空心铝合金型材挤压过程数值模拟及模具优化方法研究
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摘要
能源、环保、安全是关系到人类生存和发展的三大难题。由于铝合金型材产品具有重量轻、强度高、外形美观、易于回收等优点,因此,推广应用铝型材产品是缓解上述三大难题的重要途径之一。目前铝型材的品种规格不断增多,应用范围不断拓展,已由20世纪50~60年代民用建筑为主体,扩展到了机械制造、车辆、船舶、飞机、通讯等各个领域。
     挤压成形工艺是实现铝型材生产的关键技术,其工艺水平决定着型材制品的质量和模具的使用寿命。然而在实际生产中,挤压模具的设计和工艺参数的确定更多依赖设计师的经验,模具质量难以保证,需要多次试模和修模才能生产出合格产品。而采用数值仿真技术模拟实际的挤压过程,可以实时跟踪描述金属的流动行为,揭示金属的真实流动规律,获得速度、温度、应力、应变等实验现场难以测量的物理量,预测型材在挤压过程中可能出现的缺陷,并及时对模具结构及工艺参数进行调整,有效减少了试模修模次数,不仅能够提高挤压型材质量,同时也可降低生产成本,缩短模具生产周期。
     铝型材挤压成形是一个处在大变形、高温、高压、复杂摩擦条件下的非线性成形过程,涉及力学中的几何非线性和物理非线性,难以采用传统的测量和分析方法研究挤压模具型腔内材料的流动规律和变形机理。本文围绕空心铝型材挤压成形问题,采用数值仿真方法,对铝型材挤压成形工艺进行系统研究,总结模具结构参数和工艺参数对挤压成形过程的影响规律,建立挤压模具的多目标优化模型,开发挤压模具分流孔自动优化系统,探讨复杂大断面型材挤压模具的设计方法,并实验研究大断面型材的机械性能、内部组织缺陷及断裂机理。论文的主要研究工作和成果如下:
     (1)建立了空心铝型材稳态挤压过程的有限元模型,研究了挤压模具型腔内材料的流动规律及变形机理,获得了挤压模具结构(如焊合室级数、分流孔数量及布局等)和挤压工艺参数(如挤压比、挤压温度和挤压速度等)对材料流动、温度分布情况、焊缝质量、挤压力、模具磨损行为、模具受力状态及变形情况的影响规律。
     (2)建立了两种集成有限元模拟技术和人工智能算法为一体的挤压模具优化设计模型。在第一种优化模型中,以获得均匀的型材截面速度分布、最小的模具应力和模芯变形为目标,采用拉丁超立方法进行实验设计,并结合Kriging代理模型和基于Pareto法的多目标遗传算法对一异形空心型材挤压模具进行了优化设计。在第二种优化模型中,选取分流孔形状作为设计变量,结合Box-Behnken实验设计和响应曲面法,分别建立了以型材截面速度均方差、最大挤压力和型材截面最高温度为目标的预测模型,并利用粒子群算法实现了一多腔壁板型材挤压模具分流孔结构的优化设计。
     (3)基于各个分流孔通量与其所填充型材面积比的一致性原则,并结合稳态挤压过程的有限体积法,建立了挤压模具分流孔自动优化模型,开发了相应的计算程序。采用上述系统对模具型腔内的金属流动规律进行了模拟分析,并自动修改分流孔形状和位置,实现了模腔内金属的流动平衡。
     (4)建立了高速列车车体用材料AA6N01铝合金的本构方程,针对高速列车壁板型材,提出了一种数字化模具设计方法,解决了型材截面速度分布不均的问题,同时提高了型材的焊缝质量。通过测试发现,型材的尺寸精度、机械性能及内部组织均满足工程应用的要求。
Energy, environmental protection and security are three difficult problems that concern human existence and development. Because of its advantages of light weight, high strength, beautiful appearance, and ease of recycling, promoting the application of aluminum profiles is an important approach to alleviate the above problems. In recent years, the application scope of aluminum profiles has been expanded continuously. In the1950s and1960s, the aluminum profiles were mainly applied in civil architecture, but now it has been widely used in many fields, such as machinery manufacturing, traffic transportation, aviation, aerospace and communication, etc.
     Extrusion die structures and process parameters play a key role in aluminum profile production, which determine product quality and service life of extrusion die. Yet in practice, the die design and the selection of process parameters are mainly dependent on the experience and intuition of the die designer. Thus it is impossible to guarantee product quality and productivity, and many times of modifications and experiments should be undergone until the acceptable product is gained. On the contrary, the numerical simulation can describe the extrusion process on the computer and gain the information of stress state, strain state, temperature and velocity distribution of the aluminum profile, which are usually unmeasurable in the production field. In addition, with numerical simulation, one can predict the potential defects in the real extrusion process, so proper adjustments could be taken to the process parameters and die structures in time before the die is manufactured. Thus the numerical method can not only improve the profile quality, but also shorten the die design cycle and reduce the cost of production.
     Usually, the extrusion process is a non-linear one with large deformation, high temperature, high pressure and complex friction, thus the flow behavior of material and deformation mechanism in porthole die are difficult to investigate by means of traditional measurement techniques. In this paper, firstly, aluminum profile extrusion process is systematically investigated by means of numerical simulation, and the effects of extrusion die structures and process parameters on extrusion process are summarized. Secondly, the multi-objective optimization model for extrusion die is established, and the porthole automatic optimization system is developed. Thirdly, the extrusion die design method for wallboard profiles with large and complex cross-sections is presented, and its mechanical property, microstructure and fracture mechanism are investigated by experimental method. The main contents and conclusions in this paper are as follows:
     (1) Numerical simulation models of hollow aluminum profile extrusion process have been established on the basis of HyperXtrude software. The effects of extrusion die structures (the step of welding chamber, the number and layout of portholes, etc.) and process parameters (extrusion ratio, extrusion temperature, ram speed, etc.) on metal flow, temperature distribution, welding quality, extrusion load, die wear behavior, die stress status and deflection have been investigated. The metal flow rules and deformation mechanism in die cavity have been obtained.
     (2) Two optimization models for porthole extrusion dies based on modern intelligence algorithms have been established. In the first optimization model, choosing standard deviation of the velocity field, maximum die stress and mandrel deflection as optimization objectives, Pareto-based genetic algorithm with Kriging model is applied to optimize porthole extrusion die of irregular cross-section profile. In the second one, combining with Box-Behnken experimental design and response surface method, prediction models for standard deviation of the velocity field, maximum extrusion force and maximum temperature in the extrudate are established, and the porthole shape of the extrusion die is optimized by means of particle swarm optimization method.
     (3) Considering the consistency rule of the ratio of mass flux in each porthole to area of corresponding part of the extrudate, an automatic optimization program has been developed for porthole structure based on finite volume method during steady extrusion process. With the developed program, porthole shapes and locations could be adjusted and optimized by analyzing status of metal flow in die cavity.
     (4) The constitutive equation of AA6N01aluminum alloy used in high-speed train is established and die design methods for large and complex cross-section profiles are proposed. Through optimization design of extrusion die, the flow velocity distribution becomes more uniform and the weld quality of the extrudate is improved. Through experimental examinations, its dimensional accuracy, mechanical property and micro structure satisfy practical engineering requirements.
引文
[1]吴向红,赵国群,马新武,赵新海.模具锥角对铝型材挤压过程影响规律的研究[J].锻压装备与制造技术,2005,5:75-78.
    [2]赵云路,唐志玉.铝塑型材挤压成形技术[M].北京:机械工业出版社,2000.
    [3]陈泽中,娄臻亮,阮雪榆,包忠诩.复杂铝型材挤压成形有限体积仿真[J].上海交通大学学报,2005,39(1):27-40.
    [4]牟华.铝型材矩形管挤压模具的参数优化设计[D].东南大学硕士学位论文,2007.
    [5]胡龙飞.铝型材壁板挤压模具结构优化设计研究[D].合肥工业大学博士学位论文,2008.
    [6]刘静安.铝型材挤压模具设计,制造,使用及维修[M].北京:冶金工业出版社,2002.
    [7]蔡薇,柳瑞清.高温挤压变形的模拟试验研究[J].锻压技术,1999,1:8-9.
    [8]C.D. Smith. Numerical solutions of partial difference equations (finite difference methods)[M]. Oxford:Clarendon Press,1985.
    [9]R.D. Richtmyer, K.M. Morton. Difference methods for initial problems[M]. New York: Interscience Publishers,1967.
    [10]A.J. Baker. Finite element computational fluid mechanic[M]. New York:McGraw-Hill, 1983.
    [11]V. Girault, P. A. Raviart. Finite element methods for naver-storks squations[M]. Berlin: Springer,1986.
    [12]S.V. Patankar. Numerical heat transfer and fluid flow[M]. New York:Hemisphere Publishing Corporation,1980.
    [13]H.K. Versteeg, W. Malalasekera. An introduction to computational fluid dynamics:the finite volume method [M]. New York:Longman Scientific & Technical,1995.
    [14]J. Lof, A.H. van den Boogaard. Adaptive return mapping algorithms for J2 elasto-viscoplasitc flow[J]. International Journal for Numerical Methods in Engineering, 2001,51:1283-1298.
    [15]G. Li, J.T. Jinn. Recent development and applications of three-dimensional finite element modeling in bulk forming processes[J]. Journal of Materials Processing Technology,2001, 133:40-45.
    [16]赵国群.金属体积塑性成形过程数值模拟技术与仿真系统[J].金属成形工艺,2003,21(5):5-8.
    [17]闫洪,夏巨谌,胡国安,王高潮.双孔模型材挤压过程的有限元分析[J].塑性工程学报,2003,10(1):28-31.
    [18]X. Velay. Prediction and control of subgrain size in the hot extrusion of aluminium alloys with feeder plates[J]. Journal of Materials Processing Technology,2009,209:3610-3620.
    [19]R. Shivpuri, S. Momin. Computer-aided design of dies to control dimensional quality of extruded shaped[J]. Annals of the CIRP,1992,41:275-279.
    [20]H.W. Shin, D.W. Kim, N.S. Kim. A simplified three dimensional finite-element analysis of the non-axisymmetric extrusion processes[J]. Journal of Materials Processing Technology, 1993,38:567-587.
    [21]K.J. Bathe. Finite element procedures in engineering analysis[M]. Englewood Cliffs: Prentice-Hall,1982.
    [22]C.A.J. Computational techniques for fluid dynamic[J]. Berlin:Spring-Verlag,1991,15-132.
    [23]H.K. Versteeg, W. Malalasekera. An introduction to computational fluid dynamics—The finite volume method[M]. England:Longman Group Ltd,1995.
    [24]苏丹.有限体积法模拟金属塑性成形技术研究[D].上海交通大学硕士学位论文,2003.
    [25]周飞,苏丹,彭颖红,阮雪榆.有限体积法模拟铝型材挤压成形过程[J].中国有色金属学报,2003,13(1):65-70.
    [26]王锐,赵国群,吴向红,娄淑梅.基于非正交结构网格有限体积法的铝型材挤压过程数值模拟关键技术[J].塑性工程学报,2009,16(2):134-139.
    [27]S.M. Lou, G.Q. Zhao, R. Wang, X.H. Wu. Modeling of aluminum alloy profile extrusion process using finite volume method[J]. Journal of Materials Processing Technology,2008, 206(1-3):481-490.
    [28]J. Zhou, L. Li, J. Duszczyk. Computer simulated and experimentally verified isothermal extrusion of 7075 aluminium through continuous ram speed variation[J]. Journal of Materials Processing Technology,2004,146:203-212.
    [29]S.H. Kim, S.W. Chung, S. Padmanaban. Investigation of lubrication effect on the backward extrusion of thin-walled rectangular aluminum case with large aspect ratio[J]. Journal of Materials Processing Technology,2006,180:185-192.
    [30]R. Codina, G. Houzeaux, H. Coppola-Owen, J. Baiges. The fixed-mesh ALE approach for the numerical approximation of flows in moving domains[J]. Journal of Computational Physics,2009,228:1591-1611.
    [31]H.H. Wisselink, J. Huetink.3D FEM simulation of stationary metal forming processes with applications to slitting and rolling[J]. Journal of Materials Processing Technology,2004, 148:328-341.
    [32]M.S. Gadala, J. Wang. ALE formulation and its application in solid mechanics[J]. Computer methods in applied mechanics and engineering,1998,167:33-55.
    [33]张雄,陆明万,王建军.任意拉格朗日-欧拉描述法研究进展[J].计算力学学报,1997,14(1):91-102.
    [34]王尧,周照耀,潘健怡,刘亮,吴苑标.基于ALE有限元法的铝型材挤压成形的数值模拟[J].锻压技术,2010,35(1):149-153.
    [35]潘健怡,周照耀,王尧,吴苑标,谭炽东,陈合霭.复杂横截面铝型材挤压模具的设计与数值模拟分析[J].塑性工程学报,2010,17(1):46-51.
    [36]E.H. Atzema, J. Huetink. Finite element analysis of forward/backword extrusion using ALE techniques[A]. Proceedings of Iternational Conference of Numerical Methods in Industrial Forming Processes, NUMIFORM 95[C], Ithaca,1995:383-388.
    [37]H.G. Mooi. Simulation of complex aluminum extrusion using an arbitrary eulerian lagrangian formulation[A]. In Simulation of Materials Processing:Throry and Applications[C], Shen SF, Dawson PR(eds), Balkema:Rotterdam,1995:869-874.
    [38]H.N. Bayomi, M.S. Gadala. Simulation of large deformation problems using the arbitrary lagrangian-eulerian formulation[A]. Proceedings of the European Conference on Computational Mechanics, ECCM'99[C], Munchen,1999.
    [39]Y.S. Kang, D.Y. Yang. Rigid-viscoplastic finite element anlysis of hot square die extrusion of complicated profiles with flow guides and lands by arbitrary langrangian-eulerian formulation[A]. In Simulation of Materials Processing:Theory and Applications[C], Shen SF, Dawson PR (eds). Balkema:Rotterdam,1995:841-846.
    [40]G. Fang, J. Zhou, J. Duszczyk. FEM simulation of aluminium extrusion through two-hole multi-step pocket dies[J]. Journal of Materials Processing Technology,2009,209: 1891-1900.
    [41]L. Donati, L. Tomesani. The effect of die design on the production and seam weld quality of extruded aluminum profiles[J]. Journal of Material Processing Technology,2005, 164-165:1025-1031.
    [42]X.H.Wu, G.Q. Zhao, Y.G. Luan, X.W. Ma. Numerical simulation and die structure optimization of an aluminum rectangular hollow pipe extrusion process[J]. Materials Science and Engineering A,2006,435-436:266-274.
    [43]B.V. Mehtaa, I. Al-Zkeri, J.S. Gunasekera, A. Buijk.3D flow analysis inside shear and streamlined extrusion dies for feeder plate design[J]. Journal of Materials Processing Technology,2001,113:93-97.
    [44]J.M. Lee, B.M. Kim, C.C. Kang. Effects of chamber shapers of porthole die on elastic deformation and extrusion process in condenser tube extrusion[J]. Materials and Design, 2005,26:327-336.
    [45]Z. Peng, T. Sheppard. Simulation of multi-hole die extrusion[J]. Materials Science and Engineering A,2004,367:329-342.
    [46]K. Padmanathan, N. Thomas. Optimization of pocket design to produce a thin shape complex profile[J]. Production Engineering-Research and Development,2003,142: 23-241.
    [47]程磊,谢水生,黄国杰,和优锋.焊合室高度对分流组合模挤压成形过程的影响[J].稀有金属,2008,32(4):442-446.
    [48]黄克坚,包忠诩,陈泽中,朱永光.宽展挤压模具正交试验研究[J].锻压技术,2004,6:49-52.
    [49]L. Li, J. Zhou, J. Duszczyk. Prediction of temperature evolution during the extrusion of 7075 aluminium alloy at various ram speeds by means of 3D FEM simulation[J]. Journal of Materials Processing Technology,2004,145:360-370.
    [50]G. Liu, J. Zhou, J. Duszczyk. FE analysis of metal flow and weld seam formation in a porthole die during the extrusion of a magnesium alloy into a square tube and the effect of ram speed on weld strength[J]. Journal of Materials Processing Technology,2008,200: 185-198.
    [51]F.K. Chen, W.C. Chuang, S. Torng. Finite element analysis of multi-hole extrusion of aluminum-alloy tubes[J]. Journal of Materials Processing Technology,2008,201:150-155.
    [52]H.H. Jo, S.K. Lee, C.S. Jung, B.M. Kim. A non-steady state FE analysis of Al tubes hot extrusion by a porthole die[J]. Journal of Material Processing Technology,2006,173: 223-231.
    [53]A.F. Bastani, T. Aukrust, I. Skauvik. Study of flow balance and temperature evolution over multiple aluminum extrusion press cycles with HyperXtrude 9.0[J]. Key Engineering Materials,2010,424:257-264.
    [54]闫洪,夏巨谌,李志刚,董湘怀,杨国泰,何成宏.工艺参数对铝型材挤压变形规律的影响[J].中国有色金属学报,2002,12(6):1154-1161.
    [55]吴向红,赵国群,孙胜,娄淑梅,马新武.挤压速度和摩擦状态对铝型材挤压过程的影响[J].塑性工程学报,2007,14(1):36-41.
    [56]彭必友,殷国富,傅建,蔡鹏.铝型材挤出速度对模具磨损程度的影响[J].中国有色金属学报,2007,17(9):1453-1459.
    [57]傅建,彭必友,李军.铝型材挤出速度对模具工作带的影响[J].塑性工程学报,2005,12(3):27-30.
    [58]Z.Z. Chen, Z.L. Lou, X.Y. Ruan. Finite volume simulation and mould optimization of aluminum profile extrusion[J]. Journal of Materials Processing Technology,2007,190: 382-386.
    [59]L. Zou, J.C. Xia, X.Y. Wang, G.A. Hu. Optimization of die profile for improving die life in the hot extrusion process[J]. Journal of Materials Processing Technology,2003,142:659-664.
    [60]胡龙飞,刘全坤,王成勇,胡成亮.基于响应面模型的铝合金壁板挤压成形优化设计[J].中国机械工程,2008,19(13):1630-1633.
    [61]林高用,陈兴科,蒋杰,王芳,杨力斌.铝型材挤压模具工作带优化[J].中国有色金属学报,2006,16(4):561-566.
    [62]亢战,张洪武.挤压成形过程灵敏度分析及模具型腔参数优化设计[J].工程力学,2008, 25(2):235-240.
    [63]孙宪萍,王雷刚,黄瑶.挤压模具型腔的等磨损优化设计[J].润滑与密封,2007,32(1):56-59.
    [64]张金标,王泾文.热挤压工艺多元非线性回归与多目标优化技术研究[J].中国机械工程,2010,21(11):1338-1341.
    [65]舒洁,刘全坤,胡龙飞.铝合金挤压模具型腔曲线优化设计[J].合肥工业大学学报,2008,31(1):85-88.
    [66]D.Y. Yang, K. Park, Y.S. Kang. Integrated finite element simulation for the hot extrusion of complicated Al alloy profiles[J]. Journal of Materials Processing Technology,2001,111: 25-30.
    [67]P. Liu, S.S. Xie, L. Cheng. Die structure optimization for a large, multi-cavity alumimum profile using numerical simulation and experiments[J]. Materials and Design,2012,36: 152-160.
    [68]梁奕清,吴锡坤,黄珍媛.城市轨道交通铝合金车体型材挤压仿真技术研究[J].材料研究与应用,2010,4(2):132-136.
    [69]刘健.轨道列车车体型材用大型、复杂、精密挤压模具的研制[D].中南大学硕士学位论文,2011.
    [70]和优锋,谢水生,徐骏,程磊,黄国杰.大型复杂截面铝型材挤压过程数值模拟及模具结构的优化[J].材料研究与应用,2011,5(3):203.208.
    [71]汪明朴,王志伟,王正安,李周,尹志民等.地铁列车用7075铝合金力学性能及微光结构分析[J].中国有色金属学报,2001,11(6):1069-1073.
    [72]李学忠.地铁型材模具的探讨[J].金属成形工艺,2001,19(4):41-45.
    [73]刘静安,谢建新.大型铝合金型材挤压技术与工模具优化设计[M].北京:冶金工业出版社,2003.
    [74]程磊,谢水生,黄国杰,吴朋越,和优锋.分流组合模挤压过程的有限元分布模拟[J].系统仿真学报,2008,20(24):6603-6612.
    [75]M. Bauser, G. Sauer, K. Siegert. Extrusion[M]. Ohio:ASM International,2006.
    [76]吴向红,赵国群,赵新海,栾贻国,马新武.铝型材挤压成形过程数值模拟的研究现状及发展[J].系统仿真学报,2007,19(5):945-951.
    [77]J. Lof, Y. Blokhuis. FEM simulations of the extrusion of complex thin-walled aluminium sections[J]. Journal of Material Processing Technology,2002,122:344-354.
    [78]陈建中,熊计,吴悦梅,赖人铭,赵国忠.铝型材宽展挤压数值模拟及模具参数优化[J].轻合金加工技术,2009,37(1):43-46.
    [79]黄成华,许光明.铝合金圆棒挤压过程温度场模拟[J].轻合金加工技术,2008,36(9):27-30.
    [80]L. Li, H. Zhang, J. Zhou, J. Duszczyk, G.Y. Li, Z.H. Zhong. Numerical and experimental study on the extrusion through a porthole die to produce a hollow magnesium profile with longitudinal weld seams[J]. Materials and Design,2008,29:1190-1198.
    [81]刘长勇,张人估,颜永年,林峰,张磊.预应力钢丝缠绕部分-组合大型挤压筒的热应力分析[J].工程力学,2011,28(5):207-211.
    [82]M.K. Sinha, S. Deb, U.S. Dixit. Design of a multi-hole extrusion process[J]. Materials and Design,2009,30:330-334.
    [83]吴锡坤.铝型材加工实用技术手册[M].长沙:中南大学出版社,2006.
    [84]王桂龙,赵国群,李辉平,管延锦.薄壁注塑制品翘曲影响因素分析与工艺优化[J].中国机械工程,2009,20(4):488-492.
    [85]孙国栋,刘长华.薄壁塑件注射工艺参数的Taguchi方法优化[J].模具工业,2010,36(8):51-58.
    [86]王安麟,傅英超,刘瑜华,姜涛,刘广军.基于田口方法的电子连接器微颤振磨损自组织模型的优化[J].机械工程学报,2010,46(21):118-123.
    [87]K. Senthilkumar, P.S.S. Srinivasan. Application of taguchi method for the optimization of system parameters of centrifugal evaporative air cooler[J]. Journal of Thermal Science, 2010,19(5):473-479.
    [88]谢英,姬国华,刘萌萌,翟明.Taguci正交实验技术在微孔注塑中的应用[J].橡塑技术与装备,2009,35:7-10.
    [89]吴向红.铝型材挤压过程有限体积数值模拟及软件开发技术的研究[D].山东大学博士学位论文,2006.
    [90]J.L. Lin, K.S. Wang, B.H. Yan, Y.S. Tarng. Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics[J]. Journal of Materials Processing Technology,2000,102:48-55.
    [91]R.S. Lee, J.L. Jou. Application of numerical simulation for wear analysis of warm forging die[J]. Journal of Materials Processing Technology,2003,140:43-48.
    [92]刘静安,黄凯,谭炽东.铝合金挤压工模具技术[M].北京:冶金工业出版社,2009.
    [93]S. Kumar. Neural Networks[M].北京:清华大学出版社,2006.
    [94]玄光男,程润伟.遗传算法与工程优化[M].北京:清华大学出版社,2004.
    [95]J. Kennedy, R.C. Eberhart, Y. Shi. Swarm intelligence[M]. San Francisco:Morgan Kaufman Publishers,2001.
    [96]吴锡坤.铝型材加实用技术手册[M].长沙:中南大学出版社,2006.
    [97]袁志发,负海燕.试验设计与分析[M].北京:中国农业出版社,2002.
    [98]S. Sakata, F. Ashida, H. Tanaka. Stabilization of parameter estimation for Kriging-based approximation with empirical semivariogram[J]. Computer Methods in Applied Mechanics and Engineering,2010,199:1710-1721.
    [99]G. Dellino, P. Lino, C. Meloril, A. Rizzo. Kriging metamodel management in the design optimization of a CNG injection system[J]. Mathematics and Computers in Simulation, 2009,79:2345-2360.
    [100]K.D. Lee, K.Y. Kim. Surrogate based optimization of a laidback fan-shaped hole for film-cooling[J]. International Journal of Heat and Fluid Flow,2011,32:226-238.
    [101]张洪伟,张以都,赵晓慈.基于Kriging模型的喷丸强化残余应力场数值模拟[J].系统仿真学报,2011,23(4):826-831.
    [102]张崎,李兴斯.基于Kriging模型的结构可靠性分析[J].计算力学学报,2006,23(2):175-179.
    [103]S. Verma, C. Balaji. Multi-parameter estimation in combined conduction-radiation from a plane parallel participating medium using genetic algorithms [J]. International Journal of Heat and Mass Transfer,2007,50:1706-1714.
    [104]D. Copiello, G. Fabbri. Multi-objective genetic optimization of the heat transfer from longitudinal wavy fins[J]. International Journal of Heat and Mass Transfer,2009,52: 1167-1176.
    [105]W. Liu, Y.Y. Yang. Multi-objective optimization of sheet metal forning process using Pareto-based genetic algorithm[J]. Journal of Materials Processing Technology,2008,208: 499-506.
    [106]朱学军,陈彤,薛量,李峻.多个体参与交叉的Pareto多目标遗传算法[J].电子学报,2001,29(1):106-109.
    [107]童晶.多目标优化的Pareto解的表达与求取[D].武汉科技大学硕士学位论文,2009.
    [108]X.D. Wang, C. Hirsch, S. Kang, C. Lacor. Multi-objective optimization of turbomachinery using improved NSGA-Ⅱand approximation model[J]. Computer Method in Applied Mechanics and Engineering,2011,200:883-895.
    [109]A. Prakash, F.T.S. Chan, S.G. Deshmukh. FMS scheduling with knowledge based genetic algorithm approach[J]. Expert Systems with Applications,2011,38:3161-3171.
    [110]A. Behroozsarand, S. Shafiei. Multi-objective optimization of reactive distillation with thermal coupling using non-dominated sorting genetic algorithm-II[J]. Journal of Natural Gas Science and Engineering,2011,3:365-374.
    [111]C.K. Kwong, K.Y Chan, Y.C Tsim. A genetic algorithm based knowledge discovery system for design of fluid dispensing processes for electronic packaging[J]. Expert Systems with Applications,2009,36:3829-3838.
    [112]X.P. Li, G.Q. Zhao, Y.J. Guan, M.X. Ma. Multi-objective optimization of heating channels for rapid heating cycle injection mold using Pareto-based genetic algorithm[J]. Polymers advanced technologies,2010,21:669-678.
    [113]Y. Kuroki, G.S. Young, S.E. Haupt. Automatic identification of weather systems from numerical weather prediction data using genetic algorithm[J]. Expert Systems with Applications,2010,35:542-555.
    [114]郭洁,洪子雯,方晓玲Box-Behnken实验设计法优化表阿霉素脂质体的处理工艺[J].复旦学报医学版,2007,34(6):816-820.
    [115]J. Adamczyk, N. Horny, A. Tricoteaux, P.-Y. Jouan, M. Zadam. On the use of response surface methodology to predict and interpret the preferred c-axis orientation of sputtered AIN thin films[J]. Applied Surface Science,2008,254(6):1744-1750.
    [116]V.I. Vitanov, N. Javaid, D.J. Stephenson. Application of response surface methodology for the optimization of microfriction surfacing process[J]. Surface and Coatings Technology, 2010,204(21-22):3501-3508.
    [117]C.S. Zhang, G.Q. Zhao, H. Chen, Y.J. Guan. Optimization design of aluminium radiator extrusion die using response surface method[J]. Materials Research Innovations,2011,15: 288-290.
    [118]梁艳迁,赵震,吴彦骏,高崇晖,胡成亮.基于响应面的多工位锻造工艺优化[J].上海交通大学学报,2009,43(5):713-721.
    [119]贺连芳,赵国群,李辉平,相楠.基于响应曲面方法的热冲压硼钢 B1500HS淬火工艺参数优化[J].机械工程学报,2011,47(8):77-82.
    [120]周驰,高海兵,高亮,章万国.粒子群优化算法[J].计算机应用研究,2003,12:7-11.
    [121]谭文,刘振宇,吴迪,刘相华,王国栋.基于粒子群优化算法的热轧厚板工艺性能优化[J].轧钢.2007,24(1):15-18.
    [122]李宁,邹彤,孙德宝,秦元庆.基于粒子群的多目标优化算法[J].计算机工程与应用,2005,23:43-46.
    [123]Y. Zhang, L. Wang, Q. Kang, Q.D. Wu. Summary of particle swarm optimization and its improved algorithms[J]. Computer Engineering and Applications,2005,41(2):1-3.
    [124]C.A. Coello, G.T. Pulido, M.S. Lechuga. Handing multiple multiple objectives with particle swarm optimization[J]. IEEE Trans on Evolutionary Computation,2004,8(3):256-279.
    [125]闫洪,包忠诩,柳和生.铝型材挤压模CAD/CAE/CAM研究进展[J].轻合金加工技,1999,27(10):1-4.
    [126]闫洪,包忠诩,江雄心等.型材挤压成形技术的研究[J].锻压机械,1999,34(6):50-52.
    [127]李靖媛,黄东男.三孔双芯模挤压方管型材的金属流动行为分析[J].材料科学与工艺,2010,18(2):251-255.
    [128]郑弃非,石力开,谢水生.空心铝型材挤压时金属流动的计算机辅助(CAD)分析[J].轻合金加工技术,1997,25(2):22-27.
    []29]梁文华.关于薄壁多型孔空心模分流孔的设计[J].轻金属,1991,6:58-59.
    [130]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004.
    [131]M. Peric. Analysis of pressure-velocity coupling on nonorthogonal grids[J]. Numerical Heat Transfer Part B:Fundamentals,1990,17(1):63-82.
    [132]H. Xu, C. Zhang. Non-orthogonality for non-straggred grid—the results[J]. International Journal for Numerical Methods in Fluids,1999,29:625-644.
    [133]王锐.铝型材挤压非正交网格有限体积数值模拟关键技术研究[D].山东大学博士学位论文,2009.
    [134]钱立新.世界高速铁路技术[M].北京:中国铁道出版社,2003.
    [135]李芾,安琪.国内外高速动车组的发展[J].电力机车与城轨车辆,2007,30(5):1-5.
    [136]L. Donati, L. Tomesani. The prediction of seam welds quality in aluminum extrusion[J]. Journal of Material Processing Technology,2004,153-154:366-373.
    [137]彭建,周绸,张丁非.高速列车用6N01铝合金焊接接头的组织与性能[J].金属热处理,2010,35(11):33-36.
    [138]杨尚磊,孟立春,吕任远,陈强,王洪峰.高速车辆用A6N01铝合金的脉冲MIG焊[J].焊接,2008,9:33-35.