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Adaptive on-line compensation model on positioning error of ball screw feed drive systems used in computerized numerical controlled machine tools

The positioning error of ball screw feed systems is mainly caused by thermal elongation of the screw shaft in machine tools. In this article, an adaptive on-line compensation method of positioning error for the ball screw shaft is established. In order to explore the thermal–solid mechanism of ball screw feed drive systems, the experiments were carried out. An exponential fitting equation is presented to obtain the temperature relationship between the temperature sensitive point and its center of each heat source based on the finite element method of the feed drive system. Consequently, based on time and position exponential distribution functions, a variable separation model of heat transfer is established. Furthermore, based on the heat transfer model of multiple varying and moving heat sources, an adaptive on-line analytical compensation model of positioning error is presented. Finally, the effect of the adaptive on-line analytical compensation model of positioning error is verified through the experiments. And, this model has self-adaptive ability and robustness. Therefore, this adaptive on-line analytical compensation model based on the heat transfer theory can be applied in real-time compensation of positioning error.