Essential chaotic dynamics of chatter in turning processes.

Large-amplitude oscillations of turning operations are investigated, which can be modelled by a one degree-of-freedom damped oscillator subjected to the regenerative effect that introduces a relevant time delay in the system. In the case of large oscillations, when the cutting tool loses contact with the surface of the workpiece, the time delay is switched off, leading to a non-smooth delay differential equation. To explore the geometric structure of the global dynamics of the system, the mathematical model is approximated by means of the essential part of the spectrum in the region where the stationary cutting process may lose its stability. The trajectories embedded in the infinite-dimensional phase space are interpreted in a three-dimensional subspace and then analyzed by means of a discrete Lorenz-map. The bifurcation diagrams of the non-smooth system include chaotic windows, which are presented by numerical and semi-analytical tools and compared to the existing results in the literature.

[1]  P. S. Heyns,et al.  An industrial tool wear monitoring system for interrupted turning , 2004 .

[2]  Jokin Munoa,et al.  Identification of cutting force characteristics based on chatter experiments , 2011 .

[3]  Marian Wiercigroch,et al.  Chaotic Vibration of a Simple Model of the Machine Tool-Cutting Process System , 1997 .

[4]  Pankaj Wahi,et al.  Self-interrupted regenerative metal cutting in turning , 2008 .

[5]  B. Mann,et al.  Stability of Interrupted Cutting by Temporal Finite Element Analysis , 2003 .

[6]  Reimund Neugebauer,et al.  Nonlinear Dynamics of Production Systems: RADONS:NONLIN.DYN.PROD.SY O-BK , 2005 .

[7]  Gábor Stépán,et al.  Global dynamics of low immersion high-speed milling. , 2004, Chaos.

[8]  Gábor Stépán,et al.  Modelling nonlinear regenerative effects in metal cutting , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Günter Radons,et al.  Application of spindle speed variation for chatter suppression in turning , 2013 .

[10]  R. E. Wilson,et al.  Estimates of the bistable region in metal cutting , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  Eric A. Butcher,et al.  On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations , 2011 .

[12]  Steffen Ihlenfeldt,et al.  Stability of milling with non-uniform pitch and variable helix Tools , 2017 .

[13]  Zoltan Dombovari,et al.  On the Global Dynamics of Chatter in the Orthogonal Cutting Model , 2011 .

[14]  Yusuf Altintas,et al.  A novel magnetic actuator design for active damping of machining tools , 2014 .

[15]  Tamás Insperger,et al.  On the Approximation of Delayed Systems by Taylor Series Expansion , 2015 .

[16]  E.J.A. Armarego,et al.  Computerized Predictive Cutting Models for Forces in End-Milling Including Eccentricity Effects , 1989 .

[17]  Rafal Bogacz,et al.  Improved conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network , 2012, BMC Neuroscience.

[18]  Gilles Dessein,et al.  On the stability of high-speed milling with spindle speed variation , 2010 .

[19]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[20]  Wadia Faid Hassan Al-shameri,et al.  Some dynamical properties of the family of tent maps , 2013 .

[21]  Dénes Takács,et al.  On stability of emulated turning processes in HIL environment , 2019, CIRP Annals.

[22]  Tamás Kalmár-Nagy,et al.  Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations , 2001 .