<p>This work describes an alternative formulation of a system of nonlinear state-dependent delay differential equations (SDDDEs) that governs the coupled axial and torsional vibrations of a 2 DOF drillstring model considering a PDC bit with realistic cutter layout. Such considerations result in up to 100 state-dependent delays due to the regenerative effect of the drilling process, which renders the computational efficiency of conventional solution strategies unacceptable. The regeneration of the rock surface, associated with the bit motion history, can be described using the bit trajectory function, the evolution of which is governed by a partial differential equation (PDE). Thus the original system of SDDDEs can be replaced by a nonlinear coupled system of a PDE and various ordinary differential equations (ODEs). Via the application of the Galerkin method, this system of PDE-ODEs is transformed into a system of coupled ODEs, which can be readily solved. Furthermore, this algorithm is extended to a linear stability analysis for the bit dynamics. The resulting stability boundaries are verified with the time-domain simulations. The reported algorithm in principle can be incorporated with a more complex drillstring model, which may lead to a more in-depth understanding of the mitigation of self-excited vibrations through PDC bit designs.</p>

An Alternative Formulation for Modeling Drillstring Self-Excited Oscillations Considering PDC Bits With Realistic Cutter Layout

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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