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Articles

Third-order least squares modelling of milling state term for improved computation of stability boundaries

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Pages 46-64 | Received 25 Feb 2014, Accepted 24 May 2016, Published online: 27 Jun 2016

References

  • Altintas, Y. (2001). Analytical prediction of three dimensional chatter stability in milling. JSME International Journal Series C, 44, 717–723.10.1299/jsmec.44.717
  • Altintas, Y., & Budak, E. (1995). Analytical prediction of stability lobes in milling. CIRP Annals – Manufacturing Technology, 44, 357–362.
  • Bayly, P. V., Halley, J. E., Mann, B. P., & Davies, M. A. (2003). Stability of interrupted cutting by temporal finite element analysis. Journal of Manufacturing Science and Engineering, 125, 220–225.10.1115/1.1556860
  • Bayly, P. V., Schmitz, T. L., Stepan, G., Mann, B. P., Peters, D. A., & Insperger T. (2002). Effects of radial immersion and cutting direction on chatter instability in end-milling. Proceedings of IMECE’02 2002 ASME International Mechanical Engineering Conference & Exhibition New Orleans, LA, November 17–22.
  • Bobrenkov, O. A., Khasawneh, F. A., Butcher, E. A., & Mann, B. P. (2010). Analysis of milling dynamics for simultaneously engaged cutting teeth. Journal of Sound and Vibration, 329, 585–606.10.1016/j.jsv.2009.09.032
  • Ding, Y., Zhu, L. M., Zhang, X. J., & Ding, H. (2010a). A full-discretization method for prediction of milling stability. International Journal of Machine Tools and Manufacture, 50, 502–509.10.1016/j.ijmachtools.2010.01.003
  • Ding, Y., Zhu, L., Zhang, X., & Ding, H. (2010b). Second-order full-discretization method for milling stability prediction. International Journal of Machine Tools and Manufacture, 50, 926–932.10.1016/j.ijmachtools.2010.05.005
  • Faassen, R. P. H., van de Wouw, N., Oosterling, J. A. J., & Nijmeijer, H. (2003, November). Prediction of regenerative chatter by modelling and analysis of high-speed milling. Internati0onal Journal of Machine Tools and Manufacture, 43, 1437–1446.10.1016/S0890-6955(03)00171-8
  • Hanna, N. H., & Tobias, S. A. (1974). Theory of nonlinear regenerative chatter. Journal of Engineering for Industry, 96 Ser B(1), 247–255.10.1115/1.3438305
  • Insperger, T. (2002). Stability analysis of periodic delay-differential equations modelling machine tool chatter (PhD dissertation). Budapest University of Technology and Economics.
  • Insperger, T. (2010). Full-discretization and semi-discretization for milling stability prediction: Some comments. International Journal of Machine Tools and Manufacture, 50, 658–662.10.1016/j.ijmachtools.2010.03.010
  • Insperger, T., & Stépán, G. (2004). Updated semi-discretization method for periodic delay differential with discrete delay. International Journal for Numerical Methods in Engineering, 61, 117–141.10.1002/(ISSN)1097-0207
  • Mann, B. P., Bayly, P. V., Davies, M. A., & Halley, J. E. (2004). Limit cycles, bifurcations, and accuracy of the milling process. Journal of Sound and Vibration, 277, 31–48.10.1016/j.jsv.2003.08.040
  • Merdol, S. D., & Altintas, Y. (2004). Multi frequency solution of chatter stability for low immersion milling. Journal of Manufacturing Science and Engineering, 126, 459–467.10.1115/1.1765139
  • Merrit, H. E. (1965). Theory of self-excited machine-tool chatter. Journal of Engineering for Industry, 87, 447–454.10.1115/1.3670861
  • Moon, F. C. (1998). Dynamics and chaos in manufacturing process. New York, NY: Wiley.
  • Ozoegwu, C. G. (2011). Chatter of Plastic Milling CNC Machine (Master of Engineering thesis). Nnamdi Azikiwe University Awka.
  • Ozoegwu, C. G. (2014). Least squares approximated stability boundaries of milling process. International Journal of Machine Tools and Manufacture, 79, 24–30.10.1016/j.ijmachtools.2014.02.001
  • Ozoegwu, C. G., & Omenyi, S. N. (2013, July–August). Wave attenuation effects on the chatter instability of end-milling. Noise Control Engineering Journal, 61, 436–444.10.3397/1/3761038
  • Ozoegwu, C. G., & Omenyi, S. (2014). Reducing computational requirement of stability analysis of milling by partial averaging. Manufacturing Review, 1(14), 1–13.
  • Ozoegwu, C. G., & Omenyi, S. N. (2016). Curvature effects on circular feed end-milling, part 2: Stability analysis. International Journal of Engineering Systems Modelling and Simulation, 8(1), 20–27. Retrieved from http://www.inderscience.com/info/ingeneral/forthcoming.php?jcode=ijesms
  • Ozoegwu, C. G., Omenyi, S., & Ofochebe, S. M. (2013). Time finite element chatter stability characterization of a three tooth plastic end-milling CNC machine. American Journal of Computational and Applied Mathematics, 3(1), 1–7.
  • Ozoegwu, C. G., Omenyi, S. N., & Ofochebe, S. M. (2015). Curvature effects on circular feed end-milling, part 1: modelling and simulation. International Journal of Engineering Systems Modelling and Simulation, 7(3), 147–157. Retrieved from http://www.inderscience.com/info/ingeneral/forthcoming.php?jcode=ijesms
  • Ozoegwu, C. G., Omenyi, S. N., Ofochebe, S. M., & Achebe, C. H. (2013). Comparing up and down milling modes of end-milling using temporal finite element analysis. Applied Mathematics, 3(1), 1–11.
  • Patel, B. R., Mann, B. P., & Young, K. A. (2008). Uncharted islands of chatter instability in milling. International Journal of Machine Tools & Manufacture, 48, 124–134.
  • Quo, Q., Sun, Y., & Jiang, Y. (2012). On the accurate calculation of milling stability limits using third-order full-discretization method. International Journal of Machine Tools & Manufacture, 62, 61–66.
  • Sellmeier, V., & Denkena, B. (2011). Stable islands in the stability chart of milling processes due to unequal tooth pitch. International Journal of Machine Tools & Manufacture, 51, 152–164.
  • Stepan, G. (1989). Retarded dynamical systems. Harlow: Longman.
  • Taylor, F. W. (1907). On the art of cutting metals. Transactions of ASME, 28, 31–350.
  • Tlusty, J., & Polacek, M. (1963). The stability of machine tools against self-excited vibrations in machining. International research in production engineering, 1(1), 465–474.
  • Wiercigroch, M., & Budak, E. (2001). Sources of nonlinearities, chatter generation and suppression in metal cutting. Philosophical Transactions of the Royal Society London, 359, 663–693.10.1098/rsta.2000.0750
  • Wiercigroch, M., & Krivtsov, A. M. (2001). Frictional chatter in orthogonal metal cutting. Philosophical Transactions: Mathematical, Physical and Engineering Sciences (Series A), 359, 713–738.10.1098/rsta.2000.0752
  • Wu, B., Luo, M., & Zhang, D. (2013). An efficient approach for identifying stable lobes with discretization method. Advances in Mechanical Engineering, 2013, 1–5. doi:10.1155/2013/682684
  • Yi, S., Nelson, P. W., & Ulsoy, A. G. (2007). Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences and Engineering, 4(2), 355–368.10.3934/mbe