Dynamic stability of cutting processes such as milling and turning is mainly restricted by the phenomenon of the regenerative effect, causing self-excited vibration, which is well known as machine-tool chatter. With the semidiscretization method for periodic delay-differential equations, there exists an appropriate method for determining the stability boundary curve in the domain of technological parameters. The stability boundary is implicitly defined as a level set of a function on the parameter domain, which makes the evaluation computationally expensive when using complete enumeration. In order to reduce computational cost, we first investigate two types of curve tracking algorithms finding them not appropriate for computing stability charts as they may get stuck at cusp points or near-branch zones. We then present a new curve tracking method, which overcomes these difficulties and makes it possible to compute stability boundary curves very efficiently.
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e-mail: henninger@itm.uni-stuttgart.de
e-mail: eberhard@itm.uni-stuttgart.de
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October 2007
Research Papers
A New Curve Tracking Algorithm for Efficient Computation of Stability Boundaries of Cutting Processes
Christoph Henninger,
Christoph Henninger
Institute of Engineering and Computational Mechanics,
e-mail: henninger@itm.uni-stuttgart.de
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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Peter Eberhard
Peter Eberhard
Institute of Engineering and Computational Mechanics,
e-mail: eberhard@itm.uni-stuttgart.de
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
Search for other works by this author on:
Christoph Henninger
Institute of Engineering and Computational Mechanics,
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germanye-mail: henninger@itm.uni-stuttgart.de
Peter Eberhard
Institute of Engineering and Computational Mechanics,
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germanye-mail: eberhard@itm.uni-stuttgart.de
J. Comput. Nonlinear Dynam. Oct 2007, 2(4): 360-365 (6 pages)
Published Online: May 16, 2007
Article history
Received:
January 5, 2007
Revised:
May 16, 2007
Citation
Henninger, C., and Eberhard, P. (May 16, 2007). "A New Curve Tracking Algorithm for Efficient Computation of Stability Boundaries of Cutting Processes." ASME. J. Comput. Nonlinear Dynam. October 2007; 2(4): 360–365. https://doi.org/10.1115/1.2756077
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