Rigidity and damping characteristics of hydrodynamic sliding bearing with deformable working surfaces

The model of a hydrodynamic sliding bearing has been developed that takes into consideration the effect of the deformation of sliding surfaces on the bearing characteristics. The deformations of the sliding surfaces are determined when solving the problem of elastohydrodynamic contact of the journal and bearing with account for the pressure in the lubricating film. Variation in the clearance size at the deformation of the bearing and shaft surfaces is found by iterations when solving jointly the problems of lubricant flow and working surface deformation. Elastic deformations of the working surfaces are calculated using a two-dimensional boundary element model and a three-dimensional finite element model of the shaft and bearing. The method of finite elements is applied to calculate the parameters of lubricant flow in the bearing based on the solution of Reynolds equation in the disturbed form. The rigidity and damping characteristics of the sliding bearing with the deformable surfaces are compared to those of the bearing with the rigid surfaces; the results of the two-dimensional model of bearing deformation are compared to those of the three-dimensional one.     

Analysis of High-Speed Intershaft Cylindrical Roller Bearing with Flexible Rings

For high-precision mechanisms such as machine tools or gas-turbine engines, which operate at extreme conditions, it is particularly important to accurately predict the behavior of the included bearing. This prediction includes, among other things, its load distribution, stiffness, and power dissipation. Although shaft speeds tend to increase, rings and shaft walls are becoming thinner due to size and weight constraints. Thus, bearing behavior is no longer independent of the housing and ring stiffness. This paper focuses on the problem of elastic ring deformation and certain behaviors of high-speed intershaft cylindrical roller bearings such as heat dissipation, contact pressure, and risk of bearing failure due to scuffing. The paper presents an analytical method to account for the structural deformation of the rings based on Roark's formulas. The elastic deformation of thin cylindrical rings has been introduced in the set of displacement and load equations that describes the bearing equilibrium. A correlation with a high-speed intershaft cylindrical roller bearing application is made and the results are compared with those obtained with the finite element method for housing deformations. Heat dissipation, load distribution, contact pressure, and internal kinematics are discussed to evaluate co-rotating and contrarotating shaft design solutions.     

Theoretical Analysis of High-Speed Cylindrical Roller Bearing with Flexible Rings Mounted in a Squeeze Film Damper

For high-precision mechanical systems such as gas-turbine engines that operate under extreme conditions, it is particularly important to accurately predict the behavior of the mainshaft rolling bearings. This prediction includes, among others, the load distribution, stiffness, and power dissipation. Although the shaft speeds tends to increase, rings and shaft are becoming thinner due to size and weight constraints. Thus, the bearing behavior is now dependent on the housing and ring stiffness. Furthermore, the use of a squeeze film damper (SFD) is widespread in gas-turbine engines to significantly reduce the vibratory levels. In this case, a single thin ring provides the interface between the bearing rolling elements and the fluid film. Due to the flexibility of this ring, an elastic coupling occurs modifying the behavior of the bearing-SFD system. A global flexible bearing-SFD assembly model is proposed in this paper. Large deformations can occur, resulting in a contact between the ring common to the bearing and the SFD and its housing. To reproduce this interference, an effective mechanical stop model is also proposed. The behavior of an industrial bearing-SFD assembly is then investigated for different operating conditions. The presented results show that this coupling has a first-order influence on the behavior of the bearing-SFD system. It is also shown that such elastic coupling introduces a dissymmetry of the load distribution with respect to the applied load direction. Moreover, in certain cases, the position of the bearing in its housing can reach eccentricities larger than the radial clearance of the SFD.     

Calculation of six-lobe and eight-lobe deformable thrust sliding bearings

The paper deals with the development of a model and the calculation of characteristics of a hydrodynamic thrust sliding bearing which provides the compensation of the axial force in high-speed and low-speed rotors of stationary gas turbine units. In the framework of creating a method for determining the stiffness and damping characteristics of the bearing and calculating the parameters of lubricant flow in the gap, we develop a model of the thrust bearing based on the coupled solution of the problem of the flow of incompressible lubricant between the sliding surfaces and the problem of the deformation of the bearing parts and the shaft under the lubricant pressure. The model makes it possible to find the basic characteristics of the thrust sliding bearing at various relative displacements of the bearing and shaft. The bearing model is verified by comparing our results with the results of calculating lubricant flow in the STAR-CD software package and the results of calculations and experiments reported in the literature. The stiffness and damping characteristics are calculated for two thrust sliding bearings with six and eight lobes, depending on the sliding surfaces closure and variations in the shaft rotation angle with account of the deformation of the sliding surfaces. A significant influence of the shaft rotation angles in the bearing section and the deformations of the sliding surfaces on the integral characteristics of the bearing is demonstrated.     

Transient analysis of misaligned elastic tilting-pad journal bearing

For several reasons, almost all bearings operate in a misaligned condition, the present research work deals with analyzing the performance of a misaligned tilting-pad journal bearing under transient loading condition. The elastic and thermal distortions of the pad are considered and finite element analysis is used to calculate the pad’s elastic deformation. Using finite difference method, the Reynolds equation is simultaneously solved with the energy equation to calculate the pressure distribution and hence the other bearing performance characteristics. A modified fluid film thickness equation is used to take the effect of shaft misalignment and bearing elastic and thermal distortion into consideration.The results have shown that considering the thermo-elasto-hydrodynamic distortion improves the bearing performance in the case of misalignment shaft. And, at low values of shaft misalignment, the decrease in oil film thickness due to shaft misalignment is compensated by the increase in oil film thickness due to elastic and thermal distortions.     

Thermo-hydrodynamic analysis of herringbone grooved journal bearings

Steady-state and stability characteristics of herringbone grooved journal bearings (HGJBs) are found considering thermal effect. The temperature of the fluid film rises significantly due to the frictional heat, thereby the viscosity of the fluid and the load carrying capacity decrease. A thermodynamic analysis requires the simultaneous solution of Reynolds equation along with energy equation of the fluid and heat conduction equations in the bush and the shaft. The linearized first-order perturbation technique is employed for the prediction of stiffness and damping coefficients of the oil film. Thereafter mass parameter and whirl ratio are found from the stability analysis. It is difficult to obtain the solution due to the numerical instability when the bearing is operated at high eccentricity ratios.     

Effect of Lubricant Non-Newtonian Behavior and Elastic Deformation on the Dynamic Performance of Finite Journal Plastic Bearings

This paper presents a numerical study of the performance of a dynamically loaded finite journal plastic bearing lubricated with a non-Newtonian fluid, taking into account the elastic deformation of the bearing. The non-Newtonian characteristics are adopted in this paper through an equivalent power-law. An expression for a modified Reynolds equation is derived in order to obtain the pressure gradient. Elastic deformation of the bearing surface was estimated in a direction normal to the bearing surface using Boussinesq equations. The film shape was modified accordingly and then iterated with the hydrodynamic pressure distribution in the bearing until a convergent solution was obtained. The Reynolds equation was solved numerically, considering three values of the flow-behavior index (n = 0.6, 1, and 1.2) and a wide range of journal speeds, materials, and clearance ratios. Consequently, the finite perturbation technique was used to determine the eight values of oil film stiffness and damping coefficients. By using the dynamic coefficients, the stability characteristics of the rotor-bearing system and the critical speed were calculated. The results show that increasing the flow-behavior index enhances the rotor-bearing system stability. A considerable destabilizing effect is obtained upon decreasing the elastic deformation coefficient.     

Performance analysis of flexible multirecess hydrostatic journal bearing operating with micropolar lubricant

This paper presents the analytical study of the effect of the bearing shell flexibility on the performance of multirecess hydrostatic journal bearing system operating with micropolar lubricant. The modified Reynolds equation for the flow of micropolar lubricant through constant flow valve‐compensated hydrostatic journal bearing has been solved by finite element technique based on Galerkins method, and the resulting elastic deformation in the bearing shell due to fluid‐film pressure has been determined iteratively, in which the deformation coefficient accounts for the bearing shell flexibility. The computed results suggest that the influence of the micropolar effect on bearing performance characteristics is significantly affected by the bearing shell flexibility. Copyright © 2012 John Wiley & Sons, Ltd.     

Controllable high speed journal bearings, lubricated with electro-rheological fluids. An analytical and experimental approach

The problem of journal bearings control is of great importance in mechanical engineering. A very recent method for doing this is the creation of ‘smart' journal bearings using electro-rheological (ER) fluids. If such a fluid is used to lubricate a journal bearing system, it is expected that the imposition of an electric field between the rotor and the stator will cause an alteration in the dynamic properties of the journal bearing. In this paper an experiment in a high speed journal bearing (16 000 to 35 000 s⁻¹), with small radial clearance is presented. The alternation of the attitude locus (eccentricity and attitude angle) and the stiffness coefficients in a loaded journal bearing lubricated with ER fluid is investigated and presented. The Reynolds equation is solved using the finite element method in order to get the dynamic characteristics of the ER bearings vs the electric field and to simulate its dynamic behavior. The Bingham plastic model of non-Newtonian fluid flow behavior is used to described the ER lubricant. The accuracy of the algorithm is obtained by comparing the results published by previous investigators and the experimental data described in this paper. It is concluded that ER fluids can be used to create ‘smart' journal bearings. and vibration controllers can be constructed to control the dynamics and stability of the ER fluid lubricated bearings.     

Consideration of the multizone hydrodynamic friction,the misalignment of axes,and the contact compliance of a shaft and a bush of sliding bearings

The second version of the original Bearing Builder Finite Element Method (BBFEM) software and its application for analyzing the hydrodynamics of cylindrical sliding bearings has been briefly described. The two-dimensional problem of the lubricating fluid flow in a bearing clearance taking into consideration the different types of deviations in the contact surface from a cylindrical shape has been solved by the finite element method. The bearing design that leads to the formation of several hydrodynamic friction zones (fluid wedges) has been considered. The role of the contact compliance of a shaft and a bush and the operation factors that cause the deviation from the initial cylindrical shape of a bearing, including the deformations and the misalignment of the shaft and bush is shown by citing specific examples of antifriction composites of different compositions.     

卧式水电机组用径向滑动轴承热弹流特性分析

研究轴颈挠度和瓦块表面热弹变形对卧式水电机组径向滑动轴承静态润滑性能的影响。推导考虑轴颈挠度和轴瓦热弹变形后的油膜厚度表达式;用中心差分法结合ANSYS软件联立求解雷诺方程、能量方程、固体热传导方程、密度方程、黏度方程和轴瓦热弹变形等,得到径向滑动轴承的热弹流润滑(TEHD)特性,并与不计入轴颈挠度及轴瓦热弹变形的油膜动压润滑特性进行比较。结果表明:在考虑轴颈挠度和轴瓦瓦面热弹变形的影响后,油膜压力、温度、厚度沿着轴承宽度中心线的对称特性消失;油膜压力峰值增大,峰值点位置由轴向中心区偏移至出口区;油膜温度峰值增大,最高温度发生在出口区;润滑区内的最小油膜厚度大幅度减小,油膜最小厚度处于出口侧边界附近;轴承润滑流量减小,损耗略有增大;轴承稳态运行时,轴颈偏位角基本一致。     

轴质量对用液体油膜轴承支承转子动特性的影响

本文研究了轴质量对支承于液体油膜轴承上的转子的影响.转子假定是位于弹性轴中部的薄盘,它考虑非零弹性轴质量由液体油膜轴承支承.该径向轴承假定为短简易型,用纵向的和相互作用的刚度及阻尼系数表示,这些系数与系统的角速度有关.假定转于由一电机加速,假定电机速度由一两阶传递函数控制.仿真结果表示质量比的小值,它由轴质量对盘质量比...     

Theoretical Prediction of Journal Bearing Stability Characteristics Based on the Extent of the Slip Region on the Bearing Surface

Journal bearing performance depends on the boundary conditions at the interfaces between the fluid and the solid surfaces. In the derivation of the Reynolds equation used to predict the bearing performance, the no-slip boundary conditions of the fluid and the solid interfaces are used. Recent research has shown that a slip can occur on specially made surfaces, the conventional no-slip boundary conditions are not valid, and the Reynolds equation is no longer applicable. If the slip is allowed to occur in certain regions, the fluid flow in the bearing can be altered, and the bearing stability characteristics can be improved. In this article, the numerical stability analysis of a journal bearing based on the extent of the slip region on the bearing surface is analyzed. An extended Reynolds equation is derived based on the slip length model, using a no-slip boundary condition against the journal surface and the slip against the bearing surface. A linearized perturbation method is used to determine the stability limit of a rigid rotor supported on two symmetrical journal bearings. Using the linear stability analysis, the linearized stiffness and damping coefficients, the threshold speed, and the critical whirl ratio are evaluated. The effects of the slip parameter on the bearing stability performance are discussed. The results show that with a critical shear stress of zero, an increase in the stability threshold can be achieved with a higher value of the nondimensional slip length and a smaller extent of the slip region on the bearing surface.     

高速主轴离心膨胀及对轴承动态特性的影响

以高速主轴系统为对象,将主轴转子和轴承内圈分别等效为等截面梁和空心圆盘,计算离心力作用下主轴转子和轴承内圈的径向弹性变形,并分析主轴转子与轴承连接状态随转速升高的变化趋势。考虑旋转部件的离心膨胀变形,建立高速主轴轴承动力学模型并进行试验验证。在此基础上,研究离心效应对主轴轴承径向预紧状态的影响,揭示高速主轴轴承动态特性随转速的变化规律。研究结果表明,离心力引起的径向膨胀变形使滚动体与轴承内、外圈之间的接触角减小,接触力增加。主轴轴承的轴向刚度和径向刚度均随转速的升高而降低。轴承内圈的离心膨胀变形对轴承轴向刚度的影响可以忽略不计,而能在一定程度上提高轴承的径向刚度。     

基于气穴模型的动压轴承动态油膜刚度计算方法

针对雷诺方程很难准确反映动压轴承高速转动过程中引起的周向惯性效应、动态挤压效应等的影响,进而导致油膜动态刚度计算精度难以满足高精度轴承设计的现状,提出用ADINA软件先求解瞬态油膜压力分布和瞬态油膜力,得到轴心轨迹,然后结合差分计算模型计算油膜动态刚度的方法。该计算方法基于流固耦合和气穴模型,定义油膜和轴的流固耦合时,采用任意的拉格朗日-欧拉(ALE)算法有效避免了油膜网格畸变的问题,再现轴心动态平衡过程和三维流场压力分布的动态发展过程,得到瞬态过程中的动态油膜力和动态油膜刚度。试验结果和基于流固耦合和气穴模型的计算结果对比分析发现两者基本吻合,说明该基于流固耦合和气穴模型的数值仿真计算方法是可行和有效的。     

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.     

Steady-state thermo-hydrodynamic analysis of cylindrical fluid film journal bearing with an axial groove

A steady-state thermohydrodynamic analysis of an axial groove journal bearings in which oil is supplied at constant pressure is performed theoretically. Thermohydrodynamic analysis requires simultaneous solution of Reynolds equation, energy equation and heat conduction equations in the bush and the shaft. From parametric study it is found that the temperature of the fluid film raises due to frictional heat thereby viscosity, load capacity decreases. Increased shaft speed resulted in increased load carrying capacity, bush temperature, flow rate and friction variable. It is difficult to obtain the solution due to numerical instability when the bearing is operated at high eccentricity ratios.     

轴颈倾斜对人字槽径向气体轴承性能影响的数值研究

由于制造误差、偏斜力矩及弹性变形等原因会导致轴颈在轴承中倾斜,使轴承气膜厚度和压力分布发生变化,会对轴承的工作性能产生影响。为研究轴颈偏斜对轴承性能的影响,通过有限元摄动法求解雷诺方程,研究轴颈偏斜角度和偏斜距离对人字槽气体轴承气膜厚度、压力场、静态和动态特性的影响,并分析轴颈倾斜对人字槽径向轴承临界质量等参数的影响规律。结果表明:轴颈偏斜距离变化对轴承静态和动态性能影响较大,偏斜角度对轴承性能影响较小;随着偏斜距离增大,量纲一承载力和临界质量均大幅减小、量纲一摩擦力矩呈现小幅下降趋势。     

Analysis of orifice compensated non-recessed hole-entry hybrid journal bearing operating with micropolar lubricants

A numerical study concerning the performance of non-recessed hole-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynolds equation governing the flow of micropolar lubricant in the bearing clearance space is solved using Finite Element Method along with appropriate boundary conditions. Dependence of bearing performance characteristics upon the bearing operating, geometric and micropolar parameters, over a range, has been analyzed. The numerically simulated results are pointed to the choice of restrictor design parameter, for the chosen combination of micropolar parameters of lubricant, in order to obtain optimum values of fluid film stiffness coefficients.     

浮环弹性变形对浮环动静压轴承润滑特性的影响

浮环轴承在高速工况下运行时,浮环表面在油膜压力作用下会发生弹性变形,影响轴承润滑性能。针对带有深浅腔的浮环动静压轴承,采用有限元法和有限差分法耦合求解油膜Reynolds方程、能量方程和温黏关系式,采用变形矩阵法求解弹性变形方程,计算浮环弹性变形分布;在浮环平衡的基础上,分析浮环变形对环速比、油膜承载力、端泄流量等润滑特性参数的影响。结果表明：浮环弹性变形分布与油膜压力分布呈现一致性,转速越高,偏心越大,变形越明显;考虑浮环弹性变形,浮环达到平衡状态时,内膜偏心率增加,环速比减小,轴承承载力与摩擦力矩均有所增加;由于浮环变形对内、外膜间隙及流动液阻的不同影响,使得内膜端泄流量增加,外膜端泄流量减少。