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。     

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。     

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。     

流体动压滑动轴承-转子系统动力特性分析

研究了非线性径向轴承支承的转子系统的动力行为。引入变分约束原理修正了流体润滑的Reynolds方程的变分形式 ,在几乎不增加计算量的情况下 ,求解了具有Reynolds边界的流体润滑问题 ,使得非线性油膜力及其Jacobian矩阵同时计算完成并且具有协调一致的精度。运用Newton Raphson方法在求得转子平衡点的同时求得了轴承的动力学系数。将预估 校正机理和Newton Raphson方法相结合给出了流体动压滑动轴承 转子系统Hopf分岔点所对应线性失稳转速的计算方法。运用打靶法并结合Floquet理论计算分析了流体动压滑动轴承 转子系统的非线性不平衡周期响应及其稳定性。数值结果表明上述方法不但节约了计算量 ,而且具有很高的精度。     

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.     

挤压油膜阻尼器-滚动轴承-转子耦合系统的非线性响应分析

为了研究转子系统非线性动力学响应,建立了挤压油膜阻尼器-滚动轴承-转子耦合系统动力学模型。在转子系统模型中,考虑了转子、滚动轴承及挤压油膜阻尼器之间的相互耦合作用,并充分考虑了滚动轴承的间隙、非线性赫兹接触和挤压油膜阻尼器非线性油膜力等。运用数值积分方法分析了转子转速、支承刚度以及挤压油膜阻尼器油膜间隙对系统动力响应的影响,并结合分岔图、频谱图、Poincaré映射图和轴心轨迹图分析了转子系统的非线性动力学响应。结果表明:转子系统当转速较高、支承刚度较大或挤压油膜阻尼器油膜间隙较大时,转子系统容易出现拟周期运动。     

鼠笼式弹性支承-圆柱滚子轴承-转子系统振动分析

考虑圆柱滚子轴承非线性接触力、保持架能量、鼠笼刚度、转子不平衡以及它们之间的力学耦合关系,基于拉格朗日方程建立鼠笼式弹性支承-圆柱滚子轴承-单转子系统动力学分析模型,结合龙格库塔数值积分方法,并对该模型动力学仿真分析,分析了不同转速区域鼠笼式弹性支承-滚动轴承-转子系统振动响应的分岔特性,结果表明:两支点的鼠笼式弹性支...     

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。     

考虑支承跨距的非线性转子系统动力学特性研究

根据主轴变形几何模型求得主轴前端总位移关系式,依据前端最小位移确定主轴的最佳支承跨距,进而建立了考虑支承跨距的转子轴承系统非线性动力学模型.运用数值积分方法,给出最优跨距支承下转子系统的非线性动力学响应,采用轴心轨迹、相图及Poincar6图分析了转速对系统动力学响应的影响.结果表明:当转子轴承系统在最佳支承跨距下运行...     

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.     

Nonlinear dynamic and bifurcation analysis of short aerodynamic journal bearings

A numerical analysis of a rigid rotor supported by relative short aerodynamic journal bearings is presented for nonlinear dynamic behaviors and bifurcation. The compressible Reynolds' equation is solved by the finite differences method and the successive over relation method and a time-dependent mathematical model for aerodynamic journal bearings is studied. A comparison of the results for the system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams is made and dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions is analyzed. The analysis shows how the existence of a complex dynamic behavior comprises periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in bearing number and squeeze number.     

Nonlinear Dynamic Analysis of a Rigid Rotor Supported By a Spiral-Grooved Opposed-Hemisphere Gas Bearing

The nonlinear dynamic behavior of a rigid rotor supported by a spiral-grooved opposed-hemisphere gas bearing is investigated in this article, focusing particular attention on its whirl motion. The finite element method combined with the finite difference method is employed to solve the time-dependent Reynolds equation that is coupled with the rotor motion considering five degrees of freedom. The rotor responses to the initial disturbance and synchronous and nonsynchronous excitations are investigated. To analyze the complicated dynamic behavior of the rotor–bearing system, the trajectories of the rotor centerline, time responses, phase portraits, power spectra, Poincare maps, and bifurcation diagrams are obtained from the numerical procedure. The results show that the conical whirl instability appears earlier than the cylindrical whirl instability with increasing rotational speed for the rotor–bearing system with no unbalance mass. Moreover, it reveals that the complex dynamic behavior of the system excited by unbalance mass varies with rotational speed and rotor mass. In addition, bifurcation diagrams employing the rotating speed and rotor mass as bifurcation parameters are obtained. Finally, the nonsynchronous excitation responses are presented, which behave in a different way than the synchronous excitation responses. The results of this study offer a further understanding of the nonlinear characteristics of spiral-grooved opposed-hemisphere gas bearings.     

Theoretical analysis of the non-linear behavior of a flexible rotor supported by herringbone grooved gas journal bearings

This paper studies the behavior of a flexible rotor supported by a herringbone-grooved gas journal-bearing system. A hybrid method is employed to develop a time-dependent mathematical model of the bearing system. The finite difference method is employed with the successive over relaxation technique to solve the Reynolds equation. The system state trajectories, Poincaré maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and the journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and quasi-periodic responses of the rotor and the journal center. The present numerical study illustrates the relationship between the dynamic behavior of this type of system and the rotor mass and bearing number. As such, the present results provide a deeper understanding of the non-linear dynamics of gas film rotor-bearing systems.     

Nonlinear dynamic analysis of a relatively short spherical gas journal bearing system

This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by two relatively short spherical gas journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM). The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic and quasi-periodic responses as the rotor mass and bearing number are increased. The results obtained using the hybrid DTM&FDM scheme are found to be in good agreement with those of a hybrid scheme comprising the successive over relaxation (SOR) method and the FDM scheme. Therefore, the DTM&FDM method provides an effective means of gaining insights into the nonlinear dynamics of relatively short spherical gas rotor-bearing systems.     

不同轴承支撑下碰摩转子系统的动力学特性

研究了不同类型轴承支撑下的转子碰摩故障振动特征。首先,采用了计及回转效应、剪切效应及横向扭转的梁单元建立了实验装置转子的有限元分析模型;然后,通过二维计算流体力学方法得到不同类型轴承的动力学参数;最后,在此基础上,结合非线性动力学理论,分析比较了转子在圆柱轴承、可倾瓦轴承等5种轴承支撑下的碰摩非线性动力学行为。研究结果表明：在椭圆轴承、五瓦轴承和四瓦可倾瓦轴承支撑下,系统主要表现为同频周期运动;而对于圆柱轴承和四油叶轴承支撑,系统会出现较复杂的运动。本研究工作是对之前转子碰摩非线性动力学研究的扩展,所得计算结果可为大型高速旋转机械系统动态设计制造和碰摩故障的诊断和控制提供理论参考。     

气体动压径向短轴承动力学和分岔分析

径向气体润滑轴承是精确定位以及微旋转机械中的重要部件,其非线性动力学特性对整个器件的稳定性和可靠性具有重要的影响。文中以气体动压径向短轴承—转子系统为研究对象,建立气体轴承—转子系统耦合非线性动力学方程,以轴承数为分岔参数,分析长径比为0.75时在不同初始偏心率条件下,系统动力学特性随转子转速变化的影响。     

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.     

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.