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Power Series Solution for Isoscallop Tool Path Generation on Free-form Surface with Ball-end Cutter

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Abstract

In this paper we propose a method to compute symbolically a curve of constant scallop height on the surface swept by a ball-end cutter when it traces a free-form cutter-contact curve on a free-form surface. We give explicit formulas for power series solutions to the curve of constant scallop height and the next cutter-contact curve, when the initial cutter-contact curve is given. To make the symbolic results useful in practice, we propose a method to approximate the solutions unilaterally in the parametric plane by piecewise Chebyshev polynomials and exponential functions.

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References

  1. Agrawal R., Pratihar D., Choudhury A.: Optimization of CNC isoscallop free-form surface machining using a genetic algorithm. Int. J. Mach. Tools Manuf. 46, 811–819 (2006)

    Article  Google Scholar 

  2. Farouki R.: The approximation of non-degenerate offset surfaces. Comput. Aided Geom. Des. 3, 15–43 (1986)

    Article  MATH  Google Scholar 

  3. Feng H., Li H.: Constant scallop height tool path generation for three axis sculptured surface machining. Comput. Aided. Des. 34, 647–654 (2002)

    Article  Google Scholar 

  4. Kim T.: Constant cusp height tool paths as geodesic parallels on an abstract Riemannian manifold. Comput. Aided. Des. 39, 477–489 (2007)

    Article  MATH  Google Scholar 

  5. Radzevich S.: Conditions of proper sculptured surface machining. Comput. Aided. Des. 34, 727–740 (2002)

    Article  Google Scholar 

  6. Snyder A.: Chebyshev Methods in Numerical Approximation. Prentice Hall, Englewood Cliff (1966)

    MATH  Google Scholar 

  7. Suresh K., Yang D.: Constant scallop-height machining of free-form surfaces. J. Eng. Ind. 116, 253–259 (1994)

    Article  Google Scholar 

  8. Tournier C., Duc E.: A surface based approach for constant scallop height tool-path generation. Int. J. Adv. Manuf. Technol. 19, 318–324 (2002)

    Article  Google Scholar 

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Correspondence to Hongbo Li.

Additional information

This work was partially supported by Program 2011CB302404, NSFC 10925105, 60821002/F02.

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Li, H., Yao, S., Li, G. et al. Power Series Solution for Isoscallop Tool Path Generation on Free-form Surface with Ball-end Cutter. Math.Comput.Sci. 6, 281–296 (2012). https://doi.org/10.1007/s11786-012-0124-7

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  • DOI: https://doi.org/10.1007/s11786-012-0124-7

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