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Model Order Reduction of a Drill‐String‐Model with Self‐Excited Stick‐Slip Vibrations
Author(s) -
Kreuzer Edwin,
Steidl Michael
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910121
Subject(s) - drill string , vibration , nonlinear system , galerkin method , inertia , slip (aerodynamics) , physics , reduction (mathematics) , finite element method , classical mechanics , control theory (sociology) , mechanics , mathematics , engineering , drill , structural engineering , computer science , geometry , mechanical engineering , acoustics , control (management) , quantum mechanics , artificial intelligence , thermodynamics
The dynamical behavior of a drill‐string is defined by its small diameter‐to‐length ratio, which makes the string vulnerable to torsional vibrations. In combination with the nonlinear friction characteristic at the drill bit, this can lead to self‐excited stick‐slip vibrations which are detrimental to the drilling process. The string can be modeled by the Finite Element Method or as a Multi‐Body system to represent the distributed character of the system. The analysis of the resulting high‐dimensional model is, however, elaborate and time‐consuming. We show that through Galerkin Projection onto the first two Characteristic Functions gained from Karhunen‐Loève‐Transformation, a reduced system can be obtained which reproduces the essential dynamical properties of the original system, e.g. the stick‐slip motion. With the reduced system, the linear stability of the drill‐string can be analyzed. We show that by reducing the inertia of the rotary table the system can be stabilized. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)