Chaotic dynamics of the cutting process

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Abstract

In the article a manufacturing system is treated as a simple two dimensional elastic structure in which the cutting force is generated by material flow against the tool. Generalized empirical relations corresponding to orthogonal cutting are applied to describe the non-linear dependence of a cutting force on chip velocity and thickness. The formulated mechanical model of a two dimensional coupled oscillator thus represents a typical example of a non-linear dissipative system, the dynamics of which require description in a four dimensional phase space. The numerical solutions of the governing dynamical equations reveal chaotic oscillations if the characteristic cutting parameter is selected in a region corresponding to intensive cutting. The properties of chaotic oscillations are illustrated by the time dependence of tool displacement, acceleration, cutting force, and power dissipated for material deformation or exchanged with an oscillating tool. The manufactured surface profile is found to resemble a wavy water surface. The phase portraits, Lissajoux figures and spectral densities of calculated signals indicate a similarity with quasiperiodic movement. The information dimension of a corresponding strange attractor, estimated by the correlation exponent, is approximately 3 for a typical example of cutting chaos. The tool displacement X in the direction of input velocity appears to be the most characteristic variable. Its return map is constructed by successive observations of maximal displacement values. The corresponding approximate analytical expression Xn+1=5 Xn(1.1-Xn)-0.70 is similar to the prototypical map which is frequently applied in the study of chaotic phenomena.

References (19)

  • I. Grabec, Proc. 2nd Int. Conf. Manuf. Sci. Technol. Syst. Future Ljubljana, in...
  • S.A. Tobias
  • J. Peklenik et al.J. Peklenik et al.
  • P.J. Thompson et al.
  • W.F. Hastings et al.
  • W.F. Hastings et al.

    Proc. R. Soc. Lond. A

    (1980)
  • Lichtenberg A.J. et al.
  • R.K. Ritala

    Physica Scripta

    (1985)
  • L.P. Kadanoff

    Physica Scripta

    (1985)
There are more references available in the full text version of this article.

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