Numerical Simulation of Uniform Extrusion Forming and Die Structure Optimization of Lightweight Empennage-shaped Component Based on Response Surface Method

doi:10.12382/bgxb.2023.0187

Abstract

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

CLC Number:

TG379

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.

Figures/Tables 26

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

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

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

Fig.4 Finite element model

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fig.17 Optimized “metal reservoir” die structure

Fig.18 Physical experimental forming load

Fig.19 Physical forming component maps

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

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

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