基于Dual-Kriging模型的稳健设计方法在板料成形中的应用
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摘要
板料成形作为现代工业的一种非常重要的加工方法,用以生产各种板材零件,在航空航天、国防、汽车等领域得到了广泛的应用。随着数值模拟技术的不断发展,对板料成形进行有限元分析,可以缩短模具的生产周期和降低生产成本。然而,对于较为复杂的成形件,数值模拟需要耗费大量的时间,同时成形件在生产过程中受到工艺条件、材料性能等波动的影响,成形件的质量可能达不到要求。因此,需要对板料的成形过程进行稳健设计,使得板料成形质量对于工艺条件、材料性能等参数的波动不敏感。
将Kriging代理模型应用于板料成形优化中,可以减少板料成形数值模拟的时间,提高优化效率。结合灰色关联分析对Kring模型的随机分布部分中的θ值进行优化,在不增加样本点的情况下提高了Kriging模型的精度。将改进后的Kriging模型应用于NUMISHEET93会议中方盒件的成形缺陷的预测,与未优化的Kriging模型相比,模型的精度大大提高。
为了使得板料的成形质量对于工艺条件、材料性能等参数波动的不敏感,提出了基于Dual-Kriging的多目标稳健设计方法。筛选影响油底壳成形质量的可控以及噪声因子并且确定其相应的波动范围；基于有限元分析应用改进的Kriging模型建立可控与噪声因子与成形件质量的映射关系；根据参数波动,基于第一重Kriging模型、蒙特卡罗模拟得到成形质量的期望与方差,建立成形质量期望与方差的第二重Kriging模型；应用基于拥挤距离的多目标粒子群算法对稳健模型进行优化。结果表明,与传统确定性优化相比,成形件质量的波动范围明显减小,提高了成形件的稳健性。
As one of the important processing method in the modem industry, sheet metal forming is used to produce a variety of sheet metal parts and has been widely applied in aerospace, defense, automotive and other fields. With the continuous development of the numerical simulation technology, the cycle of the mold production and product cost can be shortened by using the finite element to analyze the sheet metal forming. However, for the more complex forming parts, numerical simulation takes too much time. At the same time, the quality of the forming parts will be below the standard, affected by the fluctuations of the process conditions and the material properties in the production process. Therefore, the robust design should be applied for the metal forming process. It will make the forming quality of the sheet be not sensitive to the process conditions, material properties and so on.
Kriging surrogate model is applied to optimize the sheet metal forming and it can reduce the time of the numerical simulation and enhance the optimization efficiency. The theta value of the random distribution of the Kriging model is optimized with the grey relational analysis and it can improve the accuracy of Kriging model without increasing the other sample points. Improved Kriging model is applied to predict the forming defects of the square box in Numisheet93. Compared to the unoptimized Kriging model, the accuracy of the model is greatly improved.
To make the forming quality of the sheet metal be not sensitive to the fluctuation of the process condition, the material properties and so on, the robust design based on the Dual-Kriging model is put forward. The controllable factors and noise factors which affect the forming quality are chosen and their corresponding fluctuation range is determined. The function of the controllable factors and noise factors and quality of the forming parts is established using the improved Kriging model based on the numerical simulation. The second layer Kriging model of the forming quality and variance is built based on the first layer Kriging model and Monte Carlo simulation according to the parameters fluctuation. The robust model is optimized with the multi-objective particle swarm optimization algorithm based on the crowding distance. The result shows that, compared to the traditional deterministic optimization, the fluctuation range of the quality of the forming part is effectively reduced and the robustness is improved.
将Kriging代理模型应用于板料成形优化中,可以减少板料成形数值模拟的时间,提高优化效率。结合灰色关联分析对Kring模型的随机分布部分中的θ值进行优化,在不增加样本点的情况下提高了Kriging模型的精度。将改进后的Kriging模型应用于NUMISHEET93会议中方盒件的成形缺陷的预测,与未优化的Kriging模型相比,模型的精度大大提高。
为了使得板料的成形质量对于工艺条件、材料性能等参数波动的不敏感,提出了基于Dual-Kriging的多目标稳健设计方法。筛选影响油底壳成形质量的可控以及噪声因子并且确定其相应的波动范围；基于有限元分析应用改进的Kriging模型建立可控与噪声因子与成形件质量的映射关系；根据参数波动,基于第一重Kriging模型、蒙特卡罗模拟得到成形质量的期望与方差,建立成形质量期望与方差的第二重Kriging模型；应用基于拥挤距离的多目标粒子群算法对稳健模型进行优化。结果表明,与传统确定性优化相比,成形件质量的波动范围明显减小,提高了成形件的稳健性。
As one of the important processing method in the modem industry, sheet metal forming is used to produce a variety of sheet metal parts and has been widely applied in aerospace, defense, automotive and other fields. With the continuous development of the numerical simulation technology, the cycle of the mold production and product cost can be shortened by using the finite element to analyze the sheet metal forming. However, for the more complex forming parts, numerical simulation takes too much time. At the same time, the quality of the forming parts will be below the standard, affected by the fluctuations of the process conditions and the material properties in the production process. Therefore, the robust design should be applied for the metal forming process. It will make the forming quality of the sheet be not sensitive to the process conditions, material properties and so on.
Kriging surrogate model is applied to optimize the sheet metal forming and it can reduce the time of the numerical simulation and enhance the optimization efficiency. The theta value of the random distribution of the Kriging model is optimized with the grey relational analysis and it can improve the accuracy of Kriging model without increasing the other sample points. Improved Kriging model is applied to predict the forming defects of the square box in Numisheet93. Compared to the unoptimized Kriging model, the accuracy of the model is greatly improved.
To make the forming quality of the sheet metal be not sensitive to the fluctuation of the process condition, the material properties and so on, the robust design based on the Dual-Kriging model is put forward. The controllable factors and noise factors which affect the forming quality are chosen and their corresponding fluctuation range is determined. The function of the controllable factors and noise factors and quality of the forming parts is established using the improved Kriging model based on the numerical simulation. The second layer Kriging model of the forming quality and variance is built based on the first layer Kriging model and Monte Carlo simulation according to the parameters fluctuation. The robust model is optimized with the multi-objective particle swarm optimization algorithm based on the crowding distance. The result shows that, compared to the traditional deterministic optimization, the fluctuation range of the quality of the forming part is effectively reduced and the robustness is improved.
引文
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[3]龚红英.板料成形CAE实用教程[M].北京：化学工业出版社,2010
[4]苏春建,于涛.金属板材成形CAE分析及应用[M].北京：国防工业出版社,2011
[5]李玉强,崔振山,张冬娟,等.板料成形优化技术进展与质量工程研究[J].塑性工程学报,2005,12(2)：11-16
[6]谢延敏,于沪平,陈军,等.基于代理模型的板料成形优化技术进展[J].塑性工程学报,2006,13(2)：20-24
[7]林忠钦,艾健,张卫国,等.冲压稳健设计方法及其应用[J].塑性工程学报,2004,11(4)：56-60
[8]谢延敏,于沪平,陈军,等.韧性断裂准则在板料成形中应用研究进展[J].哈尔滨工业大学学报,2009,41(1)：169-173
[9]孙光永,李光耀,张勇,等.基于有限元的板料拉延成形质量评价准则及工艺参数优化研究[J].固体力学学报,2009,30(1)：70-77
[10]赵茂俞,薛克敏,李萍.多目标质量的覆盖件成形工艺参数优化[J].机械工程学报,2009,45(8)：276-282
[11]Lematire J. Continuous Damage Mechanics Model for Ductile Fracture[J]. Journal of Engineering Materials and Technology,1985,107(1):83-89
[12]Oyane M, Sato T, Okimoto K, et al. Criteria for ductile fracture and their applications[J]. Journal of Mechanical Working Technology,1980,4(1):65-81
[13]Cockcroft M..G, Latham D.J. Ductility and the workability of Metals[J]. Journal of the Institute of Metals,1968,96:33-39
[14]余心宏,瞿妮芝,瞿江波.基于Oyane韧性断裂准则的板料成形极限预测[J].材料科学与工艺,2009,17(5)：738-740
[15]谢延敏.基于Kriging模型和灰色关联分析的板料成形工艺稳健优化设计研究[D].上海：上海交通大学,2007
[16]崔令江,杨玉英,朱玉萍.利用神经网络构建方盒件成形数值模拟模型[J].塑性工程学报,2005,12(1)：20-23
[17]韩飞,莫健华,龚攀.基于遗传神经网络的数字化渐进成形回弹分析[J].华中科技大学学报,2008,36(1)：121-124
[18]阳湘安,沅峰.车身覆盖件回弹控制的成形工艺多目标优化[J].上海交通大学学报,2011,45(11)：1673-1683
[19].张剑,陈文亮,鲍益东.基于响应面近似模型的拉延筋优化[J].南京航空航天大学学报,2012,44：97-100
[20]张峻,柯映林.基于动态序列响应面方法的钣金成形过程参数优化[J].中国机械工程,2005,16(4)：307-310
[21]谢延敏,徐笑梅,罗征志.基于Kriging模型的翻边成形参数优化[J].塑性工程学报,2010,17(5)：4-9
[22]卿启湘,陈哲吾,文桂林.基于Kriging插值的汽车行李箱盖冲压成形参数的优化设计[J].中国机械工程,2011,22(17)：2122-2126
[23]陈立周.稳健设计.机械工业出版社,1999
[24]陈永亮,刘双,王汉涛,等.基于Kriging代理模型的主轴箱稳健设计[J].天津大学学报,2011,44(12)：1111-1117
[25]高月华.基于Kriging代理模型的优化设计方法及其在注塑成形中的应用[D].大连：大连理工大学,2009
[26]黄风立,林建平,钟美鹏,等.注塑成型工艺多目标稳健设计及优化算法[J].同济大学学报,2011,39(2)：287-298
[27]潘尔顺,徐小芸.基于有限元法与田口法的V型件冲压仿真参数稳健设计[J].上海
交通大学学报,2005,39(7)：1077-1081
[28]申丽娟,杨军,赵宇.基于方差传递模型的飞机蒙皮拉形工艺稳健设计[J].机械工程学报,2011,47(1)：145-151
[29]孙光永,李光耀,陈涛,等.基于6σ的稳健优化设计在薄板冲压成形中的应用[J].机械工程学报,2008,44(11)：248-254
[30]Bo Hou, Wurong Wang, Shuhui Li. Stochastic analysis and robust optimization for a deck lid inner panel stamping [J]. Materials and Design,2010,31:1191-1199
[31]汤禹成,陈军.基于支持向量机和重要度抽样的高强度钢板冲压成形工艺稳健设计[J].材料科学与工艺,2010,18(5)：735-740
[32]王武荣,游洁,张新鹏,等.基于材料性能波动统计学分析的特征件冲压成形稳健设计[J].上海交通大学学报,2011,45(1)：1-5
[33]李人宪.有限元基础[M].北京：国防工业出版社,2009
[34]童宏永.U形件弯曲回弹的数值模拟[D].天津：河北工业大学,2006
[35]陈文亮.板料成形CAE分析教程[M].北京：机械工业出版社,2005
[36]刘继涛,刘飞,张为华Kriging模型在固体火箭发动机装药可靠性分析中的应用[J].航空动力学报,2010,25(1)：193-197
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