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。     

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.     

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.     

非线性油膜力轴承上不平衡弹性转子的稳定裕度

探讨了弹性转子系统的稳定性和稳定裕度问题,采用短轴承油膜力的解析表达式和数值模拟的方法研究了系统的分岔和混沌特性。希望把电力系统广泛应用的高维轨线约化扩展相平面稳定性量化理论推广到非线性转子系统中,提出了相比正面积准则,给出了转子系统稳定裕度的定义,对滑动轴承不平衡转子系统进行了稳定性量化分析。     

滚动轴承转子系统的非线性动力学特性分析

接触非线性和间隙非线性耦合导致滚动轴承 转子系统表现出复杂的动力学特性 ,在工作转速范围内系统会产生分岔混沌振动 ,从而影响系统工作的稳定性和可靠性 ;在计及轴承接触非线性和径向间隙的条件下 ,建立了滚动轴承支承的水平刚性转子系统的非线性动力学模型 ,用数值积分方法得到系统在不同参数域中的相图、轴心轨迹、频谱图及Poincar啨映射图 ,研究了系统响应随转子转速的变化趋势。结果表明 :轴承的径向间隙是决定轴承 转子系统动态响应的一个重要参数。随着间隙的增大 ,混沌响应区变宽 ,轴承的动态刚度减小 ,故在设计滚动轴承 转子系统时 ,应对径向间隙进行优选。     

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.     

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.     

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-转子系统的分岔与混沌特性研究

利用一种精确的非稳态非线性油膜力模型求得油膜力。以无量纲偏心和一个反映多种影响因素的综合参数为分岔变量,用数值积分法在广泛的参数变化范围内研究了轴承一转子系统运动的变化规律,作出了分岔图。借助Poincare映射和Lyapunov指数分析了系统的运动形态。结果表明,利用该油膜力模型可从不同角度发现由倍周期分岔导致的混沌现象和概周期运动等复杂的非线性动力学行为。随着参数的变化,复杂的运动区域中间会出现简单的运动区域。这为合理设计系统参数以避开危险区域提供了依据。     

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。     

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。     

Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery

The fluid dynamics of gas-lubricated journal bearings in micro-rotating machinery is different from those of larger size. One point to be considered is a slip flow effect. In this paper, the slip flow effect is considered in order to estimate load-carrying capacity and dynamic coefficients of micro gas-lubricated journal bearings. Based on a modified compressible Reynolds equation including slip flow effect, the first slip approximation was applied. To extract dynamic coefficients, the linearized dynamic equations were formulated by the perturbation method. Numerical predictions compared the static and dynamic characteristics considering slip flow at room-to-high temperature in a range of bearing numbers. The results including load-carrying capacity and dynamic coefficients demonstrate that the slip flow effect becomes significant with temperature increase as well as in the lower range of bearing numbers.     

Application of Hopf bifurcation theory to rotor-bearing systems with consideration of turbulent effects

This paper shows that the steady state and the dynamic characteristics of a rotor-bearing system with turbulent effects can be conveniently evaluated by applying the Hopf bifurcation theory to the equations of motion of a rigid rotor symmetrically supported by two identical fluid-film journal bearings. Results are presented for stiffness and damping coefficients and stability characteristics of a journal bearing, which take turbulence into consideration.     

柔性转子滚动轴承系统混沌行为研究

研究了滚动轴承支承的柔性转子系统的混沌行为。考虑空间Euler-Bernoulli杆单元、刚性圆盘、圆柱滚子轴承非线性接触力、不平衡力,使用有限单元法建立了柔性转子轴承系统的非线性动力学方程组。根据FPA修正法确定求解周期,采用Runge-Kutta法、Newton-Raphson法求解非线性动力学方程组,用获得的系统最大Lyapunov指数判断系统的混沌行为。以某滚子轴承柔性转子系统为例,研究了该类转子系统在径向间隙、不平衡力、转轴刚度比对柔性转子系统混沌特性的影响规律,发现随着轴承径向间隙的增大,系统的混沌区间逐渐增大、变多。不平衡力的存在使得系统混沌的转速及范围变大。随着刚度比增大,振幅峰值及对应的转速均逐渐增大,系统混沌区间也增多,轴承非线性振动对柔性转子系统非线性行为的影响逐渐增强。     

Nonlinear Simulation of Rotor Dynamics Coupled with Journal and Thrust Bearing Dynamics under Nonlinear Suspension

This study performs a dynamic analysis of a rotor supported by an oil-film journal and thrust bearings. The analysis of the rotor-bearing system is investigated under the assumptions of an incompressible lubricant, a flexible rotor, and negligible side leakage in the thrust bearing. The numerical results show that the nonlinear dynamics of the system vary with the nondimensional speed ratio and the initial value of the displacements in the horizontal, vertical, and axial directions. Specifically, some routes of periodic responses, subharmonic motions into chaos, out of chaos to subharmonic responses, or suddenly into chaos, suddenly out of chaos to periodic ones were found.     

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。     

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。     

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.     

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.