A Novel Stability Analysis of Systems with Multiple Time Delays

1
A Novel Stability Analysis of Systems with
Multiple Time Delays and Its Application to
High Speed Milling Chatter
Hassan Fazelinia Department of Mechanical
Engineering University of Connecticut
2
Problem Statement

• A, Bj constant matrices in ?n?n
• ? (?1, ?2, , ?p) ? ?p rationally independent
  delays

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Variable Pitch Milling and Multiple Delay

• Notable earlier works
• Slavicek, J., 1965, 6th MTDR Conference,
  London, Pergamon Press.
• Minis, I. and Yanushevsky, R. , 1993, ASME
  Journal of Engineering for Industry 115(1), 1-8.
• Altintas, Y. and Budak, E., 1995, Annals of the
  CIRP 44(1), 357-362.

4
Process Dynamics

• Olgac, N. and Sipahi, R., ASME Journal of
  Manufacturing Science and Engineering, 2005.
  127(4).
• Sipahi, R. and Olgac, N. , IMECE 2006

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CTCR Results and Experimental Comparison
CTCR results (red) Altintas, Y. 1999 (black)
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Optimization of Variable Pitch Milling

• Maximizing the metal removal rate while
  avoiding the onset of chatter

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Optimization results