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An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms
An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms
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An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms
An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms

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An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms
An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms
Journal Article

An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms

2023
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Overview
Higher-order error terms (HOET) occur inevitably during the geometric error modelling and compensation of a machine tool using both screw theory and multi-body system (MBS) theory. Though the HOET has little influence on machining accuracy, it will make analysis and compensation of geometric errors complicated and tedious. Especially, it is necessary to eliminate the higher-order error terms artificially when deriving the analytical expressions for geometric error compensation. Hence, a novel geometric error modelling and compensation algorithm without the interference of HOET is proposed in this paper. Taking a three-axis CNC machine tool as an example. A new summation operation rule for geometric error modelling was defined according to the homogeneous transformation matrix (HTM) method, which has no multiplication between error matrices. And the analytical expressions of motion-axis commands for error compensation could be calculated directly according to the new modelling algorithm without manual deletion of HOET. Active elimination of HOET can simplify the process of geometric error modelling and compensation and can significantly improve efficiency. The results show that the acquisition efficiency of symbolic compensation expressions can be improved by at least 70% compared to the traditional actual inverse kinematics. Moreover, the HOET are automatically eliminated and has a small influence on the compensation accuracy. Finally, a cutting experiment was conducted and analyzed to verify the high efficiency and effectiveness of the proposed method.