Roundness error evaluation by minimum zone circle via microscope inspection

Utilizing the convex hull theory, a novel minimum zone circle （MZC） method, named im- proved minimum zone circle （IMZC） was developed in this paper. There were three steps for IMZC to evaluate the roundness error. Firstly, with the convex hull algorithm, data points on the circle contour were categorized into two sets to determine two concentric circles which contained all points of the contour. Secondly, vertexes of the minimum circumscribed circle and the maximum inscribed circle were found out from the previously determined two sets, and then four tangent points for de- termining the two concentric circles were also found out. Lastly, according to the evaluation using the MZC method, the roundness error was figured out. In this paper l IMZC was used to evaluate roundness errors of some micro parts. The evaluation results showed that the measurement precision using the IMZC method was higher than the least squared circle （LSC） method for the same set of data points, and IMZC had the same accuracy as the traditional MZC but dramatically shortened com- putation time. The computation time of IMZC was 6. 89% of the traditional MZC.

RESEARCH ON THE MINIMUM ZONE CYLINDRICITY EVALUATION BASED ON GENETIC ALGORITHMS

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

基于改进乌鸦搜索算法评定圆度误差

针对传统启发式智能优化算法评定圆度误差计算效率低且容易陷入局部最优解的问题,提出采用改进乌鸦搜索算法评定圆度误差。根据最小区域拟合准则建立乌鸦搜索算法评定圆度误差数学模型,并引入权重系数,提高算法全局搜索能力,同时设定最小二乘圆心附近为乌鸦搜索初始位置,提高算法搜索效率。最后通过模拟和实验验证了所提算法的准确性和高效性,并通过多组数据对比发现改进乌鸦搜索算法的全局搜索能力较遗传算法(GA)、粒子群算法(PSO)和传统乌鸦搜索算法(CSA)得到明显提升。

基于fminimax优化函数的圆度误差评定

依据圆度误差标注代号和附加符号的含义,基于最小外接法、最大内切法和最小区域法分别建立了参考圆的圆心坐标优化目标函数和圆度误差评定模型,采用MATLAB软件编写了参考圆的圆心坐标优化目标函数子程序和圆度误差评定子程序,给出了圆度误差评定中fminimax优化函数调用方法。用Talyrond 585LT圆柱度测量仪对三个试样的圆周轮廓进行了提取,基于最小二乘法、最小外接法、最大内切法和最小区域法对提取的圆周轮廓分别进行了圆度误差评定。研究了优化搜索范围对圆度误差评定结果的影响,并将fminimax优化函数圆度误差评定的优化符合度与其他优化方法圆度误差评定的优化符合度进行了比较。fminimax优化函数的应用结果表明,评定结果精度高于或等于其他优化方法评定结果的精度,可满足圆度误差评定的需要。

基于机器视觉的小型零件圆度测量

针对小型零件圆度误差测量效率低、精度不稳定等问题,提出了一种基于机器视觉的小型零件圆度测量方法。通过建立机器视觉检测平台,获得零件图像。经过预处理后,通过Canny算子结合8领域扩张算法划定感兴趣区域,采用多项式插值亚像素边缘检测算法获得边缘坐标;然后,利用改进区域搜索算法确定准圆心,并通过最小区域法的几何结构找出最小区域圆心,从而计算圆度误差。实验结果表明,圆度误差的测量重复精度为8.1μm,能够实现小型零件的非接触测量。

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（IlEA） 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.

ALGORITHM FOR SPHERICITY ERROR AND THE NUMBER OF MEASURED POINTS

The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine （CMM）. The consummate criterion for the minimum zone of spherical surface is analyzed first, and then an approximation technique searching for the minimum sphericity error from the form data is studied. In order to obtain the minimum zone of spherical surface, the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps. Therefore the algorithm is precise and efficient. After the appropriate mathematical model for the approximation technique is created, a data processing program is developed accordingly. By processing the metrical data with the developed program, the spherical errors are evaluated when different numbers of measured points are taken from the same sample, and then the corresponding scatter diagram and fit curve for the sample are graphically represented. The optimal number of measured points is determined through regression analysis. Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective. On average, the obtained sphericity error is 5.78 μm smaller than the least square solution, whose accuracy is increased by 8.63%; The obtained optimal number of measured points is half of the number usually measured.

Monte Carlo Method for the Uncertainty Evaluation of Spatial Straightness Error Based on New Generation Geometrical Product Specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

Geometric Approximation Searching Algorithm for Spatial Straightness Error Evaluation

Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.

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。

基于改进麻雀搜索算法的平面度误差评定方法

针对在平面度误差最小区域评定过程中易出现陷入局部最优、收敛速度慢和精度低的问题,提出了一种基于改进麻雀搜索算法(ISSA)的平面度误差评定方法。首先,采用具有更好遍历性的Kent混沌映射代替传统的Logistic混沌映射生成初始化种群,以增强算法的全局搜索能力;然后,应用一种基于光学透镜成像原理的反向学习策略以避免算法无法跳出局部最优;选用经典测试函数验证了ISSA算法的有效性,相对于SSA能够取得更好的寻优效果;最后,应用该方法对平面度误差进行评定,并与引用的其它方法进行比较。实验结果表明:基于ISSA算法的平面度误差评估方法用时0.4884 s能够解得最小包容平面,与应用SSA算法相比减少了0.3705 s,其计算精度与应用最小二乘法、遗传算法和粒子群算法的平面度误差评定方法相比分别减小了18.0325μm、2.3325μm、6.1325μm。基于ISSA算法的平面度误差评估方法在优化效率、求解质量、计算精度和稳定性上均有优势,可应用于三坐标测量机等形位误差测量仪器。

改进序列二次规划算法用于轴对称非球面轮廓度误差评定

为了高效率、高精度的评定轴对称非球面零件,提出一种改进序列二次规划算法并结合非线性方程组牛顿迭代法来评定非球面的轮廓度误差。对于测量仪器检测时存在的设计坐标系与测量坐标系不重合的问题,使用坐标变换矩阵来消除测量坐标系存在的位置误差;针对非球面的特点,构建二元非线性方程组来表示非球面的投影点,并采用牛顿迭代法精准计算投影距离;为解决计算的复杂性,采用改进序列二次规划算法构建误差子问题求解,并利用拟牛顿法求解大规模无约束非线性问题。最后,对多种非球面镜片进行仿真和实验分析,并与最小二乘法和熵函数法对比。结果表明,所设计的算法有效提高了计算轮廓度误差过程中的数据处理效率和精度。

改进的穷举算法在圆度误差评定中的应用

本文提出一种改进的穷举算法的圆度误差评定方法,并应用于圆度误差最小区域评定中,详细阐述了改进的穷举算法的计算过程及思路流程图。该算法摒弃传统穷举算法运算繁杂的缺点,根据初始检测数据找出具有X和Y坐标的最大最小四个极值位置点,依据四个极值位置点建立初始圆度误差区域,不仅使初始误差范围接近理想区域,而且减少程序的循环次数及计算量。基于接触式影像仪软件开发平台,利用C++语言设计出圆度误差评定软件,能够快速求出圆度误差值,为现场检测提供方便。

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0.436s可找到最优平面,比ABC算法节省0.411s,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6.13μm。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0.9μm。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。

平面度误差最小区域新算法——有序判别法

提出一种平面度误差最小区域新算法———有序判别法。该方法以最小区域准则为基础，直接以排序的高点和低点构成的初始评定平面进行最小包容区域的判定和搜索，最终求得平面度误差值。该方法易于理解和掌握，搜索判别有序。实例运算表明，首轮搜索成功率高、速度快。

浮点数编码改进遗传算法在平面度误差评定中的研究

随着智能制造系统的迅猛发展,应用元启发模式计算方法快速、准确地求解平面度误差值凸显出重大现实意义。为进一步提高平面度误差计算精度,研究了一种基于浮点数编码的改进遗传算法,在原有遗传算法的交叉变异基础之上,引入模拟退火思想,建立最小包容区域法的数学模型,通过计算机仿真获得了最佳适应度收敛曲线和平均适应度收敛曲线,优化结果表明相比传统遗传算法,平面度误差计算精度提高了33.67%。本算法采用浮点数编码、三段式交叉、转轮式选择和最优保存策略,借助模拟退火算法的局部搜索优势,提升了算法的整体性能,且更便于计算机编程,可进一步推广应用到智能测量仪器的其他高精度形位尺寸计算问题领域。

三维测头探测误差的评定准则及高精度评定方法研究

在对三维测头探测误差进行分析的基础上,参照球度误差的定义,给出了探测误差的4种评定准则及相应评定算法。对一组测量数据,用Powell寻优方法按最小包容区域准则对探测误差进行了评定,并与按最小二乘准则的评定结果进行了比较,分析及计算结果表明,采用最小包容区域准则与方法,消除了传统探测误差评定方法存在的原理误差,提高了检定准确度。

改进蜂群算法及其在圆度误差评定中的应用

针对基本人工蜂群算法(Artificial bee colony algorithm,ABC)的缺点,提出一种改进人工蜂群算法(Improved artificial bee colony algorithm,IABC),并应用于圆度误差最小区域评定中。该改进算法利用信息熵初始化种群,增强种群的多样性,并在引领蜂和跟随蜂搜索阶段,提出一种新的搜索策略,平衡算法的探索与开发能力。详细阐述IABC算法的基本原理与实现步骤,给出圆度误差满足最小包容区域条件的优化目标函数和收益度函数。通过基准测试函数验证IABC算法的有效性和准确性;通过对由三坐标机测得的多组测量数据进行圆度误差评定试验,结果表明IABC算法的评定精度优于最小二乘法、遗传算法以及粒子群算法等其他优化算法,且在求解质量和稳定性上优于ABC算法,验证了IABC算法不仅正确,而且适用于圆度误差的评定优化。

基于模拟植物生长算法的平面度误差评定

平面特征是最基本的几何图形元素之一,在机械零部件中发挥着重要作用。为了实现方便准确地评定平面度误差,提出将模拟植物生长算法应用于确定平面度最小包容区域的问题中。首先,根据最小区域法建立了平面度误差评定的数学模型;其次,介绍了模拟植物生长算法的仿生原理和数学理论,引入了寻优步长的自适应调整机制,并且阐述了使用该算法评定平面度误差的具体流程;最后,基于VB6.0开发了算法的计算机程序,实例运行后将评定结果和现有的评定算法进行了比较。实践证明,采用模拟植物生长算法评定平面度误差,不仅可以有效地求出最小包容区域解,而且具有良好的快速性和稳定性。

基于自适应多种群遗传算法的圆度误差评定

针对传统遗传算法在圆度误差评定方法存在搜索稳定性差、易陷入局部收敛和全局搜索能力不足的问题,改进传统遗传算法(TGA),提出了采用自适应多种群遗传算法(AMPGA)的评定方法。根据圆度误差评定的特点,建立了多种群协同进化的遗传方式,并引入了交叉概率Pc和变异概率Pm随个体适应度值变化而不断调整的遗传机制,通过编写自适应多种群遗传算法(AMPGA)程序对圆度误差进行评定,得到相应结果与三坐标测量机的实测值对比。对比分析结果表明该方法能有效的克服传统遗传算法(TGA)在圆度误差评定上存在的搜索稳定性差、易陷入局部收敛和全局搜索能力不足的问题,是一种更有效的圆度误差评定方法。