Yiang Zhang

Magnetorheological finishing is widely used in the high-precision processing of optical components, but due to the influence of multi-source system errors, the convergence of single-pass magnetorheological finishing (MRF) is limited. Although iterative processing can improve the surface accuracy, repeated tool paths tend to deteriorate mid-spatial frequency textures, and for complex surfaces such as aspheres, traditional manual alignment is time-consuming and lacks repeatability, significantly restricting the processing efficiency. To address these issues, firstly, this study systematically analyzes the effect of six-degree-of-freedom positioning errors on convergence behavior, establishes a positioning error-normal contour error transmission model, and obtains a workpiece positioning error tolerance threshold that ensures that the relative convergence ratio is not less than 80%. Further, based on these thresholds, a hybrid self-positioning method combining machine vision and a probing module is proposed. A composite data acquisition method using both a camera and probe is designed, and a stepwise global optimization model is constructed by integrating a synchronous iterative localization algorithm with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The experimental results show that, compared with the traditional alignment, the proposed method improves the convergence ratio of flat workpieces by 41.9% and reduces the alignment time by 66.7%. For the curved workpiece, the convergence ratio is improved by 25.7%, with an 80% reduction in the alignment time. The proposed method offers both theoretical and practical support for high-precision, high-efficiency MRF and intelligent optical manufacturing.

The accuracy of traditional measuring machines is affected by the measuring range and sensitive geometric errors, and it is not possible to combine large caliber and high-precision measurements. This study proposes a differential geometric error-weighting method for designing a high-precision, large-diameter measuring machine. The machine utilized a zero-Abbe arm structure and applied the rigid body theory and small-angle hypothesis to model geometric errors. Weights were calculated for 23 geometric errors, identifying eight sensitive ones. A picometer-precision laser interferometer (quDIS) with a theoretical positioning accuracy of 0.2 nm/mm and standard flat rulers are used to ensure highly accurate positioning of the Y-axis/Z-axis of the measuring platform and reduce the straightness of both axes by approximately 75%, with radial and axial runout of the rotary table under 100 nm. The development and design method of the high-precision measuring machine proposed in this study is applicable to large-diameter high-precision flexible measurement, and the accurate control of measuring machine movement accuracy is realized by calculating the geometric error weights.