An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing
The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/12/5/471 |
| _version_ | 1797536879682256896 |
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| author | Yajun Wang Yunfei Zhang Renke Kang Fang Ji |
| author_facet | Yajun Wang Yunfei Zhang Renke Kang Fang Ji |
| author_sort | Yajun Wang |
| collection | DOAJ |
| description | The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr<sub>150</sub> = 0.028 λ and PVcr<sub>100</sub> = 0.014 λ respectively. |
| first_indexed | 2024-03-10T12:07:07Z |
| format | Article |
| id | doaj.art-db9bff7d0c6f4669998de09f1814a190 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-10T12:07:07Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-db9bff7d0c6f4669998de09f1814a1902023-11-21T16:31:24ZengMDPI AGMicromachines2072-666X2021-04-0112547110.3390/mi12050471An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical SurfacingYajun Wang0Yunfei Zhang1Renke Kang2Fang Ji3School of Mechanical Engineering, Dalian University of Technology, Dalian 116023, ChinaInstitute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang 621900, ChinaSchool of Mechanical Engineering, Dalian University of Technology, Dalian 116023, ChinaInstitute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang 621900, ChinaThe dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr<sub>150</sub> = 0.028 λ and PVcr<sub>100</sub> = 0.014 λ respectively.https://www.mdpi.com/2072-666X/12/5/471ultra-precision machiningcomputer-controlled optical surfacingdwell time algorithmremoval functionelementary approximation |
| spellingShingle | Yajun Wang Yunfei Zhang Renke Kang Fang Ji An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing Micromachines ultra-precision machining computer-controlled optical surfacing dwell time algorithm removal function elementary approximation |
| title | An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing |
| title_full | An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing |
| title_fullStr | An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing |
| title_full_unstemmed | An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing |
| title_short | An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing |
| title_sort | elementary approximation of dwell time algorithm for ultra precision computer controlled optical surfacing |
| topic | ultra-precision machining computer-controlled optical surfacing dwell time algorithm removal function elementary approximation |
| url | https://www.mdpi.com/2072-666X/12/5/471 |
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