Model Order Reduction of a Drill-String-Model with Self-Excited Stick-Slip Vibrations

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)