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.     

Hydrodynamic Behavior of Viscoelastic Liquids in a Simulated Journal Bearing

The hydrodynamic effect of viscoelasticity in bearing performance was investigated experimentally by measuring the pressure distribution of viscoelastic liquids and Newtonian liquids in a simulated plain journal bearing. The pressure distribution of the viscoelastic liquids was somewhat different from that of the Newtonian liquids, showing a flattening of the pressure profile and a shift of the circumferential position of the peak pressure. Such a difference contributes to a small recovery of the loss of the load-carrying capacity due to the non-Newtonian viscosity for viscoelastic liquids. It may also contribute to a further reduction of friction beyond the effect of shear thinning. The difference of cavitation on the divergent region of the bearing for these two different kinds of liquid was evident. The viscoelastic liquids showed less extent of cavitation. The experimental conditions conform closely to those used in the classical hydrodynamic lubrication theory. The experimental data indicate that the full fluid film occupies half a bearing starting at 0° and ending at 180°, and the subatmospheric pressure in the divergent region is leveled off at a certain negative pressure. Based on this boundary condition, a computer solution in solving the Reynolds equation for a finite bearing gives very good agreement with experiment.     

The finite journal bearing considering film separation

The Reynolds equation is solved numerically for a journal bearing of finite length considering separation of the film of lubricant at the trailing edge of the pressure zone. The performance characteristics of the bearing are calculated. The solution is compared with that obtained using the conventional Swift-Stieber boundary conditions.     

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。     

Hydrodynamic load capacity of a full porous journal bearing of finite length in the turbulent regime considering slip flow and curvature

The hydrodynamic lubrication of a 360° finite porous metal journal bearing of arbitrary wall thickness press fitted in a solid housing and working with a turbulent film of newtonian lubricant was analysed in a closed form using a new generalized pressure equation. Bearings of undefined axial length and narrow bearings have been considered previously. For finite bearings the flow of lubricant in the axial clearance space is of the same order as in the azimuth. Therefore the governing differential equation is three dimensional and difficult to solve. However, Warner's method was used to reduce this equation to two second-order ordinary linear differential equations with analytically known variable coefficients which are simpler to solve. Analytical solutions of these were obtained as a boundary value problem in terms of the end conditions defining the start and termination of the load-supporting film. The half Sommerfeld boundary conditions were used for the azimuthal film extent since they are mathematically simpler, and the results obtained in the laminar regime were close to those obtained using the more complex (but realistic) Reynolds boundary conditions. Film curvature effects were included by using C/R₁ in the expression for film thickness. The curvature effect of the thick porous bearing matrix, which allows it to have an arbitrary wall thickness, was taken into account by a new direct approach which makes it possible to use the separation of variables. The collocation technique was utilized to determine the hydrodynamic pressure from which the bearing characteristics were evaluated. The results are fully analytical in nature, simple and yet exact and accurate; they permit easy and economical calculation of numerical data over a very wide range of parameters.     

A Study of Dynamically Loaded Journal Bearings Lubricated with Non-Newtonian Couple Stress Fluids

This paper is to theoretically investigate the behavior of dynamically loaded journal bearings lubricated with non-Newtonian couple stress fluids. To take into account the couple stress effects due to the lubricants blended with various additives, the modified Reynolds equation for dynamic loads governing the film pressure is derived. The film pressure is solved numerically with Reynolds boundary conditions and then various bearing characteristics are calculated. The effects of couple stresses on bearing performance characteristics are analyzed. The results conclude that couple stress fluids lubrication improves the bearing performance under dynamic loads.     

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.     

Analysis of Thermoelastohydrodynamic Performance of Journal Misaligned Engine Main Bearings

To understand the engine maln bearings’ working condition is important in order to improve the performance of engine. However, thermal effects and thermal effect deformations of engine maln bearings ar...     

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。     

内燃机曲轴主轴承压力分布的Matlab解法

以内燃机曲轴主轴承为研究对象,考虑雷诺边界条件,优化雷诺方程以求解主轴承压力分布。计算结果表明,这种计算主轴承油膜压力的方法较为合理。     

Steady state and dynamic characteristics of axial grooved journal bearings

The steady state and dynamic characteristics including whirl instability of oil journal bearings with single axial groove located at the top of the bearing and then at some angular interval from the top from which oil is supplied at constant pressure are obtained theoretically. The Reynolds equation is solved numerically by finite difference method satisfying the appropriate boundary conditions. The dynamic behaviour in terms of stiffness and damping coefficients of fluid film and stability are found using a first-order perturbation method for each location of the groove. It has been shown that both load capacity, end flow is maximum when the feeding groove is at 12° location and thereafter the load capacity falls, stability improves for smaller groove angle and groove length at higher value of eccentricity ratio and speed. The stiffness and damping coefficient magnitude is found to be higher for the bearing with smaller groove angle and groove length, the difference between the hydrodynamic and hydrostatic load increases at 12° groove location.     

圆盘止推静压气体轴承亚音速流场的简化计算

雷诺气体润滑方程仅涉及轴承气膜内的静压分布,对静压气体轴承流道特性的准确刻画还需要研究轴承流道内的气流速度场。将忽略惯性力的纯粘性等温气膜和等熵流动的供气孔拼接,建立了单供气孔环面节流圆盘止推轴承的流道简化模型,给出流道各部分气流马赫数、雷诺数和压力分布的计算公式。结果表明,气膜中气流速度随矢径变化的性质,取决于速度梯度为零的矢径位置;气膜中的气流雷诺数随矢径的增加不断减小。实际的计算结果表明,只要气膜入口截面上的气流马赫数小于临界声速,整个轴承流道将工作在亚音速,供气压力或气膜高度的变化对气膜起始区域边界层发展段长度的影响很小,供气孔始末端截面上压力和温度的变化也很小,忽略惯性力的纯粘性等温雷诺模型基本能够适用轴承的整个亚音速工况。气膜起始区域边界层发展段的长度,可以用气膜中雷诺数大于临界雷诺数的区域长度来近似。     

Theoretical hydrodynamic load capacity of an axially undefined full porous journal bearing in the turbulent regime considering slip flow and curvature

A mathematical analysis using a new generalized pressure equation is reported for the hydrodynamic lubrication of a 360° long porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. The limiting case of an axially undefined length of the bearing is considered and the axial flow of lubricant in the clearance space is neglected so that the governing differential equation is simpler to solve. Half Sommerfeld boundary conditions are used for the extent of the azimuthal film and film curvature has been included. The curvature effect of the thick porous bearing matrix is taken into account by a new direct approach in which the separation of variables is used for the first time in such a problem. The collocation technique is utilized to determine the hydrodynamic pressure from which the characteristics are evaluated. The results are fully analytical in nature, simple, yet exact and accurate, permitting easy and economical calculation of numerical data over a very wide range of parameters.     

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。     

Stability of tri-taper journal bearings under dynamic load using a non-linear transient method

Stability of a tri-taper journal bearing which is subjected to steady, periodic and variable rotating loads is studied theoretically using a non-linear transient approach. The hydrodynamic forces are initially obtained by solving the Reynolds equation, satisfying the Reynolds boundary conditions. Further, the transient behavior of rotor bearing system is predicted by substituting these hydrodynamic forces in the equations of motion and then solving them by fourth order Runge Kutta method. Stability of the rotor bearing system is determined from the journal locus. Comparative studies predict that the dynamic performance is superior for a bearing with high ramp size and aspect ratio.     

多叶动压气体滑动轴承静态特性的有限差分算法

多叶动压气体滑动轴承因其结构简单、摩擦阻力低、旋转精度高和无环境污染等优点,在高速离心分离机、空气压缩机和透平膨胀机等旋转机械中应用广泛。为探究多叶动压气体滑动轴承的静态性能,通过数学变换将三叶动压轴承的气体润滑Reynolds方程转化为标准偏微分方程形式,利用有限差分法和超松弛迭代法进行数值求解,研究气膜厚度和气膜压力分布、承载力、摩擦因数和质量流量等静态性能,随偏心率、预负荷系数、轴承数、长径比及瓦块分布位置的变化规律。结果表明：三叶轴承的承载力和轴颈表面摩擦因数随偏心率和长径比的增加而增加,而偏位角和质量流量随偏心率和预负荷系数的增加则呈现出相反的变化趋势;随着轴承数和预负荷系数的增大,承载力和摩擦因数显著提高,偏位角和质量流量则逐渐减小;瓦块分布位置对三叶动压气体滑动轴承的静态性能影响显著,其中瓦上承载方式的承载力、偏位角和质量流量明显高于瓦间承载方式。     

Analysis of Foil Journal Bearings with Backing Springs

Gas-lubricated foil journal bearings are simple, in construction, lightweight and well suited for high-temperature applications in turbomachinery. Hearing stiffness is governed primarily by the foil flexural stiffness. The bearing consists essentially of thin overlapping circular metal foils, one end of which is cantilevered to the bearing housing and. the other end rests on an adjacent foil.

An analysis of gas-lubricated foil bearings is presented with a specific type of backing spring used under the foils to control bearing preload, and stiffness. The backing spring acts like, an elastic foundation tinder the foil and radically changes the hydrodynamic pressure distribution generated in the gas film. The pressure distribution is obtained by simultaneously solving the compressible Reynolds equation and. the elasticity equations governing the compliant bearing surface, consisting of foils and backing springs. An iterative scheme is used, to obtain pressure distributions for heavily loaded cases, involving extensive computation, because of the sensitivity of pressure solution to small changes in film thickness distributions attributable to the compliant bearing surface. Pressure distribution, film thickness, bearing load capacity, iterative solution convergence characteristics and bearing power dissipation are presented as a function of journal eccentricity.     

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.     

表面织构动压滑动轴承油膜力解析模型

提出一种求解表面织构动压轴承油膜力的解析模型。基于Sommerfeld油膜边界,通过分离变量的方法,求解表面织构动压滑动轴承二阶偏微分Reynolds方程,得到表面织构动压滑动轴承油膜压力解析式。以圆形凹坑轴承为例,在油膜区域通过积分求得织构轴承的油膜力,分析织构参数对油膜压力的影响,研究发现,表面织构位于收敛区域(升压区)的轴承,其润滑与承载性能优于表面织构位于发散区域(降压区)的轴承、全织构轴承以及光滑轴承。对比了提出的解析模型与FDM和CFD模型在不同长径比和偏心率下的计算结果,结果表明,提出的解析模型能准确地描述表面织构动压滑动轴承的油膜力,且计算结果同FDM和CFD模型计算结果基本一致,验证了该模型的正确性。