Synthetic positioning error modelling of a feed axis for a precision CNC machine tool

The linear feed system is a kernel movement component in a CNC machine tool. Because of thermal generation principally caused by motor and frictional action between motion pairs, such as cutter-workpiece and ball-raceway pairs, positioning errors have not only geometrical errors but also thermal errors, which plays an important role on the machining accuracy of parts. Geometrical errors solely related to position can be extracted through coordinate rotation transformation and expressed in the form of a polynomial. Many temperature sensors are allocated at different places to acquire the overall temperature changes in the feed system. To eliminate the correlation between some temperatures, the K-means clustering algorithm is employed to categorize the temperature measurement points, and key points are selected based on grey correlation analysis to achieve representative measurements. Consequently, a thermal error model is implemented by a BP neural network to establish the relationship between temperature and thermal deformation. A synthetic model is obtained through superposition of the above two error models to predict the positioning error. A thermal characteristic experiment of the linear feed axis carried out on a precision CNC machine verifies the effectiveness of the positioning error modelling method and provides a feasible and reliable reference to compensate for feed axis positioning errors in CNC machine tools.