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.     

径向可倾瓦轴承的热弹流润滑分析

用Newton-Raphson法一次性求出了所有瓦块的压力分布和轴心的位置,用步进扫描法对轴承进行了三维温度场分析,用20节点有限元法构造了瓦块的压力变形矩阵和热变形矩阵。     

支点弹性、阻尼可倾瓦轴承动力特性数值仿真及试验研究

依据考虑瓦块摆动和沿几何预载荷方向微幅振动的可倾瓦轴承完全动力特性的解析模型及其对应的八参数简化动力模型,设计制备了支点弹性、阻尼特性可倾瓦轴承。该轴承通过在瓦块支点与轴承体之间设置弹性垫片,使瓦块支点支撑在弹性垫片上,弹性垫片与轴承体之间存在微小间隙并与轴颈润滑系统共享油路以实现局部挤压油膜效应。根据不同加工工艺,制备了两种形式的新型支点弹性、阻尼轴承,并通过理论计算模拟与试验分析对两种新型轴承的动力特性进行研究。结果表明,支点弹性、阻尼可倾瓦轴承能够增大转子的一临界阻尼,有效提高转子系统稳定性。     

可控节流参数对液体静压轴承特性的影响研究

节流器是液体静压主轴的核心元件,其节流特性对液体静压主轴的刚度和回转精度具有直接影响。针对现有节流器在主轴工作时节流特性不可控的不足,提出一款预压预调型可控节流器。在分析可控节流器工作原理和节流特性基础上,根据流体润滑理论,建立基于可控节流器的液体静压轴承承载性能的理论模型,研究可控节流器供油压力、弹簧刚度和控制油腔压力等参数对液体静压轴承承载性能的影响规律,并与固定节流液体静压轴承的承载性能进行对比。研究发现,在其他结构参数及工作参数一定的条件下,可控节流器能够显著地提高液体静压轴承的油膜刚度;在不同偏心率条件下,可控节流液体静压轴承的最佳油膜刚度对应的节流参数不同。在开发的液体静压电主轴试验台上进行了试验研究,通过对油腔压力和油膜刚度的理论计算值与试验测量值的对比,证实了可控节流方案的有效性。     

基于CFD的可倾瓦轴承静动特性研究

目前对于可倾瓦轴承的静动特性研究方法,主要是先研究单块瓦片的特性,再通过瓦片子系统的叠加得到轴承整体特性,在计算中忽略了瓦间间隙及瓦块相互之间的流场影响。用瓦块独立计算模型模拟理论计算中只考虑轴瓦与轴颈间隙流场的情况,整体计算模型考虑轴承瓦间间隙的影响,在Fluent软件中计算两种模型的静动特性参数,并进行对比和分析。计算结果表明,瓦间间隙对轴承流场的影响不能忽略,尤其是在涉及温度场计算时,瓦块独立计算模型计算的结果与整体模型计算结果相差很大。     

An analytical model for complete dynamical coefficients of a tilting-pad journal bearing

An analytical model as well as calculation method is presented for the complete dynamic characteristics of tilting-pad journal bearing. Using this model, the global oil-film forces, stiffness and damping coefficients acting on the journal and all pads can be calculated in a highly concise expression. To improve the computational efficiency, a fast algorithm for calculating the oil-film force and Jacobian of the local pad system is proposed and the Newton–Raphson method is used for solving the equilibrium positions of the journal and all pads. Taking a rigid rotor symmetrically supported on two identical five-shoe tilting-pad journal bearing as an example, the complete dynamic characteristics, damping natural frequency and the stability are calculated. Compared with the traditional reduced model, the numerical results show that the dynamic characteristics can be calculated efficiently and succinctly. The stability can also be overestimated by using the reduced model.     

Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton–Raphson method

Thermoelastohydrodynamic lubrication (TEHD) analysis is presented to investigate the static performance of tilting-pad journal bearings. A completely numerical solution is obtained. The Newton–Raphson method is employed to predict the bearing characteristics of the hydrodynamic pressure, the eccentricity and the pad attitude angles simultaneously. For the temperature calculation, three-dimensional (3D) energy equations for the fluid under each pad and 3D heat transfer equations for the pads are solved using a sequential sweeping method. The elastic deformation and thermal expansion of each pad are calculated with the 20-node isoparametric finite element method. It is found that the Newton–Raphson method is a smart and efficient method. The results show that the elastic deformation due to the hydrodynamic pressure and the influence of the temperature elevation play an important role in the calculated bearing system.     

A FEM approach to simulation of tilting-pad thrust bearing assemblies

Finite-element method (FEM) modelling is applied to analysis of the performance of hydrodynamic tilting-pad thrust bearing assemblies. A 3D model of the bearing assembly that includes the bearing pad and shaft is used to assess the influence of operating conditions on bearing parameters such as temperature and oil film distributions across the pads. The model is first applied to the investigation of a spherically pivoted-pad. Through comparison with results from experiments carried out on just such a bearing, good correlation between the model and experimental results is found for maximum oil film temperature, pressure distribution and thickness. The model is then applied to the examination of a bearing having spring-supported babbitt pads. The effect of different oil types on a spring-supported thrust bearing is analysed. Further application of the model to investigate the same spring-supported pad, this time with a resilient surface coating, is discussed.     

可倾瓦气体动压轴承承载能力的数值分析

应用MATLAB的偏微分方程工具箱,采用有限元法求解气体润滑Reynolds方程,通过完全装配分析法计算了可倾瓦动压气体轴承的承载能力,研究了轴承偏心和瓦块预负荷对可倾瓦轴承的承载能力、最小气膜厚度和最大气膜压力以及瓦块摆角的影响。计算结果表明,随轴承偏心或瓦块预负荷增大,各瓦块的承载能力和摆角发生明显变化,轴承的最小气膜厚度减小,最大气膜压力增大,承载能力增大。从理论上解释了可倾瓦轴承的承载能力与轴承偏心和瓦块预负荷的密切相关性。     

多瓦可倾瓦径向滑动轴承热润滑性能分析

考虑变黏度、密度的情况,建立多瓦可倾瓦径向滑动轴承的数学模型,用有限差分法求解其热流体动力润滑(THD)模型,分别计算12块瓦可倾瓦径向滑动轴承的最小油膜、压力分布和三维温度场分布,分析不同载荷、不同转速、不同润滑油黏度等对轴承各瓦的热润滑性能影响。结果显示,建立的模型及其计算程序能计算分析多瓦可倾瓦径向滑动轴承的热润滑问题。润滑油黏度和转子转速对多瓦可倾瓦径向滑动轴承的热润滑性能有较大的影响;瓦块绕支点的倾斜以及瓦块所处的角度位置会影响部分瓦块的热润滑性能,出现与普通圆形径向滑动轴承不一致的润滑性能变化。     

一种可控滑动轴承-转子系统性能计算方法*

针对可控滑动轴承油膜性能计算困难问题,提出一种考虑基础参振的滑动轴承性能计算的动网格模型,阐述网格更新原理,给出可控滑动轴承所支撑转子系统轴心轨迹的计算方法。在滑动轴承-转子-基础系统的性能计算时,该方法保证油膜径向网格线和轴颈表面垂直,能减小轴承油膜性能计算的累计误差。通过不平衡载荷条件下的转子轴心静平衡位置计算结果与油膜力数据库方法、经典数据进行对比,验证了该模型的正确性,并利用该方法分析受正弦位移激励的滑动轴承-刚性转子系统的工频振动情况。结果表明：选择合适相位和幅值的正弦位移激励来控制轴承座,可减小转子系统的不平衡振动。这为基于超磁致伸缩材料的轴承、基于压电陶瓷材料的轴承、柔性铰链可倾瓦轴承等可控轴承-转子系统的性能计算提供了一种新方法。     

Multi-orifice active tilting-pad journal bearings—Harnessing of synergetic coupling effects

The dynamic performance of tilting-pad journal bearings with controllable radial oil injection is theoretically investigated, exploring the synergetic effect between passive elastohydrodynamics and active radial lubricant injection.The flexible tilting-pads are modelled as linearly elastic using finite elements. To reduce computational work, a pseudo-modal reduction is applied.Curves of dynamic bearing coefficients as well as the corresponding phase-magnitude plots are presented.Strong synergy between elastohydrodynamics and active control is observed, in particular for bearings with injection orifices far from the pivot line.     

On the Adjusting of the Dynamic Coefficients of Tilting-Pad Journal Bearings

This paper gives a theoretical and experimental contribution to the problem of active modification of the dynamic coefficients of tilting-pad journal bearings, aiming to increase the damping and stability of rotating systems. The theoretical studies for the calculation of the bearing coefficients are based on the fluid dynamics, specifically on the Reynolds equation, on the dynamics of multibody systems and on some concepts of the hydraulics. The experiments are carried out by means of a test rig specially designed for this investigation. The four pads of such a bearing are mounted on four flexible hydraulic chambers which are connected to a proportional valve. The chamber pressures are changed by means of the proportional valve, resulting in a displacement of the pads and a modification of the bearing gap. By changing the gap, one can adjust the dynamic coefficients of the bearing. With help of an experimental procedure for identifying the bearing coefficients, theoretical and experimental results are compared and discussed. The advantages and the limitation of such hydrodynamic bearings in their controllable form are evaluated with regard to application on the high-speed machines.     

The effect solid particle lubricant contamination on the dynamic behavior of compliant journal bearings

The proposed work concerns a theoretical and numerical investigation of the effect of solid particle contamination of lubricant oils on the static and dynamic characteristics of a finite length compliant journal bearing operating under isothermal conditions with laminar flow. In the present investigation, we use simple models based on the Einstein's mixture theory, which is characterized by the presence of suspended rigid particles in a fluid. Using the classical assumptions of lubrication, a Reynolds equation is derived and solved numerically by the finite difference method. The displacement field at the fluid film bearing liner interface due to pressure forces is determined using the elastic thin layer model. The results obtained show that the presence of suspended rigid particles in the lubricating oil (solid contamination) has significant effects on the hydrodynamic performance characteristics such as the pressure field, friction force, flow rate, elastic surface deformation as well as stability maps of the rotor‐bearing system (critical mass and whirl frequency) especially at high volumetric concentration.     

Hydrodynamic Performance of a Thrust Bearing with Micropatterned Pads

The primary objective of this study was to investigate the influence of surface texturing on hydrodynamic lubrication of tilting-pad thrust bearings in terms of bearing power loss, operating temperature, and oil-film thickness. For this purpose, the working faces of six thrust pads from a 228.6-mm-outer-diameter bearing were textured. The textured surface consisted of a system of crossing channels of less than 10 μm in depth. Tests were conducted with a VG68 mineral turbine oil supplied to the bearings at a constant temperature of 50°C and flow rate of 15 L/min. The following parameters were measured: frictional torque, pad and collar temperatures, oil-film thickness, and pressure profiles along two circumferential lines. No significant change in collar and pad temperature could be observed when the patterned bearing was used. However, the textured bearing showed a tendency to exhibit lower power loss especially when an optimum oil flow supply rate was used. At the same time, inlet and outlet film thicknesses for the patterned bearing showed larger values than those obtained during tests on the plain babbitt pads.     

Stability of multi orifice active tilting-pad journal bearings

The stability properties of actively lubricated tilting-pad journal bearings are investigated theoretically. The bearing preload factor and control system gains are varied, and stable and unstable regions are identified. It is seen, that the control system influences bearing stability, and that the nature and magnitude of this influence depends on the rotor mass, preload factor and rotational speed. Furthermore, it is shown that assuming the bearing pads to be rigid can produce a substantial error. A rigid pad model will overpredict the stable range of the bearing, thus it may lead to failure if trusted.     

静压孔位置对油膜支承可倾瓦轴承承载性能的影响分析

为了提高汽轮机转子系统中支承轴承的油膜刚度,以三瓦油膜支承可倾瓦轴承为研究对象,研究静压孔相对位置对轴承承载性能的影响规律。建立了油膜支承可倾瓦轴承油膜润滑模型,并运用计算流体动力学方法数值求解三维N-S方程,揭示了不同静压孔相对位置下轴承压力分布、最小膜厚、偏心率、刚度等性能参数的变化规律。分析结果表明：在载荷为890 N的情况下,改变孔的位置可以提高轴承油膜刚度;当静压孔相对位置γ=5°左右时,孔位置接近油膜最大压力分布区,与γ=0°时相比,最小膜厚和偏心率分别减小9.8%和48%,主刚度kyy、kxx接近原结构的1.4倍和1.1倍,此时静压孔位置为相对最优位置区域。依据分析结果开发了新型油膜支承可倾瓦轴承（γ=5°）,通过试验对比分析了普通滑动轴承与新型油膜支承可倾瓦轴承的综合性能,结果表明,高转速时所开发的新型油膜支承可倾瓦轴承具有更好的承载性能与减振性能。研究结果对油膜支承可倾瓦轴承的性能分析具有一定的参考价值,设计轴承静压孔时可根据油膜压力分布规律对其优化以提高轴承性能。     

混合流态下径向滑动轴承的静态特性研究

以无限宽径向滑动轴承为研究对象,考虑油膜中同时存在层流和紊流两种流态,基于层流、紊流润滑理论,联立求解雷诺方程、能量方程和温黏方程,分析油膜中流态变化,得到压力分布、承载力、摩擦力和最高温度等特性参数。结果表明:随着转速的升高和偏心率的增大,油膜内流体从完全层流转变为完全紊流要经过一个复杂的流态变化过程;与单一层流流态相比,混合流态下油膜承载力和摩擦力较大,温升较高,黏度变化较大,这表明流态的改变和热效应对轴承特性有着不可忽略的影响,在计算轴承特性时,应准确判断油膜中流态,并考虑热效应的影响。     

Analysis of heavy duty tilting-pad journal bearing taking into account pad distortion and possible adoption of rubber pad segments

In this work a comparative study has been made between the thermo-hydrodynamic performance of a three shoe tilting-pad journal bearing with rigid and elastic pads subjected to unbalance load. A case study of a bearing adopting three rubber pad segments has also been studied. The distortion of the elastic pad is introduced into the distribution of the film thickness through an iterative scheme to assess its effect on the load carrying capacity of the bearing. A finite element mesh is used to calculate the distortion of the elastic pad while a finite difference mesh is used to calculate the pressure field in the lubricant film. Results have shown a number of interesting conclusions regarding the adoption of rubber pad segments instead of tilting-pads. There is an increase in minimum oil film thickness when using elastic pad or even rubber pad segments compared with rigid pads. Also the maximum pressure and load carrying capacity are not significantly affected.     

大型水轮发电机推力轴承热弹性流体动力润滑性能相似分析

本文以大型水轮发电机推力轴承热弹性液体动力润滑系统的基本方程为基础,导出了包括转动部件、双层水冷可倾瓦部件、油池和冷却器的整个系统的相似准则数。