Hennebelle F, Coorevits T, Bigerelle M
Laboratoire d'Electronique, Informatique et Image, UMR CNRS 6306, Université de Bourgogne, Auxerre Cedex, France; Centre Technique des Industries Mécaniques (CETIM), Pôle Expertise, Métrologie, Etalonnage, Senlis, France.
Scanning. 2014 Jan-Feb;36(1):161-9. doi: 10.1002/sca.21114. Epub 2013 Jul 22.
The straightness error of a coordinate measuring machine (CMM) is determined by measuring a rule standard. Thanks to a reversal technique, the straightness uncertainty of the CMM is theoretically dissociated from the straightness uncertainty of the rule. However, stochastic variations of the whole measurement system involve uncertainties of the CMM straightness error. To quantify these uncertainties, different sources of stochastic variations are listed with their associated probability density functions. Then Monte Carlo methods are performed first to quantify error and secondly to optimize measurement protocol. It is shown that a 5-measurement distance from 0.1 mm to each measurement coordinate allows a double reduction of uncertainties, principally due to the rule roughness amplitude (R(a) = 0.35 µm) and because this optimal distance of 0.1 mm is equal to the autocorrelation length of the rule roughness. With this optimal configuration, the final uncertainly on the straightness error of the CMM studied is less than 1 µm on the whole evaluated length of the rule (1 m). An algorithm, including Probe Tip Radius of the CMM and surface roughness of the piece, is finally proposed to increase CMM reliability by minimizing error measurements due to surface roughness of the measured piece.
坐标测量机（CMM）的直线度误差通过测量标准尺来确定。借助反转技术，CMM的直线度不确定度在理论上与标准尺的直线度不确定度分离。然而，整个测量系统的随机变化会带来CMM直线度误差的不确定度。为了量化这些不确定度，列出了不同的随机变化源及其相关的概率密度函数。然后首先采用蒙特卡罗方法来量化误差，其次对测量方案进行优化。结果表明，从每个测量坐标到0.1mm的5次测量距离可使不确定度降低一半，这主要归因于标准尺粗糙度幅度（R(a)=0.35µm），并且因为0.1mm的这个最佳距离等于标准尺粗糙度的自相关长度。采用这种最佳配置，在所研究的CMM直线度误差上，在标准尺的整个评估长度（1m）上最终不确定度小于1µm。最后提出了一种算法，该算法包括CMM的探头半径和工件的表面粗糙度，以通过最小化由于被测工件表面粗糙度引起的误差测量来提高CMM的可靠性。
