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。     

基于差分格式的气动制动系统管路研究

通过采用一阶迎风差分格式、中心差分格式和二阶Lax-Wendroff格式对气动制动系统（PBS）中管路部分进行精度分析。根据气体连续方程、运动方程和能量守恒式,在时间和空间上划分差分网格建立管路动态模型。为了提高研究精度,在建立管路动态模型的过程中涉及了管路的热交换和可压缩性等因素,运用MATLAB软件对气体的双曲型偏微分方程进行数值计算,并且由虚拟管路小孔模型作为管路动态模型数值计算的边界条件。通过分析3种格式下管路中的状态变量与时间的关系,选择精度较高稳定性较强的差分格式,对车辆气动制动系统的管路部分的设计和研究具有指导意义。     

基于层次模型的雷诺方程自适应变步长差分算法研究

针对传统有限差分法求解雷诺方程效率低和灵活性差等问题,提出一种基于网格层次化思想的差分算法来求解雷诺方程模型。首先建立变步长雷诺方程差分计算模型,然后提出基于压力梯度与区域积分值的区域细化算法,最后基于层次化思想给出自适应变步长差分算法的求解流程。该方法采用网格层次化思想将初始粗网格进行不断的校正,模拟构造出能满足目标的自适应网格,有效地避免了传统等分网格方法为提高求解精度而不断盲目细化风格的问题。通过不同模型的计算结果表明:基于层次化思想的自适应变步长差分算法相较传统的等分网格有限差分算法,能够用较小的自由度计算得到较好的表达油膜压力的曲面,在求解效率和灵活性上有显著提升。     

基于FINE软件的轴流泵叶轮流动分析及性能预测

应用结构化网格技术和有限体积差分格式并结合k-ε湍流模型对相对坐标系下的三维雷诺平均N-S方程进行求解,对在同一设计工况下的相同流道几何尺寸的两个轴流泵叶轮内部的三维紊流场进行了数值计算与分析,得到其内部流场、压力场的分布情况,预测了水泵的水力性能,据此选出了性能较优的水泵叶轮。     

球面配流副二维稳态压力场的数值求解方法研究

推导出基于球面坐标系的贴体网格生成方程,在贴体坐标系下利用有限差分法迭代求解雷诺方程,得到了球面配流副的二维稳态压力场,在迭代求解网格生成方程过程中利用平均近似的方法将隐式迭代方程转化为显式方程,大大缩短了求解时间。用球面配流副近似平面配流副进行了压力场计算,计算结果与电模拟法的结果非常接近。应用该方法对液压变压器球面配流副进行了压力场计算,计算结果表明,当相邻油口压力接近时过渡区域的压力场分布不能忽略。     

求解磁头/磁盘超薄气膜润滑性能的有效有限差分算法

首先给出超薄气膜润滑的基本方程.通过对方程的分析指出,在纳米尺度下工作的磁头/磁盘具有轴承数很大和剪切流项含有压力的两个特点.提出对剪切流项进行主元迭代求解可压缩气体雷诺方程的新计算方法.在推导出该方法所用的差分公式和误差分析公式基础上,利用这些公式对双轨和多轨两种磁头在5 nm和10 nm下工作压力分布进行计算.计算过程表明该方法对超薄条件下的气膜润滑计算是有效的,该方法能够有效解决大轴承数条件下容易出现失稳的现象,避免计算中数值振荡的发生,成功地将普通有限差分算法用于求解大轴承数的气体润滑数值计算中.计算结果的误差分析表明:该算法对大轴承数气体润滑问题的收敛十分有效,并具有编程简单、计算速度快等优点.     

线接触等温弹流的数值分析

本文用改进的直接迭代法求解线接触弹性流体动力润滑问题,获得了各种工况下具有典型弹流特征的完全数值解。为提高精度,推导应用了高阶有限差分格式;引进了简化压力和φ函数的变换;在对压力的循环修正计算中采用了变松弛因子和分段迭代的技巧;在弹性变形计算中采用了变形矩阵的方法,通过解析方法,避免了奇异积分。幂指数粘压方程的采用,与真实流体的情况更加接近。计算结果表明,本文算法是可行的。     

复合材料开孔层合板有限元网格划分方法研究

对复合材料开孔层合板有限元建模过程中网格划分方法进行量化研究。应用参数化的方法建立多种板宽孔径比、多种铺层比例的开孔层合板模型,逐级调整网格密度,计算单轴拉伸载荷作用下孔边最大应力集中系数。根据有限元结果,结合牛顿插值的数值计算方法,模拟出开孔层合板合理的网格密度划分方程。然后,对该网格划分方程下计算的数值解进行试验验证与解析解验证。结果表明,这种网格密度划分方程能有效地降低计算误差,可以在板宽孔径比大于3的复合材料开孔层合板的有限元计算中广泛使用。     

用多重网格法准确计算弹流润滑膜厚度的方法

应用多重网格法求解稳态等温线接触弹性流体动力润滑(EHL)问题,得到了不同工况下使用不同的差分格式并采用不同的网格时的数值解。分析了对Reynolds方程的楔形项使用不同的差分格式时,数值解随着网格层数增加的变化趋势。结果表明:各种常见工况下,对楔形项无论是采用两点差分还是三点差分,随着网格层数的增加,得到的最小膜厚、中心膜厚、第二压力峰值及其出现的位置都会趋于稳定。由数值解归纳出了准确计算中心膜厚与最小膜厚的经验公式。网格层数较少时,将对楔形项分别采用两点差分和三点差分而得到的膜厚代入该公式,即可求出与网格层数较多时的结果非常接近的膜厚值。     

滑动轴承非线性油膜力的一维直接解法

滑动轴承的油膜力,特别在雷诺边界条件下,并不存在解析解。一般采用有限差分方法或迭代算法求解方 程,因计算量偏大不适合轴承非线性动力分析。针对滑动轴承轴瓦形状比较规则和轴向压力分布较为简单的特点, 把二维变分不等方程降阶为一维形式,并提出一维变分不等方程的直接解法,无需迭代便可求出节点压力及油膜 破裂边界。与二维有限元互补算法相比,直接解法误差小于百分之一,而且其运算时间也仅为其百分之一。     

一种9杆巴氏桁架位置正解的超混沌改进牛顿法

提出非线性方程组全部实数解求解的超混沌改进牛顿法,完成了第33种非平面两耦合9杆巴氏桁架的位置正解问题。结合矢量法和复数法建立该机构4回路的4个约束方程,利用正、余弦三角函数关系增设4变量,建立4个补充方程,从而构造了该机构位置分析的8变量约束方程组。将超混沌序列和改进牛顿迭代法结合,应用超混沌离散系统产生迭代初始点,提出了应用超混沌序列的改进牛顿迭代法求解非线性方程组全部实数解的新方法,完成了该机构的位置分析。给出计算实例,并与其他方法进行了比较,实例表明该方法的正确性和有效性。     

Explicit solution for normal depth of parabolic section of open channels

To obtain the normal depth of parabolic section of open channels, multiple known parameters were incorporated into a comprehensive one by transforming basic equations, and a concept of the non-dimensional normal depth was introduced. The normal depth equations were simplified into a non-dimensional iterative formula that was proved to have a high velocity of convergence. By analyzing the comprehensive parameter and dimensionless normal depth under condition of usually adopted sizes of parabolic channels and through establishing their relationship, the iterative initial value of normal depth was obtained. The normal depth of parabolic channels was acquired by substituting the initial value into the iteration formula. The error analysis was made and a case study was provided as an application example. The case study showed that the iteration formula was very simple, convenient and precise for determining the normal depth of parabolic channels with the maximum relative error of normal depth being less than 0.34% when the ratio of width to depth was between 0.2 and 20.     

Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Iterative solution methods are usually used for solving a variety of Reynolds equations in lubrication analysis due to their simplicity and effectiveness. The objective of this study is to present a robust stopping criterion for iterative methods, by which the iterative process of the methods can be terminated for high execution efficiency without sacrificing the solution accuracy. In this study, the compressible and incompressible fluid Reynolds equations are solved by popular relaxation methods. A very efficient preconditioned conjugate gradient method is also applied in a case for verification. The proposed stopping criterion for iterative methods is based on a coarse-grid truncation error analysis. Three different gridwork groups are required for estimating the truncation errors, which involves only a small amount of additional execution time. In the numerical models examined, the amount of truncation error in a model is insensitive to the gridwork used. It is also found that in a calculation the best prediction of truncation error for terminating the iteration is obtained by using the average fluid film pressure. It is shown that for all the cases tested the proposed stopping criterion can meet the objective stated. The stopping criterion can also be applied when the efficiency of iterative methods is to be compared in solving Reynolds equations.     

A study on the finite element preprocessing for the analysis and design with discontinuous composites

A strategy of finite element (FE) preprocessing of discontinuous fiber or whisker reinforced composite materials for mechanical analysis and design has been treated in this paper. The procedures were based on the calculation of the error in energy norm for global convergence and the traction differential approach at fiber/matrix interface for local convergence. The mesh refinement strategy was intended to theh-based generalized approach using the elongated element at the fiber/matrix interface, which yields significantly different patterns from those obtained by conventional mesh refinement procedures. This difference may have a critical bearing on the subsequent thermo-mechanical properties predicted by the finite element analysis (FFA). It was found that the FE mesh design of adequate element aspect ratio at the fiber/matrix interface results in a much more rapid computational convergence rate than that obtained by the conventional approach.     

One step positive approach for sheet metal forming simulation based on quasi-conjugate-gradient method

In one step inverse finite element approach, an initial blank shape is normally predicted from the final deformed shape. The final deformed shape needs to be trimmed into a final part after stamping, the trimmed area, therefore, needs to be compensated manually before using one step inverse approach, which causes low efficiency and in consistency with the real situation. To solve this problem, one step positive approach is proposed to simulate the sheet metal stamping process. Firstly the spatial initial solution of one step positive method is preliminarily obtained by using the mapping relationship and area coordinates, then based on the deformation theory the iterative solving is carried out in three-dimensional coordinate system by using quasi-conjugate-gradient method. During iterative process the contact judgment method is introduced to ensure that the nodes on the spatial initial solution are not separated from die surface. The predicted results of sheet metal forming process that include the shape and thickness of the stamped part can be obtained after the iterative solving process. The validity of the proposed approach is verified by comparing the predicted results obtained through the proposed approach with those obtained through the module of one step inverse approach in Autoform and the real stamped part. In one step positive method, the stamped shape of regular sheet can be calculated fast and effectively. During the iterative solution, the quasi-conjugate-gradient method is proposed to take the place of solving system of equations, and it can improve the stability and precision of the algorithm.     

基于机构条件数的30m望远镜三镜Stewart平台

从误差传递的角度研究了30 m望远镜（TMT）三镜大型Stewart平台的转动精度。首先,利用奇异值分析Stewart平台速度雅克比矩阵,得出机构条件数与支腿伸长量的关系。利用条件数与系统误差传递系数的关系推导出TMT三镜特殊运动形式下支腿伸长量误差与平台姿态误差的关系,并使用MATLAB优化平台结构参数得出一组优化解。然后,利用ADAMS对之前的理论推导进行仿真验证。最后,利用已知误差传递模型结合精度实验数据进行实验,辨识得出Stewart支腿伸长误差为均匀分布、动平台转动误差向量模为双峰分布。利用MATLAB进行模拟,模拟结果显示：假设支腿伸长误差为0到1之间均匀分布,动平台转动误差向量模的期望会由优化前的5.345 4×10^-4变为优化后的4.272 1×10^-4,优化量约为20%;转动误差分布的两个肩峰相互靠拢且向0点移动。     

Egg-shaped cross section: Uniform flow direct solution and stability identification

The complexity of an egg-shaped cross section makes developing a straightforward formula to calculate the normal depth a challenging task. In this paper, the inadequacy of the power regression based model employed so far for estimating the normal depth in these conduits was presented based on the relative hydraulic sensitivity of structures. A set of precise iterative formulas for the normal depth solution was developed which facilitates the calculation of the normal depth especially using spreadsheets. Also, accurate and direct equations to determine the uniform flow depth in an egg-shaped cross section were obtained by using an alternative regression based model developed according to the concept of the relative hydraulic sensitivity. The maximum relative error associated with the proposed equations compared to the precise iterative formula results is less than 1%. In addition, to design a sewer system especially in relatively steep urban areas, direct formulas were developed to distinguish between sub- and supercritical flow regimes and to categorize the uniform flow stability condition in such channels.     

An automated methodology for performing time synchronous averaging of a gearbox signal without speed sensor

In this paper we extend a sensorless algorithm proposed by Bonnardot et al. for angular resampling of the acceleration signal of a gearbox submitted to limited speed fluctuation. The previous algorithm estimates the shaft angular position by narrow-band demodulation of one harmonic of the mesh frequency. The harmonic was chosen by trial and error. This paper proposes a solution to select automatically the mesh harmonic used for the shaft angular position estimation. To do so it evaluates the local signal-to-noise ratio associated to the mesh harmonic and deduces the associated low-pass filtering effect on the time synchronous average (TSA) of the signal. Results are compared with the TSA obtained when using a tachometer on an industrial gearbox used for wastewater treatment. The proposed methodology requires only the knowledge of an approximate value of the running speed and the number of teeth of the gears. It forms an automated scheme which can prove useful for real-time diagnostic applications based on TSA where speed measurement is not possible or not advisable due to difficult environmental conditions.     

Intelligent dimensional error pre-compensation in CNC grinding using iterative learning approach

This paper focuses on the problem of intelligent compensation of nonlinearly appeared dimensional error in the computer numerical control grinding process. An intelligent error pre-compensation scheme is proposed with intelligent controller, automatic dimensional error measurement, and feedback information. Iterative learning approach is applied to infer the error compensation of the next workpiece machining by using the historical data. The simulation results and the real system input and output responses show that the proposed intelligent error compensation scheme and the iterative learning approach have significant superiority.     

Analysis of heavy duty tilting-pad journal bearing taking into account pad distortion and possible adoption of rubber pad segments

In this work a comparative study has been made between the thermo-hydrodynamic performance of a three shoe tilting-pad journal bearing with rigid and elastic pads subjected to unbalance load. A case study of a bearing adopting three rubber pad segments has also been studied. The distortion of the elastic pad is introduced into the distribution of the film thickness through an iterative scheme to assess its effect on the load carrying capacity of the bearing. A finite element mesh is used to calculate the distortion of the elastic pad while a finite difference mesh is used to calculate the pressure field in the lubricant film. Results have shown a number of interesting conclusions regarding the adoption of rubber pad segments instead of tilting-pads. There is an increase in minimum oil film thickness when using elastic pad or even rubber pad segments compared with rigid pads. Also the maximum pressure and load carrying capacity are not significantly affected.