钻柱振动与冲击抑制技术研究现状

doi:10.11885/j.issn.1674-5086.2013.12.19.03

摘要/Abstract

摘要：

对钻柱振动和冲击的控制是井眼轨道优化设计、钻井参数优选、提高钻速及实现智能钻井的重要基础。在深
水、超深水，深井、超深井，页岩气硬脆性地层及气体钻井作业中，要用到丛式井、定向井等特殊钻井工艺，这些复杂井
建井过程中由钻柱振动和冲击造成的损失日益增加。系统阐述和对比了钻柱振动和冲击的表现形式及评价方法。将
钻柱振动和冲击分为被动控制、主动控制和半主动控制3 方面，归纳和分类探讨了近年来核心控制方法及关键控制设
备的结构、原理，给出代表性的成果，对比分析了相应方法特点、设备及适应范围，设计了钻柱振动和冲击控制程序，
探讨了未来重点研究的方向。

关键词: 钻柱振动, 钻柱冲击, 深水, 超深井, 页岩气地层, 振动控制

Abstract:

Control of drill string vibration and shockis an important basis for track optimizing，wellbore design and precise
control，optimization of drilling parameters，improving drilling speed and intelligent drilling. In deep water，ultra-deep water，
deep well，ultra deep well，hard and brittle shale gas formations and gas drilling operations，cluster wells，directional wells
and other special drilling technologies are employed，but these complex wells increases losses by vibration and shock. We
systematically explained and compared the forms and methods of performance evaluation of the drill string vibration and shock
and divided the drill string vibration and shock into passive control，active control and semi-active control. Based on a summarization
and recent classification of critical control methods and the structure and principle of critical controlling equipments，
we focused on the representative achievements and made a comparative analysis of the corresponding methodological characteristics，
equipments and application range，which resulted in the procedures of drill string vibration and shock control and
revealed the direction of future research.

Key words: drillstring vibration, drill string impact, deep water, ultra-deep well, shale gas formations, vibration control

中图分类号:

TE331.1

董广建1 *，陈平1，邓元洲2，郭昭学1. 钻柱振动与冲击抑制技术研究现状[J]. 西南石油大学学报(自然科学版), 2016, 38(3): 121-134.

DONG Guangjian1*, CHEN Ping1, DENG Yuanzhou2, GUO Zhaoxue1. A Literature Review of Researches on Drillstring Vibration Suppression[J]. 西南石油大学学报(自然科学版), 2016, 38(3): 121-134.

0
/ / 推荐

导出引用管理器 EndNote|Ris|BibTeX

链接本文: http://journal15.magtechjournal.com/Jwk_xnzk/CN/10.11885/j.issn.1674-5086.2013.12.19.03

http://journal15.magtechjournal.com/Jwk_xnzk/CN/Y2016/V38/I3/121

参考文献

[1] 胡文瑞，鲍敬伟，胡滨. 全球油气勘探进展与趋势[J].
石油勘探与开发，2013，40（4）：409 413.
HU Wenrui，BAO Jingwei，HU Bin. Trend and progress
in global oil and gas exploration[J]. Petroleum Exploration
and Development，2013，40（4）：409 413.
[2] 邹才能，杨智，张国生，等. 常规非常规油气“有序
聚集”理论认识及实践意义[J]. 石油勘探与开发. 2014，
41（1）：14 25.
ZOU Caineng，YANG Zhi，ZHANG Guosheng，et al.
Conventional and unconventional petroleum “orderly
accumulation”：Concept and practical significance[J].
Petroleum Exploration and Development. 2014，41（1）：
14 30.
[3] 董广建，陈平，马天寿，等. 深水表层钻井关键技术及
装备研究应用现状[J]. 石油机械，2013，41（6）：49 53.
DONG Guangjian，CHEN Ping，MA Tianshou，et al. Key
technology of deep water top hole drilling and current
situation of equipment research and application[J]. China
Petroleum Machinery，2013，41（6）：49 53.
[4] 石晓兵，喻著成，陈平. 侧钻水平井，分支井井眼轨迹
设计与控制理论[M]. 北京：石油工业出版社，2009：
1 20.
SHI Xiaobing，YU Zhucheng，CHEN Ping. Design
and control theory of the sidetrack horizontal well and
branch wellbore trajectory[M]. Beijing：Petroleum Industry
Press，2009：1 20.
[5] 陈平，刘阳，马天寿. 页岩气“井工厂”钻井技术现状及
展望[J]. 石油钻探技术，2014，42（3）（3）：1 7.
CHEN Ping，LIU Yang，MA Tianshou. Status and
prospect of multi-well pad drilling technology in shale
gas[J]. Petroleum Drilling Techniques，2014，42（3）：
1 7.
[6] 陈平. 钻井与完井工程（第二版）[M]. 北京：石油工业
出版社，2011：1 10.
CHEN Ping. Drilling and completion engineering：The
2nd edition[M]. Beijing：Petroleum Industry Press，2011：
1 10.
[7] MITCHELL R F，ALLEN M B. Case studies of BHA vibration
failure[C]. SPE 16675，1987.
[8] VANDIVER K J，NICHOLSON J W，SHYU R. Case
studies of the bending vibration and whirling motion of
drill collars[J]. SPE Drilling Engineering，1990，5（4）：
282 290.
[9] RECKMANN H，JOGI P，KPETEHOTO F T，et al.
MWD failure rates due to drilling dynamics[C]. SPE
127413，2010.
[10] 朱荣东，陈平，周建良，等. 深水表层钻井随钻压力温
度测量仪的研制[J]. 机械，2012（S1）：93 95.
ZHU Rongdong，CHEN Ping，ZHOU Jianliang，et al. The
development of a downhole tool used in deepwater tophole
drilling that can measure pressure and temperature while
drilling[J]. Machinery，2012（S1）：93 95.
[11] 陈平，马天寿. 深水钻井溢流早期监测技术研究现
状[J]. 石油学报，2014，35（3）：602 612.
CHEN Ping，MA Tianshou. Research status of early monitoring
technology for deepwater drilling overflow[J]. Acta
Petrolei Sinica，2014，35（3）：602 612.
[12] 杨川，陈平，夏宏泉，等. 随钻地层压力测量仪研究新
进展[J]. 天然气工业，2013，33（2）：71 75.
YANG Chuan，CHEN Ping，XIA Hongquan，et al.
Progress in research and development of measurement
while drilling apparatuses[J]. Natural Gas Industry，2013，
33（2）：71 75.
[13] DUNAYEVSKY V A，ABBASSIAN F. Application of
stability approach to bit dynamics[J]. SPE Drilling &
Completion，1998，13（2）：99 107.
[14] FINNIE I，BAILEY J J. An experimental study of drill
string vibration[J]. Journal of Engineering for Industry，
ASME Transaction，1960，82（2）：129 135.
[15] PASLAY P R，BOGY D B. Drill string vibration due to
intermitent contact of bit teeth[J]．Journal of Engineering
for Industry，ASME Transaction，1963，85（5）：110 115.
[16] MILLHEIM K K. The effect of BHA dynamics on the
trajectory of a bit[J]. Journal of Petroleum Technology，
1981，33（12）：2323 2337.
[17] DAREING D W. Drill collar length is a major factor in vibration
control[J]. Petroleum Technology，1984，36（4）：
637 644.
[18] 刘清友，黄本生. 牙轮钻头横向振动模型的建立及求
解[J]. 天然气工业，2001，21（4）：55 56.
LIU Qingyou，HUANG Bensheng. Establishment of lateral
vibration dynamic model of roller cone rock bit and its
solution[J]. Natural Gas Industry，2001，21（4）：55 56.
[19] ALLEN M B. BHA lateral vibrations：case studies and
evaluation of important parameters[C]. SPE 16110，1987.
[20] ZHU X H，LIU W. The effects of drill string impacts
on wellbore stability[J]. Journal of Petroleum Science and
Engineering，2013，109：217 229.
[21] MACDONALD K A，BJUNE J V. Failure analysis of drill
strings[J]. Engineering Failure Analysis，2007，14（8）：
1641 1666.
[22] BARYSHNIKOV A，CALDERONI A，LIGRONE A，et
al. A new approach to the analysis of drillstring fatigue
behaviour[C]. SPE 30524，1997.
[23] 李鹤林，冯耀荣. 石油管材与装备失效分析案例集[M].
北京：石油工业出版社，2006：63 75
LI Helin，FENG Yaorong. The cases collection of
petroleum tubular goods and equipment failure analysis[
M]. Beijing：Petroleum Industry Press，2006：63 75.
[24] BAILEY E I，SMITH J E. The goodman diagram as an
analytical tool to optimize fatigue life of rotary shouldered
connections[C]. SPE/IADC 79874，2003.
[25] HOSSAIN M M，RAHMAN M K，RAHMAN S S，et al.
Fatigue life evaluation：a key to avoid drill pipe failure due
to die-marks[C]. SPE/IADC 47789，1998.
[26] HILL T H，ELLIS S E，LEE K，et al. An innovative design
approach to reduce drill string fatigue[J]. SPE Drilling &
Completion，2005，20（2）：94 100.
[27] WU J. Drill-pipe bending and fatigue in rotary drilling of
horizontal wells[C]. SPE 37353，1996.
[28] AI Chi，ZHANG J，GE W，et al. Prediction of fatigue
life of drillstring under axial-torsional combined vibrations[
C]. SPE 99356，2006.
[29] HOUSNER G W. Strong ground motion[J]. Earthquake
Engineering，1970：75 91.
[30] WASSELL M，STROEHLEIN B. Method of establishing
vibration limits and determining accumulative vibration
damage in drilling tools[C]. SPE 135410，2010.
[31] 臧艳彬，王瑞和，张锐，等. 基于事故树的钻柱失效分
析方法[J]. 石油学报，2011，32（1）：171 176.
ZANG Yanbin，WANG Ruihe，ZHANG Rui，et al. A failure
analysis of drill string based on fault tree[J]. Acta
Petrolei Sinica，2011，32（1）：171 176.
[32] WOLF S F，ZACKSENHOUSE M，ARIAN A. Field
measurements of downhole drillstring vibrations[C]. SPE
14330，1985.
[33] DYKSTRA M W，CHEN D，WARREN T M，et al. Experiment
evaluations of drill bit string dynamics[C]. SPE
28323，1994.
[34] MACPHERSON J D，JOGI P. Application and analysis
of simultaneous near bit and surface dynamics measurements[
C]. IADC/SPE 39397，1998.
[35] CHEN S L，BLACKWOOD K，LAMINE E. Field investigation
of the effects of stick-slip lateral and whirl vibrations
on roller-cone bit performance[J]. SPE drilling &
completion，2002，17（1）：15 20.
[36] FINGER J T，MANSURE A J，KNUDSEN S D，et al.
Development of a system for diagnostic-while-drilling
（DWD）[C]. SPE 79884，2003.
[37] COBERN M E，WASSELL M E. Laboratory testing of
an active drilling vibration monitoring & control system[
C]//AADE National Technical Conference & Exhibition，
Houston，2005：5 7.
[38] REEVES M，MACPHERSON J D，ZAEPER R，et al.
High speed drill string telemetry network enables new
real time drilling and measurement technologies[C]. SPE
99134，2006.
[39] LEDGERWOOD III L W，JAIN J R，HOFFMANN O J，
et al. Downhole measurement and monitoring lead to an
enhanced understanding of drilling vibrations and polycrystalline
diamond compact bit damage[J]. SPE Drilling
& Completion，2013，28（3）：254 262.
[40] OUESLATI H，HOHL A，MAKKAR N，et al. The need
for high frequency vibration measurement along with dynamics
modeling to understand the genesis of PDC bit
damage[C]. SPE 167993，2014.
[41] 葛亮，胡泽，陈平. 井下工程参数随钻测试系统设计[J].
传感器与微系统，2013，32（8）：105 107.
GE Liang，HU Ze，CHEN Ping. Design of down-hole
engineering parameters measurement while drilling system[
J]. Transducer and Microsystem Technologies，2013，
32（8）：105 107.
[42] AREVALO Y I，MEDINA Y，NASLAUSKY A. Quantifying
drilling vibration challenges[J]. Offshore（Tulsa），
2011，71（8）：84.
[43] AREVALO Y I，FERNANDES A J. Quantification of
drillstring-integrity-failure risk using real-time vibration
measurements[J]. SPE Drilling & Completion. 2012，
27（2）：216 222.
[44] PARK Y，ANG A H，WEN Y K. Seismic damage analysis
of reinforced concrete buildings[J]. Journal of Structural
Engineering，1985，111（4）：740 757.
[45] DENNEY D. Quantifying Drillstring-Integrity-Failure
Risk：Real-Time Vibration Measurements[J]. Journal of
Petroleum Technology，2012，64（2）：66 69.
[46] FINNIE I，BAILEY J J. An experimental study of drill
string vibration [J]. Journal of Engineering for Industry，
ASME Transaction，1960，82（2）：129 135.
[47] HALSEY G W，KYLLINGSTAD A，ARRESTAD T V，
et al. Drillstring torsional vibration：comparasion between
theory and experiments on a full scale research drilling
rig[C]. SPE 15564，1986.
[48] DAREING D W. Guidelines for controlling drill string
vibrations[J]. Journal of energy resources technology，
1984，106（2）：272 277.
[49] HEISIG G，NEUBERT M. Lateral drillstring vibrations in
extended-reach wells[C]. IADC/SPE 59235，2000.
[50] MENAND S，SELLAMI H，AKOWANOU J，et al.
How drillstring rotation affects critical buckling load[C].
IADC/SPE 112571，2008.
[51] 王珍应. 钻井液对钻柱横向振动和稳定性的影响[J]. 石
油机械，1990，18（1）：31 36.
WANG Zhenying. Effects of the lowing drill fliud on
lateral vibration and stability of the drill stem[J]. China
Petroleum Machinery，1990，18（1）：31 36.
[52] 屈展，陈军斌，刘实. 井下高温对内含钻井液钻柱振动
固有特性的影响分析[J]. 振动与冲击，1998（2）：75 78.
QU Zhan，CHEN Junbin，LIU Shi. Analysis of the downhole
temperature affection on the inherent vibration characteristics
of the drillstring containing drill fluid flow[J].
Journal of Vibration and Shock，1998（2）：75 78.
[53] 史玉才，王军，管志川. 下部钻柱涡动机理及规律的试
验研究[J]. 广西大学学报（自然科学版），2007，32（2）：
126 129.
SHI Yucai，WANG Jun，GUAN Zhichuan. Research
on whirling mechanism of bottom drillstring and its
rules by inner simulated experiments[J]. Journal of
Guangxi University（Natural Science Edition），2007，
32（2）：126 129.
[54] CHEN D C K. SMITH M，PIERRE S L． Integrated
drilling dynamics system closes the model-measureoptimize
loop in real time[C]. SPE 79888，2003.
[55] AKINNIRANYE G，MEGAT A，ELSWEISY H，et al.
Implementation of a shock and vibration mitigation process：
achieving real-time solutions and savings[J]. SPE
Drilling & Completion，2009，24（2）：301 310.
[56] 李子丰，李敬元，马兴瑞，等. 油气井杆钻柱动力学基
本方程及应用[J]. 石油学报，1999，20（3）：95 98.
LI Zifeng，LI Jingyuan，MA Xingrui，et al. Fundamental
equations and its applications for dynamical analysis
of rod and pipe string in oil and gas wells[J]. Acta Petrolei
Sinica，1999，20（3）：95 98.
[57] 张小柯，狄勤丰. 钻柱涡动时弯扭组合交变应力下的
强度计算[J]. 天然气工业，2004，24（7）：1 4.
ZHANG Xiaoke，DI Qinfeng. Strength calculation of
whirled drillstring at flexural-torsional alternate stress[J].
Natural Gas Industry，2004，24（7）：1 4.
[58] BAILEY J R，REMMERT S M. Managing drilling vibrations
through BHA design optimization[J]. SPE Drilling
& Completion，2010，25（4）：458 471.
[59] TEASDALE P，CHAFAI R，SAEED A，et al. BHA modeling
coupled with high frequency downhole vibration
data provides unique solution to inconsistent drilling performance
in south Iraq oilfield[C]. IADC/SPE 156445，
2012.
[60] BURGESS T M，MCDANIEL G L，Das P K. Improving
BHA tool reliability with drillstring vibration models：
field experience and limitations[C]. SPE/IADC 16109，
1987.
[61] SKAUGEN E． The effects of quasi-random drill bit
vibrations upon drillstring dynamic behavior[C]. SPE
16660，1987.
[62] ANDREAS P，AHMET S．Active control of stick-slip
vibrations：the role of fully coupled dynamics[C]. SPE
68093，2001.
[63] POLETTO F. Numerical modeling and interpretation of
drillstring waves[J]. Geophysics，2001，（9）：1569 1581.
[64] SINOR L A，WARREN T M，ARMAGOST W K. Development
of an antiwhirl core bit[J]. SPE Drilling & Completion，
1995，10（3）：170 177.
[65] DEFOURNY P M，ABBASSIAN F. Flexible Bit：A new
anti-vibration PDC-bit concept[J]. SPE Drilling & Completion，
1998，13（4）：237 242.
[66] JOHNSON S. A new method of producing laterally stable
PDC drill bits[J]. SPE Drilling & Completion，2008，
23（3）：314 324.
[67] BARTON S，MAY H，JOHNSON S. Gauge，cutting
structure，torque control components—what really counts
for optimal tool face control with fc drill bits? [J]. SPE
Drilling & Completion，2009，24（2）：293 300.
[68] PESSIER R，DAMSCHEN M. Hybrid bits offer distinct
advantages in selected roller-cone and PDC-bit application[
J]. SPE Drilling & Completion，2011，26（1）：
96 103.
[69] PELFRENE G，SELLAMI H，GERBAUD L. Mitigating
stick-slip in deep drilling based on optimization of PDC
bit design[C]. SPE/IADC 139839，2011.
[70] SCHWEFE T，ENDRES L，JAIN JR，et al. Development
and testing of stick/slip-resistant PDC bits[C]. IADC/SPE
168026，2014.
[71] SOWERS S F，DUPRIEST F E，BAILEY J R，et al. Roller
reamers improve drilling performance in wells limited by
bit and bottomhole assembly vibrations[C]. IADC/SPE
119375，2009.
[72] RADFORD S，LI T，JENKINS M. Novel concentric
expandable stabilizer results in increased penetration
rates and drilling efficiency with reduced vibration[C].
IADC/SPE 119534，2009.
[73] WU S X，PAEZ L. Decoupling stick-slip and whirl
to achieve breakthrough in drilling performance[C].
IADC/SPE 128767，2010.
[74] ARRESTAD T V，KYLLINGSTAD A. An experiment
and theoretical study of coupled boundary conditions for
vibration in drillstring[C]. SPE 15563，1986.
[75] JANSEN J D. Whirl and chaotic motion of stabilized drill
collars[C]. SPE 20930，1992.
[76] MCCARTHY J，KABBARA A，BURNETT T. Careful
planning and application of an asymmetric vibration
damping tool dramatically improves underreaming
while drilling performance in deepwater drilling[C]. SPE
156164，2009.
[77] THUWAINI J A，EMAD M，MOHAMED W，et al. Combination
of a unique stabilized bi-center bit and vibration
dampening tool improve hole opening performances
through interbedded formations in Saudi arabia[C]. SPE
117248，2008.
[78] 李子丰，王兆运，阳鑫军，等. 钻柱涡动分析及防涡稳
定器设计[J]. 石油钻采工艺，2008，30（3）：124 127.
LI Zifeng，WANG Zhaoyun，YANG Xinjun，et al.
Swirling analysis of drilling strings and anti-whirl stabilizers
design[J]. Oil Drilling & Production Technology，
2008，30（3）：124 127.
[79] BATES P C，BOUZIANE C，NICHOLL D，et al. Antivibration
sub allows a very high signal-to-noise ratio and
improves borehole quality[C]. SPE 166539，2013.
[80] BLEVINS R D. Flow-induced vibrations[M]. 2nd edition.
New York：Van Nostrand & Co.，1990.
[81] FENG C C. The measurement of vortex induced effects in
flow past[D]. Columbia：University of British Columbia，
1968.
[82] BLACKBURN H M， GOVARDHAN R N，
WILLIAMSON C H K. A complementary numerical
and physical investigation of vortex-induced vibration[J].
Journal of Fluids and Structures，2001，15（3）：481 488.
[83] CLAYER F，VANDIVER J K，LEE H Y. The effect of surface
and downhole boundary condition on the vibration of
drillstrings[C]. SPE 20447，1990.
[84] SELNES K S，CLEMMENSEN C，REIMERS N. Drilling
difficult formations efficiently with the use of an antistall
tool[J]. SPE Drilling & Completion，2009，24（4）：
531 536.
[85] REIMERS N. Antistall tool reduces risk in drilling difficult
formations[J]. Journal of Petroleum Technology，
2012，64（1），26 29.
[86] JANSEN J D，VAN DEN STEEN L，ZACHARIASEN E.
Active damping of torsional drillstring vibrations with a
hydraulic top drive[J]. SPE Drilling & Completion. 1995，
10（4）：250 254.
[87] SERRARENS A，VAN DE MOLENGRAFT M，KOK
J J，et al. H1 control for suppressing stick-slip in oil
well drillstrings[J]. Control Systems，IEEE. 1998，18（2）：
19 30.
[88] TUCKER R W，WANG C. Torsional vibration control and
cosserat dynamics of a drill-rig assembly[J]. Meccanica，
2003，38（1）：145 161.
[89] CHRISTOFOROU A P，YIGIT A S. Fully coupled vibrations
of actively controlled drillstrings[J]. Journal of
Sound and Vibration. 2003，267（5）：1029 1045.
[90] NAVARRO-LÓPEZ E M，SUÁREZ R. Practical approach
to modelling and controlling stick-slip oscillations in oilwell
drillstrings[C]//Control Applications，IEEE，2004，
2：1454 1460.
[91] CANUDAS-DE-WIT C，CORCHERO M A，RUBIO F
R，et al. D-oskil：A new mechanism for suppressing stickslip
in oil well drillstrings[C]//Decision and Control，44th
IEEE Conference IEEE，2005：8260 8265.
[92] PUEBLA H，ALVAREZ-RAMIREZ J. Suppression of
stick-slip in drillstrings：A control approach based on
modeling error compensation[J]. Journal of Sound and Vibration，
2008，310（4–5）：881 901.
[93] KARKOUB M，ABDEL-MAGID Y L，BALACHANDRAN
B. Drill-string torsional vibration suppression using
GA optimized controllers[J]. Journal of Canadian
Petroleum Technology，2009，48（12）：32 38.
[94] MAJEED F A，KARKI H，KARKOUB M，et al. Experimental
verification of drill string vibration suppression
using an adaptive self-tuning controller[J]. International
Journal of Acoustics and Vibration，2013，18（1）：20 26.
[95] AL-HIDDABI S A，SAMANTA B，SEIBI A. Non-linear
control of torsional and bending vibrations of oilwell drillstrings[
J]. Journal of Sound and Vibration，2003，265（2）：
401 415.
[96] ABDULGALIL F，SIGUERDIDJANE H. PID based on
sliding mode control for rotary drilling system[A]. Computer
as a Tool，2005. EUROCON 2005. The International
Conference on[C]. IEEE，2005：262 265.
[97] PAVKOVI? D，DEUR J，LISAC A. A torque estimatorbased
control strategy for oil-well drill-string torsional
vibrations active damping including an auto-tuning algorithm[
J]. Control Engineering Practice，2011，19（8）：
836 850.
[98] DEUR J，KOLEDI? T，PERI? N. Optimization of
speed control system for electric drives with elastic coupling[
C]//Control Applications，Proceedings of the 1998
IEEE International Conference，1998（1）：319 325.
[99] 李琳，努尔扎提，张奇志. 钻机旋转系统的自适应PID
控制策略[J]. 石油学报. 2011，32（1）：158 161.
LI Lin，NURZAT，ZHANG Qizhi. Adaptive PID control
strategy for the drilling-rig rotary system[J]. Acta Petrolei
Sinica，2011，32（1）：158 161.
[100] KREUZER E，STEIDL M. Controlling torsional vibrations
of drill strings via decomposition of traveling
waves[J]. Archive of Applied Mechanics，2012，82（4）：
515 531.
[101] SARKER M M，RIDEOUT D G，BUTT S D. Advantages
of an LQR controller for stick-slip and bit-bounce
mitigation in an oilwell drillstring[C]//ASME 2012 International
Mechanical Engineering Congress and Exposition.
American Society of Mechanical Engineers，2012：
1305 1313.
[102] SALDIVAR B，MONDIÉ S. Drilling vibration reduction
via attractive ellipsoid method[J]. Journal of the Franklin
Institute，2013，350（3）：485 502.
[103] JAVANMARDI K，GASPARD D T. Application of softtorque
rotary table in mobile bay[C]. SPE/IADC 23913，
1992.
[104] WASSELL M E，COBERN M E，SAHETA V，et al. Active
vibration damper improves performance and reduces
drilling costs[J]. World Oil，2008，229（9）：108 111.
[105] HUTCHINSON M. Automated Downhole Vibration
Damping[C]. SPE 166736，2013.
[106] HUTCHINSON M，BURGESS D，THOMPSON F，et
al. Self-adapting bottom hole assembly vibration suppression[
C]. SPE 166071，2013.
[107] 胡寿松. 自动控制原理（第五版）[M]. 北京：科学出版
社，2007：1 5.
HU Shousong. The principle of automatic control：Fifth
Edition[M]. Beijing：Science Press，2007：1 5.
[108] 林皋，朱彤，林蓓. 结构动力模型试验的相似技巧[J].
大连理工大学学报. 2000（1）：1 8.
LIN Gao，ZHU Tong，LIN Bei. Similarity technique for
dynamic structural model test[J]. Journal of Dalian University
of Technology，2000（1）：1 8.