Chaotic Phenomena Induced by the Fast Plastic Deformation of Metals During Cutting

[+] Author and Article Information
Zoltan Palmai

 COGITO Ltd., Budapest Alvinci ut 24, Budapest 1022, Hungarypalmay@axelero.hu

J. Appl. Mech 73(2), 240-245 (Jul 07, 2005) (6 pages) doi:10.1115/1.2074727 History: Received September 23, 2004; Revised July 07, 2005

In the present study the examination of chip formation is focused on the primary shear zone, which is divided into two layers, and the variation of shear stress and temperature in time are given by two mechanical balance equations and three energy equations. All the five evolution differential equations are autonomous and nonlinear. The material characteristics are determined by an exponential constitutive equation. The mathematical model is suitable for the qualitative description of different types of chips, such as continuous chips and periodic or aperiodic shear localized chips, which is demonstrated by the general structure and typical solutions of the equation system.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 4

The typical solutions of the mathematical model (p=1.03, ξ=2.6η=4.5, a=0.3, b=0.012, C=1). (a) Fixed point ζ=22.5, (b) bifurcation ζ=5.8, (c) chaotic ζ=11.65, (d) five-cyclic ζ=11.33.

Grahic Jump Location
Figure 3

The structure of the mathematical model’s solutions. F: Fixed point, B: Bifurcation, K+C: Chaotic and n-cyclic (n>1), p=1.03, η=4.5, a=0.3, b=0.012, and C=1.

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Figure 2

The simplified model of chip formation

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Figure 1

Longitudinal cross sections of austenitic steel chips. (a) v=0.3m∕s, (b) v=0.58m∕s, (c) v=1.17m∕s)↔:0.1mm.



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