Skip to main content
SpringerLink
Log in

Material removal model considering influence of curvature radius in bonnet polishing convex surface

  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. WALKER D D, BEAUCAMP A T H, BINGHAM R G, et al. Precessions process for efficient production of aspheric optics for large telescope and their instrumentation[J]. Proc. SPIE, 2003, 4842: 73–84.

    Article  Google Scholar 

  2. WALKER D D, BEAUCAMP A T H, BROOKS D, et al. Novel CNC polishing process for control of form and texture on aspheric surfaces[J]. Proc. SPIE, 2002, 4767: 99–106.

    Article  Google Scholar 

  3. WALKER D D, BEAUCAMP A T H, BROOKS D, et al. New results from the precession polishing process scaled to larger sizes[J]. Proc. SPIE, 2004, 5494: 71–81.

    Article  Google Scholar 

  4. WALKER D D, KIM S W, BINGHAM R G, et al. Computer-controlled polishing of moderate-sized general aspherics for instrumentation[J]. Proc. SPIE, 1998, 3355: 947–954.

    Article  Google Scholar 

  5. BINGHAM R G, WALKER D D, KIM D H, et al. Novel automated process for aspheric surfaces[J]. Proc. SPIE, 2004, 4093: 445–450.

    Article  Google Scholar 

  6. WALKER D D, BEAUCAMP A T H, BINGHAM R G, et al. Precessions asheric polishing: new results from the development program[J]. Proceeding of SPIE-The International Society for Optical Engineering, 2003, 5180: 15–28.

    Google Scholar 

  7. JACOBS S D. International innovations in optical finishing[J]. Proceedings of The Society of Photo-Opitcal Instrumentation Engineerings (SPIE), 2004, 5523: 264–272.

    Google Scholar 

  8. KIM D W, KIM S W. Novel simulation technique for efficient fabrication of 2-m class hexagonal segments for extremely large telescope primary mirrors[J]. Proc. SPIE, 2005, 5638: 48–59.

    Article  Google Scholar 

  9. KIM D W, KIM S W. Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes[J]. Optics Express, 2005, 13: 910–917.

    Article  Google Scholar 

  10. BEAUCAMP A, NAMBA Y, CHARLTON P. Corrective finishing of extreme ultraviolet photomask blanks by precessed bonnet polishier[J]. Applied Optics, 2014, 53(14): 3075–3080.

    Article  Google Scholar 

  11. BEAUCAMP A, NAMBA Y, INASAKI I, et al. Finishing of optical moulds to ?/20 by automated corrective polishing[J]. CRIP Annal-Manufacturing Technology, 2011(60): 375–378.

    Article  Google Scholar 

  12. PAN Ri, WANG Zhenzhong, WANG Chunjin, et al. Research on the precession motion control technology for free surface optical elements in bonnet polishing[J]. Journal of Mechanical Engineering, 2013, 49(3): 186–193. (in Chinese)

    Article  Google Scholar 

  13. PAN Ri, YANG Wei, WANG Zhenzhong, et al. The controllable bonnet polishing system for large diameter aspheric optical elements in bonnet polishing[J]. Laser and Particle Beams, 2012, 24(6): 1344–1348.

    Article  Google Scholar 

  14. WANG Chunjin, YANG Wei, WANG Zhenzhong, et al. Dwell-time algorithm for polishing large optics[J]. Applied Optics, 2014, 53(21): 4752–4760.

    Article  Google Scholar 

  15. WANG C, WANG Z, YANG X, et al. Modeling of the static tool influence function of bonnet polishing based on FEA[J]. International Journal of Advanced Manufacturing Technology, 2014, 74(1–4): 341–349.

    Article  Google Scholar 

  16. WANG Chunjin, YANG Wei, YE Shiwei, et al. Optimization of parameters for bonnet polishing based on the minimum residual error method[J]. Optical Engineering, 2014, 53(7): 075108(1–9).

    Article  Google Scholar 

  17. JI S M, ZHANG L, ZHANG X, et al. Spinning-inflated-ballonet polishing tool and its application in curved surface polishing[J]. Key Engineering Materials, 2007, 339: 21–25.

    Article  Google Scholar 

  18. JI SM, ZHANG X, ZHANG L, et al. Form and texture control of free-form surface polishing[J]. Key Engineering Materials, 2006, 304–305: 113–117.

    Article  Google Scholar 

  19. JI Shiming, YUAN Qiaoling, ZHANG Li, et al. Study of the removing depth of the polishing surface based on a novel spinning–inflated-ballonet polishing tool[J]. Materials Science Forum, 2006, 532–533: 452–455.

    Article  Google Scholar 

  20. JIN Mingsheng, JI Shiming, ZHANG Li, et al. The optimization of the line space and experimental research on the continuous precession in bonnet polishing[J]. China Mechanical Engineering, 2013, 24(7): 861–865.

    Google Scholar 

  21. ZHANG Li, LI Yanbiao, JIN Mingsheng, et al. Analysis of the abrasive field to polish mold free surface in new bonnet polishing[J]. China Mechanical Engineering, 2014, 25(6): 832–835.

    Google Scholar 

  22. CONG Kai. 3-PRS CNC system development of bonnet polishing parallel machine[D]. Harbin: Harbin Institute Technology, 2010.

    Google Scholar 

  23. XIE Dagang, GAO Bo, YAO Yingxue, et al. Study of local material removal model of bonnet tool polishing[J]. Key Engineering Materials, 2006, 304–305: 335–339.

    Article  Google Scholar 

  24. PRESTON F W. The theory and design of plate glass polishing[J]. Journal of the Society of Glass Technology, 1927, 11: 214–256.

    Google Scholar 

  25. JOHNSON K L. Contact mechanics[M]. Beijing: High Education Press, 1992.

    Google Scholar 

  26. SONG Jianfeng, YAO Yingxue, XIE Dagang, et al. Effects of polishing parameters on material removal for curved optical glasses in bonnet polishing[J]. Chinese Journal of Mechanical Engineering, 2008, 21(5): 29–33.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Jianfeng Song

  2. Digital Manufacturing Laboratory of Mechatronicas Engineering College, Harbin Institute Technology, Harbin, 150001, China

    Jianfeng Song & Yingxue Yao

Authors
  1. Jianfeng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingxue Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianfeng Song.

Additional information

Supported by Young Teacher Independent Research Subject of Yanshan University of China (Grant No. 15LGA002)

SONG Jianfeng is currently associate professor at College of Mechanical Engineering, Yanshan University, China. She graduated from Harbin Institute Technology, China, in October, 2009. Her research interests include intelligent manufacturing and digital manufacturing.

YAO Yingxue is currently a professor at School of Mechatronics Engineering, Harbin Institute Technology, China.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, J., Yao, Y. Material removal model considering influence of curvature radius in bonnet polishing convex surface. Chin. J. Mech. Eng. 28, 1109–1116 (2015). https://doi.org/10.3901/CJME.2015.0923.114

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2015.0923.114

Keywords

Search

Navigation