Modeling and analysis of self-excited drill bit vibrations

• Main Author: Germay, Christophe
• Other Authors: DESTINE, Jacques
• Format: Others
• Published: Universite de Liege 2009
• Subjects: discontinuous delay differential equations; stick-slip vibrations; drillstring dynamics
• Online Access: http://bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-05112009-141606/

The research reported in this thesis builds on a novel model developed at the University of Minnesota to analyze the self-excited vibrations that occur when drilling with polycrystalline diamond cutter bits. The lumped parameter model of the drilling system takes into consideration the axial and the torsional vibrations of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process combined with the quasihelical motion of the bit leads to a regenerative effect that introduces a coupling between the axial and torsional modes of vibrations and a state-dependent delay in the governing equations, while the frictional contact process is associated with discontinuities in the boundary conditions when the bit sticks in its axial and angular motion. The response of this complex system is characterized by a fast axial dynamics superposed to the slow torsional dynamics. A two time scales analysis that uses a combination of averaging methods and a singular perturbation approach is proposed to study the dynamical response of the system. An approximate model of the decoupled axial dynamics permits to derive a pseudo analytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier works. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. In this thesis, we also analyze the axial and torsional vibrations by basing the model on a continuum representation of the drillstring rather than on the low dimensional lumped parameter model. The dynamic response of the drilling structure is computed using the finite element method. While the general tendencies of the system response predicted by the discrete model are confirmed by this computational model (for example that the occurrence of stick-slip vibrations as well as the risk of bit bouncing are enhanced with an increase of the weight-on-bit or a decrease of the rotational speed), new features in the self-excited response of the drillstring are detected. In particular, stick-slip vibrations are predicted to occur at natural frequencies of the drillstring different from the fundamental one (as sometimes observed in field operations), depending on the operating parameters. Finally, we describe the experimental strategy chosen for the validation of the model and discuss results of tests conducted with DIVA, an analog experimental set-up of the lumped parameter model. Some results of the experiments conducted in an artificial rock seem to validate the model studied here although the same experiments obtained with natural rocks were unsuccessful. Different problems with the design of the experimental setup were identified. By using the outcome of the analysis of the uncoupled dynamics, we could provide critical recommendation to elaborate and to design a simpler and stiffer analog experiment (TAZ) used to study the self excitation of the axial dynamics that ultimately lead to the excitation of the torsional dynamics.