# Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

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## Abstract

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.

## Keywords

Drilling mechanics Drill string Time-delay effects Stick-slip effects Flexible rotor dynamics Nonlinear vibrations## Notes

### Acknowledgements

The authors from Shanghai Jiao Tong University gratefully acknowledge the support received through 973 Grant No. 2011CB706803.

## References

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