A helical interpolation precision truing and error compensation for arc-shaped diamond grinding wheel

  • Jiahao Zhu
  • Peng YaoEmail author
  • Wei WangEmail author
  • Chuanzhen Huang
  • Hongtao Zhu
  • Bin Zou
  • Hanlian Liu


In the grinding of aspherical optical surface, an arc-shaped diamond grinding wheel is generally employed, whereas its profile errors greatly influence the form accuracy of ground workpiece. A high efficiency helical interpolation precision truing method for the arc-shaped diamond grinding wheel is proposed in this paper. Helical interpolation trajectory and decreasing interpolation radius with the wear of a rotary truing wheel ensure a constant contact length and a uniform wear of the diamond grinding wheel and truer. The mathematical models of tool setting errors and measurement error of truer diameter in the truing process were established firstly. The prediction models considering the wear of truer are coincided well with the truing experiment results. Based on the mathematical error models, an error compensation truing process was proposed. The profile accuracy of an arc-shaped diamond grinding wheel was improved to 5 μm (PV) effectively by the error compensation truing process. An ellipsoidal surface of a fused silica workpiece was ground by the well-trued diamond grinding wheel. A form error (in PV) below 4.5 μm was obtained after precision grinding.


Aspheric lens Ultra-precision grinding Arc-shaped diamond grinding wheel Form truing Helical interpolation Error compensation 


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Funding information

This work was supported by National Key R&D Program of China (Grant No. 2017YFB1301903), National Natural Science Foundation of China (No. 51875321) Shandong Province Natural Science Foundation (Grant No. ZR2018MEE019), Key Laboratory of Optical System Advanced Manufacturing Technology (Grant No. Y6SY1FJ160).


  1. 1.
    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 Tool Manu 50(5):480–486CrossRefGoogle Scholar
  2. 2.
    Brinksmeier E, Mutlugünes Y, Klocke F, Aurich JC, Shore P, Ohmori H (2010) Ultra-precision grinding. CIRP Ann-Manuf Techn 59(2):652–671CrossRefGoogle Scholar
  3. 3.
    Jiang C, Guo Y, Li H (2013) Parallel grinding error for a noncoaxial nonaxisymmetric aspheric lens using a fixture with adjustable gradient. Int J Adv Manuf Technol 66(1–4):537–545CrossRefGoogle Scholar
  4. 4.
    Li C, Zhang F, Ma Z, Ding Y (2017) 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(1–4):13–24CrossRefGoogle Scholar
  5. 5.
    Kuriyagawa T, Zahmaty MSS, Syoji K (1996) A new grinding method for aspheric ceramic mirrors. J Mater Process Technol 62(4):387–392CrossRefGoogle Scholar
  6. 6.
    Saeki M, Kuriyagawa T, Lee JS (2001) Machining of aspherical Opto-device utilizing parallel grinding method. Aspe Annual MeetingGoogle Scholar
  7. 7.
    Chen F, Yin S, Ohmori H, Yu J (2013) Form error compensation in single-point inclined axis nanogrinding for small aspheric insert. Int J Adv Manuf Technol 65(1–4):433–441CrossRefGoogle Scholar
  8. 8.
    Lin XH, Wang ZZ, Guo YB, Peng YF, Hu CL (2014) Research on the error analysis and compensation for the precision grinding of large aspheric mirror surface. Int J Adv Manuf Technol 71(1–4):233–239CrossRefGoogle Scholar
  9. 9.
    Liu L, Zhang F (2017) Prediction model of form error influenced by grinding wheel wear in grinding process of large-scale aspheric surface with SiC ceramics. Int J Adv Manuf Technol 88(1–4):899–906CrossRefGoogle Scholar
  10. 10.
    Huang H, Chen WK, Kuriyagawa T (2007) Profile error compensation approaches for parallel nanogrinding of aspherical mould inserts. Int J Mach Tool Manu 47(15):2237–2245CrossRefGoogle Scholar
  11. 11.
    Chen B, Guo B, Zhao Q (2015) An investigation into parallel and cross grinding of aspheric surface on monocrystal silicon. Int J Adv Manuf Technol 80(5–8):737–746CrossRefGoogle Scholar
  12. 12.
    Peng Y, Dai Y, Song C, Chen S (2016) Error analysis and compensation of line contact spherical grinding with cup-shaped wheel. Int J Adv Manuf Technol 83(1–4):293–299CrossRefGoogle Scholar
  13. 13.
    Lin X, Guo Y, Wang Z (2013) Precision model and analysis of large axisymmetric aspheric grinding. Chin J Mech Eng 49(17):65–72CrossRefGoogle Scholar
  14. 14.
    Guo Y (2003) Study on truing and dressing Technology for arc-Diamond Wheel. Manufacturing Technology & Machine ToolGoogle Scholar
  15. 15.
    Xie J (2008) Experiment on CNC arc truing of diamond grinding wheel by mutual wear. Chin J Mech Eng 44(2):102–107CrossRefGoogle Scholar
  16. 16.
    Chen B, Guo B, Zhao Q, Wang J, Chen GE (2016) On-machine precision form truing of arc-shaped diamond wheels. J Mater Process Technol 223:65–74CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Advanced Jet Engineering Technologies (CaJET), School of Mechanical EngineeringShandong UniversityJinanChina
  2. 2.Key Laboratory of High Efficiency and Clean Mechanical ManufactureMinistry of Education, PR ChinaJinanChina
  3. 3.College of Mechanical and Electronic EngineeringChina University of Petroleum (East China)QingdaoChina

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