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Mathematical modeling for the design of a generic custom-engineered form mill

Abstract

This paper presents a mathematical model for the geometric design of a custom-engineered form milling (CEFM) cutter and develops an accurate 3D surface-based generic definition of the form mill. The proposed geometric definition of the CEFM cutter is developed in terms of biparametric surface patches using newly defined 3D rotational angles rather than the conventional 2D angles. The non-uniform rational B-spline curve fairing and sweep surface approaches are used to design the cutting edge and flank surface, respectively, of the cutter. To validate the methodology, an interface is developed that converts the proposed 3D parametric definition of the cutter into an intermediate neutral CAD format and then renders the cutter model in any CAD modeling environment. The accuracy of the mathematical model is verified by evaluating the deviation plot between the surfaces of the proposed cutter model and the surfaces developed using digitized data of an existing actual CEFM cutter. The satisfactory comparison verifies the shape design methodology for custom cutters presented in this paper. The method described here offers a simple and intuitive way of generating shape design of custom cutters for possible use in machining process simulations, finite element analysis, and other applications.

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References

  1. 1.

    Wilson FW (1987) ASTME: fundamentals of tool design. Prentice Hall, New Jersey

  2. 2.

    Drodza TJ, Wick C (1983) Machining, tool and manufacturing engineers handbook, vol I. Society of Manufacturing Engineers, Dearborn

  3. 3.

    Vijayaraghavan A, Dornfeld DA (2007) Automated drill modeling for drilling process simulation. J Comp and Infor Sci Engg 7:276–282

  4. 4.

    Tandon P, Khan MR (2009) Three dimensional modeling and finite element simulation of a generic end mill. Comput-Aided Des 41(2):106–114

  5. 5.

    Mortenson ME (1985) Geometric modeling. Wiley, New York

  6. 6.

    Rogers DF, Adams JA (1990) Mathematical elements of computer graphics. McGraw-Hill, New York

  7. 7.

    Tandon P, Gupta P, Dhande SG (2003) Geometric modeling of single point cutting tool surfaces. Int J Adv Manuf Tech 22(1–2):101–111

  8. 8.

    Tandon P, Gupta P, Dhande SG (2005) Geometric modeling of end mills. Computer-Aided Design and Appli 2(1–4):57–66

  9. 9.

    Kuo HC, Wu LJ (2001) A study on the evaluation of a model of the precise outside of the roller nest mill cutter. J Mat Proc Tech 117:178–182

  10. 10.

    Hsieh JM, Tsai YC (2006) Geometric modeling and grinder design for toroid-cone shaped cutters. Int J Adv Manuf Tech 29:912–921

  11. 11.

    Radzevich SP (2007) A novel method for mathematical modeling of a form-cutting-tool of the optimum design. Appl Math Model 31:2639–2654

  12. 12.

    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 Tech 34:1072–1087

  13. 13.

    Radzevich SP (2007) A novel design of cylindrical hob for machining of precision involute gears. ASME J Mech Des 129:334–345

  14. 14.

    Hsieh JK, Tseng HC, Chang SL (2009) A novel hob cutter design for the manufacture of spur-typed cutters. J Mat Proc Tech 209:847–855

  15. 15.

    Vasilis D, Nectarios V, Aristomenis A (2007) Advanced computer aided design simulation of gear hobbing by means of three-dimensional kinematics modeling. ASME J Manuf Sci Engg 129:911–918

  16. 16.

    Farin G (2002) Curves and surfaces for computer-aided geometric design—a practical guide, 5th edn. Academic, San Diego

  17. 17.

    IGES 5.3 (1996) US Product Data Association. IGES/PDES Organization, USA

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Correspondence to Puneet Tandon.

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Khan, M.R., Tandon, P. Mathematical modeling for the design of a generic custom-engineered form mill. Int J Adv Manuf Technol 54, 139–148 (2011). https://doi.org/10.1007/s00170-010-2936-4

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Keywords

  • Custom-engineered form mill
  • Geometric modeling
  • Surface patches
  • Three-dimensional angles
  • Reverse engineering