Performance of finite journal bearings in non-laminar lubrication regime

Fluid dynamic lubrication of journal bearings in a superlaminar regime, ie a transition or turbulent regime, is the subject-matter of this study.Results obtained by solving an appropriately modified Reynolds bidimensional equation have been put in the form of operating diagrams which allow the correct design of journal bearings in real conditions of flow     

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.     

球面螺旋槽动静压气体轴承动态特性分析

以半球螺旋槽动静压气体轴承为研究对象,建立球面动静压混合气体轴承的非线性动态润滑计算分析数学模型,采用偏导数法推导出扰动压力控制方程;在广义坐标系下,采用有限差分法对扰动压力控制方程离散化,推导出扰动压力的差分表达式;推导出半球螺旋槽动静压气体轴承刚度和阻尼系数与扰动压力之间的关系表达式;采用VC++6.0编制程序,数值计算出三维微气膜的瞬态扰动压力分布、非线性气膜力及动态刚度系数和动态阻尼系数。研究转速、偏心率及供气压力对气膜动态特性系数的影响规律,结果表明:随着转速、偏心率及供气压力的增大,气膜刚度和阻尼系数均有不同程度的变化。     

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...     

多油叶轴承油膜动力特性系数的计算方法

刚度系数和阻尼系数是反映滑动轴承动力响应特性的重要的特性系数。对于以液体为润滑介质的多油叶轴承,本文给出了其动力特性系数的算法,采用数值方法进行了算例计算。     

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.     

A simple sixth order numerical method for solving the Reynolds equation

A numerical iterative method is given for the solution of the Reynolds equation subject to separable boundary conditions. The iteration error for a given eigenfunction is sixth order in the step size. The method has been tested in the case of the finite exponential bearing pad for which exact analytical solutions are available. The dimensionless load capacity per unit width, W, can be calculated to 0.1% accuracy if ten terms are used in the sum for W. Only the first five terms need be calculated using the iteration, thereafter, analytical approximations given in the article may be used. Not more than twenty steps are needed in any given iteration to obtain the accuracy stated above.Calculations of the dimensionless load capacities of plane bearings show that the method is at least one order of magnitude faster than the method based on a two-dimensional rectangular array of points. The superiority is even more marked when calculations are made for a family of plane bearings having the same inclination but different breadth/length ratios.     

考虑扰动频率的可倾瓦轴承扰动压力雷诺方程数值模拟

考虑扰动频率的影响,建立流体动压润滑可倾瓦轴承扰动压力雷诺方程。针对目前可倾瓦轴承有限差分数值算法不易联立求解等问题,提出基于PDE工具箱有限元数值求解方法。理论分析和计算结果均表明,扰动压力是轴承参数、静态工作点参数和扰动频率的函数,扰动压力与扰动频率密切相关;扰动频率为0时,复数域扰动压力虚部为0;随着扰动频率的增大,扰动压力实部变化不大,虚部随之增大。     

Elasto-hydrodynamic lubrication analysis of partial arc journal bearings

Centrally loaded partial arc bearings having deformable bearing surfaces have been analysed. The coupled Reynolds equation satisfying the pressure field in the fluid and the three-dimensional elasticity equations governing the deformations in the bearing lining are solved simultaneously using the finite element method. The steady state solution for the coupled problem is obtained by using a doubly nested iteration scheme which determines the positive pressure field in the fluid film and the orientation of the load line. The influence of bearing deformation on the load capacity, attitude angle, friction coefficient parameter and oil flow are reported for 60° and 120° partial arc bearings. The analysis is extended for lubricants having pressure-dependent viscosity     

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.     

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。     

速度对三油楔滑动轴承轴心位置及摩擦力的影响

根据全收敛楔三油楔轴承模型建立了该轴承的油膜厚度方程,并利用Reynolds方程建立了油膜摩擦力矩的计算式,研究了轴旋转速度对轴心平衡位置和摩擦力的影响。通过对润滑状态的模拟,得出:随着速度的增大,偏心距和偏心方向呈非线性变化的趋势,变化速度逐渐减缓,最终趋于稳定;速度与摩擦力之间也是一种非线性关系,在启动的瞬间尤为明显,但在正常运行时可视为线性关系。     

Adaptive multilevel method for the air bearing problem in hard disk drives

An adaptive grid-generating algorithm is constructed and integrated with the multigrid method to form a numerical scheme that suits slider air-bearing simulation of hard disk drives. The relative truncation error, a by-product of the multigrid method, is used in grid adaptation criteria. Finer meshes are constructed over nodes of the current finest grid where the relative truncation error exceeds a predetermined tolerance. The union of these finer meshes forms a new level of grid, which may not cover the entire domain of the coarse grid underneath. The final grid system thus constructed is composed of levels of uniform grids with decreasing mesh sizes. This composite grid structure incorporates with numerical resolution as needed and efficiency of computation. A shaped rail, negative pressure slider is used to demonstrate the effectiveness of this numerical scheme. Compared with the traditional multigrid method, the proposed adaptive multilevel method can significantly reduce the computation work for achieving the same level of accuracy.     

考虑空穴因素的动载滑动轴承动态特性分析研究

基于JFO理论 (Jakobsson,Floberg ,Olsson)提出的质量守恒边界条件 ,对二维动载滑动轴承的线性稳定性在考虑空穴因素影响的条件下进行分析研究 ,建立相应的模型及方程 ,进而求得动力特性系数 ,以便进一步更准确的考察其稳定性。最后 ,对一个 36 0°的普通圆柱动载径向轴承进行实例计算 ,计算结果显示和实验测量数据吻合的较为一致。     

基于Reynolds边界有限宽径向轴承实用计算方法

提出了一种基于Reynolds边界有限宽径向轴承的实用计算方法。该方法是将Fuller用电模拟方法得到的离散性端泄系数首次用函数表示,并采用无限宽径向轴承按Reynolds边界条件得到的解析解答。在此基础上建立了有限宽轴承承载量系数公式,它避开了文献中轴承承载量系数的数值计困难。结果表明:利用本文中已建立了轴承承载量系数公式及文献中摩擦因数的公式,能更方便得到有限宽轴承摩擦因数的变化规律性;本文的求解方法、求解过程简单、方便并且具有实用精度;计算得到的端泄系数、承载量系数及摩擦因数与相应文献报道的结果十分逼近。     

Theoretical characteristics of hydrodynamic journal bearings lubricated with soybean‐based oil

Vegetable‐based oils are not only biodegradable but also environmentally advantageous, and the range of lubrication applications offered by them continues to grow. Recently, vegetable‐based oils have been combined with synthetic esters to produce modified vegetable‐based oils. This paper presents an investigation of the theoretical characteristics of hydrodynamic journal bearings lubricated with non‐Newtonian soybean‐based oil. The soybean‐based oil was mixed with synthetic esters and silicone oil. The relationship between the shear stress and shear strain rate of the oil was obtained experimentally. The time‐dependent modified Reynolds equation including non‐Newtonian effects was formulated for short circular journal bearings. The perturbation technique was applied to the Reynolds equation to obtain zero‐ and first‐order pressure equations. The finite difference method was used to calculate the pressure distribution numerically. The static and dynamic characteristics, such as pressure distribution, Sommerfeld number, attitude angle, and spring and damping coefficients, were obtained numerically. It was found that the nonlinear factors of the non‐Newtonian soybean‐based oil strongly affected the performance characteristics of the journal bearings.