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Vol.34 No.3Jun., 2020第34卷第3期2020年6月能源环境保护Energy Environmental Protection移动扫码阅读秦红正.浅埋薄基岩煤层开采对潜水含水层的影响及定量评价[J] •能源环境保护,2020,34(3) ：85-91.QIN Hongzheng. I nfluence of coal mining with shallow buried and thin bedrock on unconfind aquifer and quantita tive evaluationf J].Energy Environmental Protection ,2020,34(3) ：85-91.浅埋薄基岩煤层开采对潜水含水层的影响及定量评价秦红正(中煤科工集团北京华宇工程有限公司，北京100120)摘要：为研究干旱矿区浅埋薄基岩煤层开采对潜水含水层的影响程度，选择凉水井煤矿为研究对 象，在资料收集、野外调查、室内测试的基础上，采用数值模拟的手段分析潜水含水层对煤层开采 的响应规律。
研究结果表明：研究区风积沙降水入渗系数高达0.53,降水是地下水补给的主要来源(约95%),地下水总量受大气降水控制明显；开采前地下水向河流的排泄约占78%,蒸发排泄 约占22%；受采掘矿井水排泄量(34.09%)影响，河流与蒸发排泄量占比分别减少至53.07%和12.84%；利用潜水含水层地下水漏失量Q 与开采前地下水排泄总量 乞的比值来表征地下水量的扰动程度Eg = QJQ&),扰动程度高达27%。
关键词:浅埋薄基岩；煤层开采;地下水;数值模拟中图分类号：X820.3 文献标志码:A 文章编号：1006-8759(2020)03-0085-07Influence of coal mining with shallow buried and thin bedrock onunconfind aquifer and quantitative evaluationQIN Hongzheng(Beijing Huayu Engineering Company Limited , China Coal Technology and Engineering Group ,Beijing W0120,China)Abstract : Taking Liangshuijing Coal Mine as the research object , data collection , field investigation , la boratory test and numerical simulation were used to numerically simulate the response law of unconfindaquifer to coal mining in order to study the influence of coal mining with shallow buried and thin bed rock on unconfind aquifer. T he results show that the precipitation infiltration coefficient of aeolian sand in the study area is as high as 0.53. G roundwater recharge mainly comes from infiltration of precipitati on ,accounting for about 95%, therefore the total amount of groundwater is obviously controlled by at mospheric precipitation.Before mining , about 78% of groundwater is drained to rivers , and the remaining22% is lost by evaporation .Affected by the water yield of mine (34.09%) ,the proportion of drainage of the rivers and evaporation is decreased to 53.07% and 12.84%, respectively.It is proposed to use theratio of the groundwater leakage of unconfind aquifer ( Q ) and the total groundwater discharge beforemining ( ) to characterize the disturbance degree of groundwater (£q ) (£q = QJQ d ) , which was ashigh as 27%.Key Words : Shallow buried and thin bedrock ; Coal mining ； Groundwater ; Numerical simulation0引言榆神府矿区主要开采侏罗纪煤层，其厚度大、埋藏浅、开采强度高,表土层下普遍存在以非胶结 沙土、砂砾为骨架组成的松散含水层,开采导水裂 缝带发育至上部松散含水层对该含水层地下水的收稿日期：2020-03-30作者简介:秦红正（1979-）,男,陕西扶风人，高级工程卯，主要研究方向为环境滲响评价。
１０００ ０５６９／２０２１／０３７（０８） ２２７６ ８６ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ 岩石学报ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２１ ０８ ０３行星矿产及行星资源地质学初论秦克章１，２ 邹心宇１ＱＩＮＫｅＺｈａｎｇ１，２ａｎｄＺＯＵＸｉｎＹｕ１１ 中国科学院矿产资源研究重点实验室，中国科学院地质与地球物理研究所，北京 １０００２９２ 中国科学院大学地球与行星学院，北京 １０００４９１ ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＭｉｎｅｒａｌＲｅｓｏｕｒｃｅｓ，ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｌｏｇｙａｎｄＧｅｏｐｈｙｓｉｃｓ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００２９，Ｃｈｉｎａ２ ＣｏｌｌｅｇｅｏｆＥａｒｔｈａｎｄＰｌａｎｅｔａｒｙＳｃｉｅｎｃｅｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００４９，Ｃｈｉｎａ２０２１ ０５ ０９收稿，２０２１ ０７ ０３改回ＱｉｎＫＺａｎｄＺｏｕＸＹ ２０２１ Ｐｏｔｅｎｔｉａｌｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓｉｎｔｈｅｐｌａｎｅｔｓａｎｄｐｒｅｌｉｍｉｎａｒｙｄｉｓｃｕｓｓｉｏｎｏｎｐｌａｎｅｔａｒｙｒｅｓｏｕｒｃｅｇｅｏｌｏｇｙ ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ，３７（８）：２２７６－２２８６，ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２１ ０８ ０３Ａｂｓｔｒａｃｔ Ｈｏｗｔｏｕｎｄｅｒｓｔａｎｄａｎｄｕｔｉｌｉｚｅｐｌａｎｅｔａｒｙｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓａｎｄｍａｋｅａｓｕｓｔａｉｎａｂｌｅａｎｄｐｅｒｍａｎｅｎｔｄｅｖｅｌｏｐｍｅｎｔｏｆｓｐａｃｅｈａｓｂｅｃｏｍｅａｎｅｗｆｒｏｎｔｉｅｒｒｅｓｅａｒｃｈｄｉｒｅｃｔｉｏｎｏｆｐｌａｎｅｔａｒｙｓｃｉｅｎｃｅ Ｔｈｅｅｘｐｌｏｒａｔｉｏｎａｎｄｄｅｖｅｌｏｐｍｅｎｔｏｆｐｌａｎｅｔａｒｙｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓｒｅｑｕｉｒｅｔｈｅｕｎｄｅｒｓｔａｎｄｉｎｇｏｆｔｈｅｔｙｐｅｓ，ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ，ｒｅｓｅｒｖｅｓａｎｄｄｉｓｔｒｉｂｕｔｉｏｎａｎｄｅｖａｌｕａｔｉｎｇｄｅｖｅｌｏｐｍｅｎｔａｎｄｕｔｉｌｉｚａｔｉｏｎｃｏｎｄｉｔｉｏｎｓｏｆｐｌａｎｅｔａｒｙｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓ，ｂｙｕｓｉｎｇｔｈｅｂａｓｉｃｔｈｅｏｒｉｅｓｏｆｐｌａｎｅｔａｒｙｓｃｉｅｎｃｅａｎｄｇｅｏｌｏｇｙ，ｅｓｐｅｃｉａｌｌｙｅｃｏｎｏｍｉｃｇｅｏｌｏｇｙ，ｃｏｍｂｉｎｅｄｗｉｔｈｐｌａｎｅｔａｒｙｏｂｓｅｒｖａｔｉｏｎａｎｄｅｘｐｌｏｒａｔｉｏｎｔｅｃｈｎｉｑｕｅｓ Ｔｈｅｒｅｆｏｒｅ，ＰｌａｎｅｔａｒｙＲｅｓｏｕｒｃｅＧｅｏｌｏｇｙ（ＰＲＧ）ｉｓａｎｉｎｔｅｒｄｉｓｃｉｐｌｉｎａｒｙｓｕｂｊｅｃｔ，ｃｏｎｔａｉｎｓｔｈｅｓｔｕｄｙｏｆｔｈｅｖａｒｉｅｔｙ，ｔｙｐｅａｎｄｄｉｓｔｒｉｂｕｔｉｏｎｌａｗｏｆｐｌａｎｅｔａｒｙｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓ，ｇｅｎｅｔｉｃｅｖｏｌｕｔｉｏｎａｎｄｃｏｍｐａｒｉｓｏｎｏｆｐｌａｎｅｔａｒｙｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓ，ｐｌａｎｅｔａｒｙｍｅｔａｌｌｏｇｅｎｙ，ｅｘｐｌｏｒａｔｉｏｎａｎｄｅｖａｌｕａｔｉｏｎｔｅｃｈｎｏｌｏｇｙａｎｄｍｉｎｉｎｇａｎｄｕｔｉｌｉｚａｔｉｏｎｅｎｇｉｎｅｅｒｉｎｇｏｆＰＲＧ ＦｒｏｍｔｈｅｐｅｒｓｐｅｃｔｉｖｅｏｆＰＲＧ，ｗｅｔｒｙｔｏｐｒｅｄｉｃｔｔｈｅｐｏｓｓｉｂｌｅｔｙｐｅｓｏｆｍｉｎｅｒａｌｒｅｓｏｕｒｃｅｓｉｎＬｕｎａｒｆｒｏｍｔｈｅｓｉｍｉｌａｒｉｔｙｏｆＥａｒｔｈａｎｄＬｕｎａｒｉｎｔｈｅｌｉｔｈｏｓｐｈｅｒｅｓｔｒｕｃｔｕｒｅ，ｔｈｅｒｏｃｋｃｏｍｐｏｓｉｔｉｏｎａｎｄｔｈｅｓｕｐｅｒｇｅｎｅｅｎｖｉｒｏｎｍｅｎｔ Ｔｈｅｒｅｓｈｏｕｌｄｂｅｔｈｅｃｈｒｏｍｉｔｅ，Ｃｕ Ｎｉ Ｃｏｓｕｌｆｉｄｅ，ＰＧＥ（ｐｌａｔｉｎｕｍｇｒｏｕｐｅｌｅｍｅｎｔ），Ｖ Ｔｉｍａｇｎｅｔｉｔｅｍｉｎｅｒａｌｓｒｅｌａｔｅｄｔｏｔｈｅｌａｙｅｒｅｄｒｏｃｋｍａｓｓａｎｄｍａｆｉｃ ｕｌｔｒａｍａｆｉｃｓｍａｌｌｒｏｃｋｍａｓｓｏｆｔｈｅｏｒｉｇｉｎｏｆｔｈｅｌｕｎａｒｍａｎｔｌｅ（ｅｖｅｎｍａｎｔｌｅｐｌｕｍｅ）ａｎｄｍｅｔｅｏｒｉｔｅｉｍｐａｃｔ，ｔｈｅＲＥＥａｎｄＮｂ ＴａｈｏｓｔｅｄｂｙＫＲＥＥＰｒｏｃｋｓ，ｔｈｕｓｗｉｌｌｈｏｐｅｆｕｌｌｙｅｘｐａｎｄｔｈｅｐｏｓｓｉｂｌｅｔｙｐｅｓａｎｄｃｏｍｍｏｄｉｔｉｅｓａｎｄｐｒｏｖｉｄｅａｂｒｏａｄｅｒｒｅｓｏｕｒｃｅｐｅｒｓｐｅｃｔｉｖｅｆｏｒｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｔｈｅｌｕｎａｒｂａｓｅｓ Ｄｕｅｔｏｅｘｉｓｔｅｎｃｅｏｆｗａｔｅｒａｎｄｐｏｓｓｉｂｌｅｐｌａｔｅｔｅｃｔｏｎｉｃｓ，Ｍａｒｓｃａｎｈｏｓｔａｖａｒｉｅｔｙｏｆｍｅｔａｌｌｉｃａｎｄｎｏｎ ｍｅｔａｌｌｉｃｍｉｎｅｒａｌｄｅｐｏｓｉｔｓｒｅｌａｔｅｄｔｏｍａｇｍａｔｉｓｍ，ｓｅｄｉｍｅｎｔａｔｉｏｎ，ｍｅｔａｍｏｒｐｈｉｓｍ，ｃｈｅｍｉｃａｌｗｅａｔｈｅｒｉｎｇａｎｄｓｅｃｏｎｄａｒｙｅｎｒｉｃｈｍｅｎｔｗｈｉｃｈｈａｓａｌｏｔｉｎｃｏｍｍｏｎｗｉｔｈｔｈｅＥａｒｔｈ Ｉｎｔｈｅｆｕｔｕｒｅ，ｔｈｅｄｉｓｃｉｐｌｉｎｅｏｆＰＲＧｓｈｏｕｌｄｓｔｒｅｎｇｔｈｅｎｔｈｅｃｒｏｓｓ ｉｎｔｅｇｒａｔｉｏｎａｎｄｔｈｅｏｒｅｔｉｃａｌａｐｐｌｉｃａｔｉｏｎｏｆｇｅｏｌｏｇｙ，ｍｅｔａｌｌｕｒｇｉｃａｌｅｎｇｉｎｅｅｒｉｎｇ，ｍａｔｅｒｉａｌｓｓｃｉｅｎｃｅ，ｐｌａｎｅｔａｒｙｃｈｅｍｉｓｔｒｙ，ｐｌａｎｅｔａｒｙｇｅｏｌｏｇｙａｎｄｐｌａｎｅｔａｒｙｐｈｙｓｉｃｓ，ｄｅｖｅｌｏｐｐｌａｎｅｔａｒｙｇｅｏｌｏｇｉｃａｌｅｘｐｌｏｒａｔｉｏｎｔｅｃｈｎｏｌｏｇｙ，ｉｎｃｌｕｄｉｎｇｉｎｔｅｌｌｉｇｅｎｔｒｏｂｏｔｅｎｇｉｎｅｅｒｉｎｇ，ｓａｍｐｌｅｃｏｌｌｅｃｔｉｏｎ，ｍｕｌｔｉ ｓｃａｌｅｔｅｓｔａｎｄａｎａｌｙｓｉｓｕｎｄｅｒｅｘｔｒｅｍｅｈｉｇｈ／ｌｏｗｔｅｍｐｅｒａｔｕｒｅ，ｈｉｇｈｉｒｒａｄｉａｔｉｏｎａｎｄｌｏｗｍｉｃｒｏｇｒａｖｉｔｙｅｎｖｉｒｏｎｍｅｎｔ，ａｎｄｃｕｌｔｉｖａｔｅｔａｌｅｎｔｓｏｆｐｌａｎｅｔａｒｙｒｅｓｏｕｒｃｅｓ，ｇｅｏｌｏｇｉｃａｌｒｅｓｏｕｒｃｅｓｄｅｖｅｌｏｐｍｅｎｔｅｎｇｉｎｅｅｒｉｎｇＫｅｙｗｏｒｄｓ ＭｉｎｅｒａｌｒｅｓｏｕｒｃｅｓｉｎＭｏｏｎａｎｄＭａｒｓ；ＰｌａｎｅｔａｒｙＲｅｓｏｕｒｃｅＧｅｏｌｏｇｙ；Ｌｕｎａｒｍａｎｔｌｅｐｌｕｍｅａｎｄｉｍｐａｃｔ ｒｅｌａｔｅｄＣｕ Ｎｉ Ｃｏ ＰＧＥ Ｖ Ｔｉ Ｆｅ Ｃｒｍｉｎｅｒａｌｉｚａｔｉｏｎ；ＫＲＥＥＰｈｏｓｔＲＥＥａｎｄｒｅａｌｍｅｔａｌｄｅｐｏｓｉｔ；Ｒｅｇｕｌａｒｉｔｉｅｓｏｆｄｉｓｔｒｉｂｕｔｉｏｎ；Ｄｅｖｅｌｏｐｍｅｎｔａｎｄｕｔｉｌｉｚａｔｉｏｎ摘 要 了解并利用行星矿产资源、可持续永久开发太空成为行星科学与深空探测的一项重要研究任务。
装备环境工程第19卷第12期·48·EQUIPMENT ENVIRONMENTAL ENGINEERING2022年12月基于含时密度泛函理论的紫外光对太安的定性影响张宝森1，张树海1，苟瑞君1，陈亚红1，朱双飞1，马坤2（1.中北大学 环境与安全工程学院，太原 030051；2.陕西应用物理化学研究所，西安 710061）摘要：目的研究太安炸药在紫外光作用下的稳定性退化机制。
方法基于TDDFT（含时密度泛函）理论，在pbe1pbe/6-311G**水平下对太安分子50个激发态进行计算，依据计算结果，绘制吸收光谱，使用空穴–电子方法对最大吸收峰3个激发态（S9、S10和S11）的激发特征进行分析，这3个激发态对最大吸收峰的总贡献率达97.31%。
将此3个激发态定为研究对象，对太安分子被特定的紫外光激发至激发态后弱键的Mayer 和Laplace键级进行分析，并基于IFCT（Interfragment Charge Transfer）方法对太安分子激发至激发态过程中的电子转移情况进行描述。
结果太安紫外吸收光谱的最大吸收峰位置为186.6 nm，小于实验测试的吸收峰位置8.4 nm。
对此吸收峰的强度贡献最大的3个激发态中，S9态贡献最高，为48.27%，其余2个激发态S10、S11为简并态，贡献相同，为24.52%。
通过空穴–电子的电荷转移分析结果可知，3个激发态均存在整体激发并带有局域电荷转移的特征。
PETN分子在吸收特定波长（187.00、186.92 nm）紫外光并激发至激发态时，O—NO2键的Mayer与Laplace键级均有所降低。
结论通过IFCT分析可知，引发键键级变化由O—NO2上的n→Pi*跃迁主导，这种效应会促使太安分子的稳定性降低。
关键词：太安；紫外光；含时密度泛函；吸收光谱；分子稳定性；激发态中图分类号：TJ450 文献标识码：A 文章编号：1672-9242(2022)12-0048-06DOI：10.7643/ issn.1672-9242.2022.12.008Qualitative Effects of Ultraviolet Light on PETN Based on TDDFTZHANG Bao-sen1, ZHANG Shu-hai1, GOU Rui-jun1, CHEN Ya-hong1, ZHU Shuang-fei1, MA Kun2(1. School of Environmental and Safety Engineering, North University of China, Taiyuan, 030051, China;2. Shaanxi Applied Physics-chemistry Research Institute, Xi'an 710061, China)ABSTRACT: The work aims to study the stability degradation mechanism of PETN explosives under the action of ultraviolet light. Based on the TDDFT (time-dependent density functional) theory, 50 excited states of PETN molecules at the收稿日期：2022–08–16；修订日期：2022–11–21Received：2022-08-16；Revised：2022-11-21基金项目：陕西应用物理化学研究所应用物理化学重点实验室基金（6142602200304）Fund：Science and Technology on Applied Physicial Chemistry Laboratory, Shaanxi Applied Physics-Chemistry Research Institute (6142602200304)作者简介：张宝森（1998—），男，硕士研究生，主要研究方向为含能材料相关计算化学。
应用化工Applied Chemical Induste Vol.07No.6 Jun.2020第47卷第6期2020年6月以硫酸氧钛为钛源制备二氧化钛粒子龚之宝，韩迈，孙伟振，马占华，李青松（中国石油大学（华东）重质油国家重点实验室，山东青岛266582）摘要：以更为廉价的钛的无机盐硫酸氧钛为钛源制备二氧化钛粒子为内容,重点介绍了实验室以及工业上以该钛源制备二氧化钛粒子以及多孔材料的方法和相应的改进措施，同时对该项粒子制备的研究现状进行了综述，并指出了各相关研究的特点和意义，且针对国内外研究现状对该项研究的未来提出了展望和建议。
关键词:硫酸氧钛；TiO5;纳米粒子;无机材料;多孔材料中图分类号:TQ028.8文献标识码:A文章编号：271-3206（2020）06-273-04Preparation of titanium dioxine particles by usingtitanium oxysdfate as titanium sturccGONG Zhi-Zao,HAN Maa-SUN Weiahen,MA Zhan-juaO^Q—g-song (S/O Key Laboetoe of Heave0/Processing,China University of Petroleum(East China):Qingdao266530,China)Abstraci:Titanium dioxide pakOlas are prepareP fem the Cxpar inorganic salt of titanium,titanium oy-ife sulOta,as the coutest of titanium dioxide pakic/s.The laboratoe and indust/al methoUs for prepa/ng titanium dioxide pakiclas and porous materials from the titanium source and cooespondWg iwprovemep-meusuras are mainly intmCxced.The research pegress of the preparatiou of the pakiclas was reviewed, and the characte/sdcs and signiUcanca of each related research were pointed out.And based on the research status a-home and adead,the future and pespects of this research are put fomarb.Key wo S s:titanyi sunata;0—4；nanoparfclas,inorganic mate/als,pomus mate/als二氧化钛是现今无机材料研究的热点，因为其具有着一些显著的优点而被逐渐用于众多领域，如其具有耐酸碱、耐高温高压、抗菌抗污染以及具有宽禁带宽度和光催化性能等特点「T,致其逐渐被广泛用于无机陶瓷膜材料,光催化降解燃料和催化剂,化妆品，传感等领域匕3。
2023年 7月下 世界有色金属129化学化工C hemical Engineering电感耦合等离子体发射光谱法测定钴镍矿中银铜铅锌铝铁镁陈尤和（甘肃省有色金属地质勘查局兰州矿产勘查院，甘肃 兰州 ７３００４６）摘 要：试样经盐酸－硝酸－氢氟酸－高氯酸混合酸消解，硝酸提取定容，采用电感耦合等离子体发射光谱法同时测定试液中银、铜、铅、锌、铝、铁、镁７个组分浓度，经计算求得组分的含量。
通过试验确定了基体元素对待测组分的光谱干扰系数，与国标方法进行比对，测定结果两者相符。
各组分方法检出限银为０．０２ｍｇ／ｋｇ、铜为０．８ｍｇ／ｋｇ、铅为２ｍｇ／ｋｇ、锌为０．６ｍｇ／ｋｇ、铝为５ｍｇ／ｋｇ、铁为１４ｍｇ／ｋｇ、镁为８ｍｇ／ｋｇ。
测定范围银为０．０８ｍｇ／ｋｇ~１０００ｍｇ／ｋｇ、铜为４ｍｇ／ｋｇ~０．２５％、铅为８ｍｇ／ｋｇ~０．２５％、锌为３ｍｇ／ｋｇ~０．２５％、铝为０．００２％~１０％、铁为０．００６％~１０％、镁为０．００４％~１０％。
标准物质测定结果的准确度精密度和正确度均满足日常要求。
关键词：钴镍矿石；电感耦合等离子体发射光谱法；多组分同时测定中图分类号：ＴＱ４２６ 文献标识码：Ａ 文章编号：１００２－５０６５（２０２３）１４－０１２９－３Determination of silver, copper, lead, zinc, aluminum, iron, magnesium in cobalt nickel oreby inductively coupled plasma atomic emission spectrometryCHEN You-he（Ｌａｎｚｈｏｕ Ｍｉｎｅｒａｌ Ｅｘｐｌｏｒａｔｉｏｎ Ｉｎｓｔｉｔｕｔｅ ｏｆ Ｇａｎｓｕ Ｎｏｎｆｅｒｒｏｕｓ Ｍｅｔａｌｓ Ｇｅｏｌｏｇｉｃａｌ Ｅｘｐｌｏｒａｔｉｏｎ Ｂｕｒｅａｕ， Ｌａｎｚｈｏｕ ７３００４６， Ｃｈｉｎａ）Abstract: Ｔｈｅ ｓａｍｐｌｅ ｗａｓ ｄｉｇｅｓｔｅｄ ｂｙ ｈｙｄｒｏｃｈｌｏｒｉｃ ａｃｉｄ ｎｉｔｒｉｃ ａｃｉｄ ｈｙｄｒｏｆｌｕｏｒｉｃ ａｃｉｄ ｐｅｒｃｈｌｏｒｉｃ ａｃｉｄ ｍｉｘｅｄ ａｃｉｄ， ｅｘｔｒａｃｔｅｄ ｂｙ ｎｉｔｒｉｃ ａｃｉｄ ｔｏ ｃｏｎｓｔａｎｔ ｖｏｌｕｍｅ， ａｎｄ ｔｈｅ ｃｏｎｃｅｎｔｒａｔｉｏｎｓ ｏｆ ｓｅｖｅｎ ｃｏｍｐｏｎｅｎｔｓ ｉｎ ｔｈｅ ｔｅｓｔ ｓｏｌｕｔｉｏｎ， ｓｉｌｖｅｒ， ｃｏｐｐｅｒ， ｌｅａｄ， ｚｉｎｃ， ａｌｕｍｉｎｕｍ， ｉｒｏｎ， ａｎｄ ｍａｇｎｅｓｉｕｍ， ｗｅｒｅ ｓｉｍｕｌｔａｎｅｏｕｓｌｙ ｄｅｔｅｒｍｉｎｅｄ ｂｙ ｉｎｄｕｃｔｉｖｅｌｙ ｃｏｕｐｌｅｄ ｐｌａｓｍａ ｅｍｉｓｓｉｏｎ ｓｐｅｃｔｒｏｍｅｔｒｙ． Ｔｈｅ ｃｏｎｔｅｎｔ ｏｆ ｔｈｅ ｃｏｍｐｏｎｅｎｔｓ ｗａｓ ｃａｌｃｕｌａｔｅｄ． Ｔｈｅ ｓｐｅｃｔｒａｌ ｉｎｔｅｒｆｅｒｅｎｃｅ ｃｏｅｆｆｉｃｉｅｎｔ ｏｆ ｔｈｅ ｍａｔｒｉｘ ｅｌｅｍｅｎｔ ｔｏ ｂｅ ｍｅａｓｕｒｅｄ ｗａｓ ｄｅｔｅｒｍｉｎｅｄ ｔｈｒｏｕｇｈ ｅｘｐｅｒｉｍｅｎｔｓ， ａｎｄ ｃｏｍｐａｒｅｄ ｗｉｔｈ ｔｈｅ ｎａｔｉｏｎａｌ ｓｔａｎｄａｒｄ ｍｅｔｈｏｄ． Ｔｈｅ ｍｅａｓｕｒｅｍｅｎｔ ｒｅｓｕｌｔｓ ｗｅｒｅ ｃｏｎｓｉｓｔｅｎｔ． Ｔｈｅ ｄｅｔｅｃｔｉｏｎ ｌｉｍｉｔ ｆｏｒ ｅａｃｈ ｃｏｍｐｏｎｅｎｔ ｍｅｔｈｏｄ ｉｓ ０．０２ｍｇ／ｋｇ ｆｏｒ ｓｉｌｖｅｒ， ０．８ｍｇ／ｋｇ ｆｏｒ ｃｏｐｐｅｒ， ２ｍｇ／ｋｇ ｆｏｒ ｌｅａｄ， ０．６ｍｇ／ｋｇ ｆｏｒ ｚｉｎｃ， ５ｍｇ／ｋｇ ｆｏｒ ａｌｕｍｉｎｕｍ， １４ｍｇ／ｋｇ ｆｏｒ ｉｒｏｎ， ａｎｄ ８ｍｇ／ｋｇ ｆｏｒ ｍａｇｎｅｓｉｕｍ． Ｔｈｅ ｍｅａｓｕｒｅｍｅｎｔ ｒａｎｇｅ ｉｓ ０．０８ｍｇ／ｋｇ~１０００ｍｇ／ｋｇ ｆｏｒ ｓｉｌｖｅｒ， ４ｍｇ／ｋｇ~０．２５％ ｆｏｒ ｃｏｐｐｅｒ， ８ｍｇ／ｋｇ~０．２５％ ｆｏｒ ｌｅａｄ， ３ｍｇ／ｋｇ~０．２５％ ｆｏｒ ｚｉｎｃ， ０．００２~１０％ ｆｏｒ ａｌｕｍｉｎｕｍ， ０．００６~１０％ ｆｏｒ ｉｒｏｎ， ａｎｄ ０．００４~１０％ ｆｏｒ ｍａｇｎｅｓｉｕｍ． Ｔｈｅ ａｃｃｕｒａｃｙ， ｐｒｅｃｉｓｉｏｎ， ａｎｄ ａｃｃｕｒａｃｙ ｏｆ ｔｈｅ ｓｔａｎｄａｒｄ ｓｕｂｓｔａｎｃｅ ｄｅｔｅｒｍｉｎａｔｉｏｎ ｒｅｓｕｌｔｓ ｍｅｅｔ ｄａｉｌｙ ｒｅｑｕｉｒｅｍｅｎｔｓ．Keywords: Ｃｏｂａｌｔ ｎｉｃｋｅｌ ｏｒｅ；ＩＣＰ－ＯＥＳ；Ｓｉｍｕｌｔａｎｅｏｕｓ ｄｅｔｅｒｍｉｎａｔｉｏｎ ｏｆ ｍｕｌｔｉｃｏｍｐｏｎｅｎｔ收稿日期：２０２３－０５作者简介：陈尤和，男，生于１９７４年，云南宣威人，本科，地质实验测试高级工程师（副高）。
㊀㊀收稿日期:20220210;改回日期:20230404㊀㊀基金项目:中海石油(中国)有限公司重大科技专项 渤海油田上产4000万吨新领域勘探关键技术 (CNOOC -KJ 135ZDXM36TJ 08TJ);中海石油(中国)有限公司综合科研项目 储层有效性录测一体化定量评价技术研究 (YXKY -2019-TJ -03)㊀㊀作者简介:李鸿儒(1985 ),男,高级工程师,2007年毕业于长江大学地球化学专业,现主要从事海上油气勘探开发作业与研究工作㊂DOI :10.3969/j.issn.1006-6535.2023.03.007基于轻烃分析的复杂储层流体随钻评价新技术李鸿儒1,谭忠健2,符㊀强1,郭明宇2,田青青3,韩明刚1,李艳霞3(1.中海油能源发展股份有限公司,天津㊀300459;2.中海石油(中国)有限公司天津分公司,天津㊀300459;3.盘锦中录油气技术服务有限公司,辽宁㊀盘锦㊀124010)摘要:针对渤中西南环古近系储层流体性质随钻评价难度大㊁多解性强㊁录井与测井资料响应特征矛盾等问题,在深度研究轻烃录井数据的基础上,建立了基于轻烃敏感参数的含水性分析㊁井场轻烃碳环优势分析㊁基于烷烃系列对比的生物降解分析以及基于主成分分析和支持向量机的数学算法等的井场轻烃流体评价方法,并进行了实例应用㊂评价结果表明:基于轻烃敏感参数的储层含水性图版及烷烃系列对比的生物降解程度解释图版,识别研究区流体性质效果好;井场轻烃碳环优势分析法可用于对比分析油气藏成因及来源,与常规录井方法相比,对多期次充注复杂油气藏流体评价优势明显;基于主成分分析和支持向量机的数学算法的轻烃分析方法评价复杂储层流体性质符合率较高,可达85%左右㊂该技术方法在研究区应用效果良好,为复杂储层流体随钻评价提供了新的思路,具有较好的应用前景㊂关键词:流体随钻评价;轻烃分析;复杂储层;渤中西南环;古近系中图分类号:TE353㊀㊀文献标识码:A ㊀㊀文章编号:1006-6535(2023)03-0056-07A New Technique for the Evaluation of Complex Reservoir FluidsWhile Drilling on Light Hydrocarbon AnalysisLi Hongru 1,Tan Zhongjian 2,Fu Qiang 1,Guo Mingyu 2,Tian Qingqing 3,Han Minggang 1,Li Yanxia 3(OOC Energy Development Co.,Ltd.,Tianjin 300459,China ;OOC (China )Tianjin Company ,Tianjin 300459,China ;3.Panjin Zhonglu Oil &Gas Technology Service Co.,Ltd ,Panjin ,Liaoning 124010,China )Abstract :To address the problems of difficult fluid evaluation while drilling for Palaeocene reservoirs in the South-west Zone of Bozhong Sag ,strong multi -solution ,and contradictory response characteristics of mud logging and well logging data ,a water content analysis based on light hydrocarbon sensitive parameters ,well field light hydrocarbon carbon ring dominance analysis ,biodegradation analysis based on alkane series comparison ,and a method for eval-uating well field light hydrocarbon fluids based on mathematical algorithms such as principal component analysis and support vector machine were established ,and the example applications were performed.The evaluation results showthat the reservoir water content plate based on light hydrocarbon sensitive parameters and the biodegradation degree interpretation plate based on alkane series comparison are effective in identifying fluid properties in the study area ;the well field light hydrocarbon carbon ring dominance analysis method can be used for comparative analysis of res-ervoir genesis and origin ,and has obvious advantages over conventional mud logging methods in evaluating fluids in complex reservoirs with multi -stage charging ;the light hydrocarbon analysis method based on mathematical algo-rithms such as principal component analysis and support vector machine has a high compliance rate of about 85%in evaluating the fluid properties of complex reservoirs.This technical method has been applied in the study area with good results ,which provides a new idea for the evaluation of complex reservoir fluids while drilling and has a goodapplication prospect.Key words :evaluation of fluid while drilling ;light hydrocarbon analysis ;complex reservoir ;southwest zone of㊀第3期李鸿儒等:基于轻烃分析的复杂储层流体随钻评价新技术57㊀㊀Bozhong Sag;Paleocene0㊀引㊀言轻烃分析技术出现于1978年左右,Leythae-user㊁Schaefer㊁Thompson和Hunt等阐述了轻烃分析方法及其应用[1-6]㊂Mango及Ten等[7-10]形成的轻烃稳态动力学成因模型使得轻烃分析技术应用更加广泛㊂1983年以来,中国开始建立并推广轻烃分析方法,林壬子㊁张春明㊁段毅等[11-13]针对轻烃成因以及轻烃分析方法在勘探中的应用开展了广泛研究㊂近年来,轻烃录井随钻分析技术的研究与应用逐步兴起,轻烃录井分析以其检测参数丰富的特点弥补了气测录井分析的不足,且轻烃参数对油气藏信息极为敏感,在复杂储层精细评价及油气层含水识别方面具有一定的技术优势,在中国部分含油区块已经形成了一些可行的解释方法[14-15]㊂轻烃录井技术参数及其衍生参数超过200个,但常用的参数不到20个,且部分参数与储层流体性质匹配度并不高,需要深度数据挖掘技术来处理轻烃参数,提升分析评价的时效,提高分析评价的精度㊂渤中西南环位于渤中凹陷西南洼㊁南洼和中洼之间的近南北向构造脊上,成藏条件优越,是渤海海域勘探热点区域[16-17]㊂随着渤中西南环油气勘探程度不断深入,对储层认识不断深化,发现中深储层孔隙结构更加复杂且非均质性更强,油气藏类型多变[18],储层岩性㊁物性㊁流体的变化导致储层含油气性在常规录测井上响应特征不够明显,流体解释易产生多解性[19-20],给决策者带来很大困扰㊂为此,选取渤中西南环32口井㊁1398层井场轻烃数据,在前人研究基础上,通过敏感参数建立解释评价图版,结合轻烃碳环优势分析技术及数据挖掘分析技术,建立基于轻烃分析的复杂储层流体随钻评价技术,对渤中西南环古近系储层流体进行随钻评价,在实际应用中取得较好的效果㊂1㊀区域地质概况渤中西南环探区勘探面积大,探区由西南洼凹陷㊁沙南凹陷和埕北凹陷及相邻凸起和斜坡构成,是一个具有构造圈闭和岩性圈闭的有利勘探区带㊂渤中西南环探区受新构造运动影响,晚期断裂活动强烈,油气藏在浅层㊁深层均有分布㊂区域古近系发育东营组三段(东三段)㊁沙河街组一段(沙一段)㊁沙河街组二段(沙二段)㊁沙河街组三段(沙三段)等有利储层,以近源扇三角洲沉积为主㊂东营组二段(东二段)湖相泥岩与东三段扇三角洲砂体㊁沙一段顶部湖相泥岩与下部扇三角洲砂体等形成多套良好的储盖组合㊂区域古近系发育东三段㊁沙一段和沙三段3套烃源岩,烃源岩厚度为500~2500m,其中,沙三段烃源岩有机质类型以Ⅰ型为主,沙一段烃源岩有机质类型以Ⅰ㊁Ⅱ1型为主,东三段烃源岩有机质类型以Ⅱ1型为主,有机质类型好㊁丰度较高,且烃源岩在2500m附近进入生烃门限,具有较好的烃源条件㊂长期活动的断裂形成了复杂的油气运移通道,能够有效沟通不同凹陷㊁不同烃源岩所产生的油气,但同时也造成了区域内油气关系复杂,多期的油气充注㊁水洗作用及生物降解作用改变了油气藏的原始样貌㊂2㊀基于轻烃分析的复杂储层流体随钻评价技术2.1㊀井场轻烃数据标准化处理由于分析条件差异(仪器㊁预热时间等),导致轻烃谱图保留时间不一致,后期资料处理应用难度大㊂根据各谱图中相同成分的色谱峰位置对谱图进行伸缩和平移操作,结合色谱基线线性插值法,使轻烃谱图各组分保留时间一致,从而对轻烃数据进行标准化处理,将轻烃各组分数据校正到一致的时间点㊂保留时间校正保证了研究区轻烃数据的准确性,为流体准确评价奠定数据基础㊂2.2㊀复杂储层流体随钻评价常规方法的建立选取渤中西南环32口井㊁1398层古近系(东营组㊁沙河街组)储层轻烃数据,在数据标准化处理的基础上,基于轻烃敏感参数㊁井场轻烃碳环优势分析㊁烷烃系列对比生物降解分析,并结合数据挖掘技术开展含水性分析㊁生物降解分析等流体性质识别研究,建立研究区基于轻烃分析的复杂储层流体随钻评价技术,提高流体评价准确性,有效解决古近系储层随钻评价难题㊂2.2.1㊀基于轻烃敏感参数的含水性分析方法常温下,烃类在水中的溶解度很低,按溶解度㊀58㊀特种油气藏第30卷㊀由大到小排序为芳香烃㊁烷烃㊁环烷烃[21-22],Lafar-gue [23]等用4种委内瑞拉原油进行水洗实验,其结果也符合上述规律,即在水洗实验的残留油中,甲苯含量为原来的5%,庚烷含量为原来的51%,甲基环己烷含量最高,为原来的69%㊂基于以上理论基础,通过对研究区22口探井古近系油气显示储层的轻烃数据对比分析,优选出轻烃丰度及芳香烃含量参数分析古近系储层含水性,建立古近系轻烃含水性分析图版(图1)㊂由图1可知:轻烃丰度越高,反映储层含油性越好,反之,含油性越差;芳香烃含量越高,反映储层含水的可能性越小,反之,则含水的可能性越大㊂图1㊀渤中西南环古近系轻烃含水性分析图版Fig.1㊀The plate of water content analysis of Paleocenelight hydrocarbons in the southwest zone of Bozhong Sag2.2.2㊀井场轻烃碳环优势分析方法Mango 轻烃稳态催化动力学成因理论中,提出了 稳态催化反应 的轻烃成因假说和K 1㊁K 2值,对轻烃的成因㊁组成和分布特征进行了系统研究[7-8]㊂在油气成藏研究中,轻烃参数在母质来源与沉积环境㊁有机质成熟度以及油气源对比方面具有重要的价值[13]㊂Mango 提出C 7轻烃异构体形成的不同途径,称为碳环优势路径:三元环优势(3RP)路径㊁五元环优势(5RP)路径及六元环优势(6RP)路径[9]㊂利用三元环[3RP:2-甲基己烷(2MC 6)+3-甲基己烷(3MC 6)+3-乙基戊烷(3EC 5)+2,2-二甲基戊烷(2,2DMC 5)+2,3-二甲基戊烷(2,3DMC 5)+2,4-二甲基戊烷(2,4DMC 5)+3,3-二甲基戊烷(3,3DMC 5)+2,2,3-三甲基丁烷(2,2,3TMC 4)],五元环[5RP:乙基环戊烷(ECYC 5)+1,2-正-二甲基环戊烷+1,2-反-二甲基环戊烷(1,2-(c +t )-DMCYC 5)+1,1-二甲基环戊烷(1,1-DMCYC 5)+1,3-正-二甲基环戊烷+1,3-反-二甲基环戊烷(1,3-(c +t )-DM-CYC 5)]和六元环[6RP:甲苯(TOL)+甲基环己烷(MCYC 6)]相对丰度做三角图,不同沉积环境或排烃期次会产生不同优势的轻烃产物,因此,可对油气藏的成因及来源进行对比分析[10]㊂基于渤中西南环储层流体轻烃特征,开展井场油气藏成因及来源对比分析(图2)㊂由图2可知:研究区既具有六元环优势分布,也具有三元环优势分布,其中,六元环优势是该区主体油气特征;CFD21-1-C 井㊁CFD21-3-A 井及CFD16-2-A 井位于三元环优势区;CFD22-2-A 井数据点比较分散,六元环区和三元环区均有分布,显示明显的混源特征(图2)㊂利用轻烃数据进行碳环优势分析,有助于从油气藏成因等源头上解决复杂储层流体评价的难题㊂图2㊀渤中西南环井场轻烃碳环优势分析Fig.2㊀The geochemical light hydrocarbon carbon ring advantage analysis at the wellfield in the southwest zone of Bozhong Sag2.2.3㊀基于烷烃系列对比的生物降解分析方法在石油中,异构己烷按含量从大到小的排序为:2-甲基戊烷㊁3-甲基戊烷㊁2,3-二甲基丁烷㊁2,2-二甲基丁烷,当原油遭受生物降解作用时,异构己烷抗生物作用的能力与正常原油异构己烷的含量相反,通过异构己烷含量变化可识别生物降解作用的存在㊂微生物降解作用是比较复杂的生物化学过程,不同菌种优先选择消耗的对象也存在差别,一般正构烷烃最易遭受生物降解,异构和环烷烃抗生物降解能力相对较强[13],正庚烷是在所有㊀第3期李鸿儒等:基于轻烃分析的复杂储层流体随钻评价新技术59㊀㊀C 7类烃中对生物降解作用最敏感的化合物,庚烷值和异庚烷值越小,原油降解越严重[3]㊂基于以上原理,通过分析研究区20口探井古近系储层地化轻烃参数,优选出4个敏感性参数(3-甲基戊烷与2,3-二甲基丁烷相对含量比;2-甲基戊烷与2,2-二甲基丁烷相对含量比;庚烷值;异庚烷值),并形成2套古近系储层生物降解分析解释图版,如图3所示㊂该解释图版能有效区分原油和生物降解原油,对复杂流体识别效果好㊂由图3可知,CFD22-2-A 井古近系显示层落入异构烷烃生物降解识别图版生物降解油区(图3a),且CFD22-2-A 井整体较CFD21-1-A㊁CFD21-1-B㊁CFD21-1-C 及CFD15-3-A 等井受生物降解更严重,位于严重生物降解区内(图3b)㊂研究表明,渤中西南环古近系储层降解程度变化较大,流体类型复杂㊂图3㊀渤中西南环古近系生物降解识别图版Fig.3㊀The Paleocene biodegradation identification plate in the southwest zone of Bozhong Sag2.3㊀复杂储层流体随钻评价数据挖掘方法地化轻烃技术采集的原始参数和衍生参数多达223个,其蕴含丰富的地层烃类信息,应用常规方法难以进行快速全面的分析㊂为此,应用数据挖掘分析方法对渤中西南环复杂储层流体性质进行随钻评价,利用主成分分析算法形成二维和三维的交会图版,对储层流体性质进行有效识别;利用支持向量机算法对已知样本进行训练学习,从而对未知样本进行预测㊂基于上述的数据挖掘分析方法解释符合率可达到85%左右㊂2.3.1㊀主成分分析算法主成分分析算法是多元统计分析中最常见的数据分析方法㊂其原理是设法将原变量重新组合成一组新的相互无关的几个综合变量,同时,根据实际需要从中可以取出几个较少的综合变量,尽可能多地反映原变量信息的统计方法,是一种无监督的降维方法㊂利用特征权重算法,根据不同轻烃参数和流体类别的相关性赋予不同的权重,优选出含油性相关参数(轻烃总含量㊁重中烃比率)和含水性相关参数(季碳与甲基环戊烷含量比值㊁甲苯与甲基环己烷含量比值㊁甲基环己烷与正庚烷含量比值等轻烃敏感参数),采用主成分分析算法将轻烃参数进行降维,得到m 个一维矩阵(PC 1㊁PC 2 PCm ),第1个主成分(PC 1)总是体现了数据集中的最大方差,接下来的每个主成分依次具有与之前主成分正交的最大方差,因此,依次选择PC 1㊁PC 2㊁PC 3建立二维和三维的交汇图版对储层流体性质进行区分(图4)㊂PC 1=-0.6892ωTOTAL -0.1547ωMCYC 6ωn C 7-0.3458ωMCH -0.1158ωWMH +0.5889ω4CωMCYC 5+0.1459ωTOLωMCYC 6(1)PC 2=0.5329ωTOTAL -0.3328ωMCYC 6ωn C 7-0.1985ωMCH +0.5501ωWMH +0.5030ω4C ωMCYC 5+0.1008ωTOL ωMCYC 6(2)㊀60㊀特种油气藏第30卷㊀PC 3=0.0410ωTOTAL +0.0523ωMCYC 6ωn C 7+0.8410ωMCH -0.1771ωWMH +0.5000ω4CωMCYC 5+0.0834ωTOLωMCYC 6(3)式中:ωTOTAL 为轻烃总含量;ωMCC 6为甲基环己烷含量;ωn C为正庚烷含量;ωMCH 为甲基环己烷指数,%;ωWMH 为重中烃比率,%;ω4C 为季碳含量;ωMCYC 为甲基环戊烷含量;ωTOL 为甲苯含量㊂图4㊀不同流体性质地化轻烃主成分分析解释图版Fig.4㊀The interpretation plate of principal component analysis of geochemical light hydrocarbons with different fluid properties㊀㊀由图4可知:油层㊁油水同层等不同流体性质之间分类明显,易区分;基于主成分分析算法建立的图版提高了不同流体间的分离程度,可有效地识别复杂储层流体㊂2.3.2㊀支持向量机算法支持向量机算法是一种有监督的机器学习方法,即以支持向量为核心原理的机器学习分类器,属于一般化线性分类器,其决策边界是对学习样本求解的最大边距超平面㊂该方法的基本原理是将样本的低维向量非线性地隐式映射到高维特征空间,并在2个分类之间的超平面两侧建立一对互相平行的支持超平面并使其之间的距离最大化㊂支持向量是指从2个分类样本训练集中筛选得到的一组样本子集,使得对特征空间中样本子集的划分等价于对整个训练集的划分,这组用于将2个类别划分开来的超平面上的向量即为支持向量㊂利用支持向量机算法,建立储层流体性质分类训练模型及预测模型,将22个研究区古近系储层轻烃数据做为已知样本进行训练,选取CFD22-2-A 井8个待测轻烃数据样本进行结果预判:2178~2198m 为油水同层,2210~2214m㊁2250~2275m 为含油水层㊂3㊀应用效果在CFD22-2-A 井古近系储层2178~2262m井段录测井响应特征差异大:气测TG >3.0%,岩屑荧光面积为20%,壁心为灰色油浸细砂岩,含油面积为50%,荧光面积为80%,储层油气录井显示较好,常规录井现场解释为油层(图5);地化热解岩屑Pg 值为14.96mg /g,壁心Pg 值为17.20mg /g,达到油层解释标准;常规测井电阻率偏低,测井解释含水饱和度为82.0%~92.8%,为含油水层㊂利用轻烃分析方法对CFD22-2-A 井古近系储层2178~2262m 井段进行流体性质评价:轻烃丰度及芳香烃含量整体偏低,在古近系轻烃含水图版上位于含油水层区域,含水特征明显(图1);井场轻烃碳环优势分析图中数据落点比较分散(图2),六元环优势区和三元环优势区均有分布,表明油源类型复杂,油藏为多期次充注;古近系异构烷烃生物降解识别图版分析显示(图3a),其具有明显的生物降解特征,且位于庚烷值和异庚烷值生物降解识别图版的生物降解区内(图3b),整体较CFD21-1-A㊁CFD21-1-B 等井受生物降解更严重㊂CFD22-2-A 井古近系储层数据点在不同流体性质轻烃主成分分析解释图版上主要与含油水层㊀第3期李鸿儒等:基于轻烃分析的复杂储层流体随钻评价新技术61㊀㊀数据点重合(图4);利用支持向量机算法预判分类结果:CFD22-2-A 井古近系储层8个待测轻烃数据样本中有6个预判为含油水层,2个预判为油水同层㊂基于主成分分析算法及支持向量机算法的轻烃分析方法表明该段储层含水特征明显㊂综上所述,CFD22-2-A 井古近系储层含水特征明显,油藏类型复杂,具有多期次充注特征;后期受生物降解作用,原油流动性变差,从而形成残余油,导致常规录井显示活跃,显示为 油层 的假象㊂2197.5m 电缆取样见水2700cm 3,见油花,轻烃分析结果与之相符,显示出轻烃分析技术在复杂储层流体随钻评价方面具有优势㊂图5㊀CFD22-2-A 井录测井综合图Fig.5㊀The comprehensive map of mud logging and well logging of Well CFD22-2-A4㊀结㊀论(1)基于渤中西南环32口井1398层轻烃地化数据,优选轻烃敏感参数建立了渤中西南环典型区块储层含水性及生物降解程度解释图版,应用效果良好,有效解决古近系储层流体随钻评价难题㊂(2)渤中西南环13口探井井场轻烃碳环优势分析表明,六元环优势是该区主体油气特征,也具有三元环优势分布,少数井分散在六元环优势区及三元环优势区之间,呈现出明显的混源特征㊂渤中西南环地区油源类型复杂,多油源多期次充注现象明显㊂(3)渤中西南环部分井古近系储层成藏后期受生物降解作用导致油质变重,油品变差,原油流动性变差,从而形成残余油,导致常规录井显示活跃,显示为 油层 的假象㊂(4)运用主成分分析及支持向量机数学算法,实现了机器学习算法与轻烃录井解释应用的深度融合,建立了井场轻烃油气水解释新技术,解释符合率可达到85%左右,但该方法还需进一步探索技术背后的地质意义㊂参考文献[1]LEYTHAEUSER D,SCHAEFER R G,CORNFORD C,et al.Generation and migration of light hydrocarbons(C 2-C 7)in sedimenta-ry basins[J].Organic geochemistry,1979,1(4):191-204.[2]THOMPSON K F M.Light hydrocarbons in subsurface sediments [J].Geochimica et Cosmochimica Acta,1979,43(5):657-672.[3]THOMPSON K F M.Classification and thermal history of petrole-um based on light hydrocarbons[J].Geochimica et Cosmochimica Acta,1983,47(2):303-316.[4]THOMPSON K F M.Fractionated aromatic petroleums and thegeneration of gas -condensates[J].Organic geochemistry,1987,11(6):573-590.㊀62㊀特种油气藏第30卷㊀[5]THOMPSON K F M.Gas 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高中英语世界著名科学家单选题50题1. Albert Einstein was born in ____.A. the United StatesB. GermanyC. FranceD. England答案：B。
解析：Albert Einstein（阿尔伯特·爱因斯坦）出生于德国。
本题主要考查对著名科学家爱因斯坦国籍相关的词汇知识。
在这几个选项中，the United States是美国，France是法国，England是英国，而爱因斯坦出生于德国，所以选B。
2. Isaac Newton is famous for his discovery of ____.A. electricityB. gravityC. radioactivityD. relativity答案：B。
解析：Isaac Newton 艾萨克·牛顿）以发现万有引力gravity）而闻名。
electricity是电，radioactivity是放射性，relativity 是相对论，这些都不是牛顿的主要发现，所以根据对牛顿主要成就的了解，选择B。
3. Marie Curie was the first woman to win ____ Nobel Prizes.A. oneB. twoC. threeD. four答案：B。
解析：Marie Curie 居里夫人）是第一位获得两项诺贝尔奖的女性。
这题主要考查数字相关的词汇以及对居里夫人成就的了解，她在放射性研究等方面的贡献使她两次获得诺贝尔奖，所以选B。
4. Thomas Edison is well - known for his invention of ____.A. the telephoneB. the light bulbC. the steam engineD. the computer答案：B。
解析：Thomas Edison（ 托马斯·爱迪生）以发明电灯（the light bulb）而闻名。
第40卷第2期2023年2月控制理论与应用Control Theory&ApplicationsV ol.40No.2Feb.2023基于扩张状态观测器和反步法的非线性超空泡航行体纵向控制秦华阳1,陈增强1,2,†,孙明玮1,周瑜1,孙青林1(1.南开大学人工智能学院,天津300350;2.天津市智能机器人重点实验室,天津300350)摘要:考虑空泡记忆效应的超空泡航行体控制难度较大,主要体现在滑行力的强非线性、模型中的时延特性以及运动中的未知扰动.对于此类多输入多输出的复杂非线性系统,利用传统反步法控制器设计思想,将其改进以适用于超空泡航行体的纵向运动控制.为了对系统模型中存在的未知扰动进行观测补偿,本文设计了线性扩张状态观测器(LESO),将扰动估计值与控制器设计相结合,使用Lyapunov方法分析系统稳定性.最后在不同条件下进行仿真,结果验证了所设计的LESO估计未知扰动的准确性,以及所提控制方法对超空泡航行体纵向控制的有效性.关键词:空泡记忆效应;超空泡航行体;非线性系统;反步控制;线性扩张状态观测器;Lyapunov分析引用格式:秦华阳,陈增强,孙明玮,等.基于扩张状态观测器和反步法的非线性超空泡航行体纵向控制.控制理论与应用,2023,40(2):373–380DOI:10.7641/CTA.2022.20085Longitudinal control of nonlinear supercavitating vehicle based on extended state observer and backstepping methodQIN Hua-yang1,CHEN Zeng-qiang1,2,†,SUN Ming-wei1,ZHOU Yu1,SUN Qing-lin1(1.College of Artificial Intelligence,Nankai University,Tianjin300350,China;2.Key Laboratory of Intelligent Robotics of Tianjin,Tianjin300350,China)Abstract:The control of a supercavitating vehicle considering the cavitation memory effect is difficult,which is mainly reflected in the strong nonlinearity of the planing force,time-delay properties in models and unknown perturbations in motion.For this kind of complex nonlinear system with multiple inputs and multiple outputs,the traditional backstepping controller is improved to be suitable for longitudinal motion control of supercavitational vehicle.In order to compensate the unknown disturbances in the system model,a linear extended state observer(LESO)is designed to combine the distur-bance estimation with the controller design,and the system stability is analyzed by using the Lyapunov method.Finally, simulations are carried out under different conditions.The results verify the accuracy of the designed LESO for estimating unknown disturbances,and the effectiveness of the proposed control method for the longitudinal control of supercavitating vehicles.Key words:cavitation memory effect;supercavitation vehicle;nonlinear system;backstepping control;linear extended state observer;Lyapunov analysisCitation:QIN Huayang,CHEN Zengqiang,SUN Mingwei,et al.Longitudinal control of nonlinear supercavitating vehicle based on extended state observer and backstepping method.Control Theory&Applications,023,40(2):373–3801引言超空泡航行体的航行状态具有特殊性.常规航行体在水下航行时受到的流体阻力远大于在空气中的阻力,因而其航行速度难以提高.为突破该限制,采用超空泡减阻技术,利用空化器形成空泡层(超空泡)将航行体表面包裹,使航行体在水中的阻力减少约90%,可以实现航行体在水下超高速运行.超空泡减阻技术大幅提高了航行体运行速度,对于军事应用的研发意义重大[1].然而,这种独特的减阻方式也增加了对超空泡航行体的控制难度,使其运动中存在滑行力的强非线性、模型中的时延特性.因此，针对该类系统的特性设计有效的控制方法对超空泡技术的发展具有重要意义.近20年来,诸多学者对超空泡航行体的控制问题展开研究.Dzielski等[2]建立了非线性的超空泡航行体基准模型,并设计了线性反馈控制律.Guo等[3]探索收稿日期:2022−01−28;录用日期:2022−09−16.†通信作者.E-mail:*****************.cn;Tel.:+86130****2991.本文责任编委:龙离军.国家自然科学基金项目(61973175,62073177,61973172)资助.Supported by the National Natural Science Foundation of China(61973175,62073177,61973172).374控制理论与应用第40卷了空化数对航行体动力学特性的影响,提供了线性反馈控制律设计依据.Mao等[4]考虑航行体的非线性控制,解决执行器饱和问题,设计了滑模控制器和线性变参数控制器.李洋等[5]建立了非全包裹超空泡航行体模型,提出了基于反步法的滑模控制律,实现了对超空泡航行体的纵向控制.Wang等[6]针对全包裹超空泡航行体提出了自适应滑模控制器,可以对模型的不确定和未知扰动做出估计.张珂等[7]应用圆柱后体的水洞试验方法,对滑行水动力进行测量实验.范春永等[8]对超空泡航行体的侧方来流对航行体的影响进行了研究,结果表明在受侧方来流冲击时,航行体的相对来流速度决定航行体所受阻力以及空泡形变大小.李洋等[9]研究了超空泡航行体的不确定性问题,基于Lyapunov分析,利用反演控制设计航行体的姿轨控制器,提出了神经网络与自适应控制相结合的控制方法.文献[10]设计了一种变增益鲁棒控制方法,通过增加松弛变量和Lyapunov函数来降低控制系统的保守性和实现系统稳定性,仿真结果表明该系统具有较强的抗干扰性能和鲁棒性.文献[11]设计了线性二次调节器和鲁棒反演控制两类控制器,并通过仿真验证了其有效性.针对模型中存在的时延问题,庞爱平等[12–13]通过对比时滞模型与非时滞模型的仿真曲线,验证了其根据非时滞设计的控制器同样适应于时滞模型.目前已有工作取得了一定效果,但考虑空泡记忆效应的超空泡航行体是涉及多参量、多输入与多输出的复杂非线性时延系统,与其他复杂非线性系统[14–15]不同,其非线性和时延特性主要体现在滑行力的计算上,尾舵与空化器偏转角作为控制输入会同时影响系统的状态,存在耦合特性.然而,控制的核心问题是抑制系统中未知扰动或者不确定性的负面作用[16].为解决此问题,Han[17]提出了自抗扰控制(active disturban-ce rejection control,ADRC),其关键思想是设计扩张状态观测器(extended state observer,ESO),从被控对象的输入或输出信号中提取未知扰动信息,并在控制中进行扰动补偿,可以明显降低扰动带来的负面影响.为便于参数整定,Gao[18]将ADRC简化为线性自抗扰控制(linear active disturbance rejection control,LAD-RC),设计了线性扩张状态观测器(linear extended sta-te observer,LESO),上述工作促进了各领域学者对ADRC的研究与应用[19–26].超空泡航行体运行过程中会受到未知扰动影响,借鉴ADRC的思想,为了估计超空泡航行体运行过程中的未知扰动,设计了基于该系统的LESO.进一步尝试采用较为简单的反步法设计控制器,通过Lyapunov 方法分析系统稳定性.通过与文献[3]中基于极点配置的线性反馈控制方法进行对比仿真,结果验证了所提方法的有效性,对于非线性超空泡航行体的纵向运动,能实现较高的控制品质.2超空泡航行体的非线性动力学模型考虑超空泡航行体在俯仰纵向平面内的运动,首先建立航行体坐标系,其原点位于航行体空化器的顶端面圆心,x轴沿航行体中心轴指向前,z轴垂直于x轴指向下,以地面系为惯性系,z为航行体深度,θ为俯仰角,w为纵向速度且沿航行体z轴方向,q为俯仰角速度,纵向平面内航行体x轴方向速度近似等于空化器的合速度V,并假设为常值,设FΛo=FΛg+FΛp[1L]T,其中FΛp为滑行力F p标准化后的值,定义如下:FΛp=−V2mL(1+h′1+2h′)[1−(R′h′+R′)2]αp,(1)FΛg=791736Lg.(2)根据Dzielski提出的经典基准模型[2],超空泡航行体的俯仰平面动力学方程如下:˙z=w−Vθ,˙θ=q,M[˙w˙q]=A[wq]+B[δfδc]+FΛo,(3)其中:A=CV1−nmL−nm+79C−nm−nLm+1736CL,B=CV2−nmL1mL−nm,M=791736L1736L1160R2+133405L2,δf为尾舵偏转角,δc为空化器偏转角,C=12C x0(1+σ)(R nR)2,(4) R′=(R c−R)/R,(5)K a=LR n(1.92σ−3)−1−1,(6)K b=[1−(1−4.5σ1+σ)K40/17a]1/2,(7) R c=R n[0.82(1+σ)σ]1/2K b.(8)第2期秦华阳等:基于扩张状态观测器和反步法的非线性超空泡航行体纵向控制375考虑空泡的记忆效应,浸入深度h ′和浸入角αp 都是含有状态时延变量的函数,设R 0=R −R c ,z ′(t,τ)=z (t )+θ(t )L −z (t −τ),根据Vanek 的文献[27],其计算公式如下:h ′= 1R [z ′(t,τ)+R ′],上壁接触,0,无接触,1R [R ′−z ′(t,τ)],下壁接触,(9)αp =θ(t )−θ(t −τ)+w (t −τ)−˙R c V,上壁接触,0,无接触,θ(t )−θ(t −τ)+w (t −τ)+˙R c V,下壁接触.(10)3种情形的判断条件为上壁接触,−R 0<z ′(t,τ),无接触,其他,下壁接触,R 0>z ′(t,τ),(11)其中:τ=L /V 表示时间延迟的值,˙Rc 表示空泡半径收缩率,表达式如下:˙R c =−2017(0.821+σσ)1/2V (1−4.5σ1+σ)K 23/17aK b (1.92σ−3).(12)采用超空泡航行体的模型参数见表1.表1超空泡航行体模型参数Table 1Supercavitating vehicle model parameters名称参数值重力加速度g 9.81(m ·s −2)航行体半径R 0.0508m 航行体长度L 1.8m密度比m 2尾翼效率n 0.5升力系数C x00.82空化器半径R n 0.0191m 空化数σ0.02413基于LESO 的反步法控制器设计与稳定性分析由第2节可知,超空泡航行体是涉及多参量,多输入与多输出的复杂非线性时延系统,其非线性和时延特性主要体现在滑行力F p 的计算上,此外,控制输入δf 和δc 会同时影响系统的状态,存在耦合特性.上述特性大大增加了对系统的控制器设计难度,利用反步法,基于Lyapunov 分析,可以在保证系统稳定性的同时有效简化控制器设计,对于系统中的未知扰动,设计LESO 进行扰动观测并补偿.在系统模型(3)中,M 为非奇异矩阵,为便于描述,令x 1=[z θ]T ,x 2=[w q ]T ,考虑系统中存在未知扰动D =[d 1d 2]T ,可将式(3)改写为{˙x 1=A 1x 1+x 2,˙x 2=A 2x 2+B 1u +F gp +D,(13)其中:A 1=[0−V00],A 2=M −1A,B 1=M −1B,u =[δf δc ]T ,F gp=M −1(F Λg +F Λp [1L]).设跟踪指令为x 1d =[z d θd ]T ,(14)跟踪误差为E 1=x 1d −x 1,对E 1求导可得˙E 1=˙x 1d −A 1x 1−x 2,(15)由于扰动项D 未知,将D 作为扩张状态x 3,有{˙x 2=A 2x 2+B 1u +F gp +x 3,˙x 3=˙D,(16)为估计未知扰动D ,构建对应的二阶LESO 如下:e 1=Z 1−x 2,˙Z 1=Z 2+A 2x 2+B 1u +F gp −β1e 1,˙Z 2=−β2e 1,(17)其中:Z 1和Z 2分别为状态变量x 2和未知扰动D 的估计值;β1=2ωo ,β2=ω2o ,ωo 为观测器带宽;假设未知扰动˙D有界,则由文献[18]可知,当t →∞时,有Z 1→x 2,Z 2→D.设虚拟指令x 2d =˙x 1d −A 1x 1+K 1E 1,(18)误差E 2=x 2d −x 2.假设˙x 1d ,¨x 1d 可获知,设计控制律u =B −11(E 1+¨x 1d +K 1˙x 1d −(A 1+K 1)˙x 1−A 2x 2−F gp −Z 2+K 2E 2),(19)其中K 1,K 2均为二阶正定矩阵.下面证明在控制律(19)下,系统(13)是渐近稳定的.证定义Lyapunov 候选函数V =12E T 1E 1+12E T2E 2,(20)则V 0,对V 求导有376控制理论与应用第40卷˙V =E T 1˙E 1+E T 2˙E 2=E T 1(˙x 1d −A 1x 1−x 2)+E T 2˙E 2=E T 1(˙x 1d −A 1x 1−x 2d +E 2)+E T 2˙E 2=−E T 1K 1E 1+E T 1E 2+E T 2˙E 2=−E T 1K 1E 1+E T 2(E 1+˙E 2)=−E T 1K 1E 1−E T 2K 2E 2<0.(21)故V 满足李雅普诺夫定理,系统(13)渐近稳定.证毕.图1为系统的控制原理框图.图1控制原理框图Fig.1Control block diagram4仿真结果为测试所提反步法控制律(19)和LESO(17)观测未知扰动的有效性,使用Simulink 进行仿真,设计不同情形的未知扰动D =[d 1d 2]T ,与文献[3]中的极点配置线性反馈法进行对比,该方法对应本文模型的控制律如下:u =−(B T B )−1B T (C +Ax d )−K f ˜x ,其中:x d =[z d θd 00]T ,˜x =x −x d ,反馈矩阵K f使用极点配置法计算得到,仿真中将极点配置为−2,−3,−4,−5.预设系统(13)的状态变量初值[z 0θ0w 0q 0]T =[0030.02]T ,跟踪指令x 1d =[z d θd ]T =[10]T ,考虑实际中舵角的限幅特性,仿真设定尾舵偏角δf 和空化器转角δc 的范围均为±25◦,根据经验选取观测器带宽ωo =10,K 1=[30080],K 2=[800015].情形1未知扰动D =[00]T .理想情况下,模型中不存在未知扰动,此时仿真结果如图2–6所示.图2中,由于系统状态初值较大,出现了大小约为500N 的非线性滑行力,在控制器作用下,该滑行力快速消失,4种状态均可在2s 内收敛并稳定至期望值(见图3),控制过程中尾舵偏角和空化器转角都能保证在限幅范围内(见图4–5).图6中,LESO 所估计未知扰动的量级在10−6,接近于0,这与未知扰动为0的情形符合,此时,有无LESO 的反步法控制效果几乎一致,而极点配置线性反馈法存在超调现象.图2情形1–滑行力变化曲线Fig.2F plane curves of Case1(a)深度(b)俯仰角(c)纵向速度(d)俯仰角速度图3情形1状态变化曲线Fig.3State curves of Case 1第2期秦华阳等:基于扩张状态观测器和反步法的非线性超空泡航行体纵向控制377图4情形1–δf 变化曲线Fig.4δf curves of Case1图5情形1–δc 变化曲线Fig.5δc curves of Case1Z 2图6情形1–LESO 估计未知扰动Fig.6Z 2curves of Case 1情形2未知扰动D =[103]T .将模型中的未知扰动设置为常数值,仿真结果如图7–11所示.由于此时极点配置线性反馈法控制下的系统失稳发散,因此仅在图7(a)中绘制了失稳状态下的深度曲线.图8中,由于系统初值和未知扰动的存在,导致滑行力初值达到600N,在反步法控制作用下,非线性滑行力会快速消失.由图7和图11可知,系统状态仍能在2s 内收敛,利用所设计的LESO 可以准确估计未知扰动,加入LESO 补偿未知扰动的反步法控制器可以消除由扰动引起的稳态误差,使系统状态更精确地达到期望值.将图9–10与情形1中的图4–5对比可知,要抵消扰动的作用需要更大的舵角变化范围,由于扰动为常数值,当系统达到稳态时,控制量也会稳定于常值,这与经验相符.对比结果表明,所提方法具有较好的鲁棒性.(a)深度(b)俯仰角(c)纵向速度(d)俯仰角速度图7情形2–状态变化曲线Fig.7State curves of Case2图8情形2–滑行力变化曲线Fig.8F plane curves of Case 2情形3未知扰动D =[10sin t 3sin t ]T .将模型中的未知扰动设置为随时间变化的正弦信号,仿真结果如图12–16所示.378控制理论与应用第40卷图13中,滑行力在控制器作用下,能从较大的初值500N 快速衰减至0.对照图12–16可知,LESO 可以较为准确地估计未知时变扰动,加入扰动补偿后的反步法控制效果更好,可以明显减弱由谐波扰动带来的振荡现象,能使系统在2s 内达到稳态.此外,结合情形1–2不难发现,空化器转角对航行体的俯仰角影响较大,尾舵偏角主要作用于航行体的升降运动,与实际情况相符.而对比方法控制下的系统无法抑制正弦扰动带来的影响,未能将系统状态收敛至期望值.图9情形2–δf 变化曲线Fig.9δf curves of Case2图10情形2–δc 变化曲线Fig.10δc curves of Case2Z 2图11情形2–LESO 估计未知扰动Fig.11Z 2curves of Case2(a)深度(b)俯仰角(c)纵向速度(d)俯仰角速度图12情形3–状态变化曲线Fig.12State curves of Case3图13情形3–滑行力变化曲线Fig.13F plane curves of Case3图14情形3–δf 变化曲线Fig.14δf curves of Case 3第2期秦华阳等:基于扩张状态观测器和反步法的非线性超空泡航行体纵向控制379图15情形3–δc 变化曲线Fig.15δc curves of Case3Z 2图16情形3–LESO 估计未知扰动Fig.16Z 2curves of Case 3综合3种情形下的对比仿真结果可知,所设计基于LESO 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Control,2007,13(2):159–184.作者简介:秦华阳硕士研究生,目前研究方向为超空泡航行体建模与控制、自抗扰控制、智能控制;陈增强教授,博士生导师,目前研究方向为智能控制、预测控制、自抗扰控制,E-mail:*****************.cn;孙明玮教授,博士生导师,目前研究方向为飞行器制导与控制、自抗扰控制;周瑜硕士研究生,目前研究方向为超空泡航行体建模与控制;孙青林教授,博士生导师,目前研究方向为自抗扰控制、自适应控制、嵌入式控制系统、柔性飞行器建模与控制.。
DOI： 10.16655/ki.2095-2813.2023.33.002青少年击剑运动员弓步刺速度与下肢爆发力的关联性研究(南京体育学院江苏南京210000)摘要： 目的：研究青少年击剑运动员下肢爆发力对弓步刺速度的影响。
方法：选取南京体育学院击剑队男性青少年运动员22名，进行Wingate测试、立定跳远（双侧、单侧）、单腿六级跳远等不同形式的爆发力测试及原地弓步刺速度、一步弓步刺速度的专项能力测试，采用Pearson相关系数进行下肢爆发力与弓步刺速度之间关联性分析。
结果：原地弓步刺速度与达到峰功率时间（r=-0.71，P=0.02）呈强负相关。
一步弓步刺速度与立定跳远（r=0.82，P=0.02）、单腿六级跳远左侧（r=0.84，P=0.01）和右侧（r=0.82，P=0.02）呈强相关，与达到峰功率时间（r=-0.72，P=0.03）呈强负相关。
结论：青少年击剑运动员弓步刺速度与下肢爆发力之间存在相关性。
原地弓步刺速度与到达峰功率时间呈高度相关，一步弓步刺速度与立定跳远、单腿六级跳远左侧和右侧呈高度相关。
关键词：青少年击剑运动员 下肢爆发力 原地弓步刺 一步弓步刺中图分类号：G885文献标识码：A文章编号：2095-2813(2023)33-0006-04 Research on the Correlation Between Lunge Speed and Lower Limb Explosive Power in Adolescent FencersCHEN Gangrui QIN Xuelin*(Nanjing Sport Institute，Nanjing, Jiangsu Province, 210000 China) Abstract: Objective: To study the effect of lower limb explosive power on lunge speed in adolescent fencers.Methods: 22 young male fencers from the fencing team of Nanjing Sport Institute were selected to conduct different forms of explosive power tests such as the Wingate test, standing long jump (bilateral and unilateral) and single-legged six-level long jump, as well as the special ability tests of rear lunge speed and one-step lunge speed, and the Pearson correlation coefficient was used to analyze the correlation between lower limb explosive power and lunge speed. Results: There was a strong negative correlation between rear lunge speed and the time to reach peak power (r=-0.71, P=0.02), and one-step lunge speed was strongly correlated with standing long jump (r=0.82, P=0.02) and the left side (r=84, P=0.01) and the right side (r=0.82, P=0.02) of single-legged six-level longjump, and was strongly negatively correlated with the time to reach peak power (r=-0.72, P=0.003). Conclusion:There is a correlation between lunge speed and lower limb explosive power in adolescent fencers, rear lunge speedis highly correlated with the time to reach peak power, and one-step lunge speed is highly correlated with standinglong jump and the left side and right side of single-legged six-level long jump.基金项目：江苏省运动与健康工程协同创新中心第三建设期项目（JSCIC-GP21001）。
Jeong Hoon KoPostdoctoral Research Fellowe-mail:jhko5889@Yusuf Altintas1ProfessorASME Fellowe-mail:altintas@mech.ubc.ca Department of Mechanical Engineering, The University of British Columbia, 2054-6250Applied Science Lane Vancouver,B.C.V6T1Z4Canada Dynamics and Stability of Plunge Milling OperationsPlunge milling operations are used to remove excess material rapidly in roughing op-erations.The cutter is fed in the direction of the spindle axis which has the highest structural rigidity.This paper presents a comprehensive model of plunge milling process by considering rigid body motion of the cutter,and three translational and torsional vibrations of the structure.The time domain simulation model allows prediction of cutting forces,torque,and vibrations while considering tool setting errors and time varying process parameters.The stability law is formulated as a four-dimensional eigenvalue problem,and the stability lobes are predicted directly with analytical solution in fre-quency domain.Time domain prediction of cutting forces and vibrations,as well as the frequency domain and chatter stability solution are verified with a series of plunge milling experiments.͓DOI:10.1115/1.2383070͔Keywords:plunge milling,chatter,cutting force1IntroductionSample plunge milling operations are illustrated in Fig.1.The cutter can be plunged into a solid block with full immersion like in drilling͑Fig.1͑a͒͒,or can act like a boring head to enlarge a hole͑Fig.1͑b͒͒,or can remove excess material from the periphery of a wall͑Fig.1͑c͒͒.Since the feed axis coincides with the most rigid spindle axis direction,the process tends to be more vibration-free than plane milling operations.As a result,plunge milling recently became popular in roughing of cavities in the die, mold,and aerospace industries.Process planners need to estimate chatter-free cutting conditions,and spindle designers should con-sider the magnitudes of trust and radial loads for the sizing of the bearings and shaft.There has been limited literature for the plunge milling process,and most efforts were spent on the design of cutter geometry.Wakaoka et al.͓1͔studied the intermittent plunge milling processto make vertical walls by focusing on the tool geometry and mo-tion.Li et al.͓2͔presented a plunge milling method to createcomplex chamfer patterns and estimated cutting forces while ne-glecting the structural dynamics of the system.The remainingliterature belongs to the commercial tool catalogs,which presentonly the dimensions and shape of the plunge milling cutters.There have been significant researches reported on the mechan-ics and dynamics of plane milling operations.Tlusty and Ismail ͓3͔presented the time domain simulation of helical end mills by including the structural dynamics of the system.Sutherland et al.and Devor et al.͓4,5͔presented both helical and face millingmodels,which can predict the cutting forces with the presence oftool run-outs,eccentricity,and static deflections.Montgomery andAltintas integrated rigid body kinematics and structural vibrationsof helical end mills͓6͔.The mechanics of ball end mills,taperedhelical ball end mills,and serrated cutters are also studied exten-sively by researchers using time domain models of the process ͓7–10͔.Atabey et al.͓11͔presented mechanics of boring heads with multiple inserts,but neglected the structural dynamics.How-ever,the integrated chip generation kinematics,and mechanics and dynamics of plunge milling in time and frequency domain, have not been studied before.Unlike plane milling operations, plunge milling tools move vertically towards the material and the chip generation occurs at the bottom cutting edges.Depending on the cutter geometry,lateral,torsional,and axial modes of the tool, vibrations may affect the regeneration of the chip thickness.The prediction of chip load history under combined rigid body motion and vibrations of the cutter by considering two lateral,axial,and torsional vibrations is modeled both in time and frequency do-mains in this paper.The review of past chatter research and future challenges are presented by Altintas and Weck͓12͔.The chatter stability of con-tinuous,one-dimensional cutting processes like orthogonal cutting isfirst analyzed by Tlusty͓13͔and Tobias͓14͔in frequency do-main.Minis and Yanushevksy considered the milling as a two-dimensional eigenvalue problem and solved the stability through iterations by applying Floquet theory͓15͔.They used average directional coefficients and assumed that the dynamics of the pro-cess is time invariant.Budak and Altintas developed a direct sta-bility law,which allows the prediction of stability lobes without any iteration when average directional factors are used,and ex-tended it to theory to consider time varying directional factors by including higher harmonics terms͓16,17͔.Researchers such as Insberger et al.͓18͔,Davies et al.͓19͔,Bayly et al.͓20͔,and Corpus et al.͓21͔presented linear but analytical solutions of pe-riodic cutting processes in the time domain,where the time varia-tion of the directional factors can be accounted.The advantage of analytic time domain solution is to avoid computationally costly numerical solutions at the expense of ignoring the nonlinearities in comparison to numerical solutions.The numerical solutions are based on thefirst principles of metal cutting laws,and they are used to simulate the correctness of the mathematical models describing the physics of the system. The rigid body motion and vibrations are modeled for the predic-tion of dynamic chip thickness variation along the cutting edge. The cutting forces acting on the tool and workpiece are evaluated from the chip thickness distribution.The size effect of cutting force coefficients,varying cutting edge geometry,and loss of con-tact between the tool and workpiece can be considered as nonlin-earities and deviations from the process parameters.The degree of nonlinearity and the influence of geometric variations on the pa-rameters of the delayed differential equations,which govern the stability of the process,are also measured through numerical simulations.The limits of process linearization for linear fre-quency or time based chatter stability solutions are assessed through numerical modeling of the complete cutting process.Fur-thermore,the prediction of cutting forces acting on the bearings,1Corresponding author.Contributed by the Manufacturing Engineering Division of ASME for publicationin the J OURNAL OF M ANUFACTURING S CIENCE AND E NGINEERING.Manuscript receivedJuly15,2005;final manuscript received July3,2006.Review conducted by W.J.Endres.32/Vol.129,FEBRUARY2007Copyright©2007by ASME Transactions of the ASMEspindle shaft,tool,and holder are important to prevent overload-ing of the machine elements.Hence,both process planner andspindle designer require the time domain,numerical simulation ofthe process for improved design and productive machining.This paper presents mechanics,dynamics,and chatter stabilityof generalized plunge milling operations in both time and fre-quency domains.Section 2presents the mechanics of plunge mill-ing where the cutting force and torque prediction are modeled.The kinematics of chip generation under vibrations are modeled inSec.3.Chatter stability of the plunge milling process is modeledin the frequency domain in Sec.4.The time domain simulationsof dynamic forces,and the frequency domain stability solution ofplunge milling process are compared against experiments in Sec.5.The paper is concluded with a summary of the model in Sec.6.2Mechanics of Plunge MillingThe geometry and parameters of a plunge milling cutter are shown in Fig.2.The cutter plunges into the metal in spindle axis ͑z ͒direction.The inserts have an offset distance of l from the cutter center.The tangential cutting force ͑F t ͒is in the direction of cutting speed and distributed along the cutting edge at the bottom.The feed force ͑F f ͒is in the direction of the feed ͑z ͒axis,and the passive force ͑F a ͒acts along the cutting edge.The cutting speed decreases as the tool edge approaches to the cutter center.De-pending on the insert geometry and run-out,the effective rake angle of the cutting edge as well as the elevation in z and positions in the x ,y directions may change,which alter the cutting mechan-ics.In order to consider a general case,the insert is divided into a finite number of small differential elements in the radial direction.The chip load and corresponding differential loads for each edge element are evaluated and digitally integrated to predict the total forces in three directions and torque.The algorithm is repeated at discrete time or spindle rotation intervals to predict the time vary-ing forces in plunge milling.The angular position of the points along the cutting edge of the cutter at its bottom is evaluated from Fig.2͑b ͒.The angular posi-tion ͑j ͒of the tooth j is describedby Fig.1Plunge milling process configuration.…a …Plunge mill-ing process for making large hole.…b …Plunge milling processto enlarge a hole.…c …Intermittent plunge milling process tomake vertical wall or conduct roughcutting.Fig.2Geometry and coordinates of a sample plunge mill.Cut-ter parameters:D 1=20mm,D 2=25mm,l =5.5mm,␣f =10deg,r =10deg,Cl f =5deg …Sandvik Cutter Part No.R210-025A20-09M ….…a …Geometry of a plunge mill.…b …Angular position ofeach tooth.Journal of Manufacturing Science and Engineering FEBRUARY 2007,Vol.129/33Downloaded 23 Feb 2012 to 222.192.86.226. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmj =0+͑j −1͒p ,p =2/N ͑1͒where 0is the rotation angle of the reference tooth measuredfrom the y axis and N is the number of teeth on the cutter.Thearea of chip cut by a differential element is h ͑j ͒⌬a ,where h ͑j ͒is the instantaneous chip thickness removed by the edge segmentwith a differential length of ⌬a .The tangential ͑F tj ͒,radial ͑F aj ͒,feed forces ͑F f j ͒,and torque ͑T cj ͒acting on the differential cutting edge element k of tooth j are given bydF tj =K tc h ͑j ͒⌬a +K te ⌬a ,dF aj =K ac h ͑j ͒⌬a +K ae ⌬a͑2͒dF f j =K fc h ͑j ͒⌬a +K fe ⌬a ,dT cj =−dF tj r k where the torque arm is r k =͑k −1/2͒⌬a +l .͑K tc ,K ac ,K fc ͒and ͑K te ,K ae ,K fe ͒are the material and tool geometry dependent cut-ting and edge force coefficients,respectively ͓22͔.The tangential,radial,and feed forces acting on the cutting edge can be transformed into three orthogonal force components in Cartesian coordinates of the cutter axes as follows:ΆF xj F yj F zj T cj ·=΄−cos j −sin j 00sin j cos j 0000100001΅ΆF tj F aj F f j T cj ·͑3͒The total instantaneous cutting forces and torque are evaluated by digitally integrating the contributions of all differential edge segments of the inserts,which are in cut when the reference toothis at an angular position ͑0͒:ΆF xj ͑0͒F yj ͑0͒F zj ͑0͒T cj ͑0͒·=͚j =0N −1͚k =0M −1⌬a ΄−͓K tc h ͑j ͒+K te ͔cos j −͓K ac h ͑j ͒+K ae ͔sin j ͓K tc h ͑j ͒+K te ͔sin j −͓K ac h ͑j ͒+K ae ͔cos j K fc h ͑j ͒+K fe͓K tc h ͑j ͒+K te ͔ͫͩk −l 2ͪ⌬a +l ͬ΅͑4͒where N ,M are the number of teeth on the cutter and the numberof elements on each cutting edge,respectively.The reference im-mersion angle is incremented as the spindle rotates 0=⍀t ,where ⍀is the angular speed of the spindle.3Kinematics of Dynamic Plunge MillingThe plunge milling cutter is fed into the material axially ͑i.e.,inthe z direction ͒with a feed rate of c ͑mm/rev/tooth ͒and angularspeed of ⍀͑rad/s ͒.Depending on the cutter geometry,cuttinginsert type and distribution,and cutting conditions as shown inFig.1,the tool may experience lateral ͑x ,y ͒,axial ͑z ͒,and tor-sional ͑͒vibrations.The general formulation of dynamic chipthickness,which contains both rigid body motion and structuralvibrations,is formulated based on the kinematics of the plungemilling.Montgomery and Altintas ͓7͔developed an exact kine-matic model of dynamic milling by digitizing the surface finish atdiscrete time intervals.Although their model accurately predictsthe exact chip thickness with regenerative vibration effects inmilling process,it is computationally costly and not robust whentorsional vibrations are included.An alternative but still an accu-rate kinematic model of dynamic chip thickness is formulatedhere by considering the structural vibrations in the lateral ͑x ,y ͒,axial ͑z ͒,and torsional ͑͒directions at the cutter center.Thetranslational vibrations at the cutting edge locations are simplypredicted by using the tool geometry.The torsional vibrations ͑͒are defined at the cutting edge but relative to the spindle axispassing through the cuttercenter,͑5͒where ͑1͒R r represents the radial eccentricity of the cutter center.The vibrations are estimated from the transfer function ͓͑⌽͑s ͔͒͒of thestructure:͑6͒It must be noted that the terms inside the transfer function ma-trix represent the flexibilities in each direction,and some of them,especially the cross terms in translational directions,may be zero depending on the cutter geometry and machine configuration.However,a general formulation is considered here since the pro-posed model is applicable to plunge milling and indexed boring cutters,which may have various flexibility configurations depend-ing on each application and cutter type.Each transfer function term is represented in Laplace domain as:⌽͑s ͒=͚h =1K nh 2/k h s 2+2h nh s +nh 2͑7͒where nh ,k h ,and h are the natural frequency,modal stiffness,and damping ratio of mode number h ,respectively.The vibrations ͑Eq.͑6͒͒are predicted by applying the predicted cutting force at each discrete time interval on the transfer function of the structure ͑Eq.͑7͒͒by using a fourth-order Runge Kutta digital integration scheme.The coordinates of the points along the cutting edge are evalu-ated by using the cutter geometry information given in Fig.2.Asthe cutter rotates and vibrates,the cut surface is digitized at dis-crete time intervals by tracking the positions of discrete cuttingedge elements.The coordinates ͑X e ,Y e ,Z e ͒of a point along thecutting edge of tooth j are expressed as:X e ,j ͑t ͒=X c ͑t ͒+r k sin ͑j ͒,Y e ,j =Y c ͑t ͒+r k cos ͑j ͒,Z e ,j ͑t ͒=Z c +R aj +͑r k −l ͒tan r͑8͒where the angular immersion angle j =⍀t +͑j −1͒p is updated with time t .The Z coordinate of the cutting edge of the previoustooth ͑j −1͒is given as follows:34/Vol.129,FEBRUARY 2007Transactions of the ASME͓6–9,22͔proposed a linear model that separates the shearing ͑K tc,K ac,K fc͒andflank contacts͑K te,K ae,K fe͒as shown in Eq.͑2͒.Such a separation makes the chatter stability linear without sacrificing the accuracy in both time and frequency domain solu-tions.The identified cutting coefficients for the particular plunge milling cutter͑Fig.2͒and aluminum material͑Al7050-T7451͒are identified from chatter-free plunge milling force measurements according to procedures given in͓10,22͔and suggested in Table1.5.1Identification of Modal Parameters.The FRFs of the plunge mill attached to the Mori Seiki SH403machining center with HSK63E interface are identified through impact modal tests. The mostflexible modes,which may contribute to the regenera-tion mechanism,are considered as shown in Table2.The torsional mode is measured by attaching a miniature accelerometer on one tooth while exerting impact blows on the opposite tooth with a miniature hammer.The torsional-axial mode is also measured by the same instruments.The impact is applied on the tool radially while mounting the accelerometer on the axial direction of the opposing tooth.The torsional-axial coupling mode around12,000Hz is verified with afinite element model of the cutter to ensure that the mea-surements are correct.Thefinite element model predicted the tor-sional mode at12,600Hz.Although the cutter is moreflexible in lateral͑x,y͒directions,where the dynamic stiffness is the least, the regenerative chip thickness is most affected by the vibrations projected in the direction of plunging͑i.e.,z͒.The axial modes͑z z͒of the cutter are quite stiff,and the torsional vibration does not bring significant change in the chip load and regenerative phase͑Eq.͑11͒͒.However,there is a strong coupling between the torsional and axial vibrations due to chip evacuation cavities in the plunge milling cutters.The coupling mode at12,000Hz cre-ates axial vibration,which directly contributes to the regenerative chip thickness͑Eq.͑11͒͒,hence it is most dominant in this par-ticular plunge milling chatter problem.The small discrepancy be-tween the measured and predicted frequencies is attributed to the errors during sensitive measurements andfinite element modeling of the cutter.Nevertheless,the stability formulation is general,and the FRF matrix can be populated withflexibilities in all threetranslational directions and one rotational direction depending oneach cutter geometry and plunge milling application.5.2Verification of Plunge Milling Model.Plunge milling tests at n=1000rev/min spindle speed but at various immersionand feed rates are given in Fig.5.The predicted and measuredcutting forces are in good agreement,which indicates the correct-ness of rigid body kinematics of plunge milling,chip thicknessevaluation from digitized surfaces cut by successive teeth,theprocess mechanics,and the linear cutting coefficient model.One insert had20m axial and1.5m radial run-outs,which are measured relative to the reference insert and included in the timedomain simulation model.The chatter stability law presented in the article has been veri-fied with plunge milling experiments.The cutter geometry isgiven in Fig.2,and the cutting force coefficients for the aluminum material Al7050-T7451were identified as K tc=956N/mm2,K a =396/K tc,and K f=371/K tc͑see Table1͒.The stability lobes pre-dicted by the proposed theory͑Eq.͑20͒͒are given in Fig.6.The presence of chatter is identified when the resulting cut surface is rough,and the process is dominated by a high pitch sound that does not correspond to the harmonics of the tooth passing fre-quency,but close to one of the natural frequencies.More than100 plunge milling tests were performed to validate the theory,and an overwhelming number of predictions were in good agreement with the experiments as shown in Fig.6.The lobes were domi-nated by the torsional-axial coupled mode͑z͒around12,000Hz. If this torsional-axial coupled mode͑12KHz͒is disabled in the simulation,the lobes,which limit the axial depth of cut most, disappear and are replaced by less dominant lateral modes. Sample cutting force and vibration measurements at unstable ͑point A͒and stable͑point B͒conditions are shown as an ex-Table1Identified cutting coefficients in plunge milling of alu-minum alloy Al7050-T7451K tc͑N/mm2͒K te͑N/mm͒K ac͑N/mm2͒K ae͑N/mm͒K fc͑N/mm2͒K fe͑N/mm͒952463963037162 Table2Modal parameters of the plunge mill attached to Mori Seiki SH403with HSK63interfaceMode no.Naturalfrequency͑Hz͒Dampingratio͑͒Modalstiffness͑k͒Dynamicstiffness͑2k͒x x 15080.0235121.00N/m 5.68N/m 230400.024241.10N/m 1.99N/m 340350.017967.50N/m 2.42N/my y 15150.051044.30N/m 4.52N/m 231000.030580.40N/m 4.90N/m 339610.018351.00N/m 1.87N/mz z 13210.0482242.00N/m23.30N/m 24050.0379790.00N/m59.80N/mz112,0900.0015321.20Nm/m0.0649Nm/m 112,0000.00243 1.106E+04Nm/rad53.80Nm/rad Fig.5Comparison of the predicted and measured cutting forces under chatter-free cutting conditions.Work material: Al7050-T7451.Cutting configuration of Fig.1…c….…a…Cutting conditions:spindle speed=1000rpm,feed per tooth =0.05mm/tooth,and radial depth of cut=4mm.…b…Cutting conditions:spindle speed=1000rpm,feed per tooth =0.125mm/tooth,and radial depth of cut=3mm.Journal of Manufacturing Science and Engineering FEBRUARY2007,Vol.129/37ample.The unstable cutting condition at point A corresponds tospindle speed of 16,000rev/min and 5mm radial depth of cut.The chatter occurs due to coupling of torsional-axial vibrations at12,360Hz.Although the lateral cutting forces F x and F y are sig-nificantly cancelled due to the symmetry of the geometry,thetorque generated by each tooth is summed as the total torque.Thedynamic torque leads to torsional vibrations,which in turn causeaxial vibrations due to coupling effect ͓23͔.The spindle speed andradial depth of cut at stable cutting condition ͑point B ͒were17,142rev/min and 5.75mm,respectively.The measured cutting forces and sound spectrum are dominated by the spindle speed ͑285.7Hz ͒due to run out.It is important to predict the amplitude and frequency of cutting forces and elastic displacements in machining under stable,chat-ter,and forced vibration conditions.The dynamic loads are trans-mitted to the spindle bearings and tool holders,and the spindle designer must forecast their magnitude by consideringchatter Fig.6Experimental verification of numerical and analytical stability lobes in plunge milling.Cutting conditions:full immersion plunge milling mode …i.e.,Fig.1…b ……,c =0.075mm/rev/tooth,and tool:Fig.2.38/Vol.129,FEBRUARY 2007Transactions of the ASMElows the analysis of various tool geometry,cutter-part engage-ment,and cutting conditions and predicts process performance measures such as forces and vibrations.AcknowledgmentThis work is supported by National Sciences and Engineering Research Council of Canada͑NSERC͒and Pratt&Whitney Canada under Industrial Research Chair and Strategic Grants of the second author.The cutting tools and tool holders were pro-vided by Mitsubishi Materials and Sandvik Coromant Companies, and the high speed SH403horizontal machining center was con-tributed by Mori Seiki Machine Tool Company. NomenclatureD1,D2ϭshank and effective cutting diam-eters of the cutter,respectively␣f,r,Cl f,pϭaxial rake,cutting edge,axial re-lief angles of the tool,and cutterpitch angle,respectivelyaϭradial depth of cut⌬aϭlength of edge element along ra-dial directionNϭnumber offlutescϭfeed per tooth͑mm/tooth/rev͒⍀ϭspindle speed͑rad/s͒F t,F a,F f,Tϭtangential force,radial force,feedforce,and torque,respectivelyhϭuncut chip thicknessx,y,z,ϭtool vibrationsX c,Y c,Z c,cϭpresent cutter center position de-termined by rigid body motionand vibration͑X e,j,Y e,j,Z e,j,e,j͒ϭpresent cutting edge position͑X e,j−1,Y e,j−1,Z e,j−1,e,j−1͒ϭprevious cutting edge positionK tc,K ac,K fcϭtangential,radial,and frictionalcutting force coefficientsK te,K ae,K feϭtangential,radial,and frictionaledge force coefficientsl dϭdistance between the previouscutter center and the present edgepositionnh,k h,andhϭnatural frequency,modal stiffness,and damping ratioR r,R aϭradial and axial runout,respectivelyh0,h dϭstatic and dynamic chip thickness,respectively⌬dϭdynamic displacement in x-yplane⌬x,⌬y,⌬z,⌬ϭregenerative displacements inx,y,z,anddirectionsA0ϭtime-invariant directionalcoefficientsTϭtooth passing periodj,pϭimmersion angle of tooth j andcutter pitch angle,respectivelyst,exϭentry and exit angles⌽͑i͒ϭfrequency response function⌽0ϭoriented frequency responsefunctioncϭchatter frequencya limϭcritical depth of cutϭphase shifts of the regenerativechip modulationsReferences͓1͔Wakaoka,S.,Yamane,Y.,Sekiya,K.,and Narutaki,N.,2002,“High-Speed and High-Accuracy Plunge Cutting for Vertical Walls,”J.Mater.Process.Technol.,127,pp.246–250.͓2͔Li,Y.,Liang,S.Y.,Petrof,R.C.,and Seth,B.B.,2004,“Force Modelling for Cylindrical Plunge Cutting,”Int.J.Adv.Manuf.Technol.,16,pp.863–870.͓3͔Tlusty,J.,and Ismail,F.,1981,“Basic Nonlinearity in Machining Chatter,”CIRP Ann.,30,pp.21–25.͓4͔Sutherland,J.W.,and DeV or,R.E.,1986,“An Improved Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems,”ASME J.Eng.Ind.,108,pp.269–279.͓5͔DeV or,R.E.,Kapoor,S.G.,Fu,H.J.,and Subbarao,P.C.,1983,“Effect of Variable Chip Load on Machining Performance in Face Milling,”Trans.North Am.Manuf.Res.Inst.SME,11,pp.348–355.͓6͔Montgomery,D.,and Altintas,Y.,1991,“Mechanism of Cutting Force and Surface Generation in Dynamic Milling,”ASME J.Eng.Ind.,113͑2͒,pp.160–168.͓7͔Altintas,Y.,and Lee,P.,1998,“Mechanics and Dynamics of Ball End Mill-ing,”ASME J.Manuf.Sci.Eng.,120,pp.684–692.͓8͔Altintas,Y.,and Engin,S.,2001,“Generalized Modeling of Mechanics and Dynamics of Milling Cutters,”CIRP Ann.,50͑1͒,pp.25–30.͓9͔Merdol,S.E.,and Altintas,Y.,2004,“Mechanics and Dynamics of Serrated Cylindrical and Tapered End Mills,”ASME J.Manuf.Sci.Eng.,126,pp.318–326.͓10͔Ko,J.H.,and Cho,D.-W.,2005,“3D Ball-End Milling Force Model Using Instantaneous Cutting Force Coefficients,”ASME J.Manuf.Sci.Eng.,127, pp.1–12.͓11͔Atabey,F.,Lazoglu,I.,and Altintas,Y.,2002,“Mechanics of Boring Pro-cesses:Part II-Multi-insert Boring Heads,”Int.J.Mach.Tools Manuf.,43͑5͒, pp.477–484.͓12͔Altintas,Y.,and Weck,M.,2004,“Chatter Stability in Metal Cutting and Grinding,”CIRP Ann.,53͑2͒,pp.619–642.͓13͔Tlusty,J.,and Polacek,M.,1957,“Besipiele der behandlung der selbsterregten Schwingung der Werkzeugmaschinen,”FoKoMa,Hanser Verlag,Munchen.͓14͔Tobias,S.A.,and Fiswick,W.,1958,Theory of Regenerative Machine Tool Chatter,Engineering,London,p.258.͓15͔Minis,I.,and Yanushevsky,T.,1993,“A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling,”ASME J.Eng.Ind.,115,pp.1–8.͓16͔Budak,E.,and Altintas,Y.,1998,“Analytical Prediction of Chatter Stability Conditions for Multi-Degree of Systems in Milling.Part I:Modelling,”ASME J.Dyn.Syst.,Meas.,Control,120,pp.22–30.͓17͔Merdol,D.,and Altintas,Y.,2004,“Multi Frequency Solution of Chatter Sta-bility for Low Immersion Milling,”ASME J.Manuf.Sci.Eng.,126͑3͒,pp.459–466.͓18͔Insberger,T.,and Stepan,G.,2000,“Stability of the Milling Process,”Period.Polytech.,Mech.Eng.-Masinostr.,44͑1͒,pp.47–57.͓19͔Davies,M.,Pratt,J.R.,Dutterer,B.,and Burns,T.J.,2000,“The Stability of Low Radial Immersion Milling,”CIRP Ann.,49͑1͒,pp.37–40.͓20͔Bayly,P.V.,Halley,J.E.,Mann,B.P.,and Davies,M.A.,2003,“Stability of Interrupted Cutting by Temporal Finite Element Analysis,”ASME J.Manuf.Sci.Eng.,125,pp.220–225.͓21͔Corpus,W.T.,and Endres,W.J.,2004,“Added Stability Lobes for Machining Processes that Exhibit Periodic Time Variation–Part1:An Analytical Solu-tion,”ASME J.Manuf.Sci.Eng.,126,pp.467–474.͓22͔Altintas,Y.,2000,Manufacturing Automation:Metal Cutting Mechanics,Ma-chine Tool Vibrations,and CNC Design,Cambridge University Press,Cam-bridge.͓23͔Bayly,P.V.,Metzler,S.A.,Schaut,A.J.,and Young,S.G.,2001,“Theory of Torsional Chatter in Twist Drills:Model,Stability Analysis and Composition to Test,”ASME J.Manuf.Sci.Eng.,124͑4͒,pp.552–561.40/Vol.129,FEBRUARY2007Transactions of the ASME。
