Shape optimization of generic rotary tool for five-axis flank milling

ORIGINAL ARTICLE
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Abstract

This paper presents an approach to optimize the shape of a general rotary cutter for five-axis flank milling of ruled and non-ruled surfaces. Based on the observation that tool shape optimization is equivalent to repositioning the control points of its B-spline meridian, the optimization of tool surface is reduced to that of a B-spline curve. Then, the meridian of rotary tool surface is represented by cubic B-spline curve, and it is used to obtain the analytic tool envelope surface. Subsequently, the flank milling error is measured by the distance between a point sampled from envelope surface and the design surface. On this basis, shape optimization of a general rotary cutter is formulated as an optimization problem from the perspective of approximating the tool envelope surface to the designed surface. Two examples are given to confirm the validity of the proposed method. The approach also applied to multi-pass five-axis flank milling.

Keywords

Flank milling Envelope surface B-spline curve Rotary tool Optimization model 

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References

  1. 1.
    Harik RF, Gong H, Bernard A (2013) 5-axis flank milling: a state-of-the-art review. Comput Aided Des 45(3):796–808CrossRefGoogle Scholar
  2. 2.
    Davim JP (2012) Machining of complex sculptured surfaces. Springer, LondonCrossRefGoogle Scholar
  3. 3.
    Xiong-Wei L (1995) Five-axis NC cylindrical milling of sculptured surfaces. Comput Aided Des 27(12):887–894CrossRefGoogle Scholar
  4. 4.
    Redonnet JM, Rubio W, Dessein G (1998) Side milling of ruled surfaces: optimum positioning of the milling cutter and calculation of interference. Int J Adv Manuf Technol 14(7):459–465CrossRefGoogle Scholar
  5. 5.
    Monies F, Redonnet JM, Rubio W, Lagarrigue P (2000) Improved positioning of a conical mill for machining ruled surfaces: application to turbine blades. Proc Inst Mech Eng Part B J Eng Manuf 214(7):625–634CrossRefGoogle Scholar
  6. 6.
    Bedi S, Mann S, Menzel C (2003) Flank milling with flat end milling cutters. Comput Aided Des 35(3):293–300CrossRefGoogle Scholar
  7. 7.
    Menzel C, Bedi S, Mann S (2004) Triple tangent flank milling of ruled surfaces. Comput Aided Des 36(3):289–296CrossRefGoogle Scholar
  8. 8.
    Chiou JCJ (2004) Accurate tool position for five-axis ruled surface machining by swept envelope approach. Comput Aided Des 36(10):967–974CrossRefGoogle Scholar
  9. 9.
    Lartigue C, Duc E, Affouard A (2003) Tool path deformation in 5-axis flank milling using envelope surface. Comput Aided Des 35(4):375–382CrossRefGoogle Scholar
  10. 10.
    Gong H, Cao LX, Liu H (2005) Improved positioning of cylindrical cutter for flank milling ruled surfaces. Comput Aided Des 37(12):1205–1213CrossRefGoogle Scholar
  11. 11.
    Gong H, Wang N (2009) Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface. Comput Aided Des 41(12):981–989CrossRefGoogle Scholar
  12. 12.
    Li-Min Z, XiaoMing Z, Gang Z, Han D (2009) Analytical expression of the swept surface of a rotary cutter using the envelope theory of sphere congruence. J Manuf Sci Eng Trans ASME 131(4):0410171–0410177Google Scholar
  13. 13.
    Zhu LM, Zhang XM, Ding H, Xiong YL (2010) Geometry of signed point-to-surface distance function and its application to surface approximation. J Comput Inf Sci Eng 10(4)Google Scholar
  14. 14.
    Ding H, Zhu L (2009) Global optimization of tool path for five-axis flank milling with a cylindrical cutter. Sci China Ser E Technol Sci 52(8):2449–2459CrossRefMATHGoogle Scholar
  15. 15.
    Zhu L, Zheng G, Ding H, Xiong Y (2010) Global optimization of tool path for five-axis flank milling with a conical cutter. Comput Aided Des 42(10):903–910CrossRefGoogle Scholar
  16. 16.
    Li Z-L, Zhu L-M (2014) Envelope surface modeling and tool path optimization for five-axis flank milling considering cutter runout. J Manuf Sci Eng Trans ASME 136(4):0410211–0410219MathSciNetGoogle Scholar
  17. 17.
    Chu C-H, Chen J-T (2006) Tool path planning for five-axis flank milling with developable surface approximation. Int J Adv Manuf Technol 29(7–8):707–713MathSciNetCrossRefGoogle Scholar
  18. 18.
    CY Wu (1986) Multiple cutter pass flank milling. U.S. Patent No.4596501Google Scholar
  19. 19.
    CY Wu (1995) Arbitrary surface flank milling of fan, compressor and impeller blades. Trans ASME, J Eng Gas Turbines Power 117(3):534–539Google Scholar
  20. 20.
    Zhu L, Lu Y (2015) Geometric conditions for tangent continuity of swept tool envelopes with application to multi-pass flank milling. Comput Aided Des 59:43–49CrossRefGoogle Scholar
  21. 21.
    Elber G, Fish R (1997) 5-axis freeform surface milling using piecewise ruled surface approximation. J Manuf Sci Eng Trans ASME 119(3):383–387CrossRefGoogle Scholar
  22. 22.
    Wang CCL, Elber G (2014) Multi-dimensional dynamic programming in ruled surface fitting. Comput Aided Des 51:39–49CrossRefGoogle Scholar
  23. 23.
    Monies F, Felices JN, Rubio W, Redonnet JM, Lagarrigue P (2002) Five-axis NC milling of ruled surfaces: optimal geometry of a conical tool. Int J Prod Res 40(12):2901–2922CrossRefGoogle Scholar
  24. 24.
    Gang Z, Limin Z, Qingzhen B (2012) Cutter size optimisation and interference-free tool path generation for five-axis flank milling of centrifugal impellers. Int J Prod Res 50(23):6667–6678CrossRefGoogle Scholar
  25. 25.
    Zhu L, Ding H, Xiong Y (2012) Simultaneous optimization of tool path and shape for five-axis flank milling. Comput Aided Des 44(12):1229–1234CrossRefGoogle Scholar
  26. 26.
    Patel K, Bolanos GS, Bassi R, Bedi S (2011) Optimal tool shape selection based on surface geometry for three-axis CNC machining. Int J Adv Manuf Technol 57(5–8):655–670CrossRefGoogle Scholar
  27. 27.
    Luo M, Yan D, Wu B, Zhang D (2016) Barrel cutter design and toolpath planning for high-efficiency machining of freeform surface. Int J Adv Manuf Technol 85(9–12):2495–2503CrossRefGoogle Scholar
  28. 28.
    Meng F-J, Chen Z-T, Xu R-F, Li X (2014) Optimal barrel cutter selection for the CNC machining of blisk. Comput Aided Des 53:36–45CrossRefGoogle Scholar
  29. 29.
    He Y, Chen Z, Xu R (2016) Research on five-axis flank milling of convex edge surface with a concave cutter. Int J Adv Manuf Technol 86(9–12):2401–2409Google Scholar
  30. 30.
    Chen T, Liu XL, Wang CH, Wang GY (2015) Design and fabrication of double-circular-arc torus milling cutter. Int J Adv Manuf Technol 80(1–4):567–579CrossRefGoogle Scholar
  31. 31.
    Wang GC, Fuh KH, Yan BH (2007) Geometry design model of a precise form-milling cutter based on the machining characteristics. Int J Adv Manuf Technol 34(11–12):1072–1087CrossRefGoogle Scholar
  32. 32.
    Chen WF (2004) A precision design for computer numerical control machining models of involute-generator revolving cutters. Proc Inst Mech Eng Part B J Eng Manuf 218(5):517–531CrossRefGoogle Scholar
  33. 33.
    Liu XL, Fan MC, Ji W, Wang GY, Chen T (2016) Research on models of design and NC manufacturing for ellipsoid end mill. Int J Adv Manuf Technol 85(9–12):2729–2744CrossRefGoogle Scholar
  34. 34.
    Rababah MM (2015) Five-axis CNC grinding of end-mills with generic revolving profiles. Jordan J Mech Ind Eng 9(3):159–165Google Scholar
  35. 35.
    Chaves-Jacob J, Poulachon G, Duc E (2009) New approach to 5-axis flank milling of free-form surfaces: computation of adapted tool shape. Comput Aided Des 41(12):918–929CrossRefGoogle Scholar
  36. 36.
    ChungY W (2012) Arbitrary surface flank milling & flank SAM in the design & manufacturing of jet engine fan and compressor airfoils. In: Proceedings of the ASME IGTI turbo expo conference in CopenhagenGoogle Scholar
  37. 37.
    Bo P, Barton M, Plakhotnik D, Pottmann H (2016) Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution. Comput Aided Des 79:1–11CrossRefGoogle Scholar
  38. 38.
    Piegl LTW (1997) The NURBS book, 2nd edn. Springer, BerlinCrossRefMATHGoogle Scholar
  39. 39.
    Zhu LM, Zheng G, Ding H (2009) Formulating the swept envelope of rotary cutter undergoing general spatial motion for multi-axis NC machining. Int J Mach Tools Manuf 49(2):199–202CrossRefGoogle Scholar
  40. 40.
    Yu L, Wang YH, Jin YQ (2013) Envelope surface formed by cutting edge under runout error in five-axis flank milling. Int J Adv Manuf Technol 69(1–4):543–553CrossRefGoogle Scholar
  41. 41.
    Philip J, Schneider DHE (2003) Geometric tools for computer graphics. Morgan Kaufmann, San FranciscoGoogle Scholar
  42. 42.
    Joge Nocedal SJW (2006) Numerical optimization, 2nd edn. Springer, BerlinGoogle Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical System and Vibration, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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