Numerical stability analysis of the rotary drilling system on the basis of state-dependent delay

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (22) : 233-240.

ZHANG He1,DI Qinfeng1,2,WANG Wenchang1,2,CHEN Feng3,DUAN Haoyu1

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Abstract

The bit-rock interaction introduces state-dependent delays in the rotary drilling systems, which cause the instability of the system and thus the self-excited vibrations of the drill string. These vibrations lead to the wear of drill bit as well as fatigue failure of the drill string and hence decrease the drilling efficiency. Therefore, stability analysis of the rotary drilling system helps to optimize the drilling parameters and bit design so as to reduce or eliminate the undesirable self-excited vibrations. In this paper, the state-dependent delay differential equations (SDDDEs) are derived with considering the torsional damping of drilling mud. The delay-related variable is reformulated via the introduction of the bit trajectory function, which transforms the SDDDEs into a system of nonlinear coupled partial differential equation (PDE) and ordinary differential equations (ODEs). The combination of spectral method and Galerkin method is utilized to analyze the linear stability of the coupled PDE-ODEs, which obtains the stability map of the system in the plane of drilling parameters. The fidelity of the proposed method is confirmed in comparison with the published results and the numerical simulation results. Finally, the effects of damping on the stability of the system are studied. The proposed numerical method in this paper could be extended to analyze the stability for a more generic lumped-parameter model with multiple degrees-of-freedom.
Key words bit-rock interaction; state-dependent delay; stability analysis; stick-slip oscillation; drillstring

Key words

bit-rock interaction / state-dependent delay / stability analysis / stick-slip oscillation / drillstring

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ZHANG He1,DI Qinfeng1,2,WANG Wenchang1,2,CHEN Feng3,DUAN Haoyu1. Numerical stability analysis of the rotary drilling system on the basis of state-dependent delay[J]. Journal of Vibration and Shock, 2022, 41(22): 233-240

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