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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
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.

Grahic Jump Location
Figure 2

The simplified model of chip formation

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.

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.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In