Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature
Over the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/15/12/1415 |
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| author | Jiadai Xue Yuhao Li Mingyang Gao Dongyun Gu Yanlin Wu Yanwen Liu Yuxin Fan Peng Zheng Wentao Chen Zhigao Chen Zheng Qiao Yuan Jin Fei Ding Yangong Wu Bo Wang |
| author_facet | Jiadai Xue Yuhao Li Mingyang Gao Dongyun Gu Yanlin Wu Yanwen Liu Yuxin Fan Peng Zheng Wentao Chen Zhigao Chen Zheng Qiao Yuan Jin Fei Ding Yangong Wu Bo Wang |
| author_sort | Jiadai Xue |
| collection | DOAJ |
| description | Over the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechanisms for variable-curvature X-ray mandrels, which are crucial for achieving the desired surface roughness and form accuracy, especially in reducing mid-spatial frequency (MSF) errors. It is essential to incorporate flexible control in deterministic small-tool polishing to improve the tool’s adaptability to curvature variations and achieve stable, Gaussian-like tool influence functions (TIFs). In this paper, we introduce a curvature-adaptive prediction model for compliance figuring, based on the Preston hypothesis, using a compliant shaping tool with high slurry absorption and retention capabilities. This model predicts the compliance figuring process of variable-curvature symmetrical mandrels for X-ray grazing incidence mirrors by utilizing planar tool influence functions. Initially, a variable-curvature pressure model was developed to account for the parabolic and hyperbolic optical surfaces’ curvature characteristics. By introducing time-varying removal functions for material removal, the model establishes a variable-curvature factor function, which correlates actual downward pressure with parameters such as contact radius and contact angle, thus linking the variable-curvature surface with a planar reference. Subsequently, through analysis of the residence time distribution across different TIF models, hierarchical filtering, and PSD distribution, real-time correction of the TIFs was achieved to enable customized variable-curvature polishing. Furthermore, by applying a time-varying deconvolution algorithm, multiple rounds of flexible polishing iterations were conducted on the mandrels of a rotationally symmetric variable-curvature optical component, and the experimental results demonstrate a significant improvement in form accuracy, surface quality, and the optical performance of the mirror. |
| format | Article |
| id | doaj-art-9ab12c8c4ebb4358bb17fb09fb2e7b76 |
| institution | DOAJ |
| issn | 2072-666X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj-art-9ab12c8c4ebb4358bb17fb09fb2e7b762025-08-20T02:39:41ZengMDPI AGMicromachines2072-666X2024-11-011512141510.3390/mi15121415Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable CurvatureJiadai Xue0Yuhao Li1Mingyang Gao2Dongyun Gu3Yanlin Wu4Yanwen Liu5Yuxin Fan6Peng Zheng7Wentao Chen8Zhigao Chen9Zheng Qiao10Yuan Jin11Fei Ding12Yangong Wu13Bo Wang14Center for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mechanical and Electrical Engineering, China University of Mining and Technology-Beijing, Beijing 100083, ChinaCollege of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCenter for Precision Engineering, Harbin Institute of Technology, Harbin 150001, ChinaOver the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechanisms for variable-curvature X-ray mandrels, which are crucial for achieving the desired surface roughness and form accuracy, especially in reducing mid-spatial frequency (MSF) errors. It is essential to incorporate flexible control in deterministic small-tool polishing to improve the tool’s adaptability to curvature variations and achieve stable, Gaussian-like tool influence functions (TIFs). In this paper, we introduce a curvature-adaptive prediction model for compliance figuring, based on the Preston hypothesis, using a compliant shaping tool with high slurry absorption and retention capabilities. This model predicts the compliance figuring process of variable-curvature symmetrical mandrels for X-ray grazing incidence mirrors by utilizing planar tool influence functions. Initially, a variable-curvature pressure model was developed to account for the parabolic and hyperbolic optical surfaces’ curvature characteristics. By introducing time-varying removal functions for material removal, the model establishes a variable-curvature factor function, which correlates actual downward pressure with parameters such as contact radius and contact angle, thus linking the variable-curvature surface with a planar reference. Subsequently, through analysis of the residence time distribution across different TIF models, hierarchical filtering, and PSD distribution, real-time correction of the TIFs was achieved to enable customized variable-curvature polishing. Furthermore, by applying a time-varying deconvolution algorithm, multiple rounds of flexible polishing iterations were conducted on the mandrels of a rotationally symmetric variable-curvature optical component, and the experimental results demonstrate a significant improvement in form accuracy, surface quality, and the optical performance of the mirror.https://www.mdpi.com/2072-666X/15/12/1415variable-curvature mandrelcompliant figuring processthe mid-spatial frequency errorreal-time correction of TIFs |
| spellingShingle | Jiadai Xue Yuhao Li Mingyang Gao Dongyun Gu Yanlin Wu Yanwen Liu Yuxin Fan Peng Zheng Wentao Chen Zhigao Chen Zheng Qiao Yuan Jin Fei Ding Yangong Wu Bo Wang Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature Micromachines variable-curvature mandrel compliant figuring process the mid-spatial frequency error real-time correction of TIFs |
| title | Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature |
| title_full | Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature |
| title_fullStr | Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature |
| title_full_unstemmed | Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature |
| title_short | Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature |
| title_sort | research on stability of removal function in figuring process of mandrel of x ray focusing mirror with variable curvature |
| topic | variable-curvature mandrel compliant figuring process the mid-spatial frequency error real-time correction of TIFs |
| url | https://www.mdpi.com/2072-666X/15/12/1415 |
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