Modeling of curved diamond wheel errors for improvement of freeform grinding accuracy

Abstract

A superhard diamond grinding can machine the hard and brittle freeform workpiece, but it is difficult to control the form-truing errors of curved wheel-profile in multiaxial grinding. Generally, it needs multiple compensation grindings through the on-machine measurement of the ground surface, leading to inefficiency. Hence, the model of 2D wheel-profile errors is proposed to directly compensate for 3D curved wheel errors in automatic grinding. This is because the wheel-profile form-truing errors mainly influence the ground freeform errors. The objective is to improve the freeform accuracy without inefficient measurement-to-compensation in the grinding system. First, the on-machine form-truing of the torus-shaped diamond wheel was employed in freeform grinding; then, the form-truing errors were systematically analyzed in connection to the ground freeform errors. It is shown that the curved form-truing errors may be parameterized by the dresser width, the wheel-profile width, and the wheel-profile in the case of large wheel positioning error. The simulated results also display that the freeform form errors decrease by increasing the wheel-profile curvature and decreasing the workpiece curvature in the case of same form-truing errors. Moreover, the simulated wheel-profile errors may directly be compensated to freeform grinding without any on-machine measurement.

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References

  1. 1.

    Tsai CY (2015) Improved irradiance distribution on high concentration solar cell using free-form concentrator. Sol Energy 115:694–707

    Article  Google Scholar 

  2. 2.

    Chen WH, Zhang XD, Liu XL, Fang FZ (2015) Optical design and simulation of a compact multi-aperture camera based on a freeform microlens array. Opt Commun 338:300–306

    Article  Google Scholar 

  3. 3.

    Wu H, Zhang XM, Ge P (2015) Design method of a light emitting diode front fog lamp based on a freeform reflector. Opt Laser Technol 72:125–133

    Article  Google Scholar 

  4. 4.

    Tang Q, Pang SY, Chen BB, Suo HB, Zhou JX (2014) A three dimensional transient model for heat transfer and fluid flow of weld pool during electron beam freeform fabrication of Ti-6-Al-4-V alloy. Int J Heat Mass Transf 78:203–215

    Article  Google Scholar 

  5. 5.

    Poniatowska M (2015) Free-form surface machining error compensation applying 3D CAD machining pattern model. Comput Aided Des 62:227–235

    Article  Google Scholar 

  6. 6.

    Jiang XN, Scott PJ, Whitehouse DJ, Blunt L (2007) Paradigm shifts in surface metrology. Part II. The current shift. Proc: Math, Phys Eng Sci 463(2085):2071–2099

    Google Scholar 

  7. 7.

    Jung J, Mayor R, Ni J (2005) Development of freeform grinding methods for complex drill flank surfaces and cutting edge contours. Int J Mach Tools Manuf 45(1):93–103

    Article  Google Scholar 

  8. 8.

    Sidpara A, Jain VK (2013) Analysis of forces on the freeform surface in magnetorheological fluid based finishing process. Int J Mach Tools Manuf 69:1–10

    Article  Google Scholar 

  9. 9.

    Sun GP, Wright P (2005) Simulation-based cutting parameter selection for ball end milling. J Manuf Syst 24(4):352–365

    Article  Google Scholar 

  10. 10.

    Erkorkmaz K, Layegh SE, Lazoglu I, Erdim H (2013) Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics. CIRP Ann 62(1):395–398

    Article  Google Scholar 

  11. 11.

    Zhang XF, Xie J, Xie HF, Li LH (2011) Experimental investigation on various tool path strategies influencing surface quality and form accuracy of CNC milled complex freeform surface. Int J Adv Manuf Technol 59(5–8):647–654

    Google Scholar 

  12. 12.

    Xu XH, Zhu DH, Wang JS, Yan SJ, Ding H (2018) Calibration and accuracy analysis of robotic belt grinding system using the ruby probe and criteria sphere. Robot Comput Integr Manuf 51:189–201

    Article  Google Scholar 

  13. 13.

    Denkena B, Turger A, Behrens L, Krawczyk T (2012) Five-axis-grinding with toric tools: a status review. J Manuf Sci Eng 134(5):054001

    Article  Google Scholar 

  14. 14.

    Nishiguchi T, Koizumi Y, Maeda Y, Masuda M, Nagayama K (1991) Improvement of productivity in aspherical precision machining with in-situ metrology. CIRP Ann Manuf Technol 40(1):367–370

    Article  Google Scholar 

  15. 15.

    Zhong Z, Nakagawa T (1996) Grinding of aspherical SiC mirrors. J Mater Process Technol 56(1–4):37–44

    Article  Google Scholar 

  16. 16.

    Chen WK, Kuriyagawa T, Huang H, Yosihara N (2005) Machining of micro aspherical mould inserts. Precis Eng 29(3):315–323

    Article  Google Scholar 

  17. 17.

    Saeki M, Kuriyagawa T, Syoji K (2002) Machining of aspherical molding dies utilizing parallel grinding method[J]. J Jpn Soc Precis Eng 68(8):1067–1071

  18. 18.

    Xie J, Zhou RM, Xu J, Zhong YG (2009) Form-truing error compensation of diamond grinding wheel in CNC envelope grinding of free-form surface. Int J Adv Manuf Technol 48(9–12):905–912

    Google Scholar 

  19. 19.

    Xie J, Li Q, Sun JX, Li YH (2015) Study on ductile-mode mirror grinding of SiC ceramic freeform surface using an elliptical torus-shaped diamond wheel. J Mater Process Technol 222:422–433

    Article  Google Scholar 

  20. 20.

    Kuriyagawa T, Zahmaty MSS, Syoji K (1996) A new grinding method for aspheric ceramic mirrors. J Mater Process Technol 62(4):387–392

    Article  Google Scholar 

  21. 21.

    Sazedur Rahman M, 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

    Article  Google Scholar 

  22. 22.

    Chen B, Guo B, Zhao QL (2015) On-machine precision form truing of arc-shaped diamond wheels. J Mater Process Technol 223:65–74

    Article  Google Scholar 

  23. 23.

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

    Article  Google Scholar 

  24. 24.

    Xie J, Zheng JH, Zhou RM, Lin B (2011) Dispersed grinding wheel profiles for accurate freeform surfaces. Int J Mach Tools Manuf 51(6):536–542

    Article  Google Scholar 

  25. 25.

    Liu Y, Wan M, Xing WJ, Zhang WH (2018) Identification of position independent geometric errors of rotary axes for five-axis machine tools with structural restrictions. Robot Comput Integr Manuf 53:45–57

    Article  Google Scholar 

  26. 26.

    Maeng SR, Baek N, Shin SY, Choi BK (2003) A Z-map update method for linearly moving tools. Comput Aided Des 35(11):995–1009

    Article  Google Scholar 

Download references

Funding

The project was sponsored by the Natural Science Foundation of Guangdong (Grant No. 2015A030311015) and the Natural Science Foundation of China (Grant No. 61475046).

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Correspondence to J. Xie.

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Liao, J.Y., Xie, J., Yang, H. et al. Modeling of curved diamond wheel errors for improvement of freeform grinding accuracy. Int J Adv Manuf Technol 103, 1879–1892 (2019). https://doi.org/10.1007/s00170-019-03679-1

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Keywords

  • Automatic grinding
  • NC errors compensation
  • Grinding wheel errors
  • Freeform errors