A new approach to stability analysis of variable speed machining systems

Tsu Chin Tsao, Mark W. McCarthy, Shiv G. Kapoor

Research output: Contribution to journalArticlepeer-review


This paper presents a new method for the stability analysis of variable speed machining systems. By using spindle angular position as the independent variable, the system dynamics are modeled as a linear periodic time-varying system with fixed delay. This representation is proven much easier to analyze and to numerically simulate than the time-varying delay representation, which traditionally uses the real-time as the independent variable. With a finite difference scheme, the infinite dimensional periodic time-varying system is approximated by a finite dimensional periodic time-varying discrete system, which in turn is converted to a time-invariant system by multiplying the time-varying state transition matrix over one period of speed variation. System-relative stability becomes tractable by spectral radius analysis. This approach makes possible the quantitative characterization of system stability as a function of variable speed profiles as well as other system parameters such as stiffness and damping of the cutting process and the tool/workpiece structure. Verifications for the face milling process by numerical simulation and experiment for both constant and variable speed are given.

Original languageEnglish (US)
Pages (from-to)791-808
Number of pages18
JournalInternational Journal of Machine Tools and Manufacture
Issue number6
StatePublished - Dec 1993

ASJC Scopus subject areas

  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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