半可燃药筒火炮密封结构多目标优化设计
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摘要
旋转药室密封技术是埋头弹火炮系统的关键技术之一。某型埋头弹火炮采用半可燃药筒结构用以旋转药室的密封,在实现密封的同时,也带来了火炮抽筒的技术问题。本文以某国防预研课题为背景,应用有限元、弹塑性力学、结构优化设计等理论对某型半可燃药筒火炮的密封问题与抽筒问题的机理进行了深入研究,不仅为解决工程中的实际问题提供了理论依据和决策参考,而且文中采用的兼顾计算精度和效率的优化策略为工程领域相关问题的解决提供了一种新的思路。主要研究内容如下：
(1)分析了某型半可燃药筒火炮的密封机制,找到了其密封的关键区域,并在此基础之上建立起了该型半可燃药筒可靠密封的评判准则,即将密封通道B的密封开始时间作为整体密封效果的评判依据。同时,运用有限元动态响应分析的方法对密封结构的强度和闭气性等能进行了综合分析,揭示了密封问题和抽筒问题的内在联系,明确了在保证密封前提条件下,尽可能减小抽筒力的设计原则和目标。
(2)运用Python语言对非线性有限元软件ABAQUS进行了二次开发,将对抽筒力大小影响较大的设计变量进行参数化处理,从而建立起密封结构的参数化模型,为实现优化过程的自动化提供保证。
(3)通过对该型火炮抽筒物理过程的研究,确定了半可燃药筒残余接触力是导致抽筒困难的主要原因。同时,提出了针对该型火炮密封结构材料特性的基本假设,并对贴膛前、贴膛后至最大膛压、卸载三个阶段中,药筒与身管药室之间的相互作用情况进行了分析,推导了基于静态弹塑性理论的某型火炮抽筒力计算模型。通过与有限元计算结果对比,验证了模型的合理性。通过进一步对模型的讨论,确定了优选材料和优化半可燃药筒设计参数组合作为减小抽筒力的两个重要途径,同时,也为后续密封结构设计参数的优化工作提供了待优化设计变量。
(4)基于所建立的密封结构参数化模型,结合对抽筒力影响因素的分析,建立起以半可燃药筒密封结构的三个设计变量,即密封段长度、密封段厚度和初始间隙作为待优化的设计变量,以密封可靠作为约束前提条件,以密封时间最短、抽筒阻力最小、密封结构总质量最小为目标函数,适用于该型半可燃药筒密封结构的优化数学模型。同时,从工程实际的角度确定了这三个设计变量的取值范围及“步长”。最后,基于多学科优化集成软件平台mode-FRONTIER,对该优化模型进行了构建和计算,确定出了一组既满足密封要求,又可大幅减小抽筒力,同时密封段总质量不大的设计参数组合。
(5)针对动态非线性有限元计算需要占用大量机时的特点,在优化过程中引入了响应面方法。提出了三种基于响应面法的优化方案,并从设计试验、响应面模型的建立及检验等角度对这三种方案进行了比较分析,最终确定了自编程正交多项式拟合法作为响应面法在此文中应用的最终方案。采用响应面法和其他优化算法相结合的优化策略,可以兼顾计算精度和计算效率,为该类密封结构的优化设计提供一种新的思路。
The sealing technology of the swing chamber is one of the CTA gun's key Technologies. Semi-combustible cartridge structure was used in a new-type CTA gun to seal the swing chamber. While achieving the goal of sealing, the extracting problems was brought. Based on the background of Defense Pre-research project, finite element method, elastic-plastic mechanics, and optimal design theory were used to research the principle of the sealing and extracting problems, which can not only provide theoretical foundation and design decision for engineering practice of such weapon systems, but a new way of thinking for solving the engineering-related problems. The main research content is as follows:
(1) The principle of a new-type swing chamber gun was analyzed, the key sealing area was found. The reliable criterion of the semi-combustible cartridge, the sealing time of the channel B, was established to judge the effect of the whole sealing system.
(2) The large-scale nonlinear FEA software ABAQUS was further developed with Python language, the design variables which had great impact on the extracting force were parameterized and the parametrical finite element model for the seal structure was created to achieve the automation of the optimization process.
(3) By studying the physical process of extracting ammunition, the main reason leading to the extracting problem was found. Meanwhile, the basic assumptions for the structure's material properties were proposed. The interaction between the cartridge and the chamber during the 3 stages, paste chamber, from paste chamber to maximum chamber pressure and unloading, was analyzed. The calculation model for the new-type gun was derived based on the static elastic-plastic theory. By comparing the finite element results, the model was verified reasonable. Through further discussion of the model, the two important ways, optimal materials and optimize design parameters, were found to reduce the extracting force.
(4) Based on the parametrical finite element model mentioned before, the mathematic model for the sealing structure was created, with the length, the thickness and the initial seal clearance as design variables, the reliable seal as restriction, the residual contact stress, the time for establishing a reliable seal and the mass of the sealing structure as objective. Meanwhile, the range of the 3 parameters and the "step" were determined from the engineering point of view. Finally, based on the multidisciplinary design optimization software mode-FRONTIER, the seal structure was optimized via combining multi-objective genetic algorithm and the response surface method. Check the effect of the optimal parameter compounding during the entire time domain, showing it satisfied the requirement.
(5) Taking the characteristic which nonlinear finite element requires a lot of time into account, the respond surface methodology was used in the optimization.3 plans were proposed based on RSM. Comparing the design of experiment (DOE), establishment and validation of response surface of the 3 plans, finally the programming orthogonal polynomial fitting method was selected as the only RSM in the paper. It is suggested that, the optimize method used in this paper guarantees balance between accuracy and efficiency, it is a promising design method for solving related engineering problem.
(1)分析了某型半可燃药筒火炮的密封机制,找到了其密封的关键区域,并在此基础之上建立起了该型半可燃药筒可靠密封的评判准则,即将密封通道B的密封开始时间作为整体密封效果的评判依据。同时,运用有限元动态响应分析的方法对密封结构的强度和闭气性等能进行了综合分析,揭示了密封问题和抽筒问题的内在联系,明确了在保证密封前提条件下,尽可能减小抽筒力的设计原则和目标。
(2)运用Python语言对非线性有限元软件ABAQUS进行了二次开发,将对抽筒力大小影响较大的设计变量进行参数化处理,从而建立起密封结构的参数化模型,为实现优化过程的自动化提供保证。
(3)通过对该型火炮抽筒物理过程的研究,确定了半可燃药筒残余接触力是导致抽筒困难的主要原因。同时,提出了针对该型火炮密封结构材料特性的基本假设,并对贴膛前、贴膛后至最大膛压、卸载三个阶段中,药筒与身管药室之间的相互作用情况进行了分析,推导了基于静态弹塑性理论的某型火炮抽筒力计算模型。通过与有限元计算结果对比,验证了模型的合理性。通过进一步对模型的讨论,确定了优选材料和优化半可燃药筒设计参数组合作为减小抽筒力的两个重要途径,同时,也为后续密封结构设计参数的优化工作提供了待优化设计变量。
(4)基于所建立的密封结构参数化模型,结合对抽筒力影响因素的分析,建立起以半可燃药筒密封结构的三个设计变量,即密封段长度、密封段厚度和初始间隙作为待优化的设计变量,以密封可靠作为约束前提条件,以密封时间最短、抽筒阻力最小、密封结构总质量最小为目标函数,适用于该型半可燃药筒密封结构的优化数学模型。同时,从工程实际的角度确定了这三个设计变量的取值范围及“步长”。最后,基于多学科优化集成软件平台mode-FRONTIER,对该优化模型进行了构建和计算,确定出了一组既满足密封要求,又可大幅减小抽筒力,同时密封段总质量不大的设计参数组合。
(5)针对动态非线性有限元计算需要占用大量机时的特点,在优化过程中引入了响应面方法。提出了三种基于响应面法的优化方案,并从设计试验、响应面模型的建立及检验等角度对这三种方案进行了比较分析,最终确定了自编程正交多项式拟合法作为响应面法在此文中应用的最终方案。采用响应面法和其他优化算法相结合的优化策略,可以兼顾计算精度和计算效率,为该类密封结构的优化设计提供一种新的思路。
The sealing technology of the swing chamber is one of the CTA gun's key Technologies. Semi-combustible cartridge structure was used in a new-type CTA gun to seal the swing chamber. While achieving the goal of sealing, the extracting problems was brought. Based on the background of Defense Pre-research project, finite element method, elastic-plastic mechanics, and optimal design theory were used to research the principle of the sealing and extracting problems, which can not only provide theoretical foundation and design decision for engineering practice of such weapon systems, but a new way of thinking for solving the engineering-related problems. The main research content is as follows:
(1) The principle of a new-type swing chamber gun was analyzed, the key sealing area was found. The reliable criterion of the semi-combustible cartridge, the sealing time of the channel B, was established to judge the effect of the whole sealing system.
(2) The large-scale nonlinear FEA software ABAQUS was further developed with Python language, the design variables which had great impact on the extracting force were parameterized and the parametrical finite element model for the seal structure was created to achieve the automation of the optimization process.
(3) By studying the physical process of extracting ammunition, the main reason leading to the extracting problem was found. Meanwhile, the basic assumptions for the structure's material properties were proposed. The interaction between the cartridge and the chamber during the 3 stages, paste chamber, from paste chamber to maximum chamber pressure and unloading, was analyzed. The calculation model for the new-type gun was derived based on the static elastic-plastic theory. By comparing the finite element results, the model was verified reasonable. Through further discussion of the model, the two important ways, optimal materials and optimize design parameters, were found to reduce the extracting force.
(4) Based on the parametrical finite element model mentioned before, the mathematic model for the sealing structure was created, with the length, the thickness and the initial seal clearance as design variables, the reliable seal as restriction, the residual contact stress, the time for establishing a reliable seal and the mass of the sealing structure as objective. Meanwhile, the range of the 3 parameters and the "step" were determined from the engineering point of view. Finally, based on the multidisciplinary design optimization software mode-FRONTIER, the seal structure was optimized via combining multi-objective genetic algorithm and the response surface method. Check the effect of the optimal parameter compounding during the entire time domain, showing it satisfied the requirement.
(5) Taking the characteristic which nonlinear finite element requires a lot of time into account, the respond surface methodology was used in the optimization.3 plans were proposed based on RSM. Comparing the design of experiment (DOE), establishment and validation of response surface of the 3 plans, finally the programming orthogonal polynomial fitting method was selected as the only RSM in the paper. It is suggested that, the optimize method used in this paper guarantees balance between accuracy and efficiency, it is a promising design method for solving related engineering problem.
引文
[1]陆欣,周彦煌,余永刚.埋头弹火炮的现状及发展趋势.火炮发射与控制学报,2002,2(31)：54-56.
[2]沈卫.埋头弹火炮及其弹药技术.现代军事,2004,19(37)：48-51.
[3]张浩,陆欣,余永刚,周彦煌.某口径埋头弹火炮的密封与装药设计.兵工学报,2006,4(27)：630-633.
[4]William J. Kelly and William D. Marcher. Cased Telescoped Ammunition Smart Seal Development, Army TACOM-ARDEC,2002.
[5]Michael J. Nusca, Albert W. Horst and James F. Newill. Simulations of Notional Telescoped Ammunition Propelling Charge, ARL-TR-3306,2004.
[6]Michael J. Nusca and Albert W. Horst Progress in Modeling Ignition in a Solid Propellant Charge for Telescoped Ammunition, ARL-TR-3673,2005.
[7]董巧云.埋头弹火炮内弹道实验与数值模拟.南京：南京理工大学,2007.
[8]彭旭东,王玉明,黄兴,李鲲.密封技术的现状与发展趋势.液压气动与密封,2009,4(23)：4-10.
[9]徐灏.密封.北京：冶金工业出版社,1999.
[10]龚雪婷,蔡纪宁,张秋翔,李双喜.金属W形密封环的弹塑性接触有限元分析.润滑与密封,2010,11(35)：82-85.
[11]杨春明,谢禹钧,韩春雨.基于Ansys的橡胶O形密封圈密封性能的有限元分析.石油与化工设备,2010,4(13)：21-24.
[12]于振波,蔡永梅,唐晓初.C形密封圈结构的有限元分析.石油化工设备,2008,2(37)：25-28.
[13]高朝鲜.大口径埋头弹内弹道设计和数值模拟.南京：南京理工大学,2009.
[14]张讯,张相炎.新型组合式炮膛密封结构的接触有限元分析.润滑与密封,2008,11(33)：69-72.
[15]张讯,张相炎.新型组合式炮膛密封结构仿真研究.弹道学报,2008,1(21)：63-66.
[16]武瑞文,顾克秋,张国栋.某自行加榴炮闭气结构非线性有限元分析.南京理工大学学报,2004,3(28)：261-264.
[17]张浩,周彦煌,林君毅.埋头弹火炮活动药室的组合自紧密封设计.火炮发射与控制学报,2005,2(21)：38-42.
[18]顾克秋,杨军荣.浮动炮闩闭气结构的强度和闭气性能分析.弹道学报,2003, 1(15)：17-20.
[19]孙兵晓,常新龙,胡成荣,马章海.固体火箭发动机密封结构随机有限元可靠性分析.火箭推进,2008,5(34)：22-26.
[20]顾克秋,钱林方,常秀英,李少峰.大口径火炮焊接药筒射击变形机理的启发式反演.爆炸与冲击,2004,6(24)：553-557.
[21]卫丰,张光.药筒发射应力和抽筒力的有限元分析.爆炸与冲击,2001,1(21)：72-75.
[22]侯保林,钱林方,于子平.大口径火炮抽筒故障分析.弹道学报,2002,2(14)：52-55.
[23]康艳祥,张以都,白绍鹏.自动武器抽筒过程仿真及抽筒力相关研究.计算机仿真,2007,3(24)：18-22.
[24]陈红磊,王文祥.药筒射击时出现卡壳原因分析及测试方法.兵工自动化,2010,1(29)：83-84.
[25]何清,田晓丽,陈国光.焊接药筒发射强度应力场分析.弹箭与制导,2006,1(26)：82-83.
[26]王慧霖,肖男.焊接钢质药筒表面处理质量与药筒退壳性关系的研究.太原重型机械学院学报,1999,2(20)：189-196.
[27]汪衡,韩卿,陶敏.焊接药筒发射强度分析及退壳力计算.国防技术基础,2009,7(35)：54-57.
[28]曾志银,宁变芳.抽筒力数值模拟.火炮发射与控制学报,2003,1(12)：44-47.
[29]钟同圣,卫丰,智友海等.Python语言和ABAQUS前处理二次开发.郑州大学学报(理学版),2006,1(2)：21-34.
[30]张国栋.结构优化与非线性有限元技术在炮闩闭气结构中的应用研究.南京：南京理工大学硕士论文,2002.
[31]马洪峰.迫击炮座钣的结构分析与优化设计.南京：南京理工大学硕士论文,2009.
[32]Roy Szweda. Contributing Editor.Tactile sensor interprets stress istribution and magnitude in O-rings and gaskets Sealing Technolo.2000.
[33]SYWoo, Y J Lee, I M Choi, B S Kim and H. Shin. Effects of the O-ring used for sealing in high-pressure balances on measurements of pressure. Korea Research Institute of Standards and Science,2003
[34]Veronica Argesanu, Lucian Madaras. MODEL AND ANALYSIS OF A MECHANICAL SEAL BY FINITE ELEMENT METHOD.INTERFACE TENSION DISTRIBUTION. Mechanics, Automatic Control and Robotics 2003,3(15).
[35]Itzhak Green and Capel English. STRESSES AND DEFORMATION OF COMPRESSED ELASTOMERIC O-RING SEALS.14th International Conference on Fluid Sealing,2004.
[36]Nosratollahi. Multidisciplinary design optimization of a reentry vehicle using genetic algorithm. Aircraft Engineering and Aerospace Technology,2010.
[37]Hussain, Z. Tokhi, M.O. Parameter Optimization of FES-Assisted Indoor Rowing Exercise Using MOGA. Asia Modelling Symposium. Proceedings 4th Asia International Conference on Mathematical Modelling and Computer Simulation, 2010.
[38]Hou, Tung-Hsu. An integrated MOGA approach to determine the Pareto-optimal kanban number and size for a JIT system. Expert Systems with Applications,2011.
[39]Shankar, Tumuluru Jaya, Sokhansanj, Shahab. A case study on optimization of biomass flow during single-screw extrusion cooking using genetic algorithm (GA) and response surface method (RSM). Food and Bioprocess Technology 2010.
[40]Azadi, Mohammad, Zahedi, Farshad. Multidisciplinary optimization of a car component under NVH and weight constraints using RSM. ASME International Mechanical Engineering Congress and Exposition,2010.
[41]Peter, J., Doloi, B., Bhattacharyya, B. Optimization of Nd:YAG Laser Marking of Alumina Ceramic Using RSM.2011.
[42]Lucian, G., Nicolae, Z. Mechanical packing (axial seal with sliding rings) study using finite element method with "ANSYS 9 WORKBENCH" program Journal of Marine Technology and Environment,2010.
[43]戴继双,马辉,孟磊,闻邦椿.大型离心压缩机转子系统结构参数优化设计.机电一体化技术,2009,8(36)：23-26.
[44]刘忠,刘莹,刘向锋.双螺旋槽端面密封结构参数的优化设计.中国科学,2007,7(37)：888-903.
[45]严云.基于ANSYS参数化设计语言的结构优化设计.华东交通大学学报,2004,4(21)：52-55.
[46]张国栋,顾克秋.基于遗传算法和参数化建模的非线性结构优化.计算力学学报,2003,6(20)：764-768.
[47]杨冬平,高卓,李文勇,李兆勇,翟东锋.基于APDL语言的喷砂罐结构参数优化设计.石油矿场机械,2007,4(36)：31-33.
[48]赵万军,张大可.ANSYS中基于参数化的液压机结构优化设计.机械设计与制造,2007,12(45)：6-8.
[49]石敬.减摇水舱优化设计与控制研究.哈尔滨：哈尔滨工程大学硕士论文,2008.
[50]赵旅.炮尾炮门结构的多目标优化及稳健设计.南京：南京理工大学硕士论文,2005.
[51]赵瑞学.某战车炮自动机关键技术研究.南京：南京理工大学博士论文,2011.
[52]戴磊.基于集成技术的开放式参数化结构形状优化设计平台.大连：大连理工大学博士论文,2008.
[53]戴春来.参数化设计理论的研究.南京：南京航空航天大学博士论文,2002.
[54]赵腾伦.ABAQUS6.6在工程机械中的应用.北京中国水利水电出版社,2007.
[55]王勖成.有限单元法.北京：清华大学出版社,2003.
[56]陈立周.稳健设计.北京：机械工业出版社,1999.
[57]杜正刚,李茂,金平,蔡国飙.大流量气-气喷嘴响应面法优化设计.北京航空航天大学学报,2010,4(36)：25-30.
[58]姜琬,金海波,孙卫平.基于多级响应面法的翼梢小翼气动优化设计.航空学报,2010,9(31)：1746-1750.
[59]李强,郭云健,李鹏辉,武云飞.一种基于响应面法的火炮身管设计参数灵敏度分析计算方法.火炮发射与控制学报,2010,3(23)：56-59.
[60]孙宝寿,吴真繁,陈哲.响应面法与遗传算法相结合的注塑工艺优化.中国机械工程,2010,9(21)：1115-1118.
[61]王延克,丁渭平,杜飞龙,何森东.基于响应面法的悬架结构改进及优化设计.机械科学与技术,2009,1(28)：10-14.
[62]张斌,张维刚,杨济匡,钟志华.基于响应面法的汽车侧撞安全性仿真优化.系统仿真学报,2009,12(21)：3850-3854.
[63]王仕松,郑坚,贾长治,崔英杰.基于响应面法的炮口制退器优化研究.机械工程与自动化,2010,6(16)：69-71.
[64]马东立,楚亮,张朔.基于响应面法的联结翼气动设计及优化.空气动力学学报,2010,1(28)：113-117.
[65]郝琪,杨林松,曹立波.基于响应面法的车身刚度特性的优化设计.机械科学与技术,2010,11(29)：1569-1577.
[66]潘翀.多元稳健设计方法及其应用研究.南京：南京理工大学硕士论文,2009.
[2]沈卫.埋头弹火炮及其弹药技术.现代军事,2004,19(37)：48-51.
[3]张浩,陆欣,余永刚,周彦煌.某口径埋头弹火炮的密封与装药设计.兵工学报,2006,4(27)：630-633.
[4]William J. Kelly and William D. Marcher. Cased Telescoped Ammunition Smart Seal Development, Army TACOM-ARDEC,2002.
[5]Michael J. Nusca, Albert W. Horst and James F. Newill. Simulations of Notional Telescoped Ammunition Propelling Charge, ARL-TR-3306,2004.
[6]Michael J. Nusca and Albert W. Horst Progress in Modeling Ignition in a Solid Propellant Charge for Telescoped Ammunition, ARL-TR-3673,2005.
[7]董巧云.埋头弹火炮内弹道实验与数值模拟.南京：南京理工大学,2007.
[8]彭旭东,王玉明,黄兴,李鲲.密封技术的现状与发展趋势.液压气动与密封,2009,4(23)：4-10.
[9]徐灏.密封.北京：冶金工业出版社,1999.
[10]龚雪婷,蔡纪宁,张秋翔,李双喜.金属W形密封环的弹塑性接触有限元分析.润滑与密封,2010,11(35)：82-85.
[11]杨春明,谢禹钧,韩春雨.基于Ansys的橡胶O形密封圈密封性能的有限元分析.石油与化工设备,2010,4(13)：21-24.
[12]于振波,蔡永梅,唐晓初.C形密封圈结构的有限元分析.石油化工设备,2008,2(37)：25-28.
[13]高朝鲜.大口径埋头弹内弹道设计和数值模拟.南京：南京理工大学,2009.
[14]张讯,张相炎.新型组合式炮膛密封结构的接触有限元分析.润滑与密封,2008,11(33)：69-72.
[15]张讯,张相炎.新型组合式炮膛密封结构仿真研究.弹道学报,2008,1(21)：63-66.
[16]武瑞文,顾克秋,张国栋.某自行加榴炮闭气结构非线性有限元分析.南京理工大学学报,2004,3(28)：261-264.
[17]张浩,周彦煌,林君毅.埋头弹火炮活动药室的组合自紧密封设计.火炮发射与控制学报,2005,2(21)：38-42.
[18]顾克秋,杨军荣.浮动炮闩闭气结构的强度和闭气性能分析.弹道学报,2003, 1(15)：17-20.
[19]孙兵晓,常新龙,胡成荣,马章海.固体火箭发动机密封结构随机有限元可靠性分析.火箭推进,2008,5(34)：22-26.
[20]顾克秋,钱林方,常秀英,李少峰.大口径火炮焊接药筒射击变形机理的启发式反演.爆炸与冲击,2004,6(24)：553-557.
[21]卫丰,张光.药筒发射应力和抽筒力的有限元分析.爆炸与冲击,2001,1(21)：72-75.
[22]侯保林,钱林方,于子平.大口径火炮抽筒故障分析.弹道学报,2002,2(14)：52-55.
[23]康艳祥,张以都,白绍鹏.自动武器抽筒过程仿真及抽筒力相关研究.计算机仿真,2007,3(24)：18-22.
[24]陈红磊,王文祥.药筒射击时出现卡壳原因分析及测试方法.兵工自动化,2010,1(29)：83-84.
[25]何清,田晓丽,陈国光.焊接药筒发射强度应力场分析.弹箭与制导,2006,1(26)：82-83.
[26]王慧霖,肖男.焊接钢质药筒表面处理质量与药筒退壳性关系的研究.太原重型机械学院学报,1999,2(20)：189-196.
[27]汪衡,韩卿,陶敏.焊接药筒发射强度分析及退壳力计算.国防技术基础,2009,7(35)：54-57.
[28]曾志银,宁变芳.抽筒力数值模拟.火炮发射与控制学报,2003,1(12)：44-47.
[29]钟同圣,卫丰,智友海等.Python语言和ABAQUS前处理二次开发.郑州大学学报(理学版),2006,1(2)：21-34.
[30]张国栋.结构优化与非线性有限元技术在炮闩闭气结构中的应用研究.南京：南京理工大学硕士论文,2002.
[31]马洪峰.迫击炮座钣的结构分析与优化设计.南京：南京理工大学硕士论文,2009.
[32]Roy Szweda. Contributing Editor.Tactile sensor interprets stress istribution and magnitude in O-rings and gaskets Sealing Technolo.2000.
[33]SYWoo, Y J Lee, I M Choi, B S Kim and H. Shin. Effects of the O-ring used for sealing in high-pressure balances on measurements of pressure. Korea Research Institute of Standards and Science,2003
[34]Veronica Argesanu, Lucian Madaras. MODEL AND ANALYSIS OF A MECHANICAL SEAL BY FINITE ELEMENT METHOD.INTERFACE TENSION DISTRIBUTION. Mechanics, Automatic Control and Robotics 2003,3(15).
[35]Itzhak Green and Capel English. STRESSES AND DEFORMATION OF COMPRESSED ELASTOMERIC O-RING SEALS.14th International Conference on Fluid Sealing,2004.
[36]Nosratollahi. Multidisciplinary design optimization of a reentry vehicle using genetic algorithm. Aircraft Engineering and Aerospace Technology,2010.
[37]Hussain, Z. Tokhi, M.O. Parameter Optimization of FES-Assisted Indoor Rowing Exercise Using MOGA. Asia Modelling Symposium. Proceedings 4th Asia International Conference on Mathematical Modelling and Computer Simulation, 2010.
[38]Hou, Tung-Hsu. An integrated MOGA approach to determine the Pareto-optimal kanban number and size for a JIT system. Expert Systems with Applications,2011.
[39]Shankar, Tumuluru Jaya, Sokhansanj, Shahab. A case study on optimization of biomass flow during single-screw extrusion cooking using genetic algorithm (GA) and response surface method (RSM). Food and Bioprocess Technology 2010.
[40]Azadi, Mohammad, Zahedi, Farshad. Multidisciplinary optimization of a car component under NVH and weight constraints using RSM. ASME International Mechanical Engineering Congress and Exposition,2010.
[41]Peter, J., Doloi, B., Bhattacharyya, B. Optimization of Nd:YAG Laser Marking of Alumina Ceramic Using RSM.2011.
[42]Lucian, G., Nicolae, Z. Mechanical packing (axial seal with sliding rings) study using finite element method with "ANSYS 9 WORKBENCH" program Journal of Marine Technology and Environment,2010.
[43]戴继双,马辉,孟磊,闻邦椿.大型离心压缩机转子系统结构参数优化设计.机电一体化技术,2009,8(36)：23-26.
[44]刘忠,刘莹,刘向锋.双螺旋槽端面密封结构参数的优化设计.中国科学,2007,7(37)：888-903.
[45]严云.基于ANSYS参数化设计语言的结构优化设计.华东交通大学学报,2004,4(21)：52-55.
[46]张国栋,顾克秋.基于遗传算法和参数化建模的非线性结构优化.计算力学学报,2003,6(20)：764-768.
[47]杨冬平,高卓,李文勇,李兆勇,翟东锋.基于APDL语言的喷砂罐结构参数优化设计.石油矿场机械,2007,4(36)：31-33.
[48]赵万军,张大可.ANSYS中基于参数化的液压机结构优化设计.机械设计与制造,2007,12(45)：6-8.
[49]石敬.减摇水舱优化设计与控制研究.哈尔滨：哈尔滨工程大学硕士论文,2008.
[50]赵旅.炮尾炮门结构的多目标优化及稳健设计.南京：南京理工大学硕士论文,2005.
[51]赵瑞学.某战车炮自动机关键技术研究.南京：南京理工大学博士论文,2011.
[52]戴磊.基于集成技术的开放式参数化结构形状优化设计平台.大连：大连理工大学博士论文,2008.
[53]戴春来.参数化设计理论的研究.南京：南京航空航天大学博士论文,2002.
[54]赵腾伦.ABAQUS6.6在工程机械中的应用.北京中国水利水电出版社,2007.
[55]王勖成.有限单元法.北京：清华大学出版社,2003.
[56]陈立周.稳健设计.北京：机械工业出版社,1999.
[57]杜正刚,李茂,金平,蔡国飙.大流量气-气喷嘴响应面法优化设计.北京航空航天大学学报,2010,4(36)：25-30.
[58]姜琬,金海波,孙卫平.基于多级响应面法的翼梢小翼气动优化设计.航空学报,2010,9(31)：1746-1750.
[59]李强,郭云健,李鹏辉,武云飞.一种基于响应面法的火炮身管设计参数灵敏度分析计算方法.火炮发射与控制学报,2010,3(23)：56-59.
[60]孙宝寿,吴真繁,陈哲.响应面法与遗传算法相结合的注塑工艺优化.中国机械工程,2010,9(21)：1115-1118.
[61]王延克,丁渭平,杜飞龙,何森东.基于响应面法的悬架结构改进及优化设计.机械科学与技术,2009,1(28)：10-14.
[62]张斌,张维刚,杨济匡,钟志华.基于响应面法的汽车侧撞安全性仿真优化.系统仿真学报,2009,12(21)：3850-3854.
[63]王仕松,郑坚,贾长治,崔英杰.基于响应面法的炮口制退器优化研究.机械工程与自动化,2010,6(16)：69-71.
[64]马东立,楚亮,张朔.基于响应面法的联结翼气动设计及优化.空气动力学学报,2010,1(28)：113-117.
[65]郝琪,杨林松,曹立波.基于响应面法的车身刚度特性的优化设计.机械科学与技术,2010,11(29)：1569-1577.
[66]潘翀.多元稳健设计方法及其应用研究.南京：南京理工大学硕士论文,2009.