摘要
为了能够在接触式自由曲面轮廓测量过程中放宽对工件位置调整的要求并提供高精度的测量结果,本文运用最小二乘法的基本原理,提出了一个可通过测量数据拟合出一个最佳位置放置参数的数学模型。该模型能同时校正自由曲面放置时存在的绕X、Y、Z轴的微小旋转量及沿X、Y、Z方向上的微小偏离量所造成的测量误差。大量数学模拟结果表明,该模型在恢复上述误差源上具有很高的精度,可精确地恢复1cm以下的偏心和0.1°以下的旋转量。对一实际自由曲面的测量结果表明,该模型可靠有效,为接触式三坐标测量自由曲面轮廓提供了宽松的镜子放置条件,同时提供了可靠的测量结果。其分析数据的基本原理对其它非接触式的自由曲面的轮廓测量同样具有较高的参考价值。
To unwind the requirement of a freeform surface for the position adjustment and to provide high precision measurement results in a high precision contacting freeform surface contour measure- ment, this paper proposes a mathematical model based on the least square method. The model can fit the measured dada to obtain optimized position parameters. After analysis of possible causes for the measurement error of Coordinate Measuring Machine（CMM）, the model can be used to correct the er- rors caused by the rotation in the X, Y, Z axes and the eccentricity in the X, Y, Z direction that exist in the positioning of freeform surface. By mathematical simulations, it is proved that this model a- chieves high precision in correction of the errors for eccentricity less than 1 cm and inclination less than 0.1 °and shows a very reliable and effective result. It provides loose workpieee positioning condi- tions, high precision and reliable measurement results. The analysis principles proposed also offer a reference for other contacting freeform surface contour measurement methods.
出处
《光学精密工程》
EI
CAS
CSCD
北大核心
2013年第11期2813-2820,共8页
Optics and Precision Engineering
基金
国家自然科学基金资助项目(No.61108042
No.61008034)
关键词
自由曲面
轮廓测量
三坐标测量仪
数据处理模型
最小二乘法
freeform surface
contour measurement
Coordinate Measuring Machine（CMM）
mathe-matical model
Least square method
