# A Novel High-Precision Workpiece Self-Positioning Method for Improving the Convergence Ratio of Optical Components in Magnetorheological Finishing

## TL;DR

This paper introduces a new method for positioning workpieces in magnetorheological finishing to improve optical component manufacturing efficiency and precision.

## Contribution

A hybrid self-positioning method combining machine vision and a probing module is proposed to enhance convergence and reduce alignment time.

## Key findings

- The proposed method improves flat workpiece convergence by 41.9% and reduces alignment time by 66.7%.
- For curved workpieces, convergence improves by 25.7% with an 80% reduction in alignment time.
- A positioning error-normal contour error transmission model is established to set error tolerance thresholds.

## Abstract

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.