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 Mathematical model for active lap to achieve unsymmetrical fabrication Liu, Haitao1,2; Zeng, Zhige1; Wu, Fan1; Fan, Bin1; Liu, H. Volume 8416 Pages 841622 2012 Language 英语 ISSN 0277786X DOI 10.1117/12.975689 Indexed By Ei Subtype 会议论文 Abstract A new mathematical model is proposed to calculate the Material Removal (MR) on any point of the mirror's surface during Computer Controlled Active Lap (CCAL)'s grinding and polishing. In this model, the workpiece rotation rate ω1, lap rotation rate ω2 and the pressure P which applied on the workpiece surface by active lap are binary functions in the mirror polar coordinate system whose polar axis is from workpiece center to lap center's initial position. The independent variables ρ and θ are the coordinates of lap center during fabrication, so the rotation rate and pressure is become to ω1(ρ, θ), ω2(ρ, θ) and P(ρ, θ). According to the simulation, this model can produce unsymmetrical material removal by choosing unsymmetrical ω1(ρ, θ), ω2(ρ, θ) or P(ρ, θ). This means it is possible to get the optimal ω1, ω2 and P functions for the demanded material removal map, and make the effects of single circle manufacture much better. This model can give active lap the unsymmetrical fabrication capability, and suitable for correcting the astigmatism or grinding off-axis aspheric surface. © 2012 SPIE.; A new mathematical model is proposed to calculate the Material Removal (MR) on any point of the mirror's surface during Computer Controlled Active Lap (CCAL)'s grinding and polishing. In this model, the workpiece rotation rate ω1, lap rotation rate ω2 and the pressure P which applied on the workpiece surface by active lap are binary functions in the mirror polar coordinate system whose polar axis is from workpiece center to lap center's initial position. The independent variables ρ and θ are the coordinates of lap center during fabrication, so the rotation rate and pressure is become to ω1(ρ, θ), ω2(ρ, θ) and P(ρ, θ). According to the simulation, this model can produce unsymmetrical material removal by choosing unsymmetrical ω1(ρ, θ), ω2(ρ, θ) or P(ρ, θ). This means it is possible to get the optimal ω1, ω2 and P functions for the demanded material removal map, and make the effects of single circle manufacture much better. This model can give active lap the unsymmetrical fabrication capability, and suitable for correcting the astigmatism or grinding off-axis aspheric surface. © 2012 SPIE. Conference Name Proceedings of SPIE: 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Advanced Optical Manufacturing Technologies Conference Date 2012 Citation statistics Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS] Document Type 会议论文 Identifier http://ir.ioe.ac.cn/handle/181551/7579 Collection 先光中心 Corresponding Author Liu, H. Affiliation 1. Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China2. Graduate University, Chinese Academy of Sciences, Beijing 100039, China Recommended CitationGB/T 7714 Liu, Haitao,Zeng, Zhige,Wu, Fan,et al. Mathematical model for active lap to achieve unsymmetrical fabrication[C],2012:841622.
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