基于响应面法的轻质尾翼均匀挤压成形数值模拟及模具结构优化

doi:10.12382/bgxb.2023.0187

摘要/Abstract

摘要：

针对轻质镁合金尾翼正挤压成形金属流动不均匀和力学性能各向异性大的问题,提出一种可调控金属均匀流动的金属蓄料池模具结构。基于Deform-3D有限元模拟分析,采用Box-Behnken响应曲面法以金属蓄料池结构参数:深度h、池壁距尾翼芯部型腔长度D₁、池壁距翼片型腔长度D₂和池壁与翼片型腔之间夹角α为变量,建立出模口金属流速均方差和成形载荷与金属蓄料池结构参数之间的响应关系。响应曲面分析结果表明:最佳的金属蓄料池结构参数为h=7mm,D₁=13mm,D₂=6mm,α=11°。采用优化后的模具结构参数进行模拟验证和物理试验,金属流动不均匀和力学性能各向异性均得到改善,并成功试制出形状尺寸和力学性能指标满足要求的尾翼形零件。

关键词: 尾翼构件, 均匀流动, 有限元模拟, 模具优化, Box-Behnken响应曲面

Abstract:

In order to solve the problems of non-uniform metal flow and large anisotropy of mechanical properties in forward extrusion forming of lightweight magnesium alloy empennage-shaped component, a metal reservoir die structure is proposedto regulate the uniform metal flow. Based on Deform-3D finite element simulation, the Box-Behnken response surface method is used to establish the response relationship among the mean square difference of metal flow velocity at the exit of die, the forming load and the structural parameters of metal reservoir by taking the depth of h, the length D₁ of metal reservoir tank wall from the empennage-shaped core cavity, the length D₂ of metal reservoir tank wall from the empennage-shaped cavity, and the angle α between the metal reservoir tank wall and the empennage-shaped cavity as variables. The results of response surface analysis show that the optimal structural parameters of metal reservoir are h=7mm, D₁=13mm, D₂=6mm, and α=11°. The inhomogeneity of metal flow and the anisotropy of mechanical properties are improvedand the empennage-shaped component with dimensions and mechanical properties that meet the requirements are successfully manufactured using the optimized die structure parameters.

Key words: empennage-shaped component, uniform flow, finite element simulation, die optimization, Box-Behnken response surface

中图分类号:

TG379

贾晶晶, 张治民, 于建民, 薛勇, 吴昂. 基于响应面法的轻质尾翼均匀挤压成形数值模拟及模具结构优化[J]. 兵工学报, 2024, 45(6): 1824-1839.

JIA Jingjing, ZHANG Zhimin, YU Jianmin, XUE Yong, WU Ang. Numerical Simulation of Uniform Extrusion Forming and Die Structure Optimization of Lightweight Empennage-shaped Component Based on Response Surface Method[J]. Acta Armamentarii, 2024, 45(6): 1824-1839.

图/表 26

图1 尾翼挤压件三维立体图

Fig.1 Three-dimensional map of the extrusion part of empennage-shaped component

图2 凹模结构及金属流动示意图

Fig.2 Schematic diagram of female die structure and metal flow

图3 不同温度和应变速率下AZ80+Ce合金的真应力应变曲线[23]

Fig.3 True stress-true strain curves of AZ80+Ce alloy at different temperatures and strain rates[23]

图4 有限元模型

Fig.4 Finite element model

图5 平面凹模结构金属流速分布

Fig.5 Metal flow velocity distribution of flat-surface female die structure

图6 平面凹模的金属流速分布图

Fig.6 Metal flow velocity distribution of flat-surface female die

图7 金属蓄料池凹模的金属流速分布图

Fig.7 Metal flow velocity distribution of female die structure with metal reservoir

图8 金属蓄料池凹模的等效应力分布图

Fig.8 Equivalent stress distribution maps of female die structure with metal reservoir

图9 平面凹模与优化后凹模成形载荷对比图

Fig.9 Comparison of forming loads of flat-surface female die and the optimized female die structure with “metal reservoir”

表1 平面凹模和不同深度金属蓄料池凹模不同步数对应的金属流动速度分布

Table 1 Metal flow velocity distributions for different steps of flat-surface female die structure and female die structure with metal reservoir

图10 不同深度“金属蓄料池”凹模对应的等效应变分布图

Fig.10 Equivalent strain distribution map of female die with metal reservoir with different depths

图11 不同深度金属蓄料池对应的等效应变和成形翼片端部高度差折线图

Fig.11 The equivalent strain and the line chart of height difference at the end of empennage vane of metal reservoir with different depths

图12 尾翼构件横截面示意图

Fig.12 Schematic diagram of cross section of empennage-shaped component

图13 正挤压棒材直筒部分和出模口受力分析

Fig.13 Stress analysis of straight tube part and die outlet of forward extrusion

表2 响应面试验因素与水平

Table 2 Analytical factors and levels for response surface methodology

水平	因素
水平	h/mm	D₁/mm	D₂/mm	α/(°)
1	3	6	6	1
2	6	10.5	9	6
3	9	15	12	11

表3 Box-Behnken 试验设计及试验结果

Table 3 Experimental design and results of Box-Behnken response surface analysis

组号	h/ mm	D₁/ mm	D₂/ mm	α/ (°)	$γ ¯$ / (mm·s^-1)	F/ MPa
1	3	10.5	9	1	1.91	258.4
2	6	6	9	11	3.10	253.6
3	6	10.5	12	11	1.65	250.3
4	9	10.5	9	1	1.46	251.4
5	6	10.5	9	6	1.88	251.5
6	6	6	12	6	2.28	248
7	9	15	9	6	1.61	252.1
8	9	10.5	12	6	1.39	246.1
9	6	10.5	9	6	2.24	250.3
10	3	10.5	6	6	2.14	257
11	6	10.5	9	6	0.98	253.8
12	6	15	12	6	2.11	321.7
13	6	15	9	1	1.68	366.7
14	6	15	6	6	0.99	251.2
15	3	15	9	6	3.94	253.7
16	6	10.5	6	1	2.13	259.2
17	9	10.5	9	11	1.76	258
18	6	10.5	9	6	2.47	256.7
19	6	6	9	1	2.14	252
20	6	10.5	9	6	1.18	256.3
21	6	10.5	6	11	0.78	247.8
22	9	10.5	6	6	1.33	251.4
23	3	6	9	6	3.67	255.1
24	6	15	9	11	0.97	248.5
25	9	6	9	6	2.84	260
26	3	10.5	9	11	2.77	255.9
27	3	10.5	12	6	2.01	251.2
28	6	10.5	12	1	1.89	248.2
29	6	6	6	6	3.24	256.7

表3 Box-Behnken 试验设计及试验结果

Table 3 Experimental design and results of Box-Behnken response surface analysis

组号	h/ mm	D₁/ mm	D₂/ mm	α/ (°)	$γ ¯$ / (mm·s^-1)	F/ MPa
1	3	10.5	9	1	1.91	258.4
2	6	6	9	11	3.10	253.6
3	6	10.5	12	11	1.65	250.3
4	9	10.5	9	1	1.46	251.4
5	6	10.5	9	6	1.88	251.5
6	6	6	12	6	2.28	248
7	9	15	9	6	1.61	252.1
8	9	10.5	12	6	1.39	246.1
9	6	10.5	9	6	2.24	250.3
10	3	10.5	6	6	2.14	257
11	6	10.5	9	6	0.98	253.8
12	6	15	12	6	2.11	321.7
13	6	15	9	1	1.68	366.7
14	6	15	6	6	0.99	251.2
15	3	15	9	6	3.94	253.7
16	6	10.5	6	1	2.13	259.2
17	9	10.5	9	11	1.76	258
18	6	10.5	9	6	2.47	256.7
19	6	6	9	1	2.14	252
20	6	10.5	9	6	1.18	256.3
21	6	10.5	6	11	0.78	247.8
22	9	10.5	6	6	1.33	251.4
23	3	6	9	6	3.67	255.1
24	6	15	9	11	0.97	248.5
25	9	6	9	6	2.84	260
26	3	10.5	9	11	2.77	255.9
27	3	10.5	12	6	2.01	251.2
28	6	10.5	12	1	1.89	248.2
29	6	6	6	6	3.24	256.7

表4 (流速均方差)响应面模型方差分析

Table 4 (Mean square deviation of flow velocity) Analysis of variance of response surface model

因素	平方和	自由度	均方差/ (mm·s^-1)	F/MPa	P
模型	24.62	14	1.28	6.95	<0.0001
A	3.45	1	3.45	11.48	<0.0001
B	3.15	1	3.15	11.17	<0.0001
C	0.04	1	0.04	0.14	0.718
D	0.01	1	0.01	0.01	0.9276
AB	0.78	1	0.78	4.8	0.0201
AC	0.01	1	0.01	0.03	0.8581
AD	0.08	1	0.08	0.24	0.6304
BC	3.09	1	3.09	9.37	<0.0001
BD	3.69	1	3.69	10.15	<0.0001
CD	0.31	1	0.31	0.96	0.3441
A²	3.05	1	3.05	9.25	<0.0001
B²	3.49	1	3.49	11.74	<0.0001
C²	0.27	1	0.27	0.85	0.3724
D²	0.18	1	0.18	0.56	0.4673

表5 (成形载荷)响应面模型方差分析

Table 5 (Forming load) Analysis of variance of response surface model

因素	平方和	自由度	均方差/ (mm·s^-1)	F/ MPa	P
模型	16808.17	24	900.34	287.09	<0.0001
A	6	1	6	0.7464	0.4363
B	3003.04	1	3003.04	373.42	<0.0001
C	18.06	1	18.06	2.25	0.2083
D	21.62	1	21.62	2.69	0.1764
AB	10.56	1	10.56	1.31	0.3157
AC	0.0625	1	0.0625	0.0078	0.934
AD	20.7	1	20.7	2.57	0.1839
BC	2568.16	1	2568.16	295	<0.0001
BD	3588.01	1	3588.01	446.16	<0.0001
CD	45.56	1	45.56	5.67	0.076
A²	8.39	1	8.39	1.04	0.3648
B²	2084.94	1	2084.94	259.26	<0.0001
C²	181.89	1	181.89	22.62	0.0089
D²	75.25	1	75.25	9.36	0.0377
A²B	1967.15	1	1967.15	229.74	<0.0001
A²C	0.845	1	0.845	0.1051	0.7621
A²D	22.44	1	22.44	2.79	0.1701
AB²	8.4	1	8.40	1.05	0.3644
AC²	4.2	1	4.20	0.5229	0.5096
B²C	617.76	1	617.76	76.82	0.0009
B²D	1939.16	1	1939.16	228.96	<0.0001
BC²	214.24	1	214.24	26.64	0.0067
A²B²	350.63	1	350.63	43.6	0.0027
A²C²	39.69	1	39.69	4.94	0.0905

图14 4因素关于流速均方差的响应曲面图

Fig.14 Response surface diagram of four factors on the mean square error of flow velocity

图15 4因素关于成形载荷的响应曲面图

Fig.15 Response surface diagram of four factors on the forming load

图16 仿真试验值与预测值的关系对应图

Fig.16 Correspondence diagram between simulated experimental value and predicted value

图17 优化的金属蓄料池凹模结构

Fig.17 Optimized “metal reservoir” die structure

图18 试验成形载荷

Fig.18 Physical experimental forming load

图19 成形实物图

Fig.19 Physical forming component maps

图20 翼片z轴和x轴方向的拉伸性能曲线

Fig.20 Tensile property curves along the z and x directions of empennage-shaped component

表6 沿z轴和x轴方向的拉伸性能

Table 6 Tensile properties along z and x directions

凹模	力学性能
凹模	拉伸方向	σ_s/MPa	R_m/MPa	δ/%
平面	z轴	159	292	11.6
	x轴	235	332	7.4
优化	z轴	192	313	9.5
	x轴	218	332	8.5

参考文献 28

[1]	ZHANG M X, WANG C, ZHANG S Y, et al. Enhanced aging precipitation behavior and mechanical properties of 6022 Al-Mg-Si alloy with Zr addition[J]. Materials Science and Engineering: A, 2022, 840:142957.
[2]	ZHAO J, JIANG B, YUAN Y, et al. Understanding the enhanced ductility of Mg-Gd with Ca and Zn microalloying by slip trace analysis[J]. Journal of Materials Science & Technology, 2021, 95(36):20-28.
[3]	AYER Ö. A forming load analysis for extrusion process of AZ31 magnesium[J]. Transactions of Nonferrous Metals Society of China, 2019, 29(4): 741-753. doi: 10.1016/S1003-6326(19)64984-8
[4]	陈亮, 刘荣忠, 郭锐, 等. 扭曲尾翼弹箭气动外形多目标优化[J]. 兵工学报, 2016, 37(7):1187-1193. doi: 10.3969/j.issn.1000-1093.2016.07.005
	CHEN L, LIU R Z, GUO R, et al. Multi-objective optimization on aerodynamic shape of projectilewith twisted empennages[J]. Acta Armamentarii, 2016, 37(7):1187-1193. (in Chinese)
[5]	鲍键, 李全安, 陈晓亚, 等. 挤压镁合金的研究进展[J]. 材料导报, 2022, 36(10):108-119.
	BAO J, LI Q A, CHEN X Y, et al. Research progress on extruded magnesium alloys[J]. Materials Review, 2022, 36(10):108-119. (in Chinese)
[6]	ZHANG Z, HE D H, XING X F, et al. Al and Zr addition to improve the hydrogen storage kinetics of Mg-based nanocomposites: synergistic effects of multiphase nanocatalysts[J]. Journal of Alloys and Compounds, 2023, 942: 169098.
[7]	LI B, WU J, TENG B G. Influences of the texture characteristic and interdendritic LPSO phase distribution on the tensile properties of Mg-Gd-Y-Zn-Zr sheets through hot rolling[J]. Acta Metallurgica Sinica (English Letters), 2021, 34(8):1051-1064.
[8]	ZHAO D J, LU S L, LI J Y. A novel continuous squeeze casting-extrusion process for grain refinement and property improvement in AZ31 alloy[J]. Materials Science and Engineering A, 2021, 808:1409-1422.
[9]	郑建新, 刘威成, 段玉涛. 7075铝合金二维超声挤压加工表面质量影响因素及其交互作用研究[J]. 兵工学报, 2017, 38(6):1231-1238. doi: 10.3969/j.issn.1000-1093.2017.06.024
	ZHENG J X, LIU W C, DUAN Y T. Interaction effects of processing parameters on surface quality of two-dimensional ultrasonically extruded 7075 aluminum alloy[J]. Acta Armamentarii, 2017, 38(6):1231-1238. (in Chinese)
[10]	张吉银, 姚倡锋, 谭靓, 等. 喷丸强化残余应力对疲劳性能和变形控制影响研究进展[J]. 机械工程学报, 2022, 58(1):1-15.
	ZHANG J Y, YAO C F, TAN L, et al. Research progress of the effect of shot peening residual stress on fatigue performance and deformation control[J]. Journal of Mechanical Engineering, 2022, 58(1):1-15. (in Chinese)
[11]	LEI D, DAI W L, WANG X Y, et al. Metal flow controlled by back pressure in the forming process of rib-web parts[J]. The International Journal of Advanced Manufacturing Technology, 2018, 97(5-8):1663-1672.
[12]	ZHENG K L, HE Z R, QU H T, et al. A novel quench-form and in-die creep age process for hot forming of 2219 thin aluminum sheets with high precision and efficiency[J]. Journal of Materials Processing Technology, 2023, 315:117931.
[13]	ZENG X, FAN X G, LI H W, et al. Die filling mechanism in flow forming of thin-walled tubular parts with cross inner ribs[J]. Journal of Manufacturing Processes, 2020, 58: 832-844.
[14]	刘惠, 刘腾飞, 陈宗强, 等. 基于试验设计和响应曲面法的大型带筋薄壁铝型材挤压工艺优化[J]. 锻压技术, 2022, 47(5):144-152. doi: 10.13330/j.issn.1000-3940.2022.05.022
	LIU H, LIU T F, CHEN Z Q, et al. Optimization on extrusion process for large reinforced thin-walled aluminum profile based on experimental design and response surface method[J]. Forming & Stamping Technology, 2022, 47(5):144-152. (in Chinese)
[15]	周晓远, 陈文琳, 潘鹏林, 等. 空心薄壁铝型材挤压数值模拟与模具优化设计[J]. 模具工业, 2018, 44(12):58-65.
[28]	LIU Q K, ZHAO P, WU D Y, et al. The analysis of the force on the sealing edge of cubic anvil high-pressure apparatus based on the principal stress method[J]. Superhard Material Engineering, 2019, 31(6):16-18. (in Chinese)
[29]	吴昂, 吴莹, 李国俊, 等. 基于响应曲面法的大型锥形件缩口成形工艺设计及多几何参数优化[J]. 机械工程学报, 2019, 55(24):83-92. doi: 10.3901/JME.2019.24.083
	WU A, WU Y, LI G J, et al. Process design and multi-geometric parameter optimization of large cones based on response surface methodology[J]. Journal of Mechanical Engineering, 2019, 55(24):83-92. (in Chinese) doi: 10.3901/JME.2019.24.083
[15]	ZHOU X Y, CHEN W L, PAN P L, et al. Numerical simulation and the die optimization design of hollow thin-wall aluminum extrusion[J]. Die & Mould Industry, 2018, 44(12):58-65. (in Chinese)
[16]	刘志文, 李落星, 符纯明, 等. 薄壁中空型材分流模挤压缺陷产生机理及出口流速精确控制[J]. 中国有色金属学报, 2021, 31(4):917-930.
	LIU Z W, LI L X, FU C M, et al. Defects formation mechanism and precision control of exit flow velocity in porthole die extrusion of hollow thin-walled aluminum profile[J]. The Chinese Journal of Nonferrous Metals, 2021, 31(4):917-930. (in Chinese)
[17]	管志新. 铝挤压分流模结构优化及配套切刀设计[D]. 烟台: 烟台大学, 2022.
	GUAN Z X. Structural optimization of aluminum extrusion porthole die and design of supporting cutter[D]. Yantai: Yantai University, 2022. (in Chinese)
[18]	朱俊瑞. 铝型材平面分流挤压模具分流桥的结构研究[D]. 烟台: 烟台大学, 2021.
	ZHU J R. Structure reseach for the porthole bridge of the aluminum profile extrusion porthole die[D]. Yantai: Yantai University, 2021. (in Chinese)
[19]	祝志荣, 洁琼, 邓汝荣. 大型铝合金矩形管分流模结构的优化改进[J]. 铝加工, 2020, 254(3):58-61.
	ZHU Z R, JIE Q, DENG R R. Improvement for die structure of the large Al alloy flat tube[J]. Aluminium Frbrication, 2020, 254(3):58-61. (in Chinese)
[20]	姜建堂, 范丁歌, 赵熊爔, 等. 大型铝合金构件制造全过程残余应力预测与控制[J]. 中国材料进展, 2022, 41(11):899-908.
	JIANG J T, FAN D G, ZHAO X X, et al. Whole process prediction-control of residual stress duringthe manufacturing of large aluminum alloy components[J]. Materials China, 2022, 41(11):899-908. (in Chinese)
[21]	高伟, 王雷刚, 黄瑶, 等. 基于Deform 3D的方管挤压模模桥结构优化研究[J]. 轻合金加工技术, 2017, 45(8):40-45.
	GAO W, WANG L G, HUANG Y, et al. Optimization of the porthole bridge structure in the square-tube extrusion die based on Deform 3D[J]. Light Alloy Fabrication Technology, 2017, 45(8):40-45. (in Chinese)
[22]	王少华, 刘惠, 陈宗强, 等. 大型带筋薄壁圆管铝型材挤压成形数值模拟[J]. 锻压技术, 2022, 47(4):181-189. doi: 10.13330/j.issn.1000-3940.2022.04.025
	WANG S H, LIU H, CHEN Z Q, et al. Numerical simulation on extrusion forming for large ribbed thin-walled circular tube aluminum profile[J]. Forming & Stamping Technology, 2022, 47(4):181-189. (in Chinese)
[23]	LI Z J, WANG J G, YAN R F, et al. Effect of Ce addition on hot deformation behavior and microstructure evolution of AZ80 magnesium alloy[J]. Journal of Materials Research and Technology, 2022, 16(1): 1339-1352
[24]	赵震, 沈大为, 曹益旗, 等. 基于卷积神经网络的板料挤压成形力预测[J]. 锻压技术, 2021, 46(9):76-84. doi: 10.13330/j.issn.1000-3940.2021.09.008
	ZHAO Z, SHEN D W, CAO Y Q, et al. Prediction on sheet metal extrusion forming force based on convolutional neural network[J]. Forming & Stamping Technology, 2021, 46(9):76-84. (in Chinese)
[25]	徐宁宁, 孙朝阳, 钱凌云, 等. 镁合金板形件扭-挤成形载荷的主应力法求解模型[J]. 机械工程学报, 2021, 57(4):73-82. doi: 10.3901/JME.2021.04.073
	XU N N, SUN C Y, QIAN L Y, et al. Solution model of principal stress method for torsion-extrusion forming load of magnesium alloy plate[J]. Journal of Mechanical Engineering, 2021, 57(4):73-82. (in Chinese) doi: 10.3901/JME.2021.04.073
[26]	颜宽然. 铝合金挤压型、棒材形状系数函数研究[J]. 轻合金加工技术, 1992, 16(11):31-34.
	YAN K R. Study on the shape coefficient function of aluminum alloy extrusion and bar[J]. Light Alloy Fabrication Technology, 1992, 16(11):31-34. (in Chinese)
[27]	JIANG J F, GE N, HUANG M J, et al. Numerical simulation of squeeze casting of aluminum alloy flywheel housing with large wall thickness difference and complex[J]. Transactions of Nonferrous Metals Society of China, 2023, 33(5):1345-1360.
[28]	刘乾坤, 赵鹏, 吴定雨, 等. 基于主应力法对六面顶压机密封边受力的分析[J]. 超硬材料工程, 2019, 31(6):16-18.