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A real-time surface interpolator methodology for precision CNC machining of swept surfaces

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Abstract

A real-time surface interpolator is developed to machine a family of swept surfaces directly from their high-level procedural definitions. All the computations required for machining are performed in real time based on the exact surface geometry, including tool path planning, tool path interpolation, tool offsetting, and tool path step-over to achieve a prescribed scallop height. A G-code command (G05) is introduced to concisely communicate the precise surface geometry and all necessary process parameters to the controller. The swept surface interpolator offers profound accuracy and efficiency advantages over the traditional approach of generating voluminous piecewise–linear/circular tool path approximations as a preprocessing step. For example, in one instance, a 36,000-line piecewise-linear (G01) approximate part program file is replaced by a 3-line exact swept surface (G05) part program file. The methodology is verified by machining a variety of swept surface forms in aluminum and wax, using a 3-axis milling machine with the surface interpolator incorporated into an open-architecture CNC controller.

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References

  1. Cheng C-W, Tseng W-P (2006) Design and implementation of a real–time NURBS surface interpolator. Int J Adv Manuf Tech 30:98–104

    Article  Google Scholar 

  2. FANUC Series 30i–MODEL A, Operator’s Manual (2004), FANUC Co.

  3. Farouki RT (2008) Pythagorean–hodograph curves: algebra and geometry inseparable. Springer, Berlin

    Book  Google Scholar 

  4. Farouki RT, Han CY, Li S (2014) Inverse kinematics for optimal tool orientation control in 5–axis CNC machining. Comput Aided Geom Design 31:13–26

    Article  MathSciNet  MATH  Google Scholar 

  5. Farouki RT, Manjunathaiah J, Nicholas D, Yuan G–F, Jee S (1998) Variable feedrate CNC interpolators for constant material removal rates along Pythagorean–hodograph curves. Comput Aided Design 30:631–640

    Article  MATH  Google Scholar 

  6. Farouki RT, Manjunathaiah J, Yuan G–F (1999) G codes for the specification of Pythagorean–hodograph tool paths and associated feedrate functions on open–architecture CNC machines. Int J Mach Tools Manuf 39:123–142

    Article  Google Scholar 

  7. Farouki RT, Neff CA (1990) Analytic properties of plane offset curves. Comput Aided Geom Design 7:83–99

    Article  MathSciNet  MATH  Google Scholar 

  8. Farouki RT, Nittler KM (2015) Rational swept surface constructions based on differential and integral sweep curve properties. Comput Aided Geom Design 33:1–16

    Article  MathSciNet  Google Scholar 

  9. Farouki RT, Shah S (1996) Real–time CNC interpolators for Pythagorean–hodograph curves. Comput Aided Geom Design 13:583–600

    Article  MATH  Google Scholar 

  10. Farouki RT, Tsai Y–F (2001) Exact Taylor series coefficients for variable–feedrate CNC curve interpolators. Comput Aided Design 33:155–165

    Article  Google Scholar 

  11. Hardwick M, Zhao Y F, Proctor F M, Nassehi A, Xu X, Venkatesh S, Odendahl D, Xu L, Hedlind M, Lundgren M, Maggiano L, Loffredo D, Fritz J, Olsson B, Garrido J, Brail A (2013) A roadmap for STEP–NC–enabled interoperable manufacturing. Int J Adv Manuf Tech 68:1023–1037

    Article  Google Scholar 

  12. Hinds J K, Kuan L P (1978) Surfaces defined by curve transformations. In: Proceedings of the 15th numerical control society annual meeting & technical conference, pp 325–340

  13. Koren Y, Lin R–S (1995) Five–axis surface interpolators. CIRP Ann 44:379–382

    Article  Google Scholar 

  14. Liang H, Li X (2009) A 5–axis milling system based on a new G code for NURBS surface. In: IEEE international conference on intelligent computing and intelligent systems (ICIS), vol 2009, pp 600–606

  15. Liang H, Li X (2013) Five–axis STEP–NC controller for machining of surfaces. Int J Adv Manuf Tech 68:2791–2800

    Article  Google Scholar 

  16. Lin R–S (2000) Real–time surface interpolator for 3–D parametric surface machining on 3–axis machine tools. Int J Mach Tools Manuf 40:1513–1526

    Article  Google Scholar 

  17. Lin R–S, Koren Y (1996) Efficient tool–path planning for machining free–form surfaces. ASME J Manuf Sci Eng 118:20–28

    Google Scholar 

  18. Lin Z, Fu J, Shen H, Gan W (2014) A generic uniform scallop tool path generation method for five–axis machining of freeform surface. Comput Aided Design 56:120–132

    Article  Google Scholar 

  19. Lo C–C (1999) Real–time generation and control of cutter path for 5–axis CNC machining. Int J Mach Tools Manuf 39:471–488

    Article  Google Scholar 

  20. Lo C–C (2000) CNC machine tool surface interpolator for ball–end milling of free–form surfaces. Int J Mach Tools Manuf 40:307–326

    Article  Google Scholar 

  21. SINUMERIK 840D/840Di/810D Advanced Programming Guide (2002), Siemens Corporation

  22. Struik D J (1961) Lectures on classical differential geometry. Dover Publications (reprint, New York

    MATH  Google Scholar 

  23. Suresh K, Yang D C H (1994) Constant scallop–height machining of free–form surfaces. ASME J Manuf Sci Eng 116:253–59

    Google Scholar 

  24. Tsai M–C, Cheng C–W, Cheng M–Y (2003) A real–time NURBS surface interpolator for precision three–axis CNC machining. Int J Mach Tools Manuf 43:1217–1227

    Article  Google Scholar 

  25. Tsai Y–F, Farouki RT, Feldman B (2001) Performance analysis of CNC interpolators for time–dependent feedrates along PH curves. Comput Aided Geom Design 18:245–265

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang Y, Liu H, Yu S (2012) Curvature–based real–time NURBS surface interpolator with look–ahead ACC/DEC control. Math Comput Sci 6:315–326

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, Davis, CA, 95616, USA

    Kevin M. Nittler & Rida T. Farouki

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  1. Kevin M. Nittler
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  2. Rida T. Farouki
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Correspondence to Rida T. Farouki.

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Nittler, K.M., Farouki, R.T. A real-time surface interpolator methodology for precision CNC machining of swept surfaces. Int J Adv Manuf Technol 83, 561–574 (2016). https://doi.org/10.1007/s00170-015-7552-x

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  • DOI: https://doi.org/10.1007/s00170-015-7552-x

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