Modeling of the Positioning Error in Ultra-Precision Machine Tools

The positioning error of ultra-precision machine tools is the primary factor directly affecting the machining accuracy. It mainly depends on the machine tools guide. And its variation trend contains the same inertia as that of the machine tools movement. The variation trend of the positioning error is the derivative of a function fitted with the positioning errors of three adjacent testing points. The variation trends function is fitted with the variation trend of many points. The model of positioning error is the integral of the variation trends function. Because the variation trend of positioning error has certain inertia, the model of positioning error which is obtained in this way is more precise and more reliable than error function model which is directly fitted with limited discrete data.