The development of thermal error compensation on CNC machine tools by combining ridge parameter selection and backward elimination procedure

Abstract

Abstract The total processing error of CNC machine tools essentially comprises geometric errors and thermal errors. Therefore, reducing the influence of thermal errors is necessary. In this study, 13 temperature sensors were utilized to measure temperature variations of heat sources on a machine. These sensors work in conjunction with a non-contact optical measurement system to measure the positioning offset error of a rotating shaft. In this study, a ridge parameter selection method was devised and integrated into a backward elimination procedure to achieve ridge regression thermal error compensation modeling. The study considered three methods for selecting temperature variable combinations. The first method requires the use of all sensors, the second method selects the combination with the minimum mean-square error, and the third method considers the effect of diminishing returns. The ridge regression method, which considers the diminishing returns effect, is known as the “R–DR model”. The R-DR model is applied to the CNC machine used in this study to reduce the maximum peak-to-peak error on the Y-axis from 54.41 µm to 13.94 µm using only 3 temperature sensors, and on the Z-axis from 73.59 µm to 10.12 µm using 4 temperature sensors. Therefore, the R–DR model has two advantages: high precision (post-compensation peak-to-peak thermal error of less than 14 µm) and fewer temperature sensors, thereby allowing the thermal error compensation modeling method to demonstrate high engineering applicability and accuracy.