Bifurcation analysis of milling process with tool wear and process damping: regenerative chatter with primary resonance

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• 作者：Hamed Moradi (1) hamedmoradi@asme.org
  Mohammad R. Movahhedy (1) movahhed@sharif.edu
  Gholamreza Vossoughi (1) vossough@sharif.edu
• 关键词：Peripheral milling &#8211 ; Primary resonance &#8211 ; Regenerative chatter &#8211 ; Tool wear &#8211 ; Process Damping &#8211 ; Bifurcation
• 刊名：Nonlinear Dynamics
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：70
• 期：1
• 页码：481-509
• 全文大小：3.8 MB
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• 作者单位：1. Centre of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, PO Box 11155-9567, Tehran, Iran
• ISSN：1573-269X

文摘

In this paper, the occurrence of various types of bifurcation including symmetry breaking, period-doubling (flip) and secondary Hopf (Neimark) bifurcations in milling process with tool-wear and process damping effects are investigated. An extended dynamic model of the milling process with tool flank wear, process damping and nonlinearities in regenerative chatter terms is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. Non-autonomous parametrically excited equations of the system with time delay terms are developed. The multiple-scale approach is used to construct analytical approximate solutions under primary resonance. Periodic, quasi-periodic and chaotic behavior of the limit cycles is predicted in the presence of regenerative chatter. Detuning parameter (deviation of the tooth passing frequency from the chatter frequency), damping ratio (affected by process damping) and tool-wear width are the bifurcation parameters. Multiple period-doubling and Hopf bifurcations occur when the detuning parameter is varied. As the damping ratio changes, symmetry breaking bifurcation is observed whereas the variation of tool wear width causes both symmetry breaking and Hopf bifurcations. Also, under special damping specifications, chaotic behavior is seen following the Hopf bifurcation.