Calculation method for conjugate depths in quadratic parabolic channels

Quadratic parabolic channels are widely used in irrigation and drainage engineering projects. Up until today there are no an effective method for computing the conjugate depths of quadratic parabolic channels. In this paper, calculation method for calculating the conjugate depths of quadratic parabolic channels was studied. Dimensionless depths were selected to simplify momentum equation for determining conjugate depths. Iterative equation for downstream depth was developed by suitable mathematical transformation on the momentum equation. If one knows dimensionless upstream depth, one can obtain dimensionless downstream depth by using iterative equation. Based on a large number of data of dimensionless conjugate depths, explicit equations with simple form for conjugate depths of quadratic parabolic channels were obtained by running a MATLAB program. Relative error analysis indicates that the proposed explicit equations which are employed to calculate conjugate depths (downstream depth and upstream depth) have high accuracy and wide application range. In the practical range of downstream depth to upstream depth ratio [1, 77.33], the maximum relative error is less than 0.30%.     

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.     

Improvements to solutions for normal depth in multiple sections of tunnels

The normal depth is an essential parameter for the design, operation, and maintenance of open channels. The circular, city-gate crossing and egg-shaped sections are often used in non-pressure tunnels in hydraulic engineering, agricultural irrigation, and sewerage works. However, the equations governing the normal depth in various sections are complicated implicit transcendental equations. In order to improvements the solutions for normal depth in multiple sections of tunnels, a function model is first established for the geometric features of various sections using the mathematical transform method and while considering non-dimensional parameters. Then implement the revised PSO algorithms in MATLAB, and establish three right solution's formulas for the normal depths in different non-pressure tunnel sections through optimization. The error analysis results and project cases show that the established formula has broad applicability. The maximum relative errors of the formula for normal depths are less than 0.07%, 0.04%, and 0.07% in circular, city-gate crossing, and egg-shaped sections, respectively, which are more accurate than the existing formulas. The results of this research may be useful in design, operation, and maintenance in tunnel engineering.     

VC+ +编程计算剃前插齿刀倒棱渐开线的分度圆压力角

运用迭代法和VC + +编程求解剃前插齿刀设计中的重要参数———剃前插齿刀倒棱渐开线分度圆上的压力角α,同时证明了迭代过程的收敛性,并给出了迭代初值的选取原则。     

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.     

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(N^3)。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。     

非线性方程组求解的混沌最小二乘法及平面四杆函数机构综合

机构学问题的数学模型常可化为多元非线性方程组，一般求解多元非线性方程组需要初始值，而初始值的选择是相当困难的；同伦方法不需初始值就能求出全部解，为求解这一问题提供了可行的方法，但需要编写专用的程序，且计算量比较大；本文结合MATLAB6．5．1高级程序设计语言采用简单的最小二乘法迭代，并将非线性方程视为非线性的动力学系统，利用使得系统产生混沌的Julia集的点求解方程的全实数解，而Julia集的点集用二周期逆像函数求得，再在其邻域内求解即可。运用该算法编写了MATLAB程序，对平面四杆机构综合问题进行了研究，从而找到了实现最大精确点时该问题的全部的解，为实际机构的设计提供了多种选择方案，为机构学设计提供了全新的方法。     

混沌最小二乘法及其在机构近似综合中的应用

结合MATLAB6.5.1高级程序设计语言采用简单的最小二乘法迭代,并将非线性方程视为非线性的动力学系统,利用使系统产生混沌的Julia集的点求解方程的全实数解,而Julia集的点集用二周期逆像函数求得,再在其邻域内求解即可.运用该算法编写了MATLAB程序,对平面四杆机构近似综合问题进行了研究,从而找到了实现最大精确点时该问题的全部的解,为实际机构的设计提供了多种选择方案,为机构学设计提供了全新的方法.     

Explicit solutions for critical and normal depths in channels with different shapes

Critical and normal depths are important for computing gradually varied flow profiles and for the design, operation, and maintenance of open channels. A closed-form analytical equation for the normal depth computation can only be derived for triangular channels. For exponential channels, it is also possible to obtain such equations for the critical depth. This is not possible, however, for other geometries, such as trapezoidal, circular, and horseshoe channels. In these channels, the governing equations are implicit and thus the use of trial procedures, numerical methods, and graphical tools is common. Some channels have explicit solutions for the critical and normal depths, while others do not. This paper presents new and improved explicit regression-based equations for the critical and normal depths of open channels with different shapes. A comparison of the proposed and existing equations is also presented. The proposed equations are simple, have a maximum error of less than 1%, and are well-suited for manual calculations and computer programming.     

磁流变抛光回转对称非球面工件精确自定位

为解决磁流变抛光中回转对称非球面工件的高效率精确自定位问题,提出了基于迭代最近点的改进两级定位方法。根据磁流变抛光特性和恒浸深控制要求,确定了磁流变抛光工件非调平自定位原理。针对经典迭代最近点算法应用于回转对称非球面工件定位存在解不唯一及计算效率低的问题,构建初始迭代矩阵实现了位姿唯一的指定性匹配,并提出了空间垂直映射方法,减小匹配点云的规模,提高了计算效率。以此为基础,提出了改进后的两级迭代最近点精确定位方法。最后,以Φ100 mm凹形抛物面熔石英工件为对象进行了抛光实验。实验结果表明:改进两级精确定位方法满足磁流变抛光的定位要求,定位精度在多次实验中均优于9μm,平均定位时间为7.3 min,在保证定位精度的同时提高了工件的定位效率。     

Direct integration of gradually varied flow equation in parabolic channels

The direct integration method is used to compute water surface profiles of gradually varied flow (GVF) in a prismatic open channel. No closed-form solution is available for the GVF equation in the case of general parabolic channels. Open channels with parabolic cross-sections are often a quite good approximation of the real geometry of natural rivers. Technology is also available for constructing this shape of channels. In the present study, by applying the Manning formula, a semi-analytical solution to compute the length of the gradually-varied-flow profile for parabolic channels is developed. The proposed solution uses a single step for the computation of water surface profiles and, as such, provides an accurate and yet simple way to compute GVF flow profiles; thus, it should be of interest to practitioners in the hydraulic engineering community.     

点接触弹流润滑问题的高效直接算法

在复合直接迭代法的基础上,运用分块迭代的思想将方程组降维,通过研究弹性变形影响因子对弹性变形的影响,将压力迭代矩阵由满元阵变为稀疏的带状阵,提出一种新的求解点接触弹流问题的高效直接迭代算法.与复合直接迭代法相比,该算法大大减少了计算量,计算效率至少提高20倍,并且可适用重载工况.将新算法计算结果与Hamrock-Dowson公式计算结果进行比较,并讨论迭代矩阵半带宽与收敛速度、载荷范围、计算精度以及数值稳定性的关系.结果表明,当压力迭代矩阵密度为满阵的22％～25％时,新算法具有最高的计算精度.     

液压往复密封的摩擦特性分析

基于往复式密封的弹性流体动力润滑的数学模型,对影响密封性能的因素进行了综合分析。综合考虑了形变理论、接触力学理论以及流体-固体耦合理论,采用MATLAB数值分析法,通过数学迭代计算完成最终求解。深入研究了润滑油黏度、界面摩擦系数以及密封圈的表面粗糙度对密封性能的综合影响。结果表明:随着耦合界面摩擦系数的增加,接触摩擦力都呈现出增大的趋势;总摩擦力随着粗糙度的增加呈现出抛物线式变化趋势;润滑油的黏度存在一个临界值,当润滑油黏度小于此临界值时,随着润滑油黏度的增加,总摩擦力先增加后降低;当润滑油黏度超过此临界值时,接触摩擦力呈现出单调增加的趋势;润滑油黏度和界面粗糙度的增加会导致流体泄漏的增大。     

配点型无网格法及其迭代求解在导热微分方程中的应用

对配点型无网格法在求解导热微分方程中的应用进行研究,提出配点型无网格法的迭代求解算法,并同有限元法进行对比。结果表明,配点型无网格及其迭代方法易于编程实现,且精度与有限元法相当。采用迭代求解法甚至可以不用形成系数矩阵,求解逐点进行,占用内存空间少。选择适当的松弛因子,松弛迭代相对于 Gauss-Seidel迭代可减少迭代次数。研究表明配点型无网格法及其迭代求解方法在求解大规模工程问题时具有优势。     

平面变形回弹迭代补偿的收敛准则及应用

针对板材平面变形过程中的回弹问题,基于迭代法建立了迭代补偿机制,给出了迭代参量收敛性的判定准则。对于简单应力状态下平板单向拉伸和双向拉伸的弹塑性变形过程,证明了参量轴向长度对迭代补偿机制具有收敛性。对于宽板V形自由弯曲工艺,通过理论和实验验证了弯曲曲率和弯曲角的收敛性。进而,将迭代补偿机制应用于宽板自由弯曲工艺的回弹控制,对曲率和弯曲角分别进行了迭代补偿实验,结果表明,根据每次试验的回弹量,迭代补偿机制可以预测下一次补偿值,使弯曲工艺经过2～3次迭代,就获得了误差小于0.1%的目标曲率和误差小于0.5%的目标弯曲角,收敛速度很快。而且,对于同一材料的同一成形工艺,每次的补偿量只取决于回弹前后的迭代参量差值。     

高精度光学头部位置定位系统

针对头盔式虚拟现实系统中的头部位置跟踪,研究并实现了多摄像机下的高精度光学头部位置定位系统。通过设计初始标定方块来减小系统安装误差,使摄像机按正交方式布置,保持其光轴两两相互垂直。定位过程中以某一摄像机为基准,任意给定目标深度初值;依据摄像机成像模型计算出目标空间位置,再将该计算结果作为其他摄像机的目标深度初值进行循环迭代计算,收敛至给定精度后得到目标三维空间坐标值。最后以3个标记点空间位置为基础,依据其空间关系计算得到目标姿态角。对比实验表明,该定位方法定位精度高、计算速度快,静态位置误差为0.051 cm,动态位置误差为0.088 cm,明显超过电磁跟踪器定位精度;同时该定位系统成本低廉,不受外界金属和电磁环境干扰,可满足虚拟现实系统中高精度头部位置跟踪需求。     

Non-linear analysis of finite hydrodynamic journal bearings in laminar and turbulent flow regimes

The Navier-Stokes equations were modified by adopting the non-linear turbulence theory proposed by Constantinescu to take into account the turbulent stresses. The modified equations were solved by the finite element method using Galerkin's technique and a suitable iterative procedure.The performance characteristics of a finite hydrodynamic journal bearing (aspect ratio b = 1) were studied in terms of the load-carrying capacity, non-dimensional stiffness and damping coefficients and critical journal mass at various eccentricities for Reynolds' numbers up to 13 300. The computed results are compared with those obtained using the twodimensional triangular element formulation and the linearized turbulence theory.     

The effect of fluid inertia on the film pressure between two axially oscillating parallel circular plates with a viscoelastic lubricant

A viscoelastic incompressible fluid between two parallel circular plates separated by a small distance with sinusoidal axial vibration of the top plate including fluid inertia terms was considered. Flow phenomena were characterized by non-dimensional parameters such as the Reynolds number Re and the elastic number S. An iteration method was used to solve the non-linear equations. The effects of Re and S on the fluid pressure were studied.     

加工螺旋槽用盘形铣刀调整参数的迭代算法

研究了加工螺旋槽用盘形成形铣刀调整参数的计算机算法,利用迭代算法得出调整参数的初值,利用计算机模拟刀具廓形,对廓形误差进行迭代修正,从而可获得调整参数的最优值。     

牛顿混沌迭代方法及四杆导引机构综合应用举例

机构学问题的数学模型常可化为多元非线性方程组，一般求解多元非线性方程组需要初始值，而初始值的选择是相当困难的。同伦方法不需初始值就能求出全部解，为求解这一问题提供了可行的方法，但需要培写专用的程序，且计算量比较大。该文结合MATLAB7．1高级程序设计语言采用简单的牛顿迭代法迭代，并将非线性方程视为非线性的动力学系统，利用使得系统产生混沌的Julia集的点求解方程的全实数解，而Julia集的点集用二周期逆像函数求得，再在其邻城内求解即可。运用该算法培写了MATLAB程序，并以平面四杆刚体导引机构综合问题为例进行了运算，找到了实现最大精确点时该问题的全部解，为实际机构的设计提供了多种选择方案，为机构学设计提供了一种迭代新算法。