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.     

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.     

Direct solutions for normal depths in curved irrigation canals

The normal depth is an important hydraulic element for canal design, operation and management. Curved irrigation canals including parabola, U-shaped and catenary canals have excellent hydraulic performance and strong ability of anti-frost heave, while the normal depths in the governing equations of the current common methods have no explicit analytical solution. They are only indirect methods by using trial procedures, numerical methods, and graphical tools. This study presents new direct formulas for normal depth in curved irrigation canals by applying for Marquardt method. The maximum relative error of the proposed formulas is less than 1% within the practice range by comparative analysis, and they are simple and convenient for manual calculations. The results may provide the reliable theoretical basis and useful reference for the design and operation management of irrigation canals.     

Normal and critical depth computations for egg-shaped conduit sections

This technical note presents regression analysis based models to compute the normal and critical depths for an egg-shaped conduit section recommended by Indian Standard Code of Practice IS–4880 (1976) [13]. The consistency of the models is checked through certain application examples. It is found that the estimated normal and critical depths agree well with the actual values computed from the fundamental equations.     

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%.     

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.     

蛋形耐压壳设计与分析

基于蛋壳几何学特性,开展了蛋形耐压壳结构设计与性能分析。根据鹅蛋形状扫描、宏观尺寸统计试验,研究蛋壳圆度、体积、表面积及蛋形系数分布规律,建立体积方程、表面积方程及蛋形函数;设计了4 km水深蛋形耐压壳,并定量分析其安全性、储备浮力、空间利用率、水动力学特性等性能;采用正交试验,研究长轴、短轴、厚度对蛋形耐压壳性能影响规律。结果表明,鹅蛋壳为高度对称结构,其蛋形系数符合均值为0.69的正态分布;蛋形耐压壳具有良好的综合性能,其中厚度是影响强度的重要因素,长轴次之,短轴最小;长轴是影响屈曲的重要因素,厚度次之,短轴最小;厚度是影响浮力系数重要因素,短轴次之,长轴影响最小;长轴是影响空间利用率的重要因素,短轴次之,厚度影响最小;水动力学特性主要受短轴影响。     

Statistical modeling of the residual life of an oil and gas pipeline under alternating pressure

According to a deterministic formula, using the method of statistical modeling, it was found that the residual life of an oil and gas pipeline has a lognormal distribution, where the input arguments: Paris’ coefficients, the annual number of cycles, the diameter and the pipeline wall thickness, the initial and critical crack depth, and the maximum and minimum stresses are subject to the normal law. According to these data, limiting safe operation lifetimes of the pipeline sections analyzed are determined.     

高效深磨中磨削温度和表面烧伤研究

介绍了一种高效深磨的磨削热模型——圆弧热源模型，该模型和直线倾斜平面模型相比改进了温度的预测；给出了圆弧热源磨削温度的积分公式和量纲一温度计算式；详细分析了热流量，推导了工件、砂轮、磨削液和磨屑的对流因子计算公式，在此基础上给出了最大接触温度的计算公式；使用J形热电偶测量了磨削接触面接近磨削烧伤时的最高磨削温度和磨削液沸腾的温度。实验结果与理论计算值对比表明，测量温度与理论计算温度有极好的一致性。     

Semi-regular polygon as the best hydraulic section in practice (generalized solutions)

The best hydraulic section is usually used as a guide or starting point in open channel design. The semi-circle and semi-regular polygons such as semi-square, semi-hexagon and semi-octagon have the minimum wetted perimeter for a given area, and consequently are the best hydraulic sections from the hydraulic point of view.This study introduces two types (Type I and Type II) of semi-regular polygons as the best hydraulic sections. Both of the sections have the same wetted perimeter and area and thus are equally efficient. However, Type I semi-regular polygon with flat bottom is suitable when excavation depths are shallow, and Type II semi-regular polygon with angled bottom is used when deeper cuts are needed. In this research, general solutions of the normal depth are also presented for Type I and Type II semi-regular polygon sections.     

单点线啮合齿轮齿厚测量尺寸研究

渐开线齿轮的齿厚测量尺寸通过测量公法线长度控制。但单点线啮合齿轮中大齿轮为一个大负变位的齿轮,渐开线部分较短,公法线无法测量。当单点线啮合齿轮中大齿轮模数较大时,测量法线长度有困难。提出了两种大齿轮齿厚测量方法：测量法线长度或测量J点（渐开线齿廓曲线与过渡曲线之间的交点）法向齿厚与齿高,分别用于中小模数和大模数单点线啮合齿轮齿厚的控制。推导了测量尺寸计算公式,并通过实例进行了验证。     

快速控制反射镜两轴柔性支撑平台刚度优化设计

基于椭圆弧柔性铰链兼顾了直梁型柔性铰链运动范围大和圆弧型柔性铰链运动精度高的特点,设计了基于椭圆弧柔性铰链的二维快速控制反射镜系统两轴柔性支撑平台。为使柔性支撑平台快速响应性好,即使其低阶固有频率最大化,对该柔性支撑平台进行了结构优化设计。理论推导了单个柔性铰链最大刚度与许用应力、转角和铰链参数的理论计算公式。然后,采用集总参数的分析方法,得出了两轴柔性支撑平台低阶最大固有频率的理论计算公式。由公式可知:在转动惯量一定的情况下,低阶固有频率最大化即为工作方向刚度最大化。最后,通过有限元仿真和实验检测验证了理论计算的准确性,得到的结果显示:柔性支撑平台的最大固有频率和最大应力的理论值与仿真值的相对误差小于5%,平台工作刚度的理论值与仿真值、实测值的相对误差分别为3.86%和5.75%。仿真和实验结果表明:利用本文推导的理论公式进行柔性支撑平台刚度优化设计,既可以满足工程设计要求,又能省去繁杂的有限元计算。     

圆筒形件不用压边拉深时的皱曲预报

在建立皱由模型的基础上，根据压缩塑性失稳临界载荷公式，导出圆筒形件不用压迫拉深时的皱曲临界切向压应力表达式。由不皱曲条件给出不皱曲的判定式，以及由皱曲确定的极限拉深系数。     

板坯形状对方截面无模旋压轴向可旋深度的影响

利用实验方法对比了方形和圆形板坯形状对方截面无模旋压轴向可旋深度的影响,并对其影响机理进行了理论分析。首先采用确定初始步长的方法推导了可无限扩展的方截面旋轮路径公式,在此基础上分别模拟了方形和圆形板坯的无模旋压过程,并对模拟结果进行实验验证。然后提出了轴向可旋深度的评估方法,并以此为判据,对比分析了同轴向旋压深度下圆形和方形板坯工况的后续可旋性,发现方形板坯工况优于圆形板坯工况,进而揭示其机理为：方形板坯工况旋压过程中剩余法兰形状与旋轮路径切合性较好,促进了金属径向流动均匀化。     

椭圆导角混合柔性铰链的设计计算与性能分析

为满足柔顺机构的大柔度要求,设计了一类新型椭圆导角混合柔性铰链。首先,以卡氏第二定理为基础推导了柔度和回转精度的计算公式,在参数的极限条件下,椭圆导角结构演化出其他三种铰链形式：直圆导角、椭圆直圆和直圆柔性铰链,使得多种柔性铰链的柔度和回转精度的计算公式合并在一组方程中,通过有限元分析验证了计算公式的正确性。其次,讨论了结构参数对柔度、回转精度和柔度精度比的影响趋势,分析结果表明,柔度与回转精度随参数的变化趋势具有相反性,且减小最小厚度是提高柔度的最佳方式。再次,比较了所提四种柔性铰链的性能,椭圆导角混合柔性铰链具有最大的柔度但回转精度较低,而直圆柔性铰链具有较高的回转精度且综合性能也较优越,但柔度最小。最后,对椭圆导角和直圆柔性铰链进行了应用研究,研究结果表明,椭圆导角混合柔性铰链在回转能力和应力水平方面具有显著优势。     

高强度铝合金的腐蚀损伤分布规律研究

在飞机大修及外场维护中所检查到的铝合金翼梁缘条腐蚀损伤数据的基础上，利用数理统计的方法，对飞机结构高强度铝合金件在机场使用到一定日历年限后的最大腐蚀深度的统计规律进行了分析研究，建立了高强度铝合金结构件的腐蚀损伤失效模型及统计分布函数。统计结果表明：飞机结构使用到某一日历年限时，最大腐蚀深度较好地服从正态分布规律，在飞机维修工程应用中利用此分布规律可估算铝合金结构件的最大腐蚀深度。     

从单自由度系统衰减响应分离与辨识粘性与干摩擦混合阻尼的方法

针对正压力随位移成正比的干摩擦与粘性混合阻尼单自由度振子,从其位移自由振动响应导出了分离和辨识粘性阻尼比与干摩擦阻尼因子的理论公式,并通过数值仿真例子对公式进行了验证。结果表明,在无测量噪声条件下,本文所提出的公式是理论上的精确表达式。其数值仿真例子的参数估计结果精度非常高,完全能够满足科学研究与工程实际的需要。     

局部共轭原理及其在弧齿锥齿轮切齿计算中的应用

本文论述研究局部共轭问题的微分邻域方法。应用“密切抛物面”原理得出了调整具有滚切修正机构的弧齿轮铣齿机的全部切齿计算公式。所得出的公式可用于编制加工弧齿锥齿轮的电子计算机程序或人工用计算卡。关于由相对运动参数计算共轭法曲率的公式,目前已有多种类型[2][3][10][11][15]。为了便于工程界应用,本文另用常见的方法对于所采用的Baxter的公式给予了严格的证明,并补充了必须的计算共轭齿面的相对运动速度的普遍公式。     

实体法铣削仿真效率改善及应用算法

轴向切削深度和径向切削宽度是铣削仿真模型求解的几何边界条件,也称为啮合几何参数。根据对啮合参数提取的三类途径的比较,针对直接布尔操作途径仿真效率低的问题,运用集合论描述了实体法铣削仿真中模拟材料去除的布尔运算过程,从时间复杂性角度分析影响实体法铣削仿真效率的因素,提出改善仿真运行效率的4种途径;在此基础上,从几何造型和切削过程两方面给出在仿真计算位置处布尔运算次数由4次减少为1次的可行性分析,提出在简化布尔运算次数情况下的切削几何边界条件的识别和判断算法,对判断算法的有效性和减少布尔运算的时间复杂性进行分析、给出在铣削力仿真中的应用示例,并说明应用范围,从而在保证切削几何边界条件准确提取的同时提高仿真效率,为铣削力等仿真模型的求解奠定基础,推动相关物理仿真研究成果在工程实际中得到切实应用。     

三次设计中望目特性信噪比的讨论与改进

以实例说明了三次设计的望目特性噪比计算式在工程应用中的不足,提出了明确目标和模糊目标两种望目特性信噪比的修正计算式,通过实例表明了望目特性信噪比的修正计算式的实用性,以便在工程实际中推广使用。