一种涡旋面轮廓度误差高精度评定算法的研究

为评定涡旋压缩机涡旋齿面轮廓度误差,提出了采用一种基于最小二乘法的逼近优化算法对涡旋面轮廓检测数据进行计算,并将计算结果与德国Zeiss公司UMC 550S型三坐标测量机的计算结果进行比较.最小二乘逼近优化算法与三坐标测量机的计算结果曲线重合度达99％以上,且精度均可达0.0001mm.结果表明了该算法的正确性和实用性,对涡旋面轮廓度误差进行高精度评定具有参考意义.     

基于变尺度教与学算法的DCT换挡毂圆度误差评定研究

针对空间圆度误差评定精度较低以及计算速度较慢的问题,提出了一种变尺度教与学算法的空间圆度误差评定方法。首先,基于误差最小区域原则建立了数学模型和目标函数,随后在标准教与学算法的基础上设计变尺度法教与学算法进行优化,提高了算法的收敛速度和计算精度。最后针对某双离合变速器(DCT)换挡毂?12j6轴颈的16个数据进行求解验证,并将计算结果与粒子群算法、改进的蜂群算法和蔡司三坐标测量机结果进行对比。实例表明,变尺度教与学算法与粒子群算法、改进的蜂群算法相比,在空间圆度误差评定上的收敛速度和计算精度均有明显的优势,体现了变尺度教与学算法的优越性。     

基于机器视觉的活塞杆同轴度误差检测研究

针对活塞杆制造过程中同轴度检测出现的精度低,效率低问题,提出了基于机器视觉技术的活塞杆同轴度误差检测方法,并建立了同轴度误差数学模型。采集活塞杆图像并进行边缘特征提取;将基准圆柱表面分解成240个连续的横截面,待测圆柱表面分解成110个连续的横截面;基于最远Voronoi图计算出每个截面的最小外接圆的圆心,并用最小二乘法拟合出活塞杆圆柱面的轴线。以此方法获得基准轴线,求得零件的同轴度误差,并以某型号的活塞杆进行实验分析,结果与三坐标测量机(CMM)测得的误差结果相吻合,表明该方法可以有效、正确地进行同轴度误差的评定。     

基于CAD模型引导测量的自由曲面定位及轮廓度误差评定

提出将粒子群优化算法与拟随机序列法相结合对基于CAD模型引导测量的自由曲面进行高精度检测和轮廓度误差评定的方法。为解决用三坐标测量仪检测自由曲面时存在的设计坐标系与测量坐标系不重合问题,提出用拟粒子群优化算法来实现被测曲面与设计曲面精确定位;针对自由曲面特点,采用轮廓峰谷误差和轮廓均方根误差综合评定自由曲面的形状误差。最后,阐述了用拟粒子群优化算法实现曲面匹配时目标函数值的计算方法,确立了用拟粒子群优化算法优化求解参数向量的具体步骤。对仿真实例和大量实测零件自由曲面轮廓度误差的计算表明:采用本文方法能够实现自由曲面精确定位,其轮廓度误差评定精度比由三坐标测量仪内置软件计算的结果高8%～15%,适用于对高精度自由曲面零件形状误差的评定。     

改进蜂群算法在平面度误差评定中的应用

为了准确快速评定平面度误差,提出将改进人工蜂群( MABC)算法用于平面度误差最小区域的评定.介绍了评定平面度误差的最小包容区域法及判别准则,并给出符合最小区域条件的平面度误差评定数学模型.叙述了MABC算法,该算法在基本人工蜂群算法( ABC)模型的基础上引入两个牵引蜂和禁忌搜索策略.阐述了算法的实现步骤,通过分析选用两个经典测试函数验证了MABC算法的有效性.最后,应用MABC算法对平面度误差进行评定,其计算结果符合最小条件.对一组测量数据的评定显示,MABC算法经过0.436 s可找到最优平面,比ABC算法节省0.411 s,其计算结果比最小二乘法和遗传算法的评定结果分别小18.03μm和6.13 μm.对由三坐标机测得的5组实例同样显示,MABC算法的计算精度比遗传算法和粒子群算法更有优势,最大相差0.9 μm.实验结果表明,MABC算法在优化效率、求解质量和稳定性上优于ABC算法,计算精度优于最小二乘法、遗传算法和粒子群算法,适用于形位误差测量仪器及三坐标测量机.     

最小区域平面度的计算几何评定算法研究

目前三坐标测量机和圆度/圆柱度仪己被广泛地用于形位误差的测量,由这些测量仪器所得的数据将会被进一步地处理和分析.采用计算几何技术中凸面体建立法求解最小区域平面度,编制了相应的算法.算法已编入程序模块,并在处理实际数据中得到了验证.     

基于海鸥算法的圆柱度误差评定方法

圆柱体零件的几何精度直接影响到机械设备的总体性能，而圆柱度误差是圆柱体零件的几何误差之一，对圆柱度误差进行精确测量和评估十分重要。针对最小区域圆柱度误差评定能否达到全局最优的问题，提出了一种基于新型元启发式海鸥算法(SOA)的圆柱度误差评定方法。首先，对圆柱体轮廓要素的提取进行了阐述，并建立了基于最小区域法的圆柱度误差评定模型；然后，介绍了海鸥优化算法中海鸥的位置更新原理、算法的优化准则和算法流程；最后，用Talyrond 585LT圆柱度仪提取了6个圆柱零件的轮廓数据，并进行了评定，通过对比不同种群数的优化结果，找到了最佳种群数，同时将其所得结果与采用遗传算法(GA)所得结果进行了对比。研究结果表明：种群数的选择对海鸥算法的优化结果影响较大，在种群数为30时能达到最优解，其精度比遗传算法高，其运行时间随着种群数的增加而增加。海鸥算法优化过程稳定，在评定最小区域圆柱度误差(MZC)方面有较好的适应性。     

改进天牛须搜索算法在圆度误差评定中的研究

为了提高圆度误差的评定精度和计算收敛速度,提出了一种改进天牛须搜索算法的圆度误差评定方法。首先,通过圆度误差最小区域原则建立了数学模型和目标函数。其次,在标准天牛须算法的基础上,设计了变步长法,进一步提高算法的计算精度和收敛速度。最后通过三坐标测量的圆度测量数据进行求解验证,并将计算结果与常用的最小二乘法和粒子群算法等进行对比。实例表明,改进的天牛须搜索算法在圆度误差评定上的计算精度和收敛速度都优于传统算法,体现了该算法的优越性。     

直角坐标采样时的一种圆柱度误差评定算法

根据国家标准中圆柱度误差的定义,在直角坐标系下建立了一种适用于三坐标测量机(CMM)圆柱度误差评定的最小二乘数学模型,并给出了最优化算法以及迭代初值选取方法.该模型坐标原点可任意选择,对采样点以及被测圆柱位置和倾斜度均无特别的限制要求.该方法易于编程实现,能够方便地应用于其它复杂几何体的形状误差评定.实验证明了该模型以及算法的稳定性和正确性,该算法已用于自主研发的GMesaure1.0测量软件系统.     

改进教与学算法在圆度误差评定中的应用

为了提高圆度误差的评定精度和计算收敛速度,提出了一种改进教与学算法的圆度误差评定方法。首先,通过圆度误差最小区域原则的数学模型,建立算法的目标函数。其次,在标准教与学算法的基础上,设计了两阶段爬山搜索策略增强局部开发能力,进一步提高算法精度和收敛速度。最后通过三坐标测量的圆度测量数据进行求解验证,并将计算结果与常用的最小二乘法,遗传算法,粒子群算法等进行对比。实例表明,改进教与学算法在圆度误差评定上的计算精度和收敛速度都优于传统算法,体现了其优越性。     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

RESEARCH ON THE MINIMUM ZONE CYLINDRICITY EVALUATION BASED ON GENETIC ALGORITHMS

A genetic algorithm (GA)-based method is proposed to solve the nonlinear optimization problem of minimum zone cylindricity evaluation. First, the background of the problem is introduced. Then the mathematical model and the fitness function are derived from the mathematical definition of dimensioning and tolerancing principles. Thirdly with the least squares solution as the initial values, the whole implementation process of the algorithm is realized in which some key techniques, for example, variables representing, population initializing and such basic operations as selection, crossover and mutation, are discussed in detail. Finally, examples are quoted to verify the proposed algorithm. The computation results indicate that the GA-based optimization method performs well on cylindricity evaluation. The outstanding advantages conclude high accuracy, high efficiency and capabilities of solving complicated nonlinear and large space problems.     

Method for cylindricity error evaluation using Geometry Optimization Searching Algorithm

According to the geometrical characteristics of cylindricity error, a method for cylindricity error evaluation using Geometry Optimization Searching Algorithm (GOSA) has been presented. The optimization method and linearization method and uniform sampling could not adopt in the algorithm. The principle of the algorithm is that a hexagon are collocated based on the reference points in the starting and the end measured section respectively, the radius value of all the measured points are calculated by the line between the vertexes of the hexagon in the starting and the end measured section as the ideal axes, the cylindricity error value of corresponding evaluation method (include minimum zone cylinder method (MZC), minimum circumscribed cylinder method (MCC) and maximum inscribed cylinder method (MIC)) are obtained according to compare, judgment and arranged hexagon repeatedly. The principle and step of using the algorithm to solve the cylindricity error is detailed described and the mathematical formula and program flowchart are given. The experimental results show that the cylindricity error can be evaluated effectively and exactly using this algorithm.     

A unified approach to form error evaluation

Evaluation of form error is a critical aspect of many manufacturing processes. Machines such as the coordinate measuring machine (CMM) often employ the technique of the least squares form fitting algorithms. While based on sound mathematical principles, it is well known that the method of least squares often overestimates the tolerance zone, causing good parts to be rejected. Many methods have been proposed in efforts to improve upon results obtained via least squares, including those, which result in the minimum zone tolerance value. However, these methods are mathematically complex and often computationally slow for cases where a large number of data points are to be evaluated. Extensive amount of data is generated where measurement equipment such as laser scanners are used for inspection, as well as in reverse engineering applications.In this report, a unified linear approximation technique is introduced for use in evaluating the forms of straightness, flatness, circularity, and cylindricity. Non-linear equation for each form is linearized using Taylor expansion, then solved as a linear program using software written in C++ language. Examples are taken from the literature as well as from data collected on a coordinate measuring machine for comparison with least squares and minimum zone results. For all examples, the new formulations are found to equal or better than the least squares results and provide a good approximation to the minimum zone tolerance.     

Evaluating the geometric characteristics of cylindrical features

This paper presents mathematical models and efficient methodologies for the evaluation of geometric characteristics that define form and function of cylindrical features; namely cylindricity and straightness of median line. These two problems have similar structures and can be solved by comparable procedures. Based on the proposed methodologies, the cylindricity error evaluation can be performed using any of the following criteria: the least squares cylinders, minimum circumscribed cylinders, maximum inscribed cylinders or minimum zone cylinders. The procedures have been tested for accuracy and efficiency. The results indicate that they provide accurate results quickly.     

具有二重机制的生物地理优化算法及圆柱度 误差评定研究*

生物地理学优化算法(Biogeography-base optimization, BBO)是一种新型的智能算法,因其参数少、易于实现等优点而受到学界的广泛关注和研究,并显示出了广阔的应用前景。为了提高算法的优化性能,对BBO算法提出一种改进。改进的算法在将差分优化算法(Differential evolution, DE)中的局部搜索策略同BBO算法中的迁移策略相结合的基础上,针对迁移算子和变异算子分别做出改进,并通过基准函数的测试证明了改进后的算法在迭代过程中种群进化、寻优能力以及算法的收敛性能得到进一步提升。尝试将改进了的生物地理学优化算法应用于圆柱度误差评定。依据国家标准,结合最小区域法,以圆柱度误差数学模型为目标函数,该算法实现了误差评定优化求解。通过该寻优结果与其他方法的评定结果的比较,验证了该种算法的可行性和正确性及其优越性。     

基于误差转换的汽车曲轴圆度及圆柱度误差评价数学模型构建研究

针对国内汽车曲轴轴颈圆度误差、圆柱度误差检测普遍存在的效率低、精度低等问题,建立基于误差转换的平面曲线和空间曲线误差数学模型,结合圆和圆柱的数学表达建立满足最小包容条件的圆度和圆柱度误差评定数学模型,并采用遗传优化算法计算出符合最小评定要求的曲轴轴颈形位误差,解决了理想包容要素位姿参数不精确的问题。同时,建立基于图像域的汽车曲轴轴颈形状误差检测试验台,针对测量过程中连杆轴颈沿主轴颈公转运动,从而导致连杆轴颈图像域检测数据存在坐标不归一问题,以曲轴法兰端特征孔为基准,通过模板匹配特征与孔边缘提取实现了连杆轴颈圆度和圆柱度测量数据空间坐标归一化处理。以某型号发动机曲轴为例进行大样本误差检测试验,并与三坐标测量机测得的结果进行对比,数据分析表明提出的曲轴轴颈形状误差检测方法的精度为1μm,且重复检测误差在0.1μm以内,证明了其理论上的正确性及实践操作的可行性。     

Flatness error evaluation and verification based on new generation geometrical product specification (GPS)

New generation geometrical product specification (GPS) links the whole course of a geometrical product from the research, development, design, manufacturing and verification to its release, utilization, and maintenance. Measurement process is one of the most important part of verification/inspection in the new generation GPS. With the knowledge-intensive and globalization trend of the economy, unifying the evaluation and verification of form errors will play a vital role in international trade and technical communication. Considering the plane feature is one of the most basic geometric primitives which contribute significantly to fundamental mechanical products such as guide way of machine tool to achieve intended functionalities, the mathematical model of flatness error minimum zone solution is formulated and an improved genetic algorithm (IGA) is proposed to implement flatness error minimum zone evaluation. Then, two evaluation methods of flatness error uncertainty are proposed, which are based on the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo Method (MCM). The calculating formula and the propagation coefficients of each element and correlation coefficients based on GUM and the procedures based on MCM are developed. Finally, two examples are listed to prove the effectiveness of the proposed method. An investigation into the source and effects of different uncertainty contributors for practical measurement on CMM is carried out and the uncertainty contributors significant are analyzed for flatness error verification. Compared with conventional methods, the proposed method not only has the advantages of simple algorithm, good flexibility, more efficiency and accuracy, but also guarantees the minimum zone solution specified in the ISO/1101 standard. Furthermore, it accords with the requirement of the new generation GPS standard which the measurement uncertainty characterizing the reliability of the results is given together. And it is also extended to other form errors evaluation and verification.     

Establishing circle and circular-cylinder references using computational geometric techniques

Form deviations of cylindrical features present in the manufactured parts are measured using coordinate measuring machine (CMM) and expressed as circularity or cylindricity errors evaluated using appropriate reference features. In the present work, computational geometric techniques are used to establish a circle as reference feature, and a heuristic algorithm is proposed to get a unique convex inner hull. Using the concept of equi-distant lines and diagrams, minimum circumscribed (MC), maximum inscribed (MI), and minimum zone (MZ) circles are established. For the first time, algorithms purely based on computational geometric concepts have been developed in the present work to arrive at MC, MI, and MZ circular cylinders. As the algorithms and the implementation details are explained with simple data sets, the practitioners can easily understand these methods and implement them in CMMs for the evaluation of circularity and cylindricity errors. The algorithms are also tested on larger datasets, and in all cases, accurate results are obtained in less than a second.     

Measurement uncertainty evaluation of conicity error inspected on CMM

The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification(GPS), the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm(IIEA) is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement(GUM) method to evaluate measurement uncertainty. Adaptive Monte Carlo method(AMCM) is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine(CMM). The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error(MZCE) rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.