Advertisement

Three-Linear-Axis Grinding of Small Aperture Aspheric Surfaces

  • Guangpeng Yan
  • Kaiyuan You
  • Fengzhou FangEmail author
Regular Paper
  • 11 Downloads

Abstract

A novel approach of three-linear-axis ultra-precision grinding with wheel path generation, tool interference checking and profile compensation is proposed and systematically investigated for fabricating aspheric surfaces. The performance of the proposed techniques is evaluated by grinding an aspheric mould insert on bindless tungsten carbide. The experimental results demonstrate that the profile error can be reduced to 0.1 μm or a lower value in peak to valley (PV) after two compensation cycles. The on-machine measurement results show agreement with the off-machine measurement results when commercially available profilometers are employed. The study confirms the feasibility of the proposed wheel path determination method and the developed profile compensation approach. A mirror surface with roughness less than 8 nm in Sa is achieved.

Keywords

Ultra-precision grinding Aspheric Tool path Interference Error compensation 

List of Symbols

O

Vertex of aspheric surface

P

Grinding point

Q

Arc nose center of point P

C

Center of the fillet-end surface of grinding wheel

T

Arbitrary point on the wheel axis except the point C

D

Arbitrary point on the ideal probe center path

F

Corresponding point of point D on actual probe center path

M

Corresponding point of point F on actual ground aspheric profile

G

Point on designed aspheric profile

G

Corresponding normal point of point G on actual ground aspheric profile

C

Compensated coordination of point C

nP

Common normal vector of grinding wheel surface and aspheric surface at grinding point P

nF

Normal vector of fitted actual probe center path at point F

Ω

Ideal probe center path

Ψ

Actual probe center path

Γ

Designed aspheric profile

Θ

Actual ground aspheric profile

rw

Arc nose radius of grinding wheel

Rw

Major radius of grinding wheel

α

Angle between grinding spindle workpiece spindle

Rp

Radius of the on-machine measurement probe

kmax(1)

Maximum principle curvature of grinding wheel surface at grinding point

kmin(1)

Minimum principle curvature of grinding wheel surface at grinding point

kmax(2)

Maximum principle curvature of aspheric surface at grinding point

kmin(2)

Minimum principle curvature of aspheric surface at grinding point

θ

Angle between the maximum principle directions of grinding wheel and aspheric surfaces at grinding point at grinding point

ePQ

Unit vector of \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{\mathcal{PQ}}}\)

eQC

Unit vector of \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{\mathcal{QC}}}\)

eCT

Unit vector of \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{\mathcal{CT}}}\)

e1(1)

Unit vector in maximum principal direction of the grinding wheel surface at grinding point

e2(1)

Unit vector in minimum principal direction of the grinding wheel surface at grinding point

e1(2)

Unit vector in maximum principal direction of the aspheric surface at grinding point

e2(2)

Unit vector in minimum principal direction of the aspheric surface at grinding point

e1 t(1)

Expression of e 1 (1) in tool coordinate system

e1 g(1)

Expression of e 1 (2) in global coordinate system

e1 g(2)

Expression of e 1 (2) in global coordinate system

δzD

LVDT detected deviation distance in point D

δnG

Signed distance between point G and point G

Rbase

Radius of the base sphere at the vertex of aspheric surface

K

Conic constant of aspheric surface

A2i

Aspheric coefficients

Notes

Acknowledgements

The authors appreciate the supports of the National Natural Science Foundation (Grant nos. 61635008, 51320105009 and 91423101), the National Key Research and Development Program (Grant no. 2016YFB1102200), and the ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (Grant no. B07014).

References

  1. 1.
    Cha, D. H., Kim, H. J., Lee, J. K., Kim, H. U., Kim, S. S., & Kim, J. H. (2008). A study of mold grinding and pressing conditions in the molding of aspheric glass lenses for camera phone module. Materials and Manufacturing Processes, 23(7), 683–689.CrossRefGoogle Scholar
  2. 2.
    Kim, H.-J., Kim, H.-U., Kim, S.-S., Park, Y.-P., Kim, J.-H., & Cha, D.-H. (2007). Fabrication and optical evaluation of aspheric glass lenses for 3 megapixel zoom camera phone module. Optical Review, 14(3), 145.CrossRefGoogle Scholar
  3. 3.
    Chen, S. T., Chang, K. E., Huang, W. P., et al. (2012). Development of a cost-effective high-precision bench machine tool for multi-level micro aspheric lighting-lens mold machining. International Journal of Precision Engineering and Manufacturing, 13(12), 2225–2231.CrossRefGoogle Scholar
  4. 4.
    Kim, B. C. (2015). Development of aspheric surface profilometry using curvature method. International Journal of Precision Engineering and Manufacturing, 16(9), 1963–1968.CrossRefGoogle Scholar
  5. 5.
    Fang, F. Z., Zhang, X. D., Weckenmann, A., Zhang, G. X., & Evans, C. (2013). Manufacturing and measurement of freeform optics. CIRP Annals Manufacturing Technology, 62(2), 823–846.CrossRefGoogle Scholar
  6. 6.
    Braunecker, B., Hentschel, R., & Tiziani, H. J. (2008). Advanced optics using aspherical elements. Bellingham: SPIE Press.Google Scholar
  7. 7.
    Chen, W. K., Kuriyagawa, T., Huang, H., & Yosihara, N. (2005). Machining of micro aspherical mould inserts. Precision Engineering, 29(3), 315–323.CrossRefGoogle Scholar
  8. 8.
    Fang, F. Z., & Xu, F. (2018). Recent advances in micro/nano-cutting: Effect of tool edge and material properties. Nanomanufacturing and Metrology, 1(1), 4–31.CrossRefGoogle Scholar
  9. 9.
    Schaub, M., Schwiegerling, J., Fest, E., Shepard, R. H., & Symmons, A. (2011). Molded optics: Design and manufacture. Boca Raton: CRC Press.Google Scholar
  10. 10.
    Brinksmeier, E., Riemer, O., & Gläbe, R. (2013). Fabrication of complex optical components. Berlin Heidelberg: Springer.CrossRefGoogle Scholar
  11. 11.
    Kim, H. U., Cha, D. H., Kim, H. J., et al. (2009). Rhenium-iridium coating effect of tungsten carbide mold for aspheric glass lens. International Journal of Precision Engineering and Manufacturing, 10(3), 19–1923.CrossRefGoogle Scholar
  12. 12.
    Staasmeyer, J.-H., Kreilkamp, H., Dambon, O., & Klocke, F. (2016). Precision glass molding: Cost efficient production of glass-optics with spectral range from 180 nm ultraviolet to 13 µm thermal infrared. In Proc. SPIE, Vol. 10009, Third European Seminar on Precision Optics Manufacturing, pp. 100090 W. 1–7, 2016.Google Scholar
  13. 13.
    Hall, C., Tricard, M., Murakoshi, H., Yamamoto, Y., Kuriyama, K., & Yoko, H. (2005). New mold manufacturing techniques. In Proc. SPIE, Vol. 5868, Optical Materials and Structures Technologies II, pp. 58680 V. 1–10.Google Scholar
  14. 14.
    Brinksmeier, E., Mutlugünes, Y., Klocke, F., Aurich, J. C., Shore, P., & Ohmori, H. (2010). Ultra-precision grinding. CIRP Annual Manufacturing Technology, 59(2), 652–671.CrossRefGoogle Scholar
  15. 15.
    Chen, B., Li, S., Deng, Z., Guo, B., & Zhao, Q. (2017). Grinding marks on ultra-precision grinding spherical and aspheric surfaces. International Journal of Precision Engineering and Manufacturing-Green Technology, 4(4), 419–429.CrossRefGoogle Scholar
  16. 16.
    Suzuki, H., Kodera, S., Maekawa, S., Morita, N., Sakuerai, E., Tanaka, K., et al. (1998). Study on precision grinding of micro aspherical surface. Feasibility study of micro aspherical surface by inclined rotational grinding. Journal of the Japan Society for Precision Engineering, 64(4), 619–623.CrossRefGoogle Scholar
  17. 17.
    Yamamoto, Y., Suzuki, H., Okino, T., Moriwaki, T., Fukuta, M., Nishioka, M., et al. (2006). Study on precision grinding of micro aspherical surface (4th Report): Accuracy improvement by simultaneous 3 axes controlled tilted grinding method of grinding point fixation. Journal of the Japan Society for Precision Engineering, 72(1), 84–88.Google Scholar
  18. 18.
    Saeki, M., Kuriyagawa, T., Lee, J.-S., & Syoji, K. (2001). Machining of aspherical opto-device parallel grinding method. In Proceedings of the 16th Annual Meeting of the ASPE, Vol. 25, pp. 433–36.Google Scholar
  19. 19.
    Saeki, M., Kuriyagawa, T., & Syoji, K. (2002). Machining of aspherical molding dies utilizing parallel grinding method. Journal of the Japan Society of Precision Engineering, 68(8), 1067–1071.CrossRefGoogle Scholar
  20. 20.
    Brinksmeier, E., Riemer, O., Kai, R., & Kathrin, M. (2011). Kinematics in ultra-precision grinding of WC moulds. International Journal of Nanomanufacturing, 7(3/4), 199–213.CrossRefGoogle Scholar
  21. 21.
    Tohme, Y.E. (2007). Grinding aspheric and freeform micro-optical molds. In: Proc. SPIE, Vol. 6462, Micromachining Technology for Micro-Optics and Nano-Optics V and Microfabrication Process Technology XII, pp. 64620 K. 1–8, 2007.Google Scholar
  22. 22.
    Chen, F., Yin, S., Yu, J., & Ohmori, H. (2013). Form error compensation in single-point inclined axis nanogrinding for small aspheric insert. International Journal of Advanced Manufacturing Technology, 65(1–4), 433–441.CrossRefGoogle Scholar
  23. 23.
    Chen, F., Yin, S., Huang, H., & Ohmori, H. (2015). Fabrication of small aspheric moulds using single point inclined axis grinding. Precision Engineering, 39, 107–115.CrossRefGoogle Scholar
  24. 24.
    Yamamoto, Y., Suzuki, H., Okino, T., Hijikata, Y., & Moriwaki, T. (2004). Ultra precision grinding of micro aspherical surface—Development of a three-axes controlled single point inclined grinding method. In Proceedings of the 13th Annual Meeting of the ASPE, Vol. 34, pp. 558–561.Google Scholar
  25. 25.
    Zhang, Q., Zhao, Q., To, S., Guo, B., & Rao, Z. (2018). Precision machining of ‘water-drop’ surface by single point diamond grinding. Precision Engineering, 51, 190–197.CrossRefGoogle Scholar
  26. 26.
    Hwang, Y., Kuriyagawa, T., & Lee, S.-K. (2006). Wheel curve generation error of aspheric microgrinding in parallel grinding method. International Journal of Machine Tools and Manufacture, 46(15), 1929–1933.CrossRefGoogle Scholar
  27. 27.
    Lee, Y.-S. (1997). Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining. Computer-Aided Design, 29(7), 507–521.CrossRefGoogle Scholar
  28. 28.
    Hu, P., Tang, K., & Lee, C.-H. (2013). Global obstacle avoidance and minimum workpiece setups in five-axis machining. Computer-Aided Design, 45(10), 1222–1237.CrossRefGoogle Scholar
  29. 29.
    Lacharnay, V., Lavernhe, S., Tournier, C., & Lartigue, C. (2015). A physically-based model for global collision avoidance in 5-axis point milling. Computer-Aided Design, 64, 1–8.CrossRefGoogle Scholar
  30. 30.
    Du, J., Yan, X.-G., & Tian, X.-T. (2012). The avoidance of cutter gouging in five-axis machining with a fillet-end milling cutter. International Journal of Advanced Manufacturing Technology, 62(1), 89–97.CrossRefGoogle Scholar
  31. 31.
    Yoon, J.-H., Pottmann, H., & Lee, Y.-S. (2003). Locally optimal cutting positions for 5-axis sculptured surface machining. Computer-Aided Design, 35(1), 69–81.CrossRefGoogle Scholar
  32. 32.
    Gong, H., Cao, L.-X., & Liu, J. (2008). Second order approximation of tool envelope surface for 5-axis machining with single point contact. Computer-Aided Design, 40(5), 604–615.CrossRefGoogle Scholar
  33. 33.
    Huang, H., Chen, W. K., & Kuriyagawa, T. (2007). Profile error compensation approaches for parallel nanogrinding of aspherical mould inserts. International Journal of Machine Tools and Manufacture, 47(15), 2237–2245.CrossRefGoogle Scholar
  34. 34.
    Owen, J. D., Shultz, J. A., Suleski, T. J., & Davies, M. A. (2017). Error correction methodology for ultra-precision three-axis milling of freeform optics. CIRP Annual Manufacturing Technology, 66(1), 97–100.CrossRefGoogle Scholar
  35. 35.
    Nishiguchi, T., Koizumi, Y., Maeda, Y., Masuda, M., Nagayama, K., & Okamura, K. (1991). Improvement of Productivity in Aspherical Precision Machining with In-situ Metrology. CIRP Ann-Manuf Technol, 40(1), 367–370.CrossRefGoogle Scholar
  36. 36.
    Sazedur Rahman, M., Saleh, T., Lim, H. S., Son, S. M., & Rahman, M. (2008). Development of an on-machine profile measurement system in ELID grinding for machining aspheric surface with software compensation. International Journal of Machine Tools and Manufacture, 48(7), 887–895.CrossRefGoogle Scholar
  37. 37.
    Kim, H.-S., Lee, K.-I., Lee, K.-M., & Bang, Y.-B. (2009). Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement. International Journal of Machine Tools and Manufacture, 49(12), 991–997.CrossRefGoogle Scholar
  38. 38.
    Chen, F. J., Yin, S. H., Huang, H., & Ohmori, H. (2010). Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement. International Journal of Machine Tools and Manufacture, 50(5), 480–486.CrossRefGoogle Scholar
  39. 39.
    Boor, Cd. (1978). A practical guide to splines. New York: Springer.CrossRefzbMATHGoogle Scholar
  40. 40.
    Seewig, J. (2005). Linear and robust Gaussian regression filters. Journal of Physics: Conference Series, 13(1), 254.Google Scholar
  41. 41.
    Kim, H. U., Jeong, S. H., Lee, D. K., Kim, S. S., Kim, H. J., & Kim, J. H. (2009). A study on improvement of WC core surface roughness by feedrate control. Journal of the Korean Society for Precision Engineering, 26(1), 57–62.Google Scholar

Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Precision Measuring Technology and Instruments, Centre of Micro/Nano Manufacturing Technology-MNMTTianjin UniversityTianjinChina

Personalised recommendations