Stabilizability diagram for turning processes subjected to digital PD control

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• 作者：David Lehotzky (1)
  Janos Turi (2)
  Tamas Insperger (1)
  
• 关键词：Machine tool chatter ; Regenerative delay ; PD controller ; Sampling effect ; Semi ; discretization ; Stabilizability
• 刊名：International Journal of Dynamics and Control
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：2
• 期：1
• 页码：46-54
• 全文大小：607 KB
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• 作者单位：David Lehotzky (1)
  Janos Turi (2)
  Tamas Insperger (1)
  
  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest聽, 1521, Hungary
  2. Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX聽, 75083, USA
  
• ISSN：2195-2698

文摘

Stabilizability of the turning process subjected to a digital proportional-derivative controller is analyzed. The governing equation involves a term with continuous-time point delay due to the regenerative effect and terms with piecewise-constant arguments due to the zero-order hold of the digital control. The resulting hybrid system can be represented as a delay-differential equation with time-periodic delay, for which the stability properties are analyzed using the semi-discretization method. The critical depth of cut is determined, which limits the stabilizability of the machining process for a given spindle speed in the sense that machining operation at larger than the critical depth of cut cannot be stabilized by the applied digital controller for a fixed sampling period. The resulted stabilizability diagram shows some similarities to the traditional stability lobe diagram of machining processes.