Geometric modeling and compensation of cutting tool positioning errors for eliminating protrusion in large-radius spherical surface machining

The production of optical components with a large radius of spherical surfaces requires exceptionally high surface profile accuracy. Minor deviations in the positioning of the cutting tool caused by factors, such as mechanical backlash, thermal deformation, and incorrect tool positioning, can result in dimensional errors of the machined surface, particularly in the form of protrusions that indicate processing defects. Despite a wide range of studies focused on tool wear and general machining errors, insufficient attention has been given to the geometric modeling and correction of defects caused by tool positioning errors. This study presents a comprehensive approach to geometrically modeling the impact of cutting tool positioning errors on the machined surface profile. A mathematical model has been developed to model the interaction between the tool and the spherical surface, enabling precise estimation of the radial machining error. Based on these data, a new error compensation method is proposed, allowing for the correction of errors by modifying the tool movement trajectory. The proposed model accurately predicts the formation and characteristics of protrusions resulting from tool displacement during the machining of spherical surfaces with a large radius. Implementation of the compensation method significantly reduces the defect rate, improves geometric accuracy, and decreases the need for additional processing. Addressing defects caused by positioning errors enables the proposal of a new method that has not previously been considered in precision machining research. The proposed model and tool positioning error compensation method offer an effective and practical solution for improving the surface profile accuracy of optical components, thereby enhancing the precision and efficiency of manufacturing processes. The proposed method contributes to the advancement of highprecision optical component manufacturing with minimal post-processing costs, providing a novel approach in the fields of instrument engineering and precision mechanical engineering.

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