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工程设计学报
Chin J Eng Design  2023, Vol. 30 Issue (1): 1-12    DOI: 10.3785/j.issn.1006-754X.2023.00.006
Design Theory and Method     
Review of PDC bit cutter arrangement technology
Ya-chao MA1(),Lei TAO1,Zhun RONG2
1.School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
2.Northwest Sichuan Gas Mine, PetroChina Southwest Oil and Gas Field Company, Dazhou 635000, China
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Abstract  

PDC (polycrystalline diamond compact) bit is the main rock-breaking tool in oil and gas drilling field, which has the advantages of high abrasion, high rate of penetration and high rock-breaking efficiency. As a cutting unit, PDC cutter determines the rock-breaking performance of PDC bit. The purpose of PDC bit cutter arrangement is to determine the spatial position of each PDC cutter on the bit, so that the bit has excellent performance and reliable life when drilling and breaking rock. PDC bits designed based on different cutter arrangement technologies show different rock-breaking performance during drilling. Therefore, the PDC bit cutter arrangement technology has been widely concerned by scholars at home and abroad. At present, a large number of scholars have made corresponding research on the cutter arrangement technology of PDC bit since its birth, but there is still a lack of systematic summary. For this reason, based on the literature about PDC bit cutter arrangement technology at home and abroad in recent years, the development process of PDC bit cutter arrangement technology since its birth was summarized, mainly including the early cutter arrangement stage, the classical cutter arrangement stage and the modern cutter arrangement stage. Through analyzing and summarizing the development process of PDC bit cutter arrangement technology, it was pointed out that the cutter arrangement technology of PDC bit in composite PDC bit, compatible intelligent PDC bit, long-life PDC bit, force-balanced PDC bit, PDC bit under impact and vibration and PDC bit in special formation represented the future development trend. The research results can provide some reference for the subsequent research of PDC bit cutter arrangement technology, and are expected to promote the further development of PDC bit cutter arrangement technology.

Key words： PDC bit      PDC cutter      cutter arrangement technology      development trend     
Received: 11 May 2022      Published: 06 March 2023
CLC:  TE 921  
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Ya-chao MA
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Cite this article:

Ya-chao MA,Lei TAO,Zhun RONG. Review of PDC bit cutter arrangement technology. Chin J Eng Design, 2023, 30(1): 1-12.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.006     OR     https://www.zjujournals.com/gcsjxb/Y2023/V30/I1/1


PDC钻头布齿技术研究综述

PDC（polycrystalline diamond compact，聚晶金刚石复合片）钻头是当今油气钻井领域的主要破岩工具，具有耐磨性高、机械钻速高和破岩效率高等优点。PDC切削齿作为切削单元，决定了PDC钻头的破岩性能。PDC钻头布齿的目的是确定每颗PDC切削齿在钻头上的空间位置，使得钻头在钻井破岩时具有优良的性能和可靠的寿命。基于不同布齿技术设计的PDC钻头在钻井过程中表现出不同的破岩性能。因此，PDC钻头布齿技术得到了国内外学者的广泛关注。现已有大量学者针对PDC钻头自诞生以来的布齿技术做了相应研究，但目前仍缺乏系统性的总结。为此，以近年来国内外关于PDC钻头布齿技术的文献为基础，总结了PDC钻头自诞生以来的布齿技术的发展历程，主要包括早期布齿阶段、经典布齿阶段和现代布齿阶段。通过对PDC钻头布齿技术发展历程的分析与总结，指出复合PDC钻头、兼容智能化PDC钻头、长寿命PDC钻头、力平衡PDC钻头、冲击与振动下PDC钻头以及特殊地层下PDC钻头的布齿技术是未来的发展趋势。研究结果可为后续的PDC钻头布齿技术研究提供一定的参考，有望推动PDC钻头布齿技术的进一步发展。


关键词： PDC钻头,  PDC切削齿,  布齿技术,  发展趋势 
Fig.1 PDC bit cutter arrangement parameters
Fig.2 PDC bit cutter arrangement design process
Fig.3 Classification of PDC bit crown profile shape based on IADC
Fig.4 Crown curve shape of PDC bit
Fig.5 Several blade profile bulge shapes
Fig.6 Radial cutter arrangement design without gaps
Fig.7 Radial cutter arrangement design with minimal gaps
Fig.8 Radial cutter arrangement design with extreme gaps
Fig.9 Spiral cutter arrangement design
Fig.10 Group cutter arrangement design
Fig.11 CounterForce PDC bit and staggered PDC cutter
Fig.12 Mixed arrangement of conical PDC cutter and conventional PDC cutter
Fig.13 Distribution and structure of rotary cutter
Fig.14 Long-life chisel cutter
Fig.15 Distribution and structure of rotary cemented carbide cutter
Fig.16 Integrated PDC bit with 360° contact ring
Fig.17 PDC cutter covered by shear cap
Fig.18 PDC bit with Stega cutter arrangement technology
[1]   SCOTT D. A bit of history： overcoming early setbacks， PDC bits now drill 90%-plus of worldwide footage［J］. Drilling Contractor， 2015， 71（4）： 60-68.
[2]   思娜，王敏生，李婧，等.PDC钻头新技术及发展趋势分析［J］. 石油矿场机械，2018，47（2）：1-7. doi：10.3969/j.issn.1001-3482.2018.02.001
SI Na， WANG Min-sheng， LI Jing， et al. Abroad PDC bit technology’s research trends and development thinking［J］. Oil Field Equipment， 2018， 47（2）： 1-7.
doi: 10.3969/j.issn.1001-3482.2018.02.001
[3]   周从明，刘建风，胥建华.PDC钻头布齿软件设计［J］.石油机械，2004，32（7）：23-25. doi：10.3969/j.issn.1001-4578.2004.07.008
ZHOU Cong-ming， LIU Jian-feng， XU Jian-hua. Software design of tooth arrangement of PDC bit ［J］. China Petroleum Machinery， 2004， 32（7）： 23-25.
doi: 10.3969/j.issn.1001-4578.2004.07.008
[4]   GARCIA-GAVITO D， AZAR J J. Proper nozzle location， bit profile， and cutter arrangement affect PDC-bit performance significantly［J］. SPE Drilling & Completion， 1994， 9（3）： 167-175.
[5]   HEYDARSHAHY S A， KAREKAL S. 钻头冠部形状对破岩效果的影响［J］.石油勘探与开发，2017，44（4）：630-637. doi：10.1016/s1876-3804（17）30076-9
HEYDARSHAHY S A， KAREKAL S. Influences of bit profiles on possible fracture modes［J］. Petroleum Exploration and Development， 2017， 44（4）： 630-637.
doi: 10.1016/s1876-3804（17）30076-9
[6]   KERR C J. PDC drill bit design and field application evolution［J］. Journal of Petroleum Technology， 1988， 40（3）： 327-332.
[7]   BRANDON B D， CERKOVNIK J， KOSKIE E， et al. Development of a new IADC fixed cutter drill bit classification system［C］//IADC/SPE Drilling Conference， New Orleans， Louisiana， Feb. 18-21， 1992.
[8]   DENG Rong， LIU Yu. Optimal design of crown structure of PDC drill bit based on Kriging model［J］. International Core Journal of Engineering， 2021， 7（3）： 277-287.
[9]   杨丽.用NURBS方法进行PDC钻头冠部设计［J］.机械制造，2004，42（8）：47-48. doi：10.3969/j.issn.1000-4998.2004.08.016
YANG Li. Design of crown part of PDC drilling bits with NURBS［J］. Machinery， 2004， 42（8）： 47-48.
doi: 10.3969/j.issn.1000-4998.2004.08.016
[10]   邹德永，梁尔国.硬地层PDC钻头设计的探讨［J］.石油机械，2004，32（9）：28-31. doi：10.3969/j.issn.1001-4578.2004.09.010
ZOU De-yong， LIANG Er-guo. Design of PDC bit for hard formation［J］. China Petroleum Machinery， 2004， 32（9）： 28-31.
doi: 10.3969/j.issn.1001-4578.2004.09.010
[11]   JU P， WANG Z， ZHAI Y， et al. Numerical simulation study on the optimization design of the crown shape of PDC drill bit［J］. Journal of Petroleum Exploration and Production Technology， 2014， 4（4）： 343-350.
[12]   JU P. Cutter load distribution analysis and crown shape optimal design of complex curved PDC bit［J］. Journal of Engineering and Technological Sciences， 2019， 51（1）： 14-27.
[13]   解东品.造斜PDC钻头冠部设计［J］.辽宁化工，2013，42（3）：241-242. doi：10.3969/j.issn.1004-0935.2013.03.010
XIE Dong-pin. Design of deflecting PDC bit crown［J］. Liaoning Chemical Industry， 2013， 42（3）： 241-242.
doi: 10.3969/j.issn.1004-0935.2013.03.010
[14]   HUANG Kui-lin， AI Zhi-jiu， YANG Ying-xin， et al. The improved rock breaking efficiency of an annular-groove PDC bit［J］. Journal of Petroleum Science & Engineering， 2019， 172： 425-435.
[15]   杨迎新，刘青友，张春亮，等.一种适用于难钻地层的复合钻头：CN106437525B［P］.2019-11-05.
YANG Ying-xin， LIU Qing-you， ZHANG Chun-liang， et al. A composite drill bit suitable for difficult-to-drill formations： CN106437525B［P］. 2019-11-05.
[16]   邹德永，蔡环.布齿参数对PDC钻头破岩效率影响的试验［J］.中国石油大学学报（自然科学版），2009，33（5）：76-79.
ZOU De-yong， CAI Huan. Experiment on effect of cutter parameters of PDC bit on rate of penetration［J］. Journal of China University of Petroleum（Edition of Natural Science）， 2009， 33（5）： 76-79.
[17]   陈曦，邱巍，张坤.长庆油田南梁区块PDC钻头的研发与应用［J］.内蒙古石油化工，2012，38（16）：1-4.
CHEN Xi， QIU Wei， ZHANG Kun. Design and application of a PDC bit used in Nanliang area of Changqing oilfield［J］. Inner Mongolia Petrochemical Industry， 2012， 38（16）： 1-4.
[18]   杨延征，王镇全.刮刀式PDC钻头布齿方法探讨［J］.西部探矿工程，2009，21（5）：41-42. doi：10.3969/j.issn.1004-5716.2009.05.016
YANG Yan-zheng， WANG Zhen-quan. Discussion on tooth arrangement method of scraper type PDC bit［J］. West-China Exploration Engineering， 2009， 21（5）： 41-42.
doi: 10.3969/j.issn.1004-5716.2009.05.016
[19]   杨丽，陈康民.PDC钻头布齿方法研究［J］.石油机械，2005，33（4）：1-3. doi：10.3969/j.issn.1001-4578.2005.04.001
YANG Li， CHEN Kang-min. Research on the distribution of the teeth of PDC bits［J］. China Petroleum Machinery， 2005， 33（4）： 1-3.
doi: 10.3969/j.issn.1001-4578.2005.04.001
[20]   DEEN A， MAW J， KNULL C， et al. Departure from the norm in polycrystalline diamond bit design allows significant performance gains in highly erosive and abrasive formations［C］//SPE Annual Technical Conference and Exhibition， San Antonio， Texas， Oct. 8-10， 2012.
[21]   AL-HINAAI A， ESRY S AL， SCOTT D E， et al. Introduction of 25mm-PDC cutters in the latest drill bit technology leads to multiple drilling performance records and reduces days to production in Oman［C］//Abu Dhabi International Petroleum Exhibition & Conference， Abu Dhabi， Nov. 7-10， 2016.
[22]   HIBBS L E， FLOM D G. Diamond compact cutter studies for geothermal bit design［J］. Journal of Pressure Vessel Technology， 1978， 100（4）： 406-416.
[23]   GLOWKA D A. Implications of thermal wear phenomena for PDC bit design and operation［C］//SPE Annual Technical Conference and Exhibition， Las Vegas， Nevada， Sep. 22-26， 1985.
[24]   王福修.PDC钻头布齿方式初探［J］.石油钻采工艺，1993，15（3）：29-33.
WANG Fu-xiu. A preliminary study on the teeth arrangement of PDC bits［J］. Oil Drilling & Production Technology， 1993， 15（3）： 29-33.
[25]   李树盛，蔡镜仑，马德坤.PDC钻头冠部设计的原理与方法［J］.石油机械，1998，26（3）：1-3.
LI Shu-sheng， CAI Jing-lun， MA De-kun. Principle and method of PDC bit profile design［J］. China Petroleum Machinery， 1998， 26（3）： 1-3.
[26]   牛世伟，杨迎新，牛永超.PDC钻头布齿计算方法的研究现状及发展［J］.石油机械，2015，43（9）：6-9. doi：10.16082/j.cnki.issn.1001-4578.2015.09.002
NIU Shi-wei， YANG Ying-xin， NIU Yong-chao. Research status and development of calculation method for PDC bit tooth arrangement［J］. China Petroleum Machinery， 2015， 43（9）： 6-9.
doi: 10.16082/j.cnki.issn.1001-4578.2015.09.002
[27]   王荣，翟应虎，王克雄.PDC钻头等体积布齿设计的数值计算方法［J］.石油钻探技术，2006，34（1）：42-45. doi：10.3969/j.issn.1001-0890.2006.01.012
WANG Rong， ZHAI Ying-hu， WANG Ke-xiong. A numerical computational method for designing PDC bits with the equal-volume law［J］. Petroleum Drilling Techniques， 2006， 34（1）： 42-45.
doi: 10.3969/j.issn.1001-0890.2006.01.012
[28]   宋洵成，邹德永，管志川.PDC钻头等切削体积布齿优化设计［J］.石油矿场机械，2006，35（4）：61-64.
SONG Xun-cheng， ZOU De-yong， GUAN Zhi-chuan. Equal-cutting-volume optimization design for a PDC bit［J］. Oil Field Equipment， 2006， 35（4）： 61-64.
[29]   任海涛，杨迎新，陈炼，等.PDC钻头钻进仿真系统数字化方法研究［J］.西南石油大学学报（自然科学版），2010，32（5）：150-154.
REN Hai-tao， YANG Ying-xin， CHEN Lian， et al. Research on the digital method of the PDC bit drilling progress simulation system［J］. Journal of Southwest Petroleum University （Science & Technology Edition）， 2010， 32（5）： 150-154.
[30]   常元昊，张楠林，施欣燕.PDC钻头设计理论综述［J］.内江科技，2014，35（8）：111-112. doi：10.3969/j.issn.1006-1436.2014.08.073
CHANG Yuan-hao， ZHANG Nan-lin， SHI Xin-yan. Summary of PDC bit design theory［J］. Neijiang Science & Technology， 2014， 35（8）： 111-112.
doi: 10.3969/j.issn.1006-1436.2014.08.073
[31]   须志刚，杨宝德，刘钢.PDC钻头等功率布齿的方法［J］.石油钻探技术，1994，22（1）：37-39.
XU Zhi-gang， YANG Bao-de， LIU Gang. PDC bit equivalent power tooth placing method［J］. Petroleum Drilling Techniques， 1994， 22（1）： 37-39.
[32]   PENG Q， ZHOU Y， YANG X， et al. Research on the method of dynamic PDC cutters distribution［J］. IOP Conference Series： Earth and Environmental Science， 2021， 675（1）： 12191.
[33]   BRETT J F， WARREN T M， BEHR S M. Bit whirl： a new theory of PDC bit failure［J］. SPE Drilling & Completion， 2012， 27（1）： 158-164.
[34]   WEAVER G E. A new PDC cutting structure improves bit stabilization and extends application into harder rock types［C］//SPE/IADC Drilling Conference， Amsterdam， Netherlands， Feb. 22-25， 1993.
[35]   邹德永，王瑞和.刀翼式PDC钻头的侧向力平衡设计［J］. 中国石油大学学报（自然科学版），2005，29（2）：42-44.
ZOU De-yong， WANG Rui-he. Lateral force balancing design of blade PDC bits［J］. Journal of China University of Petroleum（Edition of Natural Science）， 2005， 29（2）： 42-44.
[36]   李辉，张鹏，马驰，等.基于蚁群粒子群混合算法的PDC钻头侧向力平衡优化［J］.钻采工艺，2009，32（2）：58-60. doi：10.3969/j.issn.1006-768X.2009.02.021
LI Hui， ZHANG Peng， MA Chi， et al. Optimization of lateral force balance of PDC bits based on ant colony particle swarm hybrid algorithm［J］. Drilling & Production Technology， 2009， 32（2）： 58-60.
doi: 10.3969/j.issn.1006-768X.2009.02.021
[37]   翟应虎，王克雄，蔡镜仑.PDC钻头的螺旋线布齿方法［J］.中国石油大学学报（自然科学版），1995，19（2）：25-29.
ZHAI Ying-hu， WANG Ke-xiong， CAI Jing-lun. Helix model for placing cutter in the design of PDC cutter［J］. Journal of China University of Petroleum（Edition of Natural Science）， 1995， 19（2）： 25-29.
[38]   WELLS M， MARVEL T， BEUERSHAUSEN C. Bit balling mitigation in PDC bit design［C］//IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition， Jakarta， Indonesia， Aug. 25-27， 2008.
[39]   汪为涛.陇东区块气探井PDC钻头的设计及选型研究［J］. 石油和化工设备，2018，21（7）：26-29. doi：10.3969/j.issn.1674-8980.2018.07.007
WANG Wei-tao. Design and selection of PDC bits for gas exploration wells in Longdong block［J］. Petro & Chemical Equipment， 2018， 21（7）： 26-29.
doi: 10.3969/j.issn.1674-8980.2018.07.007
[40]   SHEIKHREZAEI K， AKBARI B. An experimental study on the impacts of different PDC cutters arrangements on a bit on rock cutting process［C］//53rd U.S. Rock Mechanics/Geomechanics Symposium， Brooklyn， Jun. 23-26， 2019.
[41]   CHEN S， ARFELE R， ANDERLE S， et al. A new theory on cutter layout for improving PDC-bit performance in hard-and transit-formation drilling［J］. SPE Drilling & Completion， 2013， 28（4）： 338-349.
[42]   居培，王传留.弧角型PDC钻头切削齿布齿模式仿真分析［J］. 煤田地质与勘探，2020，48（5）：240-245. doi：10.3969/j.issn.1001-1986.2020.05.030
JU Pei， WANG Chuan-liu. Simulation of the cutter arrangement pattern of the arc PDC drill bit［J］. Coal Geology & Exploration， 2020， 48（5）： 240-245.
doi: 10.3969/j.issn.1001-1986.2020.05.030
[43]   宋洵成，邹德永.采用遗传算法的PDC钻头侧向力平衡优化设计［J］.中国石油大学学报（自然科学版），2006，30（4）：50-52.
SONG Xun-cheng， ZOU De-yong. Optimization design of lateral force balance of PDC bits by genetic algorithm［J］. Journal of China University of Petroleum （Edition of Natural Science）， 2006， 30（4）： 50-52.
[44]   CAO T， YU K， CHEN X， et al. Full-phase optimization of PDC bit cutter layout to reduce lateral force based on zoning method［J］. Journal of Mechanical Science and Technology， 2021， 35（3）： 1199-1207.
[45]   HOUGH C L JR. The effect of back rake angle on the performance of small-diameter polycrystalline diamond rock bits： ANOVA tests［J］. Journal of Energy Resources Technology， 1986， 108（4）： 305-309.
[46]   KARASAWA H， MISAWA S. Development of new PDC bits for drilling of geothermal wells—part 1： laboratory testing［J］. Journal of Energy Resources Technology， 1992， 114（4）： 323-331.
[47]   SINOR L A， POWERS J R， WARREN T M. Effect of PDC cutter density， back rake， size， and speed on performance［C］//IADC/SPE Drilling Conference， Dallas， Texas， Mar. 3-6， 1998.
[48]   AKBARI B， MISKA S. The effects of chamfer and back rake angle on PDC cutters friction［J］. Journal of Natural Gas Science and Engineering， 2016， 35： 347-353.
[49]   田家林，付传红，杨琳，等.基于扭转振动的PDC钻头布齿角度对复合片磨损规律的影响研究［J］.固体力学学报，2014，35（6）：574-582.
TIAN Jia-lin， FU Chuan-hong， YANG Lin， et al. Influence of the tooth-distributing angle of PDC bit on wear of composite plate under torsion vibration［J］. Chinese Journal of Solid Mechanics， 2014， 35（6）： 574-582.
[50]   McMILLAN J. Ulterra introduces ground-breaking CounterForce™ PDC bit technology［EB/OL］. （2013-04-21）［2022-05-11］. .
[51]   高科，孙阳，刘婧，等.石灰岩地层PDC钻头仿生PDC齿工作角优化试验研究［J］.探矿工程，2015，42（11）：70-73.
GAO Ke， SUN Yang， LIU Jing， et al. Experimental study on bionic PDC cutting teeth of PDC bit working angle optimization for limestone stratum［J］. Drilling Engineering， 2015， 42（11）： 70-73.
[52]   MA Y， HUANG Z， LI Q， et al. Cutter layout optimization for reduction of lateral force on PDC bit using Kriging and particle swarm optimization methods［J］. Journal of Petroleum Science and Engineering， 2018， 163： 359-370.
[53]   李百胜，孙明光.用于含砾石且软硬交错地层的新型PDC钻头设计［J］.石油机械，2004，32（9）：32-34. doi：10.3969/j.issn.1001-4578.2004.09.011
LI Bai-sheng， SUN Ming-guang. New PDC bit design for gravel-bearing formations with alternating hard and soft formations［J］. China Petroleum Machinery， 2004， 32（9）： 32-34.
doi: 10.3969/j.issn.1001-4578.2004.09.011
[54]   XIONG C， DAI X， SHI H， et al. Investigation on rock breakage mechanism of stinger PDC cutter and hybrid cutter arrangement design［C］//54th U.S. Rock Mechanics/ Geomechanics Symposium， Virtual， Online， Jun. 28-Jul. 1， 2020.
[55]   YU J P， ZOU D Y， LIU X A， et al. Simulation and experimental study on hybrid bit with different cutters［J］. International Journal of Simulation Modelling， 2021， 20（1）： 87-98.
[56]   MENSA-WILMOT G， SOZA R， HUDSON K. Advanced cutting structure improves PDC bit performance in hard rock drilling environments［C］//SPE Annual Technical Conference and Exhibition， Denver， Colorado， Oct. 5-8， 2003.
[57]   PAK M， GUMICH D， ZINNATULLIN I， et al. Unique approach to bit design coupled with innovative rolling PDC cutter sets new performance benchmark drilling extremely abrasive sandstone formations， Usinsk region Russia［C］//SPE Middle East Oil & Gas Show and Conference， Manama， Kingdom of Bahrain， Mar. 6-9， 2017.
[58]   SMITH M. Baker hughes introduces long-life PDC bit to reduce trips in high horsepower drilling operations［EB/OL］. （2017-05-04） ［2022-05-11］. .
[59]   IZBINSKI K， PATEL S G， VANDEVEN A. Innovative dual-chamfer edge technology leads to performance gains in PDC bits［C］// SPE/IADC Drilling Conference and Exhibition， London， England， Mar. 17-19， 2015.
[60]   BEATON T， WONG A， ISNOR S， et al. New type of oilfield drill bit produces new levels of performance in large diameter intervals［C］//SPE/IADC Middle East Drilling Technology Conference and Exhibition， Abu Dhabi， Jan. 26-28， 2016.
[61]   CRANE D， ZHANG Y， DOUGLAS C， et al. Innovative PDC cutter with elongated ridge combines shear and crush action to improve PDC bit performance［C］//SPE Middle East Oil & Gas Show and Conference， Manama， Kingdom of Bahrain， Mar. 6-9， 2017.
[62]   CHEN P， MENG M， MISKA S， et al. Study on integrated effect of PDC double cutters［J］. Journal of Petroleum Science and Engineering， 2019， 178： 1128-1142.
[63]   ROBERTS T S. Development of a new concept of steerable PDC bit for directional drilling［C］//IADC/SPE Drilling Conference， Dallas， Texas， Mar. 3-6， 1998.
[64]   KING W W， LEON C， RUMBOS T， et al. PDC shearing cap technology protects cutters when drilling out casing bits for increased ROP and bit life in the next hole section［C］//SPE/IADC Drilling Conference and Exhibition， London， England， Mar. 17-19， 2015.
[65]   ZHANG C， YANG Y， REN H， et al. Investigation of the cross-cutting polycrystalline diamond compact bit drilling efficiency［J］. Shock and Vibration， 2021， 2021： 1-15.
[66]   HUANG Z， MA Y， LI Q， et al. Geometry and force modeling， and mechanical properties study of polycrystalline diamond compact bit under wearing condition based on numerical analysis［J］. Advances in Mechanical Engineering， 2017， 9（6）： 2071939296.
[67]   马亚超，黄志强，练章华，等.适用复杂地层钻井的PDC钻头随机磨损侧力平衡布齿法：CN201811246893.2［P］.2019-03-12. doi：10.1177/1687814019894452
MA Ya-chao， HUANG Zhi-qiang， LIAN Zhang-hua， et al. Balanced tooth distribution method for random wear side force of PDC bit suitable for drilling in complex formation： CN201811246893.2［P］. 2019-03-12.
doi: 10.1177/1687814019894452
[68]   马亚超，张鹏，黄志强，等.全局力平衡PDC钻头布齿优化设计［J］.中国机械工程，2020，31（20）：2412-2419. doi：10.3969/j.issn.1004-132X.2020.20.003
MA Ya-chao， ZHANG Peng， HUANG Zhi-qiang， et al. Optimal design for cutter-layout of global force balanced PDC bits［J］. China Mechanical Engineering， 2020， 31（20）： 2412-2419.
doi: 10.3969/j.issn.1004-132X.2020.20.003
[69]   马亚超.基于切削齿动态磨损的PDC钻头侧向力平衡分析与布齿优化设计［D］.成都：西南石油大学，2017：69-102. doi：10.1016/j.petrol.2018.01.001
MA Ya-chao. Lateral force-balance analysis and optimal design for cutter-layout of PDC bit based on dynamic wear of cutters［D］. Chengdu： Southwest Petroleum University， 2017： 69-102.
doi: 10.1016/j.petrol.2018.01.001
[1] MA Ya-chao, ZHANG Peng, HUANG Zhi-qiang, NIU Shi-wei, XIE Dou, DENG Rong. Prediction of dynamic wear trend of PDC bit under the influence of varying temperature and load[J]. Chin J Eng Design, 2020, 27(5): 625-635.
[2] LUO Jin-wu, KUANG Yu-chun, ZHANG Rui, CHEN Hua, LIAO Wen-ling, LI Gang-jun. Research on hydraulic structure of PDC bit in horizontal well based on CFD-DEM coupling[J]. Chin J Eng Design, 2020, 27(5): 636-644.
[3] YANG Ying-xin, ZHOU Jian, HUANG Kui-lin, REN Hai-tao, CHEN Lian. Optimization design and application of PDC bit for directional reaming-while-drilling[J]. Chin J Eng Design, 2018, 25(6): 668-674.
[4] LIN Min, XIE Zong-liang, YANG Ying-xin, LI Wei-jun, CHEN Lian, REN Hai-tao. Design and field test of the new PDC bit with divided gage pad[J]. Chin J Eng Design, 2018, 25(1): 43-49.
[5] KUANG Yu-chun, WANG Yuan-ji, FENG Ming, HAN Yi-wei. Reverse design and optimization of PDC bit cutter parameters[J]. Chin J Eng Design, 2017, 24(5): 545-554.
[6] KUANG Yu-chun, WANG Fang, WEI Li-hong, DONG Zong-zheng, LUO Jin-wu. Research on the bottom hole flow field analysis platform of PDC bit based on Web service[J]. Chin J Eng Design, 2017, 24(4): 380-386.
[7] GAO Li, ZENG Qing-Liang, FAN Wen-Hui. Trend on research of multidisciplinary design optimization[J]. Chin J Eng Design, 2007, 14(6): 429-434.