铝合金轮毂低压铸造凝固过程温度场数值模拟及模具工艺优化
|
摘要
铝合金轮毂与传统的钢轮毂相比,具有重量轻、散热性好、舒适性佳、节省油耗、外表美观等优点,已经得到广泛应用。低压铸造是生产铝合金轮毂的主要方法之一,它是一种近无余量铸造工艺,相比于传统铸造具有明显的优势,是铸造的发展方向之一。
金属凝固过程数值模拟是计算机在铸造生产中应用的核心内容,涉及铸造理论、凝固理论、传热学、工程力学、数值分析、计算机图形学等多种学科,是国际上公认的用计算机拓宽和促进铸造学科向前发展的学科前沿领域。对金属凝固过程进行数值模拟,可以大大提高模具的设计精度和可靠性,缩短设计周期。
本文针对某型号铝合金轮毂生产中常出现的缩孔、缩松等铸造缺陷问题,基于传热学及有限元理论,利用Pro/e进行实体造型及模具设计,然后利用ANSYS对铸造凝固过程进行数值模拟,最后通过正交实验对模具工艺进行优化。
根据传热学理论,铝合金轮毂凝固过程中系统的温度和系统内能随时间有明显的变化,凝固过程的相变问题需要考虑凝固潜热,铸件凝固过程热分析属于非线性的。同时针对该过程有限元的特点,进行了非线性瞬态温度场热传导有限元求解。
本文采用CAD软件Pro/e与CAE软件ANSYS相结合的方法,即采用Pro/e建立实体模型,利用ANSYS划分网格,建立有限元模型,并进行数值模拟。计算中,为兼顾计算精度与计算效率,对模型进行了适当的简化处理。
利用ANSYS热分析功能,对铝合金轮毂进行瞬态非线性温度场分析和计算机模拟仿真,发现轮毂轮辋与轮辐交接部位有明显的“孤岛缺陷”,模拟结果与实际生产吻合。通过正交实验的方法对模具工艺进行优化,选取对铸件成型过程影响较大的4个因素:侧模、下模、上模冷却水道中冷却水流动速度v_1、v_2、v_3以及侧模温度T,每个因素安排3个水平。最终得到最佳优化方案为:侧模、上模、下模冷却水流速分别为0.5m/s、1m/s、1m/s,同时侧模温度由初始方案的300℃降至200℃。并通过模拟仿真证明该组合对于抑制孤岛效应、改进铸件质量、提高生产效率、延长模具寿命具有重要意义。
Compared to traditional steel wheels,aluminum alloy wheel hub has some merits as light weight,good heat dissipation,well comfort,fuel savings,aesthetic appearance etc,so that it has been widely used.Low pressure die casting is one of the main method of producting aluminum alloy wheels,which is a near non-casting margin founding technics.Compared to traditional casting,low pressure die casting has obvious advantages,and it is one of the developmental direction of casting.
This papper is according to the existing problems in the process of a particular model aluminum alloy wheels' production,such as shrinkage cavity and porosity.This papper is based on the study of thethemral-delivering and finite element theory,by using of Pro/e for entity modeling and die design,then by using of ANSYS for the numerical simulation of casting solidification process.Finally,by the way of the orthogonal experiment to optimize the process of die.
According to thethemral-delivering theoy,the temperature and internal energy of the system are significantly variant during the casting solidification process.Considering the latent heat of solidification,the thermal alnalysis about casting solidification process of the aluminum cylinder heat isnon-linear and trnasient. At the same time,according to the process's finite element characteristics,finite element solution of the nonlinear transient temperature field has been carried out.
In this paper,using the method of combining CAD software Pro/e and CAE software ANSYS,that is using Pro/e to set up solid model and using ANSYS for mesh division and the finite element model's setting up,as well as the numerical simulation's carrying out.In calculations,considerring accuracy and computational efficiency,appropriate treatment has been taken to simplify the model.
Nonlinear transient temperature field analysis and computer simulation have been carried out with ANSYS's thermal analysis function.The results showed that 'isolated island defects' was founed in the middle of wheel rim and the spokes,and it coincide with the actual production.With the method of orthogonal experiment to optimize the tooling process,choose the the four larger impact factors of molding casting process as fllow:the cooling water's flow rate in lateral die,upper die and lower die,as well as the lateral die's temperature,each factor have three levels of organization.Finally,get the best optimization program as follows:the cooling water flow rate of lateral die,upper die and lower die are 0.5m/s,1m/s,1m/s,at the same time adjust the initial temperature of lateral die from 300℃to 200℃.Simulation result showed that this method can improve the quality of casting and production efficiency,as well as lengthen the life of die.
金属凝固过程数值模拟是计算机在铸造生产中应用的核心内容,涉及铸造理论、凝固理论、传热学、工程力学、数值分析、计算机图形学等多种学科,是国际上公认的用计算机拓宽和促进铸造学科向前发展的学科前沿领域。对金属凝固过程进行数值模拟,可以大大提高模具的设计精度和可靠性,缩短设计周期。
本文针对某型号铝合金轮毂生产中常出现的缩孔、缩松等铸造缺陷问题,基于传热学及有限元理论,利用Pro/e进行实体造型及模具设计,然后利用ANSYS对铸造凝固过程进行数值模拟,最后通过正交实验对模具工艺进行优化。
根据传热学理论,铝合金轮毂凝固过程中系统的温度和系统内能随时间有明显的变化,凝固过程的相变问题需要考虑凝固潜热,铸件凝固过程热分析属于非线性的。同时针对该过程有限元的特点,进行了非线性瞬态温度场热传导有限元求解。
本文采用CAD软件Pro/e与CAE软件ANSYS相结合的方法,即采用Pro/e建立实体模型,利用ANSYS划分网格,建立有限元模型,并进行数值模拟。计算中,为兼顾计算精度与计算效率,对模型进行了适当的简化处理。
利用ANSYS热分析功能,对铝合金轮毂进行瞬态非线性温度场分析和计算机模拟仿真,发现轮毂轮辋与轮辐交接部位有明显的“孤岛缺陷”,模拟结果与实际生产吻合。通过正交实验的方法对模具工艺进行优化,选取对铸件成型过程影响较大的4个因素:侧模、下模、上模冷却水道中冷却水流动速度v_1、v_2、v_3以及侧模温度T,每个因素安排3个水平。最终得到最佳优化方案为:侧模、上模、下模冷却水流速分别为0.5m/s、1m/s、1m/s,同时侧模温度由初始方案的300℃降至200℃。并通过模拟仿真证明该组合对于抑制孤岛效应、改进铸件质量、提高生产效率、延长模具寿命具有重要意义。
Compared to traditional steel wheels,aluminum alloy wheel hub has some merits as light weight,good heat dissipation,well comfort,fuel savings,aesthetic appearance etc,so that it has been widely used.Low pressure die casting is one of the main method of producting aluminum alloy wheels,which is a near non-casting margin founding technics.Compared to traditional casting,low pressure die casting has obvious advantages,and it is one of the developmental direction of casting.
This papper is according to the existing problems in the process of a particular model aluminum alloy wheels' production,such as shrinkage cavity and porosity.This papper is based on the study of thethemral-delivering and finite element theory,by using of Pro/e for entity modeling and die design,then by using of ANSYS for the numerical simulation of casting solidification process.Finally,by the way of the orthogonal experiment to optimize the process of die.
According to thethemral-delivering theoy,the temperature and internal energy of the system are significantly variant during the casting solidification process.Considering the latent heat of solidification,the thermal alnalysis about casting solidification process of the aluminum cylinder heat isnon-linear and trnasient. At the same time,according to the process's finite element characteristics,finite element solution of the nonlinear transient temperature field has been carried out.
In this paper,using the method of combining CAD software Pro/e and CAE software ANSYS,that is using Pro/e to set up solid model and using ANSYS for mesh division and the finite element model's setting up,as well as the numerical simulation's carrying out.In calculations,considerring accuracy and computational efficiency,appropriate treatment has been taken to simplify the model.
Nonlinear transient temperature field analysis and computer simulation have been carried out with ANSYS's thermal analysis function.The results showed that 'isolated island defects' was founed in the middle of wheel rim and the spokes,and it coincide with the actual production.With the method of orthogonal experiment to optimize the tooling process,choose the the four larger impact factors of molding casting process as fllow:the cooling water's flow rate in lateral die,upper die and lower die,as well as the lateral die's temperature,each factor have three levels of organization.Finally,get the best optimization program as follows:the cooling water flow rate of lateral die,upper die and lower die are 0.5m/s,1m/s,1m/s,at the same time adjust the initial temperature of lateral die from 300℃to 200℃.Simulation result showed that this method can improve the quality of casting and production efficiency,as well as lengthen the life of die.
引文
[1]张毅.铸造工艺CAD及其应用[M].北京:机械工业出版社,1994
[2]程军.计算机在铸造中的应用[M].北京:机械工业出版社,1993
[3]王君卿.国内外铸造工艺过程计算机数值模拟的发展[C].第九届中国铸造学术会议论文集.1997:362-374
[4]柳百成.铸造工艺计算机辅助设计研究进展[J].铸造.1999(8):40-45
[5]Jolly MR.Cost Benefits of Solidification Simulation to Foundry Users [J].Foundryman.1994(1):11
[6]杨宠,林汉同等.铸件凝固过程应力场数值模拟技术[J].热加工工艺.2001(1):40-42
[7]柳百成,荆涛等.铸造工程的模拟仿真与质量控制[M].北京:机械工业出版社,2001
[8]孔祥谦.有限单元法在传热学中的应用(第三版)[M].北京:科学出版社,1998
[9]张红松,张希俊,张方.铸造过程计算机数值模拟的国内外研究概况[J].昆明理工大学学报(理工版).2003(5):55-58
[10]杨全,张真.金属凝固与铸造过程数值模拟IM]。浙江大学出版社,1996
[11]Saeed Moaveui.有限元分析与ANSYS理论与应用[M].电子工业出版社,2004
[12]J.Henzel,J.Keveran.AFS.Cast Metals Research Journal[J].1965(1):19
[13]赵健,张毅.铸件凝固电子计算机数值模拟发展概况[J].铸造.1985(5):1-6
[14]R.D.Pehllie,A.Jeyarajan.Summary of Thermal Properties for Casting Alloy and Mould Materials[J].NTIS-PB83-211003,University of Michigan,Ann Arbor,MI.1982(2):111-120
[15]新山英辅,内田敏夫.铸物[M].1980
[16]李殿中.K417合金精铸叶片组织形成过程数值模拟与质量控制[D].哈尔滨工业大学工学博士学位论文.1998:2-7
[17]杨屹,蒋玉明.铸件凝固过程中热应力场及热裂的数值模拟研究分析[J].铸造技术.2000(2):36
[18]张毅.铸件凝固数值模拟及铸造工艺CAD现代进展[J].铸造.1987(6):8-12
[19]郭可韧等.大型铸件凝固过程的数字模拟[J].大连工学院学报.1980(2):1-16
[20]陈瑶.铸件凝固过程温度场、应力场数值模拟技术的研究[D].清华大学工学博士学位论文.1998:10-13
[21]董洁.锻造用钢锭凝固过程温度场、应力场的数值模拟及应用.西安建筑科技大学硕士学位论文.2005:1-3
[22]周洁,白杉.铝合金轮毂的市场_特点和制造工艺[J].铝加工.2006(3):43-44
[23]李双寿,吕朔,武汉琦.汽车用轻合金轮毂的发展及展望[C].第四届有色合金及特种铸造国际会议论文集.2005:143-149
[24]罗庚生,张志忠等.低压铸造[M].北京:国防工业出版社,1989
[25]王锡棋等.4Cr5MoSiV钢铝合金压铸模的真空高压冷热处理[J].金属热处理.1998(5):8-10
[26]R.Brreitler,J.Mayerhofer,Bohler Edelstahl Gmbh.Advanced Hot Work Tool Steels for Die Casting[C].Dies Proceeding of the First China International Die Casting Congress.1997:122-130
[27]Hattel JP,Anderson S,Henson P.Modeling of Thermal Induced Stresses in Die Casting Dies[C].Transaction of 17~(th) International Die Casting Congress and Exposition,North American Die Casting Association,Rosemon,USA.1993:52-58
[28]LIEURADE H P,DIASA,GIUSTI I,WSNIEWSKI A.Experimental Simulation and Theoretical Modeling of Crack Initiation and Propagation Due to Thermal Cycling[J].High Temperature Technology.1990(2):137-145
[29]JOHANSSON Borje,JONSSON Lennart,WORBYE Jjohn.Some Aspects on the Properties of QRO 80M and Die Casting Die Performance[C].SDCE 13~(th) International Die Casting Congress and Exposition,Milwaukee.1985:8
[30]卢险峰.模具学导论[M].北京:化学工业出版社,2007
[31]陈光明.压铸模CAD/CAE/CAM的现状与发展对策[J].模具技术.2003(5):44-49
[32]张国智,胡仁喜,陈继刚等.ANSYS10.0热力学有限元分析实例指导教程[M].北京:机械工业出版社,2007
[33]赵镇南.传热学[M].北京:高等教育出版社,2002
[34]孙蓟全,刘庆国.传热学[M].哈尔滨:东北林业大学出版社,1997
[35]熊守美,许庆彦,康进武.铸造过程模拟仿真技术[M].北京:机械工业出版社,2004
[36]陈海清,李华基,曹阳.铸件凝固过程数值模拟[M].重庆大学出版社,1991
[37]李景涌.有限元法[M].北京:北京邮电大学出版社,1999
[38]谭建国.使用ANSYS6.0进行有限元分析[M].北京:北京大学出版社,2002
[39]王庆五,左昉.ANSYS10.0机械设计高级应用实例[M].北京:机械工业出版社,2006
[40][美]laryl L.Logna著.有限元方法基础教程(第三版)[M].北京:电子工业出版社,2003
[41]宋勇,艾宴清,梁波.精通ANSYS7.0有限元分析[M].北京:清华大学出版社,2003
[42]张洪信.有限元基础理论与ANSYS应用[M].北京:机械工业出版社,2006
[43]高咏涛.ANSYS在结构分析中的应用及与CAD的连接[J].机械工程师.2005(8):77-78
[44]孙军.CAD与ANSYS的接口技术探讨[J].化工设备与管道.2004(2):55-57
[45]林建冬,原思聪,郑建校.基于Pro_E与ANSYS的CAD_CAE数据交换方法研究[J].工程机械.2007(8):32-36
[46]黄圣杰.Pro/En neer2001高级开发实例[M].北京:电子工业出版社,2001
[47]李翔鹏.Pro/ENGINEER野火版3.0自学手册:模具设计篇[M].人民邮电出版社,2006
[48]林清安.Pro/ENGINEER 20001模具设计[M].北京:清华大学出版社,2004
[49]潘晓涛,贺伯平,阳林,邓超权.汽车铝合金轮毂低压铸造模具设计[J].模具设计.2005(9):34
[50]赵玉涛.铝合金车轮制造技术[M].北京:机械工业出版社,2004
[51]ANSYS,Inc.Connection User Guide[G]
[52]ANSYS,Inc.ANSYS Modeling and Meshing Guid[G]
[53]林慧国,火树鹏,马绍弥.模具材料应用手册[M].北京:机械工业出版社,2004
[54]黄伯云等.中国材料工程大典,第4卷,有色金属材料工程[M].北京:化学工业出版社,2006
[55]张国智,胡仁喜,陈继刚等.ANSYS10.0热力学有限元分析实例指导教程[M].北京:机械工业出版社,2007
[56]En-Gang Wang,Ji-Cheng He.Finite element numerical thermo-mechanical behavior of steel billet in continuous casting mold[J].Science Technolgy of Advance Material,2001(2):257-263
[57]Hetu.J.F,Gao.D.M,Kabanemi.K.Ketal.Numerical Modeling of Casting Processes[J].Advanced Performance Materials,1998(5):65-82
[58]杨世铭,陶文铨.传热学(第3版)[M].北京:高等教育出版社,1998
[59](美)弗兰克P,英克鲁佩勒等.传热和传质基本原理[M].北京:化学工业出版社,2007
[60](德)W.瓦格纳,A.克鲁泽.水和蒸汽的性质[M].北京:科学出版社,2003
[61]valle M,Belingardi G,Cavato rta M P,etc.Casting defects and fatigue strength of a die cast aluminum alloy acomparison between standard specimens and production components[J].In ternational Journal of Fatigue.2002(1):1-9
[62]田胜元,萧曰嵘,实验设计与数据处理[M].武汉:中国建筑工业出版社,2005
[63]方开泰,马长兴.正交与均匀实验设计[M].北京:科学出版社,2001
[64]陈立周.稳健设计[M].北京:科学出版社,2000
[65](日)奥野忠一,芳鹤敏郎.实验设计方法.北京:机械工业出版社,1985.
[66]苏大为.铝合金汽车轮毂低压铸造过程的数值模拟及工艺优化[D].江苏大学工学硕士学位论文.2008:84-85
[67]B.Zhang,D.M.Maijer,S.L.Cockcroft.Development of a 3-D thermal model of the low-pressure die-cast(LPDC) process of A356 aluminum alloy wheels[J].Materials Science and Engineering.2007(A464):295-305
[68]Shepel SV,Paolucci S.Numerical simulation of falling and solidification of permanent mold castings[J].ApplThermEng.2007(22):229-248
[2]程军.计算机在铸造中的应用[M].北京:机械工业出版社,1993
[3]王君卿.国内外铸造工艺过程计算机数值模拟的发展[C].第九届中国铸造学术会议论文集.1997:362-374
[4]柳百成.铸造工艺计算机辅助设计研究进展[J].铸造.1999(8):40-45
[5]Jolly MR.Cost Benefits of Solidification Simulation to Foundry Users [J].Foundryman.1994(1):11
[6]杨宠,林汉同等.铸件凝固过程应力场数值模拟技术[J].热加工工艺.2001(1):40-42
[7]柳百成,荆涛等.铸造工程的模拟仿真与质量控制[M].北京:机械工业出版社,2001
[8]孔祥谦.有限单元法在传热学中的应用(第三版)[M].北京:科学出版社,1998
[9]张红松,张希俊,张方.铸造过程计算机数值模拟的国内外研究概况[J].昆明理工大学学报(理工版).2003(5):55-58
[10]杨全,张真.金属凝固与铸造过程数值模拟IM]。浙江大学出版社,1996
[11]Saeed Moaveui.有限元分析与ANSYS理论与应用[M].电子工业出版社,2004
[12]J.Henzel,J.Keveran.AFS.Cast Metals Research Journal[J].1965(1):19
[13]赵健,张毅.铸件凝固电子计算机数值模拟发展概况[J].铸造.1985(5):1-6
[14]R.D.Pehllie,A.Jeyarajan.Summary of Thermal Properties for Casting Alloy and Mould Materials[J].NTIS-PB83-211003,University of Michigan,Ann Arbor,MI.1982(2):111-120
[15]新山英辅,内田敏夫.铸物[M].1980
[16]李殿中.K417合金精铸叶片组织形成过程数值模拟与质量控制[D].哈尔滨工业大学工学博士学位论文.1998:2-7
[17]杨屹,蒋玉明.铸件凝固过程中热应力场及热裂的数值模拟研究分析[J].铸造技术.2000(2):36
[18]张毅.铸件凝固数值模拟及铸造工艺CAD现代进展[J].铸造.1987(6):8-12
[19]郭可韧等.大型铸件凝固过程的数字模拟[J].大连工学院学报.1980(2):1-16
[20]陈瑶.铸件凝固过程温度场、应力场数值模拟技术的研究[D].清华大学工学博士学位论文.1998:10-13
[21]董洁.锻造用钢锭凝固过程温度场、应力场的数值模拟及应用.西安建筑科技大学硕士学位论文.2005:1-3
[22]周洁,白杉.铝合金轮毂的市场_特点和制造工艺[J].铝加工.2006(3):43-44
[23]李双寿,吕朔,武汉琦.汽车用轻合金轮毂的发展及展望[C].第四届有色合金及特种铸造国际会议论文集.2005:143-149
[24]罗庚生,张志忠等.低压铸造[M].北京:国防工业出版社,1989
[25]王锡棋等.4Cr5MoSiV钢铝合金压铸模的真空高压冷热处理[J].金属热处理.1998(5):8-10
[26]R.Brreitler,J.Mayerhofer,Bohler Edelstahl Gmbh.Advanced Hot Work Tool Steels for Die Casting[C].Dies Proceeding of the First China International Die Casting Congress.1997:122-130
[27]Hattel JP,Anderson S,Henson P.Modeling of Thermal Induced Stresses in Die Casting Dies[C].Transaction of 17~(th) International Die Casting Congress and Exposition,North American Die Casting Association,Rosemon,USA.1993:52-58
[28]LIEURADE H P,DIASA,GIUSTI I,WSNIEWSKI A.Experimental Simulation and Theoretical Modeling of Crack Initiation and Propagation Due to Thermal Cycling[J].High Temperature Technology.1990(2):137-145
[29]JOHANSSON Borje,JONSSON Lennart,WORBYE Jjohn.Some Aspects on the Properties of QRO 80M and Die Casting Die Performance[C].SDCE 13~(th) International Die Casting Congress and Exposition,Milwaukee.1985:8
[30]卢险峰.模具学导论[M].北京:化学工业出版社,2007
[31]陈光明.压铸模CAD/CAE/CAM的现状与发展对策[J].模具技术.2003(5):44-49
[32]张国智,胡仁喜,陈继刚等.ANSYS10.0热力学有限元分析实例指导教程[M].北京:机械工业出版社,2007
[33]赵镇南.传热学[M].北京:高等教育出版社,2002
[34]孙蓟全,刘庆国.传热学[M].哈尔滨:东北林业大学出版社,1997
[35]熊守美,许庆彦,康进武.铸造过程模拟仿真技术[M].北京:机械工业出版社,2004
[36]陈海清,李华基,曹阳.铸件凝固过程数值模拟[M].重庆大学出版社,1991
[37]李景涌.有限元法[M].北京:北京邮电大学出版社,1999
[38]谭建国.使用ANSYS6.0进行有限元分析[M].北京:北京大学出版社,2002
[39]王庆五,左昉.ANSYS10.0机械设计高级应用实例[M].北京:机械工业出版社,2006
[40][美]laryl L.Logna著.有限元方法基础教程(第三版)[M].北京:电子工业出版社,2003
[41]宋勇,艾宴清,梁波.精通ANSYS7.0有限元分析[M].北京:清华大学出版社,2003
[42]张洪信.有限元基础理论与ANSYS应用[M].北京:机械工业出版社,2006
[43]高咏涛.ANSYS在结构分析中的应用及与CAD的连接[J].机械工程师.2005(8):77-78
[44]孙军.CAD与ANSYS的接口技术探讨[J].化工设备与管道.2004(2):55-57
[45]林建冬,原思聪,郑建校.基于Pro_E与ANSYS的CAD_CAE数据交换方法研究[J].工程机械.2007(8):32-36
[46]黄圣杰.Pro/En neer2001高级开发实例[M].北京:电子工业出版社,2001
[47]李翔鹏.Pro/ENGINEER野火版3.0自学手册:模具设计篇[M].人民邮电出版社,2006
[48]林清安.Pro/ENGINEER 20001模具设计[M].北京:清华大学出版社,2004
[49]潘晓涛,贺伯平,阳林,邓超权.汽车铝合金轮毂低压铸造模具设计[J].模具设计.2005(9):34
[50]赵玉涛.铝合金车轮制造技术[M].北京:机械工业出版社,2004
[51]ANSYS,Inc.Connection User Guide[G]
[52]ANSYS,Inc.ANSYS Modeling and Meshing Guid[G]
[53]林慧国,火树鹏,马绍弥.模具材料应用手册[M].北京:机械工业出版社,2004
[54]黄伯云等.中国材料工程大典,第4卷,有色金属材料工程[M].北京:化学工业出版社,2006
[55]张国智,胡仁喜,陈继刚等.ANSYS10.0热力学有限元分析实例指导教程[M].北京:机械工业出版社,2007
[56]En-Gang Wang,Ji-Cheng He.Finite element numerical thermo-mechanical behavior of steel billet in continuous casting mold[J].Science Technolgy of Advance Material,2001(2):257-263
[57]Hetu.J.F,Gao.D.M,Kabanemi.K.Ketal.Numerical Modeling of Casting Processes[J].Advanced Performance Materials,1998(5):65-82
[58]杨世铭,陶文铨.传热学(第3版)[M].北京:高等教育出版社,1998
[59](美)弗兰克P,英克鲁佩勒等.传热和传质基本原理[M].北京:化学工业出版社,2007
[60](德)W.瓦格纳,A.克鲁泽.水和蒸汽的性质[M].北京:科学出版社,2003
[61]valle M,Belingardi G,Cavato rta M P,etc.Casting defects and fatigue strength of a die cast aluminum alloy acomparison between standard specimens and production components[J].In ternational Journal of Fatigue.2002(1):1-9
[62]田胜元,萧曰嵘,实验设计与数据处理[M].武汉:中国建筑工业出版社,2005
[63]方开泰,马长兴.正交与均匀实验设计[M].北京:科学出版社,2001
[64]陈立周.稳健设计[M].北京:科学出版社,2000
[65](日)奥野忠一,芳鹤敏郎.实验设计方法.北京:机械工业出版社,1985.
[66]苏大为.铝合金汽车轮毂低压铸造过程的数值模拟及工艺优化[D].江苏大学工学硕士学位论文.2008:84-85
[67]B.Zhang,D.M.Maijer,S.L.Cockcroft.Development of a 3-D thermal model of the low-pressure die-cast(LPDC) process of A356 aluminum alloy wheels[J].Materials Science and Engineering.2007(A464):295-305
[68]Shepel SV,Paolucci S.Numerical simulation of falling and solidification of permanent mold castings[J].ApplThermEng.2007(22):229-248