The optimal design of a measurement system to measure the geometric errors of linear axes

In this paper, a measurement system consisting of an L-type reference mirror and five capacitive sensors is analyzed and optimized to measure the geometric errors of linear axes more accurately. The positions of the reference coordinate system and capacitive sensors are optimized to minimize the standard uncertainty of estimated geometric errors, which is due to the standard uncertainty of the component—the L-type reference mirror and the capacitive sensors. Primarily, the flatness of the L-type reference mirror and the linearity of the capacitive sensors cause the component uncertainties. The capacitive sensors fixed on the linear axis are moved, and the L-type reference mirror is fixed on the base of the machine tool to eliminate Abbe's error, which is proportional to the command position of a linear axis. Five geometric errors of a linear axis are measured with a single setup and single measurement, simply. Finally, the optimized measurement system is applied to measure the geometric errors of linear axes X and Y of a three-axis machine tool. And the standard uncertainties of the measured geometric errors are calculated based on the specifications of the L-type reference mirror and the capacitive sensors.