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Page de résumé pour ULgetd-05112009-141606

Auteur : Germay, Christophe
E-mail de l'auteur : Christophe.Germay@student.ulg.ac.be
URN : ULgetd-05112009-141606
Langue : Français/French
Titre : Modeling and analysis of self-excited drill bit vibrations
Intitulé du diplôme : Doctorat en sciences de l'ingénieur
Département : FSA - Département d'électricité, électronique et informatique
Jury :
Nom : Titre :
DETOURNAY, Emmanuel Membre du jury/Committee Member
ERNEUX, Th Membre du jury/Committee Member
KERSCHEN, Gaëtan Membre du jury/Committee Member
VAN DE WOUW, Nathan Membre du jury/Committee Member
WIERCIGROCH, Marian Membre du jury/Committee Member
DESTINE, Jacques Président du jury/Committee Chair
SEPULCHRE, Rodolphe Promoteur/Director
Mots-clés :
  • discontinuous delay differential equations
  • stick-slip vibrations
  • drillstring dynamics
Date de soutenance : 2009-03-11
Type d'accès : Restreint/Intranet
Résumé :

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


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.

Autre version :
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