The geometric dynamic errors of CMMs in fast scanning-probing

Quasi-stiffness model is effective for the compensation of the geometric errors of coordinates measuring machines (CMMs) in slow probing, but degrade the error compensation accuracy due to the generation of dynamic errors in fast probing. It is usually regarded that acceleration is the major origin of dynamic errors; and yet the dynamic effects that rise from the quick fluctuation of geometric errors in fast probing had attracted little attentions. This paper presents a model for the dynamic effects of the geometric errors of CMMs in fast probing, and investigates their properties with experiments. The error model is built with recursive least squares (RLS) identification technique by taking probing acceleration and the 6 geometric errors of X slideway for the inputs while the positioning error of probe tip for output. Then the positioning error of probe tip is decomposed into 7 components corresponding to the 7 inputs. Analyses on the experiments show that the angular errors around Y and Z axes, ε_Y(x) and ε_Z(x), can induce remarkable dynamic effects, especially in a CMM with low stiffness air bearing. Error compensation with RLS identification seems feasible theoretically, but it is not recommendable due to the veracity uncertainty of identification. Nevertheless smoothening the sharp corners of the curves of geometric errors, especially ε_Y ∼ x and ε_Z ∼ x, in terms of probing speed and Y coordinates of probe tip is considered as a simple but effective and reliable method to improve the accuracy of CMMs errors compensation in fast probing.     

坐标测量机几何要素通用构造原理研究

本文研究坐标测量机中七项基本几何要素的构造方法，提出了实体要素与逻辑要素的参数化模型，研究了各类逻辑操作的参数方程，为在坐标测量机应用软件中采用参数法管理几何要素、构造几何要素模块和扩展几何模块奠定了基础。     

Measurement Uncertainty of Blade Surface by Coordinates Measuring Machines in Rotation and Parallel Sampling Modes

三坐标测量机在旋转探针取样和平行探针取样模式下叶片表面测量的不确定性

李亚政,黄洪雁,王峥,刘占生,张广辉

（哈尔滨工业大学 能源学院 哈尔滨 150001）

研究目的：

为解决传统三坐标测量取样时采用平行探针测量方法所存在的不足,探究采用旋转探针进行三坐标测量的技术可行性,该技术可适应于空间受限或复杂元器件表面几何精度的测量。

研究方法：

论文采用理论分析和实验研究并用的方法,使用3+2轴卡尔.蔡司三坐标测量机进行实验研究,分析了平行探针测量法和旋转探针测量法的测量不确定性。

研究结果：

分析与研究结果表明,在没有进行进一步的算法改善的条件下,旋转探针测量法的测量不确定性与平行探针法测量不确定性相当,也即可以相互替换。如旋转探针法的算法进一步得到完善,则其精度可进一步提高。

结论：

本论文分析的三坐标测量机旋转探针取样测量法测量不确定性较好,在同等精度条件下与平行探针取样测量法不确定性水平相当,且可更适应于复杂曲面或空间受限下的测量情况。

关键词：三坐标测量;测量不确定性;取样策略;叶片

     

基于Mie级数解圆极化波与异向介质的相互作用

针对手征异向介质的电磁特性问题,基于Bohren的波分解技术,将手征异向介质球中的电磁波分解为左手和右手圆极化波,应用边界条件,推导了可用于计算手征异向介质球电磁散射的Mie级数解.将理想的、阻抗匹配的异向介质散射截面与文献结果对比证明了本文算法和程序的正确性.基于Mie级数解计算了有耗手征异向介质球的后向散射截面,探讨圆极化波与手征异向介质的相互作用.     

Improvement of coordinate measuring machine probing accessibility

In this paper, the probe accessibility of coordinate measuring machines (CMM) in dimensional inspection is studied. Based on the previous methods of the accessibility map, the influence of the actual configuration of the probe on the accessibility is analyzed in detail. A method, which takes the effects of the probe length and volume into account, is proposed so that the shortcomings of abstracting the probe as an infinite half-line could be overcome completely. Finally, a feasible and efficient algorithm is given.     

关于从能力成熟度模型(CMMs)向能力成熟度模型集成(CMMI)转换的探讨

首先对能力成熟度模型（CMMs）和能力成熟度模型集成（CMMI）进行概述，并介绍两者的关系，然后介绍能力成熟度模型的各组成成员和它们相互集成时所产生的问题，以及为解决这些问题而产生的能力成熟度模型集成，并讨论了能力成熟度模型集成的构架结构及应用，最后提出了发展趋势。     

The effect of sampling in circular substitute geometries evaluation

Coordinate Measuring Machines (CMMs) are widely used in dimensional metrology applications of the manufacturing industry. CMMs perform the dimensional control of machined parts by measuring a set of points of the manufactured part and by fitting a substitute geometry, which is a geometric element with known analytical representation (line, plane, circle, etc.). The substitute geometry is then used to determine position, dimension and form of the element and the accordance of the manufactured part with the design tolerances. Therefore, the precision of the substitute geometry estimate is the basis for a reliable and accurate dimensional measurement. Two important factors that affect the precision of the estimate are the number and the position of measured (or sampled) points. The present work is addressed to the definition of the relationship between the number and position of sampled points and the errors of the estimate of radius and position of the centre of circular profiles (holes or shafts) with the Least Squares Method. A new approach to the problem is proposed and the analytical solution of the problem is presented. Using the identified equations it is possible to evaluate the distributions of the estimate errors and therefore to determine their confidence limits. As will be discussed, as the number of sampled points increases the confidence limits of the errors may increase or decrease, depending on the spectra of the machined profiles. The problem of the definition of the optimal number and angular position of the sampled points is analysed and a solution is proposed. Finally, the last part of the present work is an application of these equations to a real case of turning operation of steel.