可倾瓦轴承-转子系统非线性动力行为

运用变分约束原理,在动力积分、迭代过程中修正了流体润滑的Reynolds方程的变分形式,使其等价为变分不等式。运用八节点等参有限元方法,计算了单块瓦的非线性油膜力,并通过组装技术求解得到5瓦可倾瓦滑动轴承的非线性油膜力。运用Poincar映射和Runge-Kutta方法,分析了5瓦可倾瓦滑动轴承支承的对称刚性转子系统的不平衡响应。数据结果显示了可倾瓦轴承-转子系统的周期解、倍周期解和混沌运动等非线性现象。     

非线性轴承-转子系统的稳定性和分岔

研究了非解析径向椭圆轴承支承的转子系统的稳定性和分岔。考虑了转动惯量的影响,利用非线性油膜力以增加数值计算的精度。在不需要额外再解Reynolds方程的情况下,采用等参有限元法,求解了具有Reynolds边值条件的流体润滑椭圆型变分约束方程,使得动力积分过程中所需非线性油膜力及其Jacobian矩阵能够同时计算完成并且具有足够且协调一致的精度。在稳定性分析中,运用打靶法和轨迹预测追踪算法研究了系统非线性不平衡响应,结合Floquet理论研究了随着轴承设计参数改变时非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。     

椭圆轴承-转子系统非线性运动及稳定性分析

运行中的轴承—转子系统,由于油膜出现气穴,存在破裂区域,此时Reynolds方程的变分形式已不能满足。基于变分约束原理,按照油膜的物理特性,在动力积分、迭代过程中实时形成修正的Reynolds方程变分形式的有限元方程及其扰动方程,在不增加计算量的情况下,同时求得了非线性油膜力及其Jacobian矩阵,并且使其具有相互协调一致的精度。将预估—校正机理和Newton-Raphson方法相结合给出了一种轴承—转子系统Hopf分岔点所对应线性失稳转速及轴承动力学系数的计算方法。将时间尺度引入PNF(Poincare-Newton-Floquetl方法求得了系统Hopf分岔极限环解及其涡动周期,判断了该解的稳定性。基于PNF法及将延续算法和PNF法相结合的轨迹预测追踪算法研究了系统非线性不平衡周期响应,结合Floquet理论分析了非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。运用Lyapunov指数分析了系统响应的混沌现象。数值结果展现了系统响应具有丰富复杂的周期、拟周期、多解共存、跳跃和混沌等非线性现象。     

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.     

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。     

透平式能量回收一体机水润滑转子稳定性研究

为了保障膜法海水淡化系统中透平式能量回收一体机的稳定运行,对一体机水润滑转子的稳定性展开研究。基于流体动压滑动轴承理论,同时考虑水润滑轴承和口环间隙水膜的流体动压润滑效应,在MATLAB平台上利用有限差分法、扰动增量法求解雷诺方程,得到水润滑滑动轴承及口环的动力特性系数,并对水润滑转子系统的动力学特征方程进行求解,进而判别转子系统的稳定性,研究了临界状态下系统转速与质量的关系。结果表明：口环间隙水膜的承载力在转子稳定性分析中不可忽略,否则将产生较大误差;考虑口环产生的动压润滑效应后,滑动轴承处水膜压力约减小40%,系统动力特性系数增加,系统的临界转速相较仅考虑滑动轴承时提升了3 000 r/min,临界质量提升了8.4%;滑动轴承的主刚度系数与交叉阻尼系数受转速的影响明显高于口环处。研究结果为提高海水淡化一体机水润滑转子系统的可靠性提供了参考。     

有限长轴承支撑的转子系统非线性动力学分析

基于π油膜假设,运用变分约束原理和分离变量法求得了有限长动压轴承非线性油膜力的近似解析表达式。通过计算比较可知,该方法和有限元法的计算结果非常接近,而且可以节约大量计算时间。在此基础上,以转子的角速度、圆盘处的偏心量及转轴的刚度为控制参数,运用Newmark法分析了轴承-转子系统的非线性动力学行为。数值结果揭示系统具有周期运动、倍周期运动、准周期运动、六周期运动、十周期运动等复杂丰富的非线性动力学特征。     

固定瓦-可倾瓦动压气体轴承-转子系统的非线性运动分析

针对固定瓦-可倾瓦组合动压气体轴承-柔性转子系统,研究系统的非线性动力学行为。运用微分变换法求解了可压缩气体润滑的Reynolds方程,得到了单块瓦的非线性气膜力,通过组装技术获得了固定瓦-可倾瓦动压气体轴承非线性气膜压力的分布。基于Newmark积分法,运用轴颈中心的运动轨迹图、时间历程图和Poincaré映射图,研究了组合动压气体轴承支承的柔性转子系统的非线性不平衡动力响应。在此基础上,进一步分析了瓦块不同支点比和预负荷系数对转子系统稳定性的影响,结果表明,选取合适的支点比和较大的预负荷系数时,有助于提高转子系统的运动稳定性。     

织构分布对动压滑动轴承油膜压力的影响

以动压滑动轴承为研究对象,根据流体动压润滑原理,建立圆形微凹坑织构化动压滑动轴承油膜数学模型,推导织构化滑动轴承油膜厚度修正公式;结合Reynolds方程有限差分法的求解方法,分析全织构和织构化参数(间距、深度)对动压滑动轴承圆周方向压力分布的影响。结果表明:分布在轴承上的全织构会引起油膜压力的变化;织构位于不同的位置时对圆形微凹坑织构滑动轴承的油膜压力的影响是不同的,对于不同间距和深度的织构,当织构位于升压区时,动压滑动轴承具有较好的润滑、承载性能,而织构位于降压区和全织构时不利于轴承承载。     

动压气体轴承-转子系统的分岔和混沌

基于非线性动力学理论,研究了气体动压轴承-转子系统的不平衡响应及分岔行为。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。运用有限差分法和逐次超松弛迭代法求解动压气体润滑雷诺方程;运用轨迹图、Poincaré映射图、时间历程图、频谱图和分岔图研究了有限宽气体轴承支承的非线性转子系统的不平衡响应及分岔;数值模拟结果揭示了系统存在复杂多样的非线性现象,这对气体润滑轴承支承的实际轴承—转子系统的设计提供了理论依据。     

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     

Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.     

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.     

椭圆轴承-转子系统失稳运动数值分析

滑动轴承油膜力是一种强非线性作用力,滑动轴承转子系统是一种典型的非线性动力系统,传统的线性方法无法计算系统失稳后的运动。文中给出用数值积分瞬态模拟对轴承－转子系统非线性振动进行计算分析的方法,并以椭圆滑动轴承－刚性转子系统为例,对系统失稳后的运动状态进行了计算和分析。     

ON THE AXIAL TRANSIENT RESPONSE ANALYSIS OF THE SECTOR-SHAPED HYDRODYNAMIC THRUST BEARING-ROTOR SYSTEM IN A TURBOEXPANDER

NOTATIONS(The letters in brackets denote the dimension to be as 1)C──Damping coefficient of oil filmD──Domain of a thrust pad in the thrust bearingF──Axial external force (static load)ΔF──Increment of axial external forcesFr──Resultant of oil film forcesF1,F2──Oil film forces of thrust bearings 1 and 2ΔFr──Increment of oil film forces resultantk──Stiffness coefficient of oil filmm──Mass of rotorp()──Oil film pressure,=pδ20/μωr21p1(1),p2(2)──Oil film pressu…     

Analysis of stability and nonlinear response of rotor system with elliptical sliding bearing supports

Based on the variational constraint approach, the variational form of Reynolds equation in hydrodynamic lubrication is revised continuously to satisfy certain constraints in the cavitation zone of oil film field. According to the physical characteristic of oil film, an eight-node isoparametric finite element method is used to convert the revised variational form of Reynolds equation to a discrete form of finite dimensional algebraic variational equation. By this approach, a perturbance equation can be obtained directly on the finite element equation. Consequently, nonlinear oil film forces and their Jacobian matrices are calculated simultaneously, and compatible accuracy is obtained without increasing the computational costs. A method, which is a combination of predictor-corrector mechanism and Newton-Raphson method, is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of bearing-rotor system, as by-product dynamic coefficients of bearing are obtained. The timescale, i.e., the unknown whirling period of Hopf bifurcation solution of bearing-rotor system is drawn into the iterative process using Poincaré-Newton-Floquet method. The stability of the Hopf bifurcation solution can be detected when estimating Hopf bifurcation solution and its periods. The nonlinear unbalanced T periodic responses of the system are obtained by using PNF method and path-following technique. The local stability and bifurcation behaviors of T periodic motions are analyzed by Floquet theory. Chaotic motions are analyzed by Lyapunov exponents. The numerical results revealed the rich and complex nonlinear behavior of the system, such as periodic, quasiperiodic, jumped solution, chaos, and coexistence of multisolution, and so on. __________ Translated from Chinese Journal of Mechanical Engineering, 2006, 42(4): 88–95 [译自: 机械工程学报]     

Stability of tri-taper journal bearings under dynamic load using a non-linear transient method

Stability of a tri-taper journal bearing which is subjected to steady, periodic and variable rotating loads is studied theoretically using a non-linear transient approach. The hydrodynamic forces are initially obtained by solving the Reynolds equation, satisfying the Reynolds boundary conditions. Further, the transient behavior of rotor bearing system is predicted by substituting these hydrodynamic forces in the equations of motion and then solving them by fourth order Runge Kutta method. Stability of the rotor bearing system is determined from the journal locus. Comparative studies predict that the dynamic performance is superior for a bearing with high ramp size and aspect ratio.