基于最大内接圆法的圆度误差测量实现方法

介绍了一种在直角坐标系下利用最大内接圆法评价圆度误差的方法,建立了圆度测量模型。针对圆度误差最大内接圆评价,提出了一种最大内接圆心搜索方法,达到了快速、精确评价的目的,实现了在直角坐标系下三坐标测量机对圆度误差的最大内接圆法评价。     

一种直角坐标系下圆度误差最小区域评价实现方法

针对直角坐标系下圆周截面形状误差评价,介绍了一种圆柱体截面圆度误差的测量与评定方法.建立了基于直角坐标系下的最小区域圆度误差三维评测模型,得到利用弦线截交关系快速评价圆度误差的方法.通过多次截交产生的虚拟中心定位,可以准确确定评价点的位置,达到了快速、精确利用最小外接球法评价球度误差的目的.通过分析表明,该方法计算效率...     

最小区域球度误差评价的弦线截交方法

最小区域球度误差评价是精密测量技术中的一个非常重要并且复杂问题。针对笛卡儿坐标系下球体形状误差评价,介绍一种利用弦线截交关系求解最小区域球度误差评价方法。通过构建笛卡儿坐标系下球度误差测量模型,提出基于一般二次曲面理论的最小二乘球心计算方法。根据最小区域球度误差模型分类,利用弦线截交关系建立起最小区域球度误差评价的2+3和3+2模型,最后通过截交几何模式产生了虚拟中心,从而准确确定球度误差评价模型的最大弦线与最大截面,达到快速精确构建模型的目的。测试数据和实例应用表明,基于弦线截交关系的最小区域球度误差评价方法具有更高的计算效率,且测量空间不受测量坐标系和零件几何形状误差的影响,并显著提高了整体评价的精度与准确性。     

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。     

最小外接球法球度误差评价与实现

针对直角坐标系下球体形状的误差评价,介绍一种利用最小外接球法评价球度误差的计算方法。建立基于直角坐标系下的球度误差三维评测模型,并研究外接球体几何曲面关系,得出了利用弦线截交关系快速评价球度误差的理论。利用弦线截交关系构建最小外接球法球度误差评价的“2+1”、“3+1”、“4+1”评价模式统一体,通过两次截交产生的虚拟中心定位,可以准确确定评价点的位置,达到了快速、精确利用最小外接球法评价球度误差的目的。通过分析表明,基于弦线截交关系的最小外接球球度误差评价方法计算效率高、易于实现且具有较高的评定精度,也为球度误差评价提供一种新的方法和思路。     

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.     

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。     

一种利用坐标测量机实现圆度误差评价的方法

针对直角坐标系下圆周截面形状误差评价,介绍了一种圆柱体截面圆度误差的测量与评定方法.在研究了圆度误差定义及测量方法的基础上,建立了基于三坐标测量机的最小外接圆圆度误差三维评测模型.利用双截面最小二乘拟合轴线调整坐标系位置,减少了位姿误差对测量结果的影响.对模型进行坐标系统一转换,使得变换后的模型能更适用于计算机数据处理.然后在坐标变换的前提下,提出了一种利用几何关系搜索最小外接圆圆心的方法,开发了相应的数据分析软件.实验和数据证明,此算法优于传统最小外接圆算法,实现了在直角坐标系下三坐标测量机对圆度误差的最小外接圆法评价.     

最大内接圆法评定圆度误差的快速精确实现方法

用最大内接圆法评定圆度误差,是指把被测实际圆的最大内接圆作为内包容圆,以最大内接圆的圆心为中心,作被测实际圆的外包容圆(此圆与被测实际圆至少一点接触),将这样两个同心圆的半径差fMI作为被测实际圆的圆度误差值。若fMI≤t(t为圆度公差值),则被测圆合格。     

计算几何在测试计量技术中的应用--求解最大内接圆

本文介绍了采用计算几何知识求解最大内接圆的新方法,该方法摆脱了传统的用坐标及函数处理几何问题的常规,从图形的崭新思路分析了最大内接圆的准确中心,并且提出了一种删除无关数据点的原则、可将采样点数减至十分之一以下。相应算法的运算时间比以往的算法快１５倍以上。     

一种最小外接圆法圆度误差评价实现方法

介绍了一种在直角坐标系下利用最小外接圆法评价圆度误差的方法。提出了一种基于对称关系的最小外接圆圆心搜索思想,运用几何思想均匀分布圆心到各点的距离,达到了快速、精确评价的目的,并且实现了在直角坐标系下三坐标测量机对圆度误差的最小外接圆法评价。     

Evaluation of roundness error from coordinate data using curvature technique

Workpieces like a shaft or hole make contact on their functional boundaries and its circularity is obtained based on the functional boundaries by enveloping features. Data for evaluating roundness error can be obtained from coordinate measuring machines. A technique for roundness error based on the curvature has been proposed to deal with coordinate measurement data. The computational geometric concepts of convex hulls are used to reduce the computation. The method developed is implemented and validated with the data available in the literature.     

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.     

基于误差转换及图像域的圆度评定方法

针对工程应用中圆度误差评定方法存在理论深奥、计算复杂、检测效率低且不适用于大容量采样点的问题,提出了一种基于误差转换及图像域的圆度误差评定方法。该方法首先将图像域测量得到的原始圆度误差进行转换,使其满足误差评定的要求;然后以最小二乘圆为起始圆,寻求半径或半径差的“极大中的极小”,通过对最小二乘圆进行小尺度平移,并用遗传算法得到该平移规划坐标,从而获得平移后的理想圆并求得圆度误差值;最后对某型号零件进行试验,试验结果与用三坐标测量得到的结果相吻合,表明该方法可以有效、正确地进行圆度误差的评定。     

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.     

Intersecting chord method for minimum zone evaluation of roundness deviation using Cartesian coordinate data

Minimum zone evaluation of roundness deviation is a very important and complex problem in precision measurement. Along with the continuous development of precision machining technology, it has become an increasingly prominent issue of how to quickly and accurately evaluate the minimum zone roundness deviation from a large number of coordinate data. In this paper, an intersecting chord method is first proposed to realize the minimum zone model of roundness deviation with coordinate data. The new modelling method uses the crossing relationship of chords to construct the intersecting structure and the 2 + 2 evaluation model of the minimum zone roundness deviation, which can not only accurately determine the position of minimum zone centre but also greatly improve the computational efficiency of modelling process. Using the related chords and their extreme points to generate a virtual centre, this may reduce the deviation between the intersecting chords structure and the centre of the minimum zone evaluation. The proposed method makes use of the geometric relationship of chords, so the minimum zone roundness deviation can be obtained without the optimal method or the point-by-point method. The validation test of the proposed method is designed to analyze a coordinate dataset published in other literature. Comparing the proposed method with the published method, it is easy to show that the relative error between two results is less than 0.4%. Finally, an experiment is also given to indicate that the calculation accuracy and the evaluation efficiency of the proposed method achieve a satisfactory conclusion.