基于不同差分格式的硬盘气膜润滑方程数值求解

为提高计算效率与计算精度,采用不同差分格式求解硬盘的磁头/磁盘界面气膜润滑方程,分析不同差分格式对磁头/磁盘界面气膜润滑压力分布模拟结果的影响。给出中央格式、上风格式、混合格式、QUICK格式、指数格式、乘方格式6种差分格式相应的离散方程格式,选取气膜润滑方程的线性流率（LFR）模型进行压力模拟,并与精确解进行比较。结果表明：6种差分格式都能够模拟出磁头滑块的压力分布情况,且当网格密度足够大时,得到的数值解与精确解基本一致;指数格式在不同网格密度下,均具有很高的稳定性,较之其他格式计算效率高,模拟效果更好;当网格密度足够大时,中央格式计算效率高,优于指数格式。     

螺旋槽干气密封数值模拟网格独立性分析

对干气密封性能进行数值模拟时,计算网格的独立性非常重要。以螺旋槽干气密封为例,研究网格层数对干气密封数值模拟结果的影响。选择相同面密度的网格,在保证其正交质量的前提下,以端面开启力和气体质量泄漏率的相对变化率作为网格独立性检验的参考量,分别通过增加螺旋槽内膜厚和非槽区膜厚网格层数,考察网格层数对螺旋槽干气密封数值模拟结果的影响。结果表明:槽深为5~9μm,非槽区膜厚为1~6μm时,非槽区膜厚网格层数对数值模拟结果的影响明显大于槽内膜厚层数;螺旋槽内膜厚网格为每微米1层,对应非槽区膜厚网格层数分别为7、8和10时,开启力和气体质量泄漏率的相对变化率均分别低于2%、1%和0.5%。     

基于拟动力学的航空发动机主轴滚子轴承热弹流润滑分析

以D1842926航空发动机主轴滚子轴承典型工况为算例,基于拟动力学分析结果,获得滚动体与套圈之间的接触微区运动和受力状态,分别用Hamrock-Dowson(H-D)拟合公式,Wilson-Sheu(W-S)热修正公式和热弹流数值法得到最小膜厚,并与试验测试数据进行了对比,结果表明,H-D最小膜厚误差非常大,W-S热修正最小膜厚比H-D误差要小,但误差仍在40%以上,文中数值结果与试验数据较为一致,误差10%以内;对比不同速度下三种算法的最小膜厚分布,低速时三者较为一致,随着速度的提高,H-D最小膜厚误差越来越大,而W-S最小膜厚在速度增大到一定程度后反而降低;随着径向载荷的增大,润滑膜压力增大,膜厚减小,两端的压力略高于中间;随着转速增大,润滑膜膜厚增大,压力基本没有变化。     

基于Elrod算法的线接触乏油热弹流润滑分析

为研究中低速、中等载荷工况下不同供油条件对接触区润滑特性的影响,假设润滑剂分别为Newton流体和Ree-Eyring流体,建立考虑供油条件的线接触热弹流润滑模型。采用Elrod算法,将入口供油量作为输入参数,求解接触区油膜压力、膜厚和油膜温度的完全数值解。结果表明:随着入口供油量的降低,接触区入口气液界面位置逐渐向Hertz接触区移动;相同供油条件下,随着速度和载荷的增大,入口气液界面位置逐渐向Hertz接触区移动,乏油程度增加;随着供油量的增加,中心膜厚和最小膜厚也相应增加,且中心膜厚更易受供油量的影响;在乏油润滑条件下,Newton流体计算得到的油膜温度明显高于Ree-Eyring流体;随供油量的增加,Ree-Eyring流体的油膜最高温度增加,而Newton流体的油膜最高温度有先降低后增加的趋势;对于给定的工况,当入口等效供油膜厚接近该种工况下接触区处于充分供油状态下的最小膜厚时,接触区内的最高温升是相对最小的。     

指数率流体热弹流润滑分析

应用多重网格技术,求得了指数率非牛顿流体线接触热弹流润滑的数值解,分析了油膜压力、厚度和温度等随流变指数、速度参数、滑滚比及载荷参数的变化关系,并与相同工况下的等温解进行了比较。结果表明,随着流变指数的增加,油膜厚度和温度、入口处的当量粘度、最小膜厚、中心膜厚和最大温升均增大,而油膜压力和摩擦因数的变化较小。指数率流体弹流润滑问题的热效应不可忽略;与压缩功项相比,油膜能量方程中的热耗散项对温度的影响最大。同时,无量纲速度参数、滑滚比和载荷参数等均影响热弹流润滑特性。     

网格数对有限差分法解雷诺方程的影响

利用中差分格式将雷诺方程离散成为线性方程组,根据Neumann引理得到中差分格式下雷诺方程的精确解。根据泰勒展开公式计算中差分格式下的准确解与解析解之间的误差,并分析该误差与网格数目之间的关系。根据差分矩阵的无穷范数计算运用迭代法及中差分格式求解雷诺方程的算法复杂度下界为O(N³)。根据无穷范数和实际测试分析真实误差、迭代误差与网格数目之间的关系。结果表明,真实误差要远大于迭代误差,两者之间的比值与网格数目的平方呈强烈的线性关系。     

陶瓷球轴承的热弹流润滑分析

建立陶瓷球轴承热弹流润滑的数学模型,利用多重网格法和逐列扫描法,得到陶瓷球轴承的点接触热弹性流体动力润滑完全数值解,并与普通轴承计算结果进行比较。结果表明:转速与载荷会对陶瓷轴承的接触区的压力、膜厚、温度产生影响,其中随着转速的增加,最小膜厚增加,摩擦因数减小,滚动体表面温度下降,而随着载荷的增加,最小膜厚减小,摩擦因数增大,滚动体表面温度上升;在相同的工况参数下,陶瓷球轴承的油膜压力低于普通轴承,膜厚高于普通轴承,轴承内圈、滚动体、中层油膜的温升小于钢质轴承,因而陶瓷轴承的润滑性能更好,使用寿命更长。     

接触固体曲率半径对非稳态热弹流润滑的影响

研究接触区的当量曲率半径对弹流油膜性质的影响,利用多重网格法求得非稳态弹流润滑问题。得到了接触固体两种等效曲率半径下的热弹流润滑数值解。数值模拟的结果显示最小膜厚的变化与Hamrock和Dowson的点接触弹流润滑的最小膜厚公式一致。在其他参数不变的情况下,曲率半径增加一倍,油膜的压力大约减小一倍,其第二压力峰变钝变宽;而膜厚增大,但其增加的幅度相比压力的增加要小很多;而温度的变化减小。     

全膜点接触热弹流的油膜特性及最小膜厚热修正公式

采用简化的全膜点接触热ＥＨＬ模型及其完全数值的求解方法，通过对多种工况下数值结果的分析，本文系统地总结了全膜点接触热ＥＨＬ油膜压力及油膜厚度在各种工况参数下的变化规律。首次提出了点接触热ＥＨＬ的最小膜厚公式，该公式考虑了速度、载荷及滑滚比的影响，便于工程应用。     

弹流中心膜厚的一个新公式——兼评Грубин公式

本文在较宽的工况范围内对线接触弹流进行了完全的数值计算,根据计算结果提出了一个适用于各工况的统一的中心膜厚计算公式,这与作者早先提出的最小膜厚公式配成一套。同时也指出了公式和Dowson-Toyoda公式的局限性和它们所适用的范围。     

An implementation of the robust inviscid wall boundary condition in high-speed flow calculations

Boundary condition is one of the major factors to influence the numerical stability and solution accuracy in numerical analysis. One of the most important physical boundary conditions in the flowfield analysis is the wall boundary condition imposed on the body surface. To solve a two-dimensional Euler equation, totally four numerical wall boundary conditions should be prescribed. Two of them are supplied by the flow tangency condition. The other two conditions, therefore, should be prepared additionally in a suitable way. In this paper, four different sets of wall boundary conditions are proposed and then applied to solve high-speed flowfields around a quarter circle geometry. A two-dimensional compressible Euler solver is prepared based on the finite volume method. This solver hires three different upwind schemes; Steger-Warming’s flux vector splitting, Roe’s flux difference splitting, and Liou’s advection upstream splitting method. It is found that the way to specify the additional numerical wall boundary conditions strongly affects the overall stability and accuracy of the upwind schemes in high-speed flow calculation. The optimal wall boundary conditions should be also chosen very carefully depending on the numerical schemes used to solve the problem.     

Dynamical stability of journal-bearing devices through numerical simulation of thermohydrodynamic models

This paper considers the numerical solution of a transient thermo-hydrodynamical model for a journal-bearing device is considered. The hydrodynamical model assumes that both bush and shaft are rigid bodies and it considers dynamical phenomena in the shaft-lubricant film system through a transient two-dimensional Elrod-Adams model. The proposed model also takes into account thermal effects in the lubricant film, bush and shaft. The dynamical model is solved by a combination of different techniques for spatial discretization (including finite element, finite volume and boundary element methods) and the resulting DAE-like system is integrated with implicit schemes.The developed algorithm is then applied to analyze the stability of steady solutions of the thermo-hydrodynamical model. Existing results based on analytical solutions for simplified configurations are revisited in order to extend stability predictions to more general conditions. This analysis allows to elucidate the role of different parameters on stability, including oil supply and thermal transfer conditions in finite width journal-bearing devices.     

Hydrodynamic performance of lubricated journal bearings with axial and spiral oil feedings

The performance characteristics of hydrodynamically lubricated journal bearings are dealt with in this paper, thermal aspects are considered and axial groove and spiral oil inlet feeding conditions are assumed.A finite journal bearing was assumed and, by the aid of numerical solutions, the Reynolds equation coupled with the energy equation in finite difference form could be solved to give an adiabatic solution. A specially devised computer program has been adopted to compute the hydrodynamic pressure and temperature distributions and to predict the performance characteristics under isothermal and thermal conditions.The results indicated that axial oil feeding allows a higher load-carrying capacity at a lower frictional resistance compared with the spiral oil inlet.     

一种分析薄壁箱梁剪滞效应的高精度法

考虑了三个不同的剪滞纵向位移差函数以反映薄壁箱梁不同宽度翼板的剪滞变化幅度 ,提出一种分析薄壁箱梁剪滞效应的高精度法。应用能量变分原理 ,导出了箱梁受横向荷载作用下的剪滞控制微分方程和边界条件 ,获得闭合解 ,通过高阶有限条法计算验证了本文方法的正确性。并探讨了不同纵向位移差函数对剪力滞的影响。     

Finite element modeling discretization requirements for the laser forming process

Due to high efficiency and accuracy, 3D finite element modeling has been an effective tool to analyze the laser forming process. The discretization of a given finite element model has a significant effect on the results of simulation. To reduce the lengthy computational time caused by excessive degrees of freedom while insuring an accurate solution, the minimum discretization requirements of finite element modeling of the laser forming process need to be determined. This paper investigates the effects of temporal and spatial discretization on the final angular deformation of the plate. Numerical results under different discretization conditions are examined. The minimum requirements for discretization of 3D finite element models for laser forming are established by examining the convergence of the numerical solutions with increased discretization. The numerical results are in good agreement with the experimental measurements.     

The Application of a Gradient Method in the Finite Element Solution of Elastohydrodynamic Problems

A gradient method is described which can be used to solve problems in elastohydrodynamics. The method involves the minimization of an error function, and is compatible with such numerical schemes of solving continuum problems as the finite element or the finite difference method. A finite length slider bearing is used to illustrate the method, and numerical results for the elastohydrodynamic pressure distribution are presented.     

受扭圆轴弹性屈曲分析时边界条件的不一致性

受扭圆轴广泛存在于机械结构中。对于细长圆轴,当其两端受扭矩作用时将发生弹性屈曲。在两端简支条件下,文献中已有的解析解和基于能量法的数值近似解结果不吻合,原因是人们没有注意到边界条件的不一致性。笔者用有限元法进行了分析,给出了单元的线性刚度矩阵和增量刚度矩阵。分析发现:由能量变分方程所得到的应自动满足的自然边界条件———力边界条件和得到解析解的二阶平衡微分方程所应满足的力边界条件两者在简支情况下是不一致的。考虑到与解析解的力边界条件的等效性后用有限元数值分析方法得到的结果与解析解极为吻合。有限元解与解析解间的差异,有时并非单元性能的原因或计算误差造成的。     

平面非定常温度场的有限元素法

用有限元素法求解非定常温度场,如大家所知,在空间量纲方面,应用有限元素离散;而在时间量纲方面,通常仍采用有限差分离散。文中分析和比较了时间量纲方面用克兰克-尼可松（Crank-Nicholson）和伽辽金（Galerkin）离散的两种不同计算格式。着重讨论了初始短时精度,指出两种格式的适用条件,并以实例作了验证。对非线性边界条件下问题的求解,建议采用一种能以较快速度,经少数几次迭代就容易达到一定精度的“等正切”逐次逼近法最后还讨论了计算时步长的选择,如何以最少的机器时间求得精确数值解等问题。     

A thermohydrodynamic solution for finite journal bearings under dynamic loading conditions

A numerical solution is developed for the equations governing the thermohydrodynamic flow in a finite journal bearing. Both wedge and squeeze pressure contributions are considered. Lubricant viscosity is taken as a function of the temperature distribution in the fluid film. Computer programs are devised to obtain numerical solutions for the prescribed journal centre locus. Thermal effects are shown to be pronounced in laminar flow bearing under dynamic loading conditions.     

Numerical solution, simulation and testing of the thermal dynamic characteristics of ball-screws

This research focuses on the characteristics of how a ball-screw changes its temperature corresponding to the periodic change of the end-most heat source. Based on the theory of heat transfer, this paper supplies a numerical solution to the non-homogeneous equation of heat transfer through the group explicit (GE) finite difference approach. The temperature distribution for the ball-screw at different times and directions is shown. By simulating and modeling the temperature field and thermal deformation of the ball-screw under periodically varying heat sources, this paper describes the thermal dynamic characteristics of the ball-screw under such conditions. By testing the thermal dynamic characteristics of the ball-screw, the numerical solution is validated.