Wahi, Pankaj and Chatterjee, Anindya (2008) Self-interrupted regenerative metal cutting in turning. In: International Journal of Non-Linear Mechanics, 43 (2). pp. 111-123.
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A new approach is used to study the global dynamics of regenerative metal cutting in turning. The cut surface is modeled using a partial differential equation (PDE) coupled, via boundary conditions, to an ordinary differential equation (ODE) modeling the dynamics of the cutting tool. This approach automatically incorporates the multiple-regenerative effects accompanying self-interrupted cutting. Taylor's 3/4 power law model for the cutting force is adopted. Lower dimensional ODE approximations are obtained for the combined tool–workpiece model using Galerkin projections, and a bifurcation diagram computed. The unstable solution branch off the subcritical Hopf bifurcation meets the stable branch involving self-interrupted dynamics in a turning point bifurcation. The tool displacement at that turning point is estimated, which helps identify cutting parameter ranges where loss of stability leads to much larger self-interrupted motions than in some other ranges. Numerical bounds are also obtained on the parameter values which guarantee global stability of steady-state cutting, i.e., parameter values for which there exist neither unstable periodic motions nor self-interrupted motions about the stable equilibrium.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Keywords:||Self-interruption;Regenerative chatter;Turning;Global dynamics;Bifurcation diagram.|
|Department/Centre:||Division of Mechanical Sciences > Mechanical Engineering|
|Date Deposited:||30 Mar 2010 11:47|
|Last Modified:||19 Sep 2010 05:58|
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