阻尼和力矩的变化,周期运动将产生倍周期或Hopf分岔,分岔转速随参数变化而改变.其中力矩的存在会明显降低系统的失稳转速,可通过选择合适的结构和工况参数尽量避免滚子轴承转子系统出现非周期运动.     

非线性径向主动电磁轴承-转子系统的耦合动力学特性及稳定性

研究径向主动电磁轴承支承的不对称转子系统的动力行为及稳定性。转子模型中考虑了陀螺效应，结合分散PID(pmponional integral differential)控制器方程和转子运动方程，形成系统方程。将预估—校正机理和Newton-Raphson方法相结合，给出一种径向主动电磁轴承—转子系统线性失稳转速即Hopf分岔点所对应转速的计算方法。基于打靶法及将预估—校正机理和打靶法相结合形成的一种轨迹预测追踪的延续算法，研究系统非线性不平衡周期响应及稳定性边界。结合Floquet分岔理论研究随系统控制参数改变径向主动电磁轴承—转子系统周期运动的局部稳定性和分岔行为。     

NONLINEAR DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC JOURNAL BEARING-FLEXIBLE ROTOR SYSTEM

The nonlinear dynamic behaviors of flexible rotor system with hydrodynamic bearing supports are analyzed. The shaft is modeled by using the finite element method that takes the effect of inertia and shear into consideration. According to the nonlinearity of the hydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique with free-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system. According to physical character of oil film, variational constrain approach is introduced to continuously revise the variational form of Reynolds equation at every step of dynamic integration and iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametric finite element method without the increasing of computing efforts. Nonlinear oil film forces and their Jacobians are simultaneously calculated and their compatible accuracy is obtained. The periodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A meth     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

基于轨迹的非线性转子系统参数稳定裕度的计算

对高维非线性非自治转子系统进行数值积分后，将各自由度的运动方程中除该自由度外的所有状态变量用积分结果代换，得到n个互相解耦且含有多个时变参数的单自由度子方程。引和在电力系统中得到广泛应用的轨迹保稳降维概念，将已有的R^n轨线映射为一系列的R^1映象轨线。在R^1观察空间的外力一位移扩展相平面上利用动态中心点的动能差序列研究转子系统中常见的周期运动、倍周期运动、概周期运动和失稳运动的特点。给出对应上述几种典型运动形式的轨线稳定裕度的定量评估指标。根据轨线稳定裕度求取参数稳定裕度，以指导工程设计和控制。     

The continuous Poincare-like cell mapping method and its application to nonlinear dynamics analysis of a bearing–rotor system

Based on the idea of continuous cell mapping, an improved Poincare-like cell mapping method is developed. This method can be used for global analysis of nonlinear dynamic systems without missing the periodic solutions and the domains of attraction. A bearing–rotor system is analyzed by using this method, and the influences of initial conditions on transient movement are discussed in detail.     

齿轮系统周期运动稳定性研究

针对含间隙的强非线性齿轮系统动力学模型，用数值方法研究了当系统参数和初始条件变化时周期运动的稳定性。基于Floquet分岔理论将预测一校正算法用于讨论参数变化时周期解的稳定性，得到精确的分岔点参数值；通过胞映射法求得周期吸引子的吸引域，引入稳定性品质因子用以定量分析初始条件变化时周期运动的稳定性。该研究结果可为非线性动力学行为的分析和齿轮系统的设计提供参考。     

Minimum Film Thickness in a Gas Foil Journal Bearing with an Unbalanced Rotor

A gas-lubricated foil journal bearing consists of a compliant metal shell structure that supports a rigid journal or rotor by means of a gas film. The response of this system to the periodic forces of an unbalanced rotor supported by a single bearing is predicted using perturbation analysis. The foil structure and the gas film are modeled with an analytically perturbed finite element approach to predict the rotor dynamic coefficients. A dynamic model of the rotor is used to predict periodic journal motion. The perturbation analysis is then used with the periodic response of the rotor to calculate periodic changes in the gas film thickness. Other quantities such as the gas film pressure and the foil deflection can also be calculated. The model includes bending and membrane effects in the top foil, coupled radial and circumferential deflections in the corrugated sub-foil, and the equivalent viscous dissipation of Coulomb friction effects in the foil structure. The approach is used to investigate the effects of top-foil thickness on minimum film thickness in a bearing.