Abstract

In downhole drilling systems, self-excited torsional vibrations caused by the bit-rock interactions can affect the drilling process and lead to the premature failure of components. Especially self-excited oscillations of higher-order modes lead to critical dynamic loads. The slim drill string design and the naturally limited drilled borehole diameter limit the installation space, power supply and lead to numerous potentially critical self-excited torsional modes. Consequently, small and robust passive damping concepts are required. The variety of possible downhole boundary conditions and potential damper designs necessitates analytical solutions for effective damper design and optimization. In this paper, two nonlinear passive damper concepts are investigated regarding design and effectiveness to reduce self-excited high-frequency torsional oscillations in drill string dynamics. Based on a finite element model of a drill string, a suitable minimal model based on the identified critical mode is generated and solved analytically using the Multiple Scales Lindstedt-Poincaré (MSLP) method. The advantages of MSLP compared to conventional MS methods are shown for this example. On the basis of the analytical solution, parameter influences are determined, and design equations are derived. The analytical results are transferred to self-excited drill string vibrations and discussed using time domain simulations of the drill string model.

Highlights

  • In deep drilling applications, unwanted vibrations can reduce reliability, lead to premature failures of components, reduce the drilling efficiency and increase nonproductive time

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  • The equations derived from the analytical solutions with the aim of analytical results are simulatively validated using self-excited drill string models

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Summary

Introduction

In deep drilling applications, unwanted vibrations can reduce reliability, lead to premature failures of components, reduce the drilling efficiency and increase nonproductive time. Due to improved and new measuring tools, high-frequency oscillations have been identified as the cause of numerous drill string failures and have been intensively investigated over the last years with studies [9,10], simulations [8,11] and experiments [12,13]. The harmonic balance method [23,24,25] is one possibility to approximate nonlinear parts of a differential equation that has been used for drill string dynamic [22]. The harmonic balance method [23,24,25] is one possibility to approximate nonlinear parts of a differential equation that has been used for drill string dyn3aomf 2i2c [22]. Umsoindgest.hUe spirnegditchteivpercerditiectriivoen cdreitreivrieodninde[r8i]vaenddinde[t8e]ramnidnidnegttheermScin,kivnagluthee, the, BHvaAlucea, nthbeeBreHdAucceadntobearseidnuglceedmtoodaalsdinegglreeemoofdfraeleddeogmrereepofrefsreenedtionmg trheeprceristeicnatlinhgigthhefrcerqituiecanlcyhimghodfree.qTuheinscmy omdoadl ree. dTuhcitsiomnoodfatlhreedtourcstiioonnalodf ythneamtoircsioofnaadl driyllsntarimngiciosfdaedsrpiiltlestirtisncgoims dpelsepxiittey istsuictoamblpe,lebxeitcyaususeitawbhlee,nbeHcFauTsOe wochceunr,HmFoTsOtlyococnuer,cmriotisctalyl monoedcerditoicmalinmatoedsethdeoemnitniraetetosrtshioeneanltsiryestteomrsidoynnaal msyisctoemf thdeyBnHamAi.cInofatdhdeiBtioHnA, t.hIne laadrgdeitbiount, stlhime ladregseigbnuot fsltihme ddreislilgsntroinfgthweidthrilliltstlterianvgawilaitbhleliitntlsetaalvlaatiiloabnlespinacsetallelaatdiosntosploawcerleeaacdtisvteo eloffwecrtseaocftidvaemefpfeecrtss oonf dthame ptoerrssioonnatlhdeytonrasmioincaslodfytnhaemdircisllosfttrhinegd.riIlnl s[t8ri,n16g,.1I9n],[8a,1s6im,19il]a, ra reduction method was used to characterize downhole vibrations and in [5,19,22] ‘it is used to investigate vibration reduction strategies

Minimal Model of a Drill String and Damper
Adaption and Simplification of the Minimal Model
Applying MSLP on the Damper with Cubic Nonlinearity
Including Friction in MSLP
Parameter Dependency of the Operating Range
Influence of the Critical Torsional Mode
Comparison with Time Domain Simulations
Damper Design for Self-Excited Drill String Vibrations
Conclusions
Full Text
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