三维空间中圆度误差的评定研究

为解决三维空间中圆度误差的精确评定问题,针对三坐标测量机检测圆度误差时因存在测量误差而使各实际测点不是精确地位于同一理想截平面上的特点,根据计算几何学和误差理论,提出了基于空间测点集算术平均中心点的最小二乘平面拟合方法,推导了其数学模型;并对国家标准中圆度误差评定的最小外接圆法、最大内接圆法和最小区域圆法进行了三维扩展;还对前两种方法作了改进,建立了此3种方法的数学模型和算法流程。最后的数字实验表明:以上3种算法是有效的。     

基于遗传算法的圆度误差评估

将遗传算法应用于圆度误差的评定.首先简介了误差评定背景和遗传算法及其特点.然后根据尺寸和公差的数学定义^[1]给出满足最小区域条件的圆度公差评定的数学模型和适应度函数.接着,以最小二乘解作为初始值,对圆度误差的遗传优化过程进行了详细的论述.最后用实例对算法进行验证.优化过程和实验结果显示了遗传算法在解决形状公差的评定这类非线性问题的优越性,通过并行搜索能最大限度地保证解的全局最优,计算精度高、效率高,且易于理解和实现.     

基于改进果蝇优化的机械圆度误差评定研究

针对机械零件圆度误差的最小区域圆法评定问题,提出一种基于改进果蝇优化算法的评定圆度误差新方法。首先根据最小区域圆法圆度误差数学描述的优化模型设计了果蝇种群个体的编码方式以及新型味道浓度判定函数;其次在保持基本果蝇优化算法典型流程的基础上,引入增强搜索和交互学习机制来增强算法的学习效率以及保持种群的多样性;最后采用3个典型的圆度误差评定问题来验证算法性能。实例分析计算表明该方法是可行有效的,其结果具有较高精度且优于传统的评定方法,适用于求解圆度误差的评定优化问题。     

圆度误差评定方法的研究

圆度误差评定是否准确,将直接影响到机械产品的性能和寿命.介绍了4个简单而有效的算法来评定圆度误差,即最小外接圆、最大内接圆、最小区域法和最小二乘圆法.利用MATLAB对上述算法进行了验证,说明文中算法有效.     

基于几何优化的圆度误差评定算法

针对圆度误差的特点,提出一种基于几何优化的圆度误差评定算法。建立直角坐标采样、可同时实现圆度误差的最小区域法、最小外接圆法和最大内接圆法评定的评定模型。详细阐述利用几何优化算法求解圆度误差的过程和步骤,给出数学计算公式及计算机程序流程图。该算法不要求等间隔测量,不采用最优化及线性化方法,也无需满足小误差和小偏差假设,只需重复调用点与点之间的距离公式;其原理是以初始参考点为基准,布置一定边长的正六边形,依次以各顶点为理想圆心计算所有测点的半径值,通过比较、判断及重复设置六边形来获得相应评定方法(最小区域圆法、最小外接圆法和最大内接圆法)的圆度误差值。试验结果表明,该算法可以有效、正确地评定圆度误差。     

AutoCAD在圆度误差评定中的应用研究

在圆度误差测量中,圆度误差的数据处理和评定一般都是采用绘制简图及用同心模板逼近的方法完成,但这种方法处理效率及准确度偏低。应用AutoCAD软件的绘图和标注功能对圆度误差进行评定的方法,能够很好的弥补传统方法的不足。     

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。     

基于仿增量算法的圆度误差快速准确评定

提出按最小外接圆法和最小区域法评定圆度误差的仿增量算法.将工件轮廓看作一个点集,并在其中建立可以确定圆(环)的子集.若子集确定的圆(环)包容原点集,则可得到相应的圆度误差;否则每次给子集增加一个在包容区域外的点构成新子集,确定包容新子集的圆(环)并去掉其中不在圆(环)边界上的点.证明了该算法是单调收敛的.同时还提出以按最小外接圆法评定圆度误差时在包容边界上的点为最小区域法初值的新思路.该算法概念清楚、模型简单,易于在计算机上实现.几个实际零件圆度误差的评定验证了算法不仅正确,而且结果准确,耗时极少.     

基于测点分类的圆度误差精确评定

针对圆度误差已有评定方法的不足,提出了一种新的精确评定方法.该方法在测点分类的基础上,搜索符合最小包容区域定义的同心圆,大大提高了误差评判效率,并在实例中得到了很好的验证.     

Circularity error evaluation: Theory and algorithm

Many procedures for the evaluation of circularity error based on different criteria have been developed. The procedures that are based on the minimum radial separation criterion are either too complex or lack an algorithmic approach to find optimal solution. This paper presents an optimization-based technique to find the value of circularity error based on the minimum radial separation criterion. The problem is formulated as a nonlinear optimization problem. Based on the developed necessary and sufficient conditions a generalized nonlinear optimization procedure is presented. The performance of the developed procedure is analyzed for different size problems generated using a simulation program. Results indicate that the procedure is accurate and very efficient in solving large size real life problems.     

Fast genetic algorithm for roundness evaluation by the minimum zone tolerance (MZT) method

According to ISO 1101, “A geometrical tolerance applied to a feature defines the tolerance zone within which that feature shall be contained”.The main goal of the minimum zone tolerance (MZT) method is to achieve the best estimation of the roundness error, but it is computationally intensive. This paper describes the application of a genetic algorithm (GA) to minimize the computation time in the evaluation of CMM roundness errors of a large cloud of sampled points.Computational experiments have shown that by selecting the optimal GA parameters, namely a combination of the five genetic parameters related to population size, crossover, mutation, stop condition, and search space, the computation time can be reduced by up to one order of magnitude, allowing real-time operation.Optimization has been tested using seven CMM samples, obtained from different machining features. The performance of the optimized algorithm has been validated using four benchmark samples from the literature and with certified samples.     

Roundness error evaluation algorithm based on polar coordinate transform

A new method for roundness error evaluation using polar coordinate system, named as polar coordinate transform algorithm (PCTA), was presented in this paper. The algorithm first allocates a circular region around the least square circle center following certain rules, then calculates the polar radius for all measured points by translating polar coordinate system to each point in the region in turn, and finally obtains minimum circumscribed center point, maximum inscribed center point and minimum zone center point from comparing each polar radius relative to each polar coordinate system. With accurate center point, the algorithm could give more accurate roundness evaluation. In the paper, the process of PCTA was described in detail including the algorithm formula and flowchart. Theoretical calculation and testing results show that PCTA can evaluate roundness error effectually and accurately.     

基于改进遗传算法的机床主轴径向回转误差分离技术研究

以提高精密机床主轴回转误差的测量精度为研究目标,基于四点法矩阵算法,采用多圈重合式方法对主轴回转误差测量中的传感器输出数据进行处理。为提高传统遗传算法的收敛速度,降低优化结果对初始值的依赖性,对交叉和变异概率因子列式进行更新,并使用改进遗传算法对传感器安装角度和输出权值系数进行优化。使用改进遗传算法,收敛速率较传统遗传算法提高50%左右。利用多功能斜轨数控车床进行主轴径向回转误差测量及分离实验,分离后的标准芯棒形状误差值与标定值相比,误差在5%以内,且误差重复性低于5%。结果表明分离的结果精度较高,从而验证提出的算法的正确性和可行性。     

基于遗传算法的球度误差评定

首先对球度公差评定问题进行了综述.然后根据圆度公差的数学定义,引申提出球度公差最小区域条件下的评定模型,并给出遗传算法的适应度函数.随后给出算法实现中的中的关键问题.最后用实例对算法进行了检验,计算结果表明基于遗传算法的球度误差优化算法不仅符合最小区域的条件,而且易于理解和实现,能够获得全局最优解,保证了高精度、高效率.     

改进遗传算法与拟随机序列结合评定自由曲线轮廓度误差

为了高效率、高精度检测自由曲线和曲面零件并计算轮廓度误差,提出将改进遗传算法与拟随机序列结合来评定自由曲线轮廓度误差.首先,针对自由曲线因没有已知的解析表达式而常用离散点表示其轮廓的特点,采用非均匀有理B样条(NURBS)来表示自由曲线,并用改进遗传算法优化重建自由曲线;然后,应用拟随机Halton序列均匀产生参数值精确计算点到曲线最短距离.阐述了自由曲线重建时控制顶点及目标函数值的计算方法,确立了改进遗传算法重建自由曲线及采用拟随机序列生成参数值求解点到曲线最短距离的具体步骤.最后,针对仿真实例计算并实测零件曲线轮廓度误差.结果显示,自由曲线轮廓度误差评定精度高于99％,表明提出的方法算法简单、计算速度快、精度高,适于在工程计量中推广应用.     

Conicity error evaluation using sequential quadratic programming algorithm

Form error evaluation plays an important role in processing quality evaluation. Conicity error is evaluated as a typical example in this paper based on sequential quadratic programming (SQP) algorithm. The evaluation is carried out in three stages. Signed distance function from the measured points to conical surface is defined and the cone is located roughly by the method of traditional least-squares (LS) firstly; the fitted cone and the measured point coordinates are transformed to simplify the optimal mathematical model of conicity error evaluation secondly; and then optimization problem on conicity error evaluation satisfying the minimum zone criterion is solved by means of SQP algorithm and kinematic geometry, where approximate linear differential movement model of signed distance function is deduced in order to reduce the computational complexity. Experimental results show that the conicity error evaluation algorithm is more accurate, and has good robustness and high efficiency. The obtained conicity error is effective.     

Applying particle swarm optimization algorithm to roundness error evaluation based on minimum zone circle

Minimum zone circle (MZC) method and least square circle (LSC) method are two most commonly used methods to evaluate roundness, but only the MZC method complies with the standard definition and can obtain the minimum roundness error value. The determination of the center of MZC is a nonlinear optimization problem which is suitable to be solved by particle swarm optimization (PSO) algorithms. In this paper, the standard PSO algorithm was introduced and theory analysis about the impact of value selection of some important parameters, such as inertia weight ω, on the algorithm’s stability and convergence was carried on so as to provide basis for giving these parameters better values. Furthermore, the superiority of making ω decrease linearly with iterations was verified through a computation experiment in terms of stability and accuracy, compared with the other three cases of ω = 1, 0.5, 0. Based on the analysis, the novel PSO algorithm, with ω decreasing linearly from 0.9 to 0.4 and the LSC center as the initial positions of the particles, is implemented to obtain MZC-based roundness errors of sampling points collected from circular section profiles by a coordinate measuring machine (CMM). By comparing the novel PSO–MZC results with the LSC-based results, it is concluded that the former are a little smaller than the latter, which verifies that the novel PSO algorithm is feasible to calculate roundness error and the fact that a LSC-based one is generally larger than a MZC-based result; the values of the two roundness errors are both related to sample size and increase with an increase in the sample size with a decreasing increment.     

评定二次曲面轮廓度误差的角度分割逼近法

提出一种基于角度分割逼近算法和粒子群算法计算二次曲面轮廓度误差的最小区域评定方法来准确评定任意位姿的二次曲面轮廓度误差。首先,给出了能够实现角度分割逼近算法的两条前提假设;基于假设,给出了更合理的算法网格布局递推公式。根据曲面轮廓度误差的定义建立了误差评定的精确模型。然后,采用角度分割逼近法求取测点到拟合二次曲面轮廓的距离;通过粒子群算法,以所有的点与二次曲面距离中的最大值为适应度值拟合出二次曲面一般方程,并实现被测轮廓与理论轮廓位置的匹配。最后,采用上述方法对某抛物面天线进行了评定,并与参数分割法、SMX-Insight和最小二乘法进行比较。实验结果显示：该方法测得的天线轮廓度误差为0.659 8 mm,比其它方法准确。结论表明：基于角度分割算法能够更有效地评定任意位姿二次曲面轮廓度误差,计算准确、迅速,而且无需确定待分割区域。     

改进型遗传算法在机械优化设计中的应用研究

针对标准遗传算法局部搜索能力弱的特点,将其与随机方向法结合,提高其局部搜索能力。结合工程问题进行优化计算,结果表明,此算法优于标准遗传算法。