image: Figure 1 | The schematic diagram of the controllable spiral magnetorheological polishing method (Time-varying spacing-swing strategy).
Credit: Feng Shi et al.
Computer-Controlled Sub-Aperture Polishing enables high-precision surface correction using small tools. Material removal is controlled by dwell time modulation along toolpaths, but the discontinuous convolution perpendicular to scan directions generates mid-spatial-frequency (MSF) ripple errors. These cause beam modulation, scattering, and contrast degradation, critically limiting optical system performance.
Magnetorheological Finishing (MRF) outperforms conventional methods (small tools, ion beam) with superior determinism, surface quality, and damage-free processing. Its compliant ribbon enables conformal contact across complex geometries, while offering broader material compatibility and higher efficiency than ion beam polishing. However, MSF errors remain its primary constraint.
Current MRF MSF mitigation approaches:
1. Optimization of MRF Parameters and Combined Process Post-Processing Technology: Compromises other spatial frequencies and requires iterative steps.
2. Modification of Polishing Paths During Machining: Suppresses ripple errors but degrades low-spatial-frequency accuracy.
3. Regulation of the Spatial Morphology and Stability of MRF TIF: Maintains raster scanning processing method, failing to eliminate MSF ripple.
Therefore, a fundamentally novel approach intrinsically eliminating the MSF ripple mechanism is imperative, enabling precise control over the MSF range.
In a new paper published in Light: Advanced Manufacturing, a team of scientists, led by Professor Feng Shi and Ci Song from College of Intelligence Science and Technology, National University of Defense Technology, 109 Deya Road, Changsha 410073, China, and co-workers have developed a novel sub-aperture polishing technology: Controllable Spiral Magnetorheological Finishing (CSMRF). This method disrupts the mechanism of conventional constant tool influence function (TIF) convolution material removal to control convolution MSF error. Building upon CSMRF, the research team ingeniously integrates adaptive path spacing with spatially varying TIF. This synergistic approach enables the mitigation and homogenization of MSF ripple errors. Critically, the complementary roles of adaptive spacing and TIF variation in regulating MSF errors were experimentally validated. The team employs genetic algorithms (GA) to precisely determine the optimal combination of adaptive spacing parameters and TIF spiral angles. Implementation utilizes a non-negative gradient-constrained dwell time algorithm to realize the CSMRF process. This integrated optimization and control strategy enables directed suppression of specific MSF error bands. The CSMRF methodology provides effective control over targeted MSF error distributions based on specific optical fabrication requirements. Furthermore, this pioneering sub-aperture polishing framework utilizing a spatially modulated convolution kernel presents a novel paradigm for full-spatial-frequency error cooperative control in precision optics manufacturing.
The research team conducted an in-depth analysis of MSF ripple error morphology evolution, grounded in sub-aperture polishing convolution theory. This investigation specifically addressed material removal under discontinuous line-feed machining conditions. We comparatively examined MSF ripple evolution across three scanning methodologies: conventional raster patterns, time-varying line feed raster paths, and time-varying spiral tool-influence function (TIF) trajectories, as visualized in Fig. 2. Further spectral analysis via Fourier transform elucidated the constructive interference mechanisms governing MSF ripples across these strategies. Results demonstrate that the time-varying line feed raster strategy induces phase misalignment during spectral summation, thereby attenuating periodic ripple peaks. Concurrently, the spiral TIF's spatial superposition generates an "erasure effect" that effectively smooths emerging spectral spikes. Consequently, synergistic integration of time-varying path spacing and controllable spiral MRF processing delivers complementary MSF error control: the former intrinsically eliminates periodic MSF ripple, while the latter suppresses multi-frequency ripple structures through spike-smoothing action.
CSMRF employs a time-variant TIF, rendering conventional convolution-based material removal models inapplicable. This operational paradigm invalidates dwell time algorithms derived from discrete convolution principles. To resolve this, the research team implemented a non-negative gradient-constrained dwell time algorithm founded on linear equations. Subsequent integration of genetic algorithm optimization co-optimized adaptive path spacing and CSMRF spiral angles. We designed a fitness function explicitly targeting suppression of MSF band errors, thereby optimizing performance under diverse constraints. This approach ultimately derived the adaptive spacing-spiral angle combination that minimizes errors within targeted MSF bands (Fig.3). The developed algorithm demonstrates universal applicability for multi-objective TIF optimization and dwell time solving in other time-variant finishing methods. Significantly, this work establishes the first documented implementation of time-variant TIFs within multi-objective optimization frameworks for manufacturing processes.
Journal
Light: Advanced Manufacturing
Article Title
Novel suppression strategy of mid-spatial-frequency errors in sub-aperture polishing: adaptive spacing-swing controllable spiral magnetorheological finishing (CSMRF) method