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Variable feed rates and variable machine forces for a constant material removal rate and constant cutting force along Pythagorean-hodograph curves

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Abstract

This paper proposes a new machining strategy to realize better dimensional accuracy as well as surface finish. The strategy attempts to keep cutting force and the material removal rate approximately constant and force the tool to move along a so-called Pythagorean-hodograph curve, which is a group of analytic curves with special properties, in a milling operation. In conventional milling operations, a constant feed rate is frequently used. This would invariably lead to higher material removal rates in concave regions and lower material removal rates in convex regions, and affects dimensional accuracy. This work aims to establish the theoretical basis to show how the above-mentioned phenomenon can be predicted. Additionally, chattering is a well-known problem in machining. In this work, it is postulated that keeping certain machining conditions approximately constant would help in reducing chattering during machining. A numerical example is given to illustrate the proposed machining strategy.

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References

  1. Shpitalni M, Koren Y, Lo CC (1994) Realtime curve interpolators. CAD Comput Aided Des 26(11):832–838

    Article  MATH  Google Scholar 

  2. Yeh SS, Hsu PL (1999) Speed-controlled interpolator for machining parametric curves. CAD Comput Aided Des 31(5):349–357

    Article  MATH  Google Scholar 

  3. Chang YF, Hong RC (2005) Parametric curve machining of a CNC milling EDM. Int J Mach Tools Manuf 45(7–8):941–948

    Article  Google Scholar 

  4. Sun Y, Wang J, Guo D (2006) Guide curve based interpolation scheme of parametric curves for precision CNC machining. Int J Mach Tools Manuf 46(3–4):235–242

    Article  Google Scholar 

  5. Farouki RT, Sakkalis I (1990) Pythagorean hodographs. IBM J Res Develop 34(5):736–752

    Article  MathSciNet  Google Scholar 

  6. Perwass CBU, Farouki RT, Noakes L (2007) A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation. Comput Aided Geom Des 24(4):220–237

    Article  MathSciNet  MATH  Google Scholar 

  7. Farouki RT, Al-Kandari M, Sakkalis T (2002) Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves. Adv Comput Math 17(4):369–383

    Article  MATH  MathSciNet  Google Scholar 

  8. Pelosi F, Farouki RT, Manni C, Sestini A (2005) Geometric hermite interpolation by spatial pythagorean-hodograph cubics. Adv Comput Math 22(4):325–352

    Article  MATH  MathSciNet  Google Scholar 

  9. Farouki RT, Shah S (1996) Real-time CNC interpolators for Pythagorean-hodograph curves. Comput Aided Geom Des 13(7):583–600

    Article  MATH  Google Scholar 

  10. Farouki RT, Manjunathaiah T, Yuan GF (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(1):123–142

    Article  Google Scholar 

  11. Farouki RT, Tsai YF, Yuan GF (1999) Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Comput Aided Geom Des 16(1):61–76

    Article  MATH  MathSciNet  Google Scholar 

  12. Faroukit RT, Manjunathaiaht J, Nicholast D, Yuant GF, Jee S (1998) Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves. CAD Comput Aided Des 30(8):631–640

    Article  Google Scholar 

  13. Tsai YF, Farouki RT, Feldman B (2001) Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Comput Aided Geom Des 18(3):245–265

    Article  MATH  MathSciNet  Google Scholar 

  14. Faroukit RT, Neff CA (1990) Analytic properties of plane offset curves. Algebraic properties of plane offset curves. Comput Aided Geom Des 7:83–127

    Article  Google Scholar 

  15. Meriam JL, Kraige LG (2007) Kinetics of particles, engineering mechanics dynamics. Wiley, United states of America, pp 119–156

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    B. Lotfi, Z. W. Zhong & L. P. Khoo

Authors
  1. B. Lotfi
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  2. Z. W. Zhong
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  3. L. P. Khoo
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Corresponding author

Correspondence to Z. W. Zhong.

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Lotfi, B., Zhong, Z.W. & Khoo, L.P. Variable feed rates and variable machine forces for a constant material removal rate and constant cutting force along Pythagorean-hodograph curves. Int J Adv Manuf Technol 40, 171–178 (2009). https://doi.org/10.1007/s00170-007-1317-0

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  • DOI: https://doi.org/10.1007/s00170-007-1317-0

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