Abstract
Grinding wheel geometry error and wheel wear are the major error sources in SiC mirror grinding. In this paper, a segmented mirror containing seven hexagonal SiC blocks is ground with a fewer-axis grinding machine with an arc-shaped grinding wheel in simulation. Error model with both grinding wheel geometry error and wheel wear error is established. The error model is linearized, and a corresponding measurement strategy is given. A method using only one measuring process of error separation and compensation for both geometry error and wheel wear error is then given to reduce the profile error of the mirror. A simulation method considering the wheel wear is used to generate measurement data of the mirror with errors. Separation and compensation processes are carried out using the simulation data. Separation results correspond with simulation settings. Grinding trajectories are modified, and the profile error of the segmented mirror after compensation drops from 37.1 to 1.6 μm. A grinding experiment is also conducted, and the profile error of the mirror drops from 44.8 to 4.9 μm.
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References
Kasai T, Harvey J E, Thompson A K (1995) Scattering effects from residual optical fabrication errors. In: International Conference on Optical Fabrication and Testing. SPIE, Tokyo
Stepp L M, Johns M, McCarthy P, Raybould K, Bouchez A, Farahani A, Filgueira J, Jacoby G, Shectman S, Sheehan M, Gilmozzi R, Hall H J (2012) Giant Magellan telescope: overview. In: Ground-based and airborne telescopes IV. SPIE, Amsterdam
Gardner JP, Mather JC, Clampin M, Doyon R, Greenhouse MA, Hammel HB, Hutchings JB, Jakobsen P, Lilly SJ, Long KS, Lunine JI, McCaughrean MJ, Mountain M, Nella J, Rieke GH, Rieke MJ, Rix H-W, Smith EP, Sonneborn G, Stiavelli M, Stockman HS, Windhorst RA, Wright GS (2006) The James Webb Space Telescope. Space Sci Rev 123:485–606
Comley P, Morantz P, Shore P, Tonnellier X (2011) Grinding metre scale mirror segments for the E-ELT ground based telescope. CIRP Ann 60:379–382
Yin J, Li M, Xu J, Ding W, Su H (2022) Edge chipping characteristics in grinding SiCf/SiC composite. Ceram Int 48:7126–7135
Zhang Y, Zhao Y, Xu J, Rao M, Yin Y (2021) A new strategy to reduce edge chipping using stress wave impedance matching. CIRP Ann 70:277–280
Wahr JM (1985) Deformation induced by polar motion. J Geophys Res 90:9363–9368
Tonnellier X (2009) Precision grinding for rapid manufacturing of large optics. Ph.D. dissertation. Cranfield University
Tsunemoto K, Mohammad SSZ, Katsuo S (1996) A new grinding method for aspheric ceramic mirrors. J Mater Process Technol 62:387–392
Yu S, Yao P, Huang C, Chu D, Zhu H, Zou B, Liu H (2022) On-machine precision truing of ultrathin arc-shaped diamond wheels for grinding aspherical microstructure arrays. Precis Eng 73:40–50
Deng H, Xu Z (2021) Laser dressing of arc-shaped resin-bonded diamond grinding wheels. J Mater Process Technol 288:1–12
Lin XH, Wang ZZ, Guo YB, Peng YF, Hu CL (2013) Research on the error analysis and compensation for the precision grinding of large aspheric mirror surface. Int J Adv Manuf Technol 71:233–239
Jiang Z, Yin Y, Chen X (2015) Geometric error modeling, separation, and compensation of tilted toric wheel in fewer-axis grinding for large complex optical mirrors. J Manuf Sci Eng 137:1–10
Xu L, Niu M, Zhao D, Xing N, Fan F (2019) Methodology for the immediate detection and treatment of wheel wear in contour grinding. Precis Eng 60:405–412
Jiang Z, Yin Y (2013) Geometrical principium of fewer-axis grinding for large complex optical mirrors. Sci China Technol Sci 56:1667–1677
Lin S, Jiang Z, Yin Y (2019) Research on arc-shaped wheel wear and error compensation in arc envelope grinding. Int J Adv Manuf Technol 103:1847–1859
Li C, Zhang F, Ma Z, Ding Y (2016) Modeling and experiment of surface error for large-aperture aspheric SiC mirror based on residual height and wheel wear. Int J Adv Manuf Technol 91:13–24
Wegener K, Hoffmeister HW, Karpuschewski B, Kuster F, Hahmann WC, Rabiey M (2011) Conditioning and monitoring of grinding wheels. CIRP Ann 60:757–777
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Zhao, Y., Zhang, Y., Xu, J. et al. Error separation and compensation of arc wheel grinding for SiC segmented mirror considering wheel wear. Int J Adv Manuf Technol 126, 3543–3554 (2023). https://doi.org/10.1007/s00170-023-11194-7
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DOI: https://doi.org/10.1007/s00170-023-11194-7