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。     

卧式水电机组局部多油楔径向滑动轴承研究

针对卧式水电机组用径向滑动轴承载荷日益提高的现状,设计一种局部多油楔瓦面结构的径向滑动轴承。通过联立求解膜厚方程、雷诺方程、密度方程、黏度方程、能量方程和固体热传导方程等,获得轴承的热流润滑特性,并与椭圆径向滑动轴承的热流特性进行对比。结果表明,局部多油楔径向滑动轴承具有较大的动压承载区域和较小的油膜压力梯度以及较低的油膜温升,可以大幅度提高轴承的承载能力。     

ON THE AXIAL TRANSIENT RESPONSE ANALYSIS OF THE SECTOR-SHAPED HYDRODYNAMIC THRUST BEARING-ROTOR SYSTEM IN A TURBOEXPANDER

NOTATIONS(The letters in brackets denote the dimension to be as 1)C──Damping coefficient of oil filmD──Domain of a thrust pad in the thrust bearingF──Axial external force (static load)ΔF──Increment of axial external forcesFr──Resultant of oil film forcesF1,F2──Oil film forces of thrust bearings 1 and 2ΔFr──Increment of oil film forces resultantk──Stiffness coefficient of oil filmm──Mass of rotorp()──Oil film pressure,=pδ20/μωr21p1(1),p2(2)──Oil film pressu…     

瞬变载荷作用下滑动轴承轴心轨迹计算仿真

为了研究动压滑动轴承在瞬变载荷作用下的润滑状况,在考虑轴颈惯性力和非线性油膜力的基础上,建立了滑动轴承轴心轨迹的运动方程,提出了采用欧拉法求解有限长滑动轴承瞬时轴心轨迹的数值方法。分别计算了在阶跃、矩形脉冲和正弦脉冲瞬变载荷作用下轴心轨迹、最大油膜压力及最小油膜厚度的变化规律。分析结果表明,在瞬变载荷作用时,轴心轨迹、最大油膜压力及最小油膜厚度都有较大的变化并呈现出一定的振荡过程。由于脉冲载荷的作用时间有限,随着其消失,轴心乃收敛于原平衡位置,而阶跃载荷则使轴心收敛于新的平衡位置。     

基于流固耦合的滑动轴承非线性油膜动特性研究

针对采用传统静态滑动轴承动力特性系数分析转子从启动到稳定在平衡位置这段时间内瞬态响应的误差较大的问题,提出了采用有限变分法和Newmark-β法相结合的非线性油膜动特性动态分析方法。该方法首先采用有限变分法计算非线性油膜动力特性系数, 解决了采用有限差分法时多次迭代的时效问题,大大提高了计算效率;然后根据计算得到的非线性油膜动力特性系数,通过Newmark-β法分析转子系统的瞬态响应,用学科间迭代方法实现了非线性油膜动力特性系数与转子瞬态响应之间的流固耦合;最后以Jeffcott转子系统为例,对比研究了传统静态分析方法与动态分析方法。结果证明,采用动态分析方法得到的转子系统瞬态响应幅值更小,精度更高。     

The effect of inlet film boundary conditions on the steady state characteristics of hydrodynamic journal bearings

The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is added precisely at this position. Since the pressure develops smoothly because of hydrodynamic action, a correction in the Reynolds boundary conditions is proposed and a new solution for the pressure distribution is obtained. The steady state characteristics of a hydrodynamic journal bearing using the new boundary conditions are compared with the well-known characteristics using the Reynolds boundary conditions.     

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Hydrodynamic Journal Bearings with Rough Surfaces

Non-linear transient stability analysis has been performed to study the sub-synchronous whirl stability of a rigid rotor supported on two symmetric hydrodynamic bearings with rough surfaces subjected to a unidirectional constant load. A Reynolds type equation for finite hydrodynamic bearings, with different models of rough surfaces, has been solved using the stochastic finite element method. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. Results show an increase in the stability with transverse roughness and a decrease in the stability with isotropic roughness. A small improvement in stability is obtained with longitudinal roughness.     

考虑不同加速工况的滑动轴承的启停性能分析*

滑动轴承的摩擦磨损主要发生在启停阶段。为了研究启停工况下的滑动轴承的摩擦学性能,建立一种面向径向滑动轴承的混合润滑数值分析模型。采用质量守恒边界条件的雷诺方程求解流体压力,采用Greenwood和Tripp接触模型预测固体表面接触,而通过Johnson载荷分配概念将润滑模型和接触模型联系起来,从而实现对滑动轴承在启停工况下从混合润滑过渡到动压润滑的摩擦学行为分析。利用该模型,研究轴承系统在启停阶段从边界润滑、混合润滑到动压润滑演化过程中的摩擦学性能;以径向滑动轴承系统为例,结合不同的轴承转速变化函数,分析轴承加速对轴承启停性能的影响;同时研究工作工况、润滑油温度、轴承的结构参数对轴承启停性能的影响。结果表明：轴承启动加速度在合理范围内越大越好,能使轴承更快进入动压润滑;较高的转速、较低的润滑油温度和较大的径向轴承间隙能使轴承拥有更好的启停性能。     

Hybrid journal bearings with particular reference to hole-entry configurations

There is a spectrum of pressure-fed journal bearings ranging from the purely hydrostatic bearing characteristics, ie zero speed operation, to the purely hydrodynamic bearing characteristics which depend completely on speed. Between these two extremes, hybrid bearing characteristics rely on mixed modes of external pressurisation and speed-dependent pressurisation. Large high speed hydrodynamic bearings require the lubricant to be pumped under pressure for temperature control. It is therefore attractive to use this external source of pressure to enhance the start-up performance by reducing wear and improving stability. Hybrid bearings offer the possibility of improving on both the zero-speed characteristics of hydrostatic bearings and on the whole range of speed characteristics of hydrodynamic bearings. It is concluded that hole-entry bearings may be particularly effective when compared with other bearing configurations for good load support and low energy consumption, when used in any of the four modes of operation including: zero-speed hydrostatic mode; high-speed hydrodynamic mode; zero and high-speed hybrid mode; and jacking mode where areas are pressurised for start-up. A modification to the procedure for solving the Reynolds equation is introduced to cope with cavitated regions. The technique presented for solving the bearing pressures and cavitation boundaries is efficient and has relevance to any type of liquid film bearing     

Application of computational fluid dynamics and fluid structure interaction techniques for calculating the 3D transient flow of journal bearings coupled with rotor systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics (CFD)-fluid structure interaction (FSI) techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ’’dynamic mesh’’ technique. A new mesh movement approach is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the journal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function (UDF). The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.     

A comparison of techniques for identifying the configuration state of statically indeterminate rotor bearing systems

Turbomachinery rotors are frequently supported on several hydrodynamic bearings and so are statically indeterminate. In such cases, the relative locations of the bearing centres (viz. the system configuration state) affect the bearing reaction forces and hence their stiffness and damping properties, thereby significantly influencing the vibration behaviour of the rotor bearing system. Since this configuration state may differ from its value at time of installation, due to thermal effects and/or foundation settlement, it would be useful to identify its value under operating conditions. This paper illustrates how this can be done in principle, regardless of the unbalance, by measuring the locations of the rotor journals relative to their respective bearing housings at any speed at which the system has reached steady state operating conditions, provided one has good models of the rotor and the foundation. Two identification procedures are compared. Both methods rely, to varying degrees, on using the Reynolds equation for hydrodynamic lubrication to obtain the bearing reaction forces. The first procedure uses the Reynolds equation to evaluate both the magnitudes and directions of the forces (the ‘magnitude and direction’ or MAD method), whereas the second procedure uses the Reynolds equation to evaluate only the directions of the forces (the ‘direction only’ or DO method). Numerical experiments on a flexibly supported statically indeterminate four bearing flexible rotor prove that both the MAD and DO identification procedures are sound in principle, being able to identify the locations of the two inboard bearings relative to the two outboard bearings to within 0.1 μm assuming seven-digit accuracy in journal orbit eccentricity measurements. On the other hand, three-digit measurement accuracy, felt to be the best accuracy practically achievable, restricts identification of the bearing locations to within 10 μm, with somewhat better identification being achieved with the MAD procedure. Such identification accuracy presupposes that the Reynolds equation correctly predicts the bearing reaction forces and could be in error owing to the temperature dependence of the bearing clearance, the assumption of a mean lubricant viscosity and the uncertainty of the cavitation boundaries. It is shown that error in lubricant viscosity may introduce significant errors into the identification achievable with the MAD procedure, but has no effect on that achievable with the DO procedure; and error in clearance introduces more error into the identification achievable with the MAD procedure than the DO procedure. Identification errors due to assumed cavitation conditions still need to be addressed.     

A study of the dynamic characteristics of synchronously controlled hydrodynamic journal bearings

In this paper, synchronous control of bearing is employed through a control algorithm for an actively controlled hydrodynamic journal bearing in order to suppress whirl instability and to reduce the unbalance response of a rotor-bearing system. Furthermore, a cavitation algorithm, implementing the Jakobsson–Floberg–Olsson boundary condition, is adopted to predict cavitation regions in a fluid film more accurately than the conventional analysis, which uses the Reynolds condition. The unbalance responses and stability characteristics of the rotor-bearing system are investigated for various control gains and phase differences between the bearing and journal motion. It is shown that the unbalance responses of the system can be greatly decreased by synchronous control of the bearing. There is an optimum phase difference, which gives the minimum unbalance response of the system at given operating conditions. It is also found that the stability threshold of the system can be greatly increased by synchronous control of the journal bearing.     

A Study of Dynamically Loaded Finite Journal Bearings in Mixed Lubrication Using a Transient Thermohydrodynamic Analysis

A transient analysis of dynamically loaded finite journal bearings in mixed lubrication is made by solving the modified generalized Reynolds equation, 2-D energy equation in the oil, and heat conduction equation in the journal simultaneously including mass conserving cavitation. ISOADI (isothermal shaft and adiabatic bushing inner surface) thermal boundary condition is used. Journal temperature is treated as quasi-steady over one loading cycle. Two kinds of contact model are used. Numerical solutions using the finite difference method are presented. Results shows that the bearing behavior is closely tied to the roughness texture and topography, asperity contact load, bearing geometry, and operating conditions.     

The effect of modified inlet boundary conditions on the stiffness and damping characteristics of finite hydrodynamic journal bearings

The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is supplied precisely at this location. Since the pressure develops smoothly because of hydrodynamic action, a correction in the boundary conditions is applied and a modified solution for the pressure distribution is obtained. The stiffness and damping characteristics of a finite hydrodynamic journal bearing using the new boundary conditions are compared with the wellknown characteristics incorporating the Reynolds boundary conditions. There is a significant change in the dynamic characteristics particularly at low values of the eccentricity ratio which can influence the characteristics of rotor-bearing systems.     

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.     

On Performance Characteristics of Three-Lobe Porous Hydrodynamic Journal Bearings

This paper presents an analysis of a three-lobe porous hydrodynamic journal bearing for its static and dynamic performance characteristics. The performance characteristics of the bearing have been computed and presented in graphical form for a wide range of permeability parameter to investigate the effect of porosity on bearing performance. The stability margin of the three-lobe journal bearing system, in terms of crtical mass of journal, has been established using Routh's criteria. The nature of transient motion of the journal has been analyzed using the complex eigen values of characteristic equation and motion trajectories obtained by numerical integration of equations of motion.     

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.     

Dynamic analysis of a reciprocating compression mechanism considering hydrodynamic forces

In this paper, a dynamic analysis of the reciprocating compression mechanism of a small refrigeration compressor is performed. In the problem formulation of the mechanism dynamics, the viscous frictional force between the piston and the cylinder wall is considered in order to determine the coupled dynamic behaviors of the piston and the crankshaft. Simultaneous solutions are obtained for the equations of motion of the reciprocating mechanism and the time-dependent Reynolds equations for the lubricating film between the piston and the cylinder wall and for the oil films on the journal bearings. The hydrodynamic forces of the journal bearings are calculated by using a finite bearing model along with the Gümbel boundary condition. A Newton-Raphson procedure is employed in solving the nonlinear equations for the piston and crankshaft. The developed computer program can be used to calculate the complete trajectories of the piston and the crankshaft as functions of the crank angle under compressor-running conditions. The results explored the effects of the radial clearance of the piston, oil viscosity, and mass and mass moment of inertia of the piston and connecting rod on the stability of the compression mechanism.     

On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids

The present work deals with the micropolar lubrication theory to the problem of the steady-state characteristics of hydrodynamic journal bearings considering two types of misalignment, e.g. axial (vertical displacement) and twisting (horizontal displacement). Using a finite difference method, the steady-state film pressures are obtained by solving modified Reynolds equation based on the micropolar lubrication theory. With the help of the steady-state film pressures, the steady-state performance characteristics in terms of load-carrying capacity, misalignment moment and friction parameter of a journal bearing are obtained at various values of eccentricity ratio, degree of misalignment and micropolar fluid characteristic parameters viz. coupling number and non-dimensional characteristic length.     

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.