Thermally induced positioning error modelling and compensation based on thermal characteristic analysis

• The thermal characteristic of a ball screw system is analysed theoretically.
• A novel model based on thermal characteristic analysis is proposed to compensate the time-varying positioning error.
• The performance of the compensation system is good and it is utilized to improve the accuracy of machine tools.

To decrease the thermally induced positioning error of machine tools, a novel approach for modelling and compensation is proposed in this study. The cause of this error is determined to be dynamic pitch error, and its manifestations are discussed in this study. The thermal expansion of a screw shaft under the influence of friction heat is analysed theoretically, and a mathematical model of the transient temperature of the screw with regard to time is developed. A temperature calculation method in the cases of cooling in the process of warming up and warming up after cooling is also introduced. To solve the problem of heat unevenly distributed of the entire screw shaft, the screw shaft is divided into several evenly distributed heat regions, and the established model is fit for each region. The synthetic model is established by superposition of all models of the regions. In addition, an external error compensation system is developed based on a function called external mechanical origin offset in Fanuc CNC systems. Six test pieces are machined to validate the accuracy of the model and the effectiveness of the error compensation system. The result indicates that the accuracy of the pieces is significantly improved compared with that obtained without error compensation. The synthetic model of the entire screw shaft is demonstrated to be an effective approach to improve the accuracy of machine tools.