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Form error compensation in single-point inclined axis nanogrinding for small aspheric insert


Based on an examination of traditional arc-enveloped grinding method, a single-point inclined axis nanogrinding method is presented to grind an aspheric insert by compensating tool setting error, radius error, and residual form error. Profile data from on-machine measurement are used to obtain the tool setting error and radius error of grinding wheel, as well as the normal residual form error. Compensation method of single-point inclined axis nanogrinding is built up for generating new compensation path. Grinding test of aspheric tungsten carbide insert with diameter 9.5 mm is conducted to evaluate performances of the grinding mode and compensation method. A last form error of 200 nm in peak to valley and surface roughness of 2.243 nm in Ra are achieved. These results indicated that the form error compensation method and single-point inclined axis nanogrinding mode can significantly improve form accuracy and surface roughness of ground surface.

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  1. 1.

    Ohmori H (1992) Electrolytic in-process dressing (ELID) grinding technique for ultraprecision mirror surface machining. I J JSPE 26(4):273–278

  2. 2.

    Lin Y, Huang H (2008) Brittle materials in nano-abrasive fabrication of optical mirror-surfaces. Prec Eng 32:336–341

  3. 3.

    Chen FJ, Hu SJ, Yin SH (2012) A novel mathematical model for grinding ball end milling cutter with equal rake and clearance angle. Int J Adv Manuf Technol. doi:10.1007/s00170-011-3889-y

  4. 4.

    Yin SH, Morita S, Ohmori H, Uehara Y, Lin WM, Liu Q, Maihara T, Iwamuro F, Mochida D (2005) ELID precision grinding of large special Schmidt plate for fibre multi-object spectrograph for 8.2 m Subaru telescope. Int J Mach Tools Manuf 45:1598–1604

  5. 5.

    Ohmori H, Nakagawa T (1995) Analysis of mirror surface generation of hard and brittle materials by ELID (Electronic In-Process Dressing) grinding with superfine grain metallic bond wheels. CIRP Ann Manuf Technol 44(1):287–290

  6. 6.

    Chen WK, Kuriyagawa T, Huang H, Yosihara N (2005) Machining of micro aspherical mould inserts. Prec Eng 29:315–323

  7. 7.

    Yin SH, Ohmori H, Dai YT, Uehara Y, Chen FJ, Tang HN (2009) ELID grinding characteristics of glass–ceramic materials. Int J Mach Tools Manuf 49(3–4):333–338

  8. 8.

    Schmitz TL, Ziegert JC, Canning JS, Raul Z (2008) Case study: a comparison of error sources in high-speed milling. Prec Eng 32(2):126–133

  9. 9.

    Nojedeh MV, Habibi M, Arezoo B (2011) Tool path accuracy enhancement through geometrical error compensation. Int J Mach Tools Manuf 51(6):471–482

  10. 10.

    Liang JC, Li HF, Yuan JX, Ni J (1997) A comprehensive error compensation system for correcting geometric, thermal, and cutting force-induced errors. Int J Adv Manuf Technol 13(10):708–712

  11. 11.

    Lei WT, Sung MP (2008) NURBS-based fast geometric error compensation for CNC machine tools. Int J Mach Tools Manuf 48(3–4):307–319

  12. 12.

    Uddin MS, Ibaraki S, Matsubara A, Matsushita T (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Prec Eng 33(2):194–201

  13. 13.

    Khan AW, Chen WY (2011) A methodology for systematic geometric error compensation in five-axis machine tools. Int J Adv Manuf Technol 53(5–8):615–628

  14. 14.

    Wu H, Zhang HT, Guo QJ, Wang XS, Yang JG (2008) Thermal error optimization modeling and real-time compensation on a CNC turning center. J Mater Process Technol 207(1–3):172–179

  15. 15.

    Creighton E, Honegger A, Tulsian A, Mukhopadhyay D (2010) Analysis of thermal errors in a high-speed micro-milling spindle. Int J Mach Tools Manuf 50(4):386–393

  16. 16.

    Zhang YH, Wu Q, Hu DJ (2008) Research on wear detection of wheel in precision NC curve point grinding. Int J Adv Manuf Technol 35(9–10):994–999

  17. 17.

    Rahman MS, Saleh T, Lim HS, Son SM, Rahman M (2008) Development of an on-machine profile measurement system in ELID grinding for machining aspheric surface with software compensation. Int J Mach Tools Manuf 48(7–8):887–895

  18. 18.

    Suzuki H, Tanaka K, Takeda H, Kawakami K, Nishioka M (1999) Study on precision grinding of micro aspherical surface: effects of tool errors on workpiece form accuracies and its compensation methods. J Japan Soc Prec Eng 65:401–405

  19. 19.

    Lee WB, Cheung CF, Chiu WM, Leung TP (2000) An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces. J Mater Process Technol 99:129–134

  20. 20.

    Habibi M, Arezoo B, Nojedeh MV (2011) Tool deflection and geometrical error compensation by tool path modification. Int J Mach Tools Manuf 51(6):439–449

  21. 21.

    Huang H, Chen WK, Kuriyagawa T (2007) Profile error compensation approaches for parallel nanogrinding of aspheric mould inserts. Int J Mach Tools Manuf 47(15):2237–2245

  22. 22.

    Chen FJ, Yin SH, Huang H, Ohmori H, Wang Y, Fan YF, Zhu YJ (2010) Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement. Int J Mach Tools Manuf 50(5):480–486

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Correspondence to Shaohui Yin.

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Chen, F., Yin, S., Ohmori, H. et al. Form error compensation in single-point inclined axis nanogrinding for small aspheric insert. Int J Adv Manuf Technol 65, 433–441 (2013).

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  • Error compensation
  • Wheel setting error
  • Radius error
  • Residual error
  • Single-point inclined axis grinding
  • Aspheric insert