Abstract
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 Polycrystalline Diamond Compact (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 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. The algorithm is further extended to a linear stability analysis for the bit dynamics. The resulting stability boundaries are verified with time-domain simulations. The reported algorithm could, in principle, be applied to a more realistic drillstring model, which may lead to an in-depth understanding of the mitigation of self-excited vibrations through PDC bit designs.
Original language | English (US) |
---|---|
Title of host publication | 17th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC) |
Publisher | American Society of Mechanical Engineers (ASME) |
ISBN (Electronic) | 9780791885468 |
DOIs | |
State | Published - 2021 |
Event | 17th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, MSNDC 2021, Held as Part of the ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2021 - Virtual, Online Duration: Aug 17 2021 → Aug 19 2021 |
Publication series
Name | Proceedings of the ASME Design Engineering Technical Conference |
---|---|
Volume | 9 |
Conference
Conference | 17th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, MSNDC 2021, Held as Part of the ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2021 |
---|---|
City | Virtual, Online |
Period | 8/17/21 → 8/19/21 |
Bibliographical note
Publisher Copyright:© 2021 by ASME