可倾瓦轴承的完整动力分析模型及计算方法

提出求解可倾瓦径向滑动轴承完整动力特性的解析模型和计算方法,给出可倾瓦轴承完整动力特性系数矩阵的简明表达形式.基于瓦块和轴颈间的运动耦合关系,建立瓦块局部坐标系统.与瓦块和轴颈运动相关的全局广义位移矢量可以通过简练的步骤转换为局部动坐标系下轴颈的位移矢量;利用求解固定瓦轴承动力特性的方法求得的局部动坐标系下的油膜力及其Jocabian矩阵,该油膜力矢量可以精确地转换为全局广义坐标系下的表达形式.在轴承的平衡位置处,全局坐标系下的油膜力矢量关于广义位移和广义速度的Jocabian矩阵为轴承完整动力特性系数矩阵的负值.给瓦块一个设定的扰动频率,就可以得到简化的当量动力特性系数矩阵.此解析方法求解简单方便,可用于分析可倾瓦轴承-转子系统.     

流体动压润滑(二下) 滑动轴承的性能计算和分析

二、动特性当轴颈受扰动(位移、速度)而偏离其平衡位置时(图23),油膜压力及其对轴颈的合力亦发生变化。当扰动微小时,这种变化可看成线性的,因此油膜在小扰动下的动特性可用若干个线性化了的刚度系数(力随位移的变化)及阻尼系数     

基于弹性壳体模型的波箔型动压气体径向轴承动特性分析

波箔型气体轴承的动态纲度和阻尼系数是轴颈偏心率、旋转速度及轴心涡动速度的函数,是进行转子临界转速、不平衡响应计算及稳定性分析不可或缺的基本参数。用摄动法建立波箔型气体轴承动特性系数计算分析的数学模型,应用弹性板壳模型计算波箔及平箔的变形,应用有限差分法及有限元法耦合对模型进行求解,获得波箔型气体轴承的动特性系数。将所得结果与已公布的实验数据对比,证明该模型的合理性和精确性。分析偏心率和轴颈转速对动特性系数的影响,结果表明,刚度系数随偏心率和轴颈转速的增加而递增,阻尼系数随偏心率和轴颈转速的增加而递减。     

考虑轴颈与轴瓦耦合运动的可倾瓦轴承完整动力学模型的研究

从单块瓦与轴颈组成的子系统在整体坐标系和局部坐标系中的几何关系入手,建立考虑轴颈与瓦块耦合运动的可倾瓦轴承的完整动力学模型。在局部坐标系中,采用二维有限元方法求解油膜力和动力特性系数,通过坐标变换叠加到整体坐标系中从而得到可倾瓦轴承动力特性系数的解析表达式,结合Newton-Raphson迭代法计算给定载荷工况下的轴承的静平衡位置。通过2个计算实例证明提出方法的正确性,同时通过与传统折合动力学模型计算结果的比较,证明可倾瓦非本质稳定的结论。     

基于流体域仿真的高速风机气浮箔片轴承动静特性研究

气浮轴承特性对高速风机转子稳定性有显著影响,气浮轴承的静特性与动特性计算是准确获得转子系统失稳转速的基础。通过建立气浮轴承物理模型,以及对应的流体域模型,设定气浮轴承工作状况下的参数,模拟其在工作状况下的流体域分布情况,调整轴心位置,找到标准工作状况下的轴心位置,实现气浮轴承的静特性计算。在静特性计算的结果的基础上,赋予轴颈同频的扰动,模拟流体域分布情况,得到在给定扰动情况下轴颈的受力情况,根据力的变化求解得到气浮轴承对应的刚度系数与阻尼系数,实现气浮轴承动特性的计算。结果表明：随着转速的不断提升,稳定时的轴心位置会逐渐向气浮箔片轴承的圆心靠近;在一定的工作转速范围内,轴承的直接刚度系数随着转速的提升而下降,直接阻尼系数则在工作转速范围内下降到达低值后上升。分析气浮轴承的特性系数与转速之间的变化规律,可为开展转子系统动力学研究提供理论基础。     

基于动网格模型的液体动静压轴承刚度阻尼计算方法

针对雷诺方程不能反映高速油流周向惯性效应、轴颈周向动压效应和静压扩散效应之间的非线性耦合关系及其对三维流场特性的影响,进而导致动静压轴承刚度阻尼的计算精度难以满足高转速精密轴承设计需要之现状,提出基于纳维-斯托克斯方程的动网格计算轴承刚度阻尼新方法。该方法采用自定义程序实现轴颈的旋转速度、位移扰动和速度扰动以及扰动过程中油膜力的计算等功能,成功将轴颈的旋转动边界转换为静边界,有效避免因轴颈旋转引起的网格畸变,并利用弹簧光顺模型更新轴颈受速度扰动和位移扰动引起的油膜网格挤压变形。通过对比研究瞬态和稳态条件下油膜力的变化,界定计算刚度阻尼系数时速度扰动和位移扰动的合理取值范围。利用所提出的方法计算典型轴承的刚度阻尼系数,再现动静压轴承油膜厚度和三维流场压力分布的动态发展过程,并采用影响系数法对该轴承的刚度系数进行试验测试。通过对比试验数据和动网格计算结果发现两者基本吻合,表明所提出的计算方法是有效可行的。     

浮环轴承轴颈与浮环同步进动之油膜特性研究

以直接积分方法研究了同步进动状态下浮环轴承系统中轴承的内、外层油膜力特性。基于浮环轴承油膜压力场控制方程,推导了轴承内、外层油膜力的解析表达式,进而分析了平衡状态下轴颈几何中心的动态轨迹以及油膜力的变化规律。计算结果显示,轴颈与浮环同步进动时,轴颈、浮环与定子中心位置相对稳定,轴颈的直径、间隙和转速等因素对浮环轴承系统的油膜特性和稳定性有直接的影响。     

考虑扰动频率的可倾瓦轴承动力学建模及数值模拟

可倾瓦轴承瓦块的摆动性增加了系统的自由度,对轴承油膜动力系数计算有很大影响,而目前的研究在计算流体动压润滑可倾瓦轴承油膜动力系数时未考虑轴颈与瓦块扰动频率的影响。针对这一问题,对考虑扰动频率的可倾瓦轴承动力学建模及动力系数计算方法进行研究,提出考虑扰动频率的可倾瓦轴承频率-缩减(Frequecy-Reduced)动力学模型,详细推导考虑扰动频率的可倾瓦轴承频率-缩减油膜动力系数矩阵形式。采用Newton-Raphson迭代法计算给定载荷和转速工况下的轴承的静平衡位置,利用有限元数值方法求解油膜刚度系数与阻尼系数。结果表明,瓦块和轴颈的扰动频率对可倾瓦动压轴承动态刚度和阻尼影响较大,随着扰动频率增大,阻尼系数的直接项增大,阻尼系数的交叉项变化不大;刚度系数的直接项数值减小,交叉项变化不大。     

工业摩擦学 第五讲:轴承的选择与设计(中)

三、动态特性和失稳转速轴承的动态特性系数通常指油膜的弹性(刚度)和阻尼性能。一个弹簧当受到W力[kgf]压缩了α[cm],则其刚度系数为k=W/α[kgf]。对于轴承的油膜来说,情况就不是这样简单了。设轴颈中心的平衡位置为O_(10),并取座标轴xy如图8。如使轴心从O_(10)沿X向偏离ΔX到O_1(图8a),则附加的油膜力不仅沿垂直方向向上,而且还有一个水平分量。这一个水平分量在小偏心率时是向右的。这一点可以这样来理解,当载荷很轻时,轴颈中心O_(10)几乎与轴承中心O_B重合。当轴心由O_(10)向下偏离到O_1时,轴承间隙中左半部分(图中划阴影部分)具有收敛形(相对于转速)。而轴承     

一种滑动轴承油膜性能计算的动网格方法

针对应用动网格方法计算油膜轴承性能时出现网格扭曲而导致累计误差过大的现象,提出了一种基于计算流体动力学(CFD)的滑动轴承油膜性能计算的动网格更新方法。该方法保证了网格更新过程中膜厚方向的网格线沿圆周方向上等均分布,且始终垂直于轴颈表面,网格不发生扭曲变形,减小了计算累计误差,提高了轴承性能计算的准确性。通过与典型算例和实验结果对比,验证了所提方法在轴承的油膜力和转子静平衡位置计算中的有效性、可行性和稳定性,并利用该方法分析了进油压力和载荷对油膜轴承所支撑转子静平衡位置的影响。该方法可为准确计算油膜轴承转子系统的性能提供参考。     

Dynamic characteristics of gas-lubricated externally pressurized porous bearings with journal rotation: I

The dynamic stiffness and damping coefficients of an externally pressurized porous bearing with journal rotation have been calculated theoretically by assuming one-dimensional flow through the porous wall. A periodic disturbance (displacement) is imposed on the journal around its concentric position and the dynamic pressure distribution is determined by small perturbations of the modified Reynolds equation. Non-dimensional stiffness and damping coefficients for various design conditions are calculated numerically using a digital computer and presented in the form of design charts and tables.     

偏心率对高速动静压轴承动特性影响

本文分析了水润滑,五腔动静压轴承偏心率对轴承静动性能的影响。轴承量在高压力、高转速下使用。计算表明,在中小偏心下,轴承动力系统为常数;而在大偏心率下,由于流体膜空穴和油腔位置的影响,轴承动特性有较大变化。同时考虑了轴承系统稳定性。     

动压气体轴承的动态刚度和动态阻尼系数

采用偏导数法求解动压气体润滑Reynolds方程,给出动压气体轴承动态刚度和动态阻尼系数普遍适应的计算方法.进行有限元数值仿真,计算动压气体轴承的动态刚度和动态阻尼系数,并重点研究轴颈扰动频率和不同轴颈扰动频率下的轴承静态载荷及轴承数对这些系数的影响.从理论上解释动压气体轴承的动态刚度和动态阻尼系数与轴颈扰动频率的密切相关性.     

Stiffness and damping coefficients for journal bearing using the 3D transient flow calculation

The dynamic coefficients of journal bearing are necessary components in the analysis of linear stability and response of rotating dynamic systems. We propose a new method for the numerical identification of bearing support force coefficients in flexible rotor-bearing systems based on the 3D transient flow calculation. The CFD commercial software FLUENT is mainly used in this simulation, which employs a finite volume method for the discretization of the Navier-Stokes equations. To determine the dynamic coefficients, a new mesh movement approach is presented to update the volume mesh when the journal moves during the 3D transient flow calculation of a journal bearing. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. Measurements and identification are performed on a test rotor supported on a pair of identical two-lobe fluid film bearings, and the results obtained from the CFD methods agree well with experimental results. The results indicate that the methods proposed in this paper can predict the dynamic coefficients of the journal bearing in a rotor-bearing system effectively, and provide a further tool for stability analysis.     

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

The purpose of this paper is to present the two-dimensional linear stability analysis considering the fluid flow in both full film and cavitation regions for a plain cylindrical journal bearing. The Lund's infinitesimal perturbation procedure is applied to Elrod's universal equation for evaluation of unsteady pressure gradients. Based on JFO theory, the pressure distribution, film rupture, and reformation boundaries can be obtained using Elrod's universal equation, for a given operating position of the journal. In this work, it is assumed that for infinitesimal perturbation of a journal about the equilibrium position, the film rupture and film reformation boundaries are the same as those obtained for steady state. However, the unsteady pressure gradients in the full film region are evaluated taking into consideration the perturbed flow parameters in the cavitation region, i.e., at both rupture and reformation boundaries. The linearized stiffness and damping coefficients, whirl frequency ratio, and threshold speed for various values of eccentricity and L/D ratios are obtained for a plain cylindrical journal bearing with an axial groove along the load line. Measured data of dynamic coefficients for a 120° partial arc bearing are chosen for comparison with this work. Results show good agreement between the theoretical and experimental results.     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

Determination of the dynamic coefficients of the coupled journal and thrust bearings by the perturbation method

This paper proposes a method to calculate the stiffness and the damping coefficients of the coupled journal and thrust bearings. Reynolds equations and their perturbation equations of journal and thrust bearings are transformed to the finite element equations by considering the continuity of pressure and flow at the interface between the journal and the thrust bearings. It also includes the Reynolds boundary condition in the numerical analysis to simulate the cavitation phenomenon. The stiffness and damping coefficients of the proposed mathematical method are compared with those of the numerical differentiation of the bearing force with respect to finite displacements and finite velocities of bearing center. It shows that the proposed method can calculate the dynamic coefficients of a coupled journal and thrust bearing more numerically stable and computationally efficient than the differentiation method. It also investigates the coupling effect of the coupled journal and thrust bearing and it shows that the proposed method makes it possible to calculate the cross-coupled dynamic coefficients in the radial–axial direction of the coupled journal and thrust bearing.     

The influence of non-newtonian oil film short journal bearings on the stability of a rigid rotor

The stability behaviour of rotors supported in plain cylindrical cavitated non-Newtonian fluid film journal bearings is investigated. Expressions for the journal force due to the fluid film are developed for the short bearing approximate solution to the modified form of Reynolds' equation. Linearised fluid film coefficients are used for the stability analysis. The results show that the dynamic fluid film coefficients for non-Newtonian lubricants are different from Newtonian coefficients and that they have a strong influence on the stability of rotor-bearing systems.     

Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Theoretical Considerations

Compliant foil bearings operate on either gas or liquid, which makes them very attractive for use in extreme environments such as in high-temperature aircraft turbine engines and cryogenic turbopumps. However, a lack of analytical models to predict the dynamic characteristics of foil bearings forces the bearing designer to rely on prototype testing, which is time-consuming and expensive. In this paper, the authors present a theoretical model to predict the structural stiffness and damping coefficients of the bump foil strip in a journal bearing or damper. Stiffness is calculated based on the perturbation of the journal center with respect to its static equilibrium position. The equivalent viscous damping coefficients are determined based on the area of a closed hysteresis loop of the journal center motion. The authors found, theoretically, that the energy dissipated from this loop was mostly contributed by the frictional motion between contact surfaces. In addition, the source and mechanism of the nonlinear behavior of the bump foil strips were examined. With the introduction of this enhanced model, the analytical tools are now available for the design of compliant foil bearings.     

Performance Characteristics of Worn Journal Bearings in Both Laminar and Turbulent Regimes. Part II: Dynamic Characteristics

The effects of geometric change due to wear on the dynamic characteristics of journal bearings are determined theoretically in both laminar and turbulent regimes. The dynamic characteristics such as spring and damping coefficients and whirl onset speed of a rigid rotor supported by two identical symmetrically aligned bearings are analyzed by a semianalytical finite element method, and the numerical results for various wear depth parameters are indicated in graphical form.

The geometric change due to wear has significant effects on the principal spring coefficients and on the cross-coupled damping coefficients. The whirl onset speed for a worn journal bearing whose wear depth parameter is larger than 0.3 becomes higher than the speed for a nonworn bearing.