Research and evaluation of geometric element data fitting software for coordinate measurement machine

Abstract

Standard geometry element fitting software is a critical important part of the coordinate measuring machine ( CMM ). It is used for coordinate data processing and data evaluation. At present, the commercial fitting software of the coordinate machine manufacturer is not disclosed to the public. So it is inconvenient to develop secondary applications. This work developed a kind of geometric element fitting software based on open source code. The software can be used to fit CMM measurement data to common geometric elements including lines, circles, planes, spheres, cylinders, and cones. The core algorithm of software is based on a least-squares algorithm and a Gauss-Newton iterative algorithm. Least squares is a data optimization technique that seeks the best function match of the data by the sum of the squares of the smallest errors. The basic idea of the Gauss-Newton iteration method is to replace the nonlinear regression model with the Taylor series expansion approximation. Then through multiple iterations, the regression coefficient is modified several times so that the regression coefficient continuously approaches the optimal regression coefficient of the nonlinear regression model. Finally, the residual square sum of the original model is minimized. The accuracy of fitting results are verified with the standard reference data developed by national institute of standards and technology. The software can be used to the geometry element measurement uncertainty evaluation.