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.     

固定瓦-可倾瓦气体轴承支撑的拉杆转子动力学特性

针对固定瓦-可倾瓦气体轴承支撑的拉杆转子动力学特性进行了研究。将拉杆转子轮盘间的接触效应等效为一个具有非线性刚度的抗弯弹簧,从而建立了拉杆转子模型。基于固定瓦-可倾瓦气体轴承的边界条件,运用微分变化法求解了Reynolds方程,得到了在单瓦坐标系下的气膜力,采用坐标变换和组装计算最终得到固定瓦-可倾瓦气体轴承的气膜力。在计算时对比了圆柱形气体轴承和固定瓦-可倾瓦气体轴承的稳定性、拉杆转子和整体转子的稳定性。最后,以转轴刚度为控制参数,运用改进的Newmark法研究了拉杆转子的动力学特性,同时也研究了固定瓦-可倾瓦气体轴承预负荷和支点比对转子系统运动行为的影响。     

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。     

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。     

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。     

动压气体轴承-转子系统稳定性分析

本文建立了普通圆柱型动压气体轴承支承的单盘转子系统模型,写出了系统的运动方程,并引用气体轴承的动力特性数值分析所得到的8个动力特性系数,利用Routh-Hurwitz准则,研究了系统的稳定性,计算表明所设计的轴承-转子系统在设计转速范围内的运转是稳定的。讨论了气体轴承结构参数偏心率,长径比及平均径向间隙对稳定性的影响,得出了应当采用小偏心率,小长径比,大平均径向间隙提高轴承转子系统稳定性的结论。     

微转子系统径向气体轴承特性

充分考虑滑移边界条件的影响,利用数值计算方法对微机电系统(Micro-electro-mechanical systems, MEMS)中微转子系统径向气体轴承的雷诺方程进行修正求解,得到轴承内部真实的气压分布,进而求得微气体轴承的承载能力和偏位角.通过与宏观无限短轴承模型的结果进行对比分析,发现滑移效应对气体轴承特性的影响规律.宏观无限短轴承模型和无滑移边界模型均会高估气体轴承的承载能力,特别是偏心率较高时(ε>0.6),产生的偏差更大;微转子系统在高速或超高速工况下运转,可以提高气体轴承的气压和承载能力.     

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。     

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。     

滑动轴承动特性系数新算法

轴承的动特性系数与轴颈在轴承中的位置有关。对于给定工况的转子-轴承系统,必须先求出轴颈的平衡位置,然后再解得轴承动力特性系数。用Newton法迭代求轴颈平衡位置,轴承的动特性系数已在获得轴颈平衡位置的同时求得,无需额外增加求解Reynolds方程的次数。     

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.     

Elastohydrodynamically Lubricated Ball Bearings with Couple-Stress Fluids,Part II: Dynamic Analysis and Application

Stiffness and damping coefficients of isothermal elastohydrodynamically lubricated point-contact problems are evaluated numerically with couple-stress fluids. A set of equations under steady-state and dynamic conditions is derived from the modified Reynolds equation using a linearized perturbation method. This paper is the second part of the present study; the modified Reynolds equation derived from the Stokes micro-continuum theory is used in the previous article. Dynamic pressures are found after solving the set of perturbed equations using the previously obtained steady-state pressure from the modified Reynolds equation. The stiffness and damping coefficients of the film are determined using the dynamic pressures. Then the overall stiffness and damping matrices of the ball bearing are obtained from load distribution, coordinate transformation, and compatibility relations. The bearing coefficients are introduced into a rotor system to simulate the response. It has been observed that the influence of couple-stress fluids on the dynamics of a rotor supported on lubricated ball bearings is marginal; hence, Newtonian theory can be used instead for simplicity. However, with increasing content of polymer additives in lubricant, for an accurate analysis the effect of couple stresses in a fluid should not be neglected.     

Dynamic behavior of fluid‐structure coupling of hydrostatic spindle under effect of oil film slip

To better understand the dynamic characteristics of a hydrostatic spindle in fluid‐structure coupling, the impact of oil film slip on the 4 dynamic stiffness and damping coefficients of the spindle is studied. On the basis of modified Reynolds equation, which considers the microscale velocity slip effect, rotation error of the spindle is calculated. To solve the rotor axis orbit under the existence of eccentric quality, 4 dynamic stiffness and damping coefficients of the oil film, which describe the dynamics of a rotor axis orbit, are calculated by using load increment method and the pressure perturbation method. The research results show that velocity slip caused a certain impact on dynamics of bearing stiffness and damping performance. The experiment of the measuring path of the shaft verifies the correct and effect of the orbit of shaft center model.     

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。     

Stability analysis of rough journal bearings under TEHL with non-Newtonian lubricants

The combined effects of surface roughness and lubricants rheology on stability of a rigid rotor supported on finite journal bearing under thermal elastohydrodynamic lubrication have been investigated using the transient method. The newly derived time dependent modified Reynolds and the adiabatic energy equations were formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems of modified Reynolds equation, elasticity equation, energy equation, and the rotor motion equation with initial conditions were solved numerically using multigrid multi-level method with full approximation technique. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters and the elastic modulus of the bearing liner materials. The results show that stability of the bearing system deteriorates with decreasing both the power law exponent and the elastic modulus of bearing liner material. The rough surface journal bearing with transverse pattern under TEHL regime exhibits better stability when compared with the rough surface journal bearing with longitudinal pattern.     

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.     

Externally pressurized gas bearings: A comparison between two supply holes configurations

Radial vibration of a vertical rotor with externally pressurized gas bearings is analyzed. The time-dependent Reynolds equation is solved together with the journal equation of motion to obtain the response characteristics of the bearing system. The bearings are supplied with either one or two sets of supply orifices. Stiffness and flow rate are compared for both cases. Stability maps are obtained at different supply pressures and with different supply orifice diameters. The mass range from orbital stability to instability is studied as a function of supply hole downstream pressure level.     

Influence of orifices on stability of rotor-aerostatic bearing system

This paper has studied the influences of both the number and locations of entry holes on the stability of a rigid rotational rotor supported by two double-row, orifice compensated aerostatic bearings. The air is assumed to be perfect gas, undergoing the adiabatic process and passing through entry holes into the bearing clearance, is governed by Reynolds equation including the coupled effects of wedge due to rotor rotation and squeezed film due to rotor oscillation. The Ph-method is used to analyze Reynolds equation which is then solved by the finite difference method and numerical integration to yield static and dynamic characteristics of air film. The equation of motion of the rotor-bearing system is obtained by using the perturbation method and the eigen-solution method is used to determine the stability threshold and critical whirl ratio. The eccentricity, rotor speed, and restriction parameter are considered in the analysis of the whirl instability of the rotor-aerostatic bearing system for the comparisons between various designs in the number and locations of entry holes of aerostatic bearings.     

狭缝节流空气静压轴承局部气膜流场的直接数值模拟

采用3阶精度的迎风格式及2阶精度的中心差分格式,直接求解二维非定常N-S方程组,研究狭缝节流空气静压轴承压降恢复之后区域的流场特性。使用雷诺方程计算相同位置气膜中心处的流场状态,并与直接数值模拟方法的计算结果进行对比。结果表明:雷诺方程与N-S方程在计算域内计算结果基本一致,两者压力偏差为0.173%,速度偏差为1.217%;流场压力、密度沿气流方向逐渐减小,但在气膜方向几乎不变;流场速度、压力梯度沿气流方向逐渐增加,速度在流场出口处达到最大值;直接数值模拟方法得到了流场的温度变化,即整个流场的温度变化很小,温度整体呈上下高、中心低的分布,而雷诺方程无法计算得出整个流场的温度变化情况;采用雷诺方程计算轴承压降恢复之后区域的流场是合理的。