Optimization of multi⁃objective parameters for double color injection⁃molding based on grey relational analysis and entropy weight method

doi:10.19491/j.issn.1001-9278.2022.07.016

Abstract

Abstract:

Taking a double color plastic bowl as an example， a multi?objective optimization analysis was carried out in this paper. The mold temperature， melt temperature， and holding time of the first injection and the second injection were selected as factor variables. The average volume?shrinkage and total warpage rates of the second injection were selected as optimization indexes. The orthogonal experiments with six factors and five levels were designed and simulated by means of the Moldflow software. The signal/noise ratio was processed using the index parameters obtained from the experiment， and the weight of two optimization indexes was calculated using an entropy weight method. Finally， the grey relational degree was obtained， and the transformation from the multi?objective optimization to the single?objective optimization was realized. The optimized process parameters were simulated and analyzed. The maximum average volume?shrinkage rate of the second injection and the maximum total warpage rates were determined to be 15.67 % and 1.964 mm， respectively， which decreased by 7.8 % and 18.4 %， respectively， compared to the analysis results of the original process parameters. This resulted in an improvement in product quality. The experimental results indicated that a combination of orthogonal experiment， grey relational analysis and entropy weight method could effectively optimize the injection?molding process parameters.

Key words: double color injection molding, orthogonal experiment, grey relational analysis, entropy weight method, multi?objective optimization

CLC Number:

TQ320.66⁺2

WANG Xiaodong, WANG Quan, CHEN Tuo, ZHENG Yue. Optimization of multi⁃objective parameters for double color injection⁃molding based on grey relational analysis and entropy weight method[J]. China Plastics, 2022, 36(7): 115-120.

Figures/Tables 12

Fig.1. Model of double color plastic bowl

Fig.2. Results of gate matching analysis

Fig.3. Runner system

Fig.4. Cooling system

Fig.5. Analysis result under default parameter

水平	第一射参数			第二射参数
水平	A/℃	B/℃	C/%	D/℃	E/℃	F/%
1	40	250	70	30	215	70
2	45	255	75	35	220	75
3	50	260	80	40	225	80
4	55	265	85	45	230	85
5	60	270	90	50	235	90

Tab.1. Factor and level of orthogonal test table

序号	A/℃	B/℃	C/%	D/℃	E/℃	F/%	$X$ /%	$Y$ /mm
1	1	1	1	1	1	1	15.84	2.186
2	1	2	2	2	2	2	16.07	2.111
3	1	3	3	3	3	3	16.39	2.086
4	1	4	4	4	4	4	16.48	2.057
5	1	5	5	5	5	5	16.75	2.057
6	2	1	2	3	4	5	16.48	2.114
7	2	2	3	4	5	1	17.10	2.156
8	2	3	4	5	1	2	15.77	2.034
9	2	4	5	1	2	3	15.98	2.060
10	2	5	1	2	3	4	16.19	2.266
11	3	1	3	5	2	4	15.99	2.078
12	3	2	4	1	3	5	16.10	2.072
13	3	3	5	2	4	1	16.72	2.104
14	3	4	1	3	5	2	16.89	2.327
15	3	5	2	4	1	3	15.69	2.225
16	4	1	4	2	5	3	16.97	2.126
17	4	2	5	3	1	4	15.64	2.025
18	4	3	1	4	2	5	15.84	2.240
19	4	4	2	5	3	1	16.55	2.235
20	4	5	3	1	4	2	16.69	2.219
21	5	1	5	4	3	2	16.44	2.093
22	5	2	1	5	4	3	16.72	2.300
23	5	3	2	1	5	4	16.89	2.255
24	5	4	3	2	1	5	15.57	2.184
25	5	5	4	3	2	1	16.23	2.155

序号	A/℃	B/℃	C/%	D/℃	E/℃	F/%	$X$ /%	$Y$ /mm
1	1	1	1	1	1	1	15.84	2.186
2	1	2	2	2	2	2	16.07	2.111
3	1	3	3	3	3	3	16.39	2.086
4	1	4	4	4	4	4	16.48	2.057
5	1	5	5	5	5	5	16.75	2.057
6	2	1	2	3	4	5	16.48	2.114
7	2	2	3	4	5	1	17.10	2.156
8	2	3	4	5	1	2	15.77	2.034
9	2	4	5	1	2	3	15.98	2.060
10	2	5	1	2	3	4	16.19	2.266
11	3	1	3	5	2	4	15.99	2.078
12	3	2	4	1	3	5	16.10	2.072
13	3	3	5	2	4	1	16.72	2.104
14	3	4	1	3	5	2	16.89	2.327
15	3	5	2	4	1	3	15.69	2.225
16	4	1	4	2	5	3	16.97	2.126
17	4	2	5	3	1	4	15.64	2.025
18	4	3	1	4	2	5	15.84	2.240
19	4	4	2	5	3	1	16.55	2.235
20	4	5	3	1	4	2	16.69	2.219
21	5	1	5	4	3	2	16.44	2.093
22	5	2	1	5	4	3	16.72	2.300
23	5	3	2	1	5	4	16.89	2.255
24	5	4	3	2	1	5	15.57	2.184
25	5	5	4	3	2	1	16.23	2.155

Tab.2. Results of orthogonal test

实验次序	信噪比		无量纲化后结果		灰色关联度系数		灰色关联度 $γ i$	排序
实验次序	$η i (X)$	$η i (Y)$	$α i (X)$	$α i (Y)$	$ξ i (X)$	$ξ i (Y)$	灰色关联度 $γ i$	排序
1	-23.995	-6.793	0.817	0.450	0.732	0.476	0.588	12
2	-24.120	-6.490	0.663	0.701	0.597	0.626	0.613	10
3	-24.292	-6.386	0.453	0.787	0.477	0.701	0.604	11
4	-24.339	-6.265	0.394	0.888	0.452	0.816	0.658	7
5	-24.480	-6.265	0.221	0.888	0.391	0.816	0.631	8
6	-24.339	-6.502	0.394	0.691	0.452	0.618	0.546	15
7	-24.660	-6.673	0.000	0.549	0.333	0.526	0.442	20
8	-23.957	-6.167	0.864	0.969	0.786	0.941	0.873	2
9	-24.072	-6.277	0.723	0.877	0.643	0.803	0.733	3
10	-24.185	-7.105	0.584	0.191	0.546	0.382	0.453	19
11	-24.077	-6.353	0.716	0.814	0.638	0.729	0.690	5
12	-24.137	-6.328	0.643	0.835	0.583	0.752	0.679	6
13	-24.465	-6.461	0.240	0.725	0.397	0.645	0.537	16
14	-24.553	-7.336	0.132	0.000	0.365	0.333	0.347	25
15	-23.912	-6.947	0.918	0.323	0.860	0.425	0.614	9
16	-24.594	-6.551	0.082	0.650	0.352	0.588	0.486	18
17	-23.885	-6.129	0.952	1.000	0.913	1.000	0.962	1
18	-23.995	-7.005	0.817	0.274	0.732	0.408	0.549	14
19	-24.376	-6.986	0.349	0.290	0.434	0.413	0.423	21
20	-24.449	-6.923	0.259	0.342	0.403	0.432	0.419	22
21	-24.318	-6.415	0.420	0.763	0.463	0.678	0.584	13
22	-24.465	-7.235	0.240	0.084	0.397	0.353	0.372	24
23	-24.553	-7.063	0.132	0.226	0.365	0.393	0.381	23
24	-23.846	-6.785	1.000	0.456	1.000	0.479	0.706	4
25	-24.206	-6.669	0.557	0.553	0.530	0.528	0.529	17

实验次序	信噪比		无量纲化后结果		灰色关联度系数		灰色关联度 $γ i$	排序
实验次序	$η i (X)$	$η i (Y)$	$α i (X)$	$α i (Y)$	$ξ i (X)$	$ξ i (Y)$	灰色关联度 $γ i$	排序
1	-23.995	-6.793	0.817	0.450	0.732	0.476	0.588	12
2	-24.120	-6.490	0.663	0.701	0.597	0.626	0.613	10
3	-24.292	-6.386	0.453	0.787	0.477	0.701	0.604	11
4	-24.339	-6.265	0.394	0.888	0.452	0.816	0.658	7
5	-24.480	-6.265	0.221	0.888	0.391	0.816	0.631	8
6	-24.339	-6.502	0.394	0.691	0.452	0.618	0.546	15
7	-24.660	-6.673	0.000	0.549	0.333	0.526	0.442	20
8	-23.957	-6.167	0.864	0.969	0.786	0.941	0.873	2
9	-24.072	-6.277	0.723	0.877	0.643	0.803	0.733	3
10	-24.185	-7.105	0.584	0.191	0.546	0.382	0.453	19
11	-24.077	-6.353	0.716	0.814	0.638	0.729	0.690	5
12	-24.137	-6.328	0.643	0.835	0.583	0.752	0.679	6
13	-24.465	-6.461	0.240	0.725	0.397	0.645	0.537	16
14	-24.553	-7.336	0.132	0.000	0.365	0.333	0.347	25
15	-23.912	-6.947	0.918	0.323	0.860	0.425	0.614	9
16	-24.594	-6.551	0.082	0.650	0.352	0.588	0.486	18
17	-23.885	-6.129	0.952	1.000	0.913	1.000	0.962	1
18	-23.995	-7.005	0.817	0.274	0.732	0.408	0.549	14
19	-24.376	-6.986	0.349	0.290	0.434	0.413	0.423	21
20	-24.449	-6.923	0.259	0.342	0.403	0.432	0.419	22
21	-24.318	-6.415	0.420	0.763	0.463	0.678	0.584	13
22	-24.465	-7.235	0.240	0.084	0.397	0.353	0.372	24
23	-24.553	-7.063	0.132	0.226	0.365	0.393	0.381	23
24	-23.846	-6.785	1.000	0.456	1.000	0.479	0.706	4
25	-24.206	-6.669	0.557	0.553	0.530	0.528	0.529	17

Tab.3. Calculation results of each parameter

	信息熵 $e j$	信息熵冗余度 $d j$	权重 $ω j$
$X$	0.999 42	0.000 58	43.6 %
$Y$	0.999 25	0.000 75	56.4 %

	信息熵 $e j$	信息熵冗余度 $d j$	权重 $ω j$
$X$	0.999 42	0.000 58	43.6 %
$Y$	0.999 25	0.000 75	56.4 %

Tab.4. Each indicator’s information entropy， redundancy and weight

水平	A	B	C	D	E	F
1	0.619	0.579	0.462	0.560	0.749	0.504
2	0.610	0.614	0.515	0.559	0.623	0.567
3	0.573	0.589	0.572	0.597	0.549	0.562
4	0.568	0.573	0.645	0.569	0.506	0.629
5	0.514	0.529	0.689	0.598	0.457	0.622
极差	0.105	0.085	0.227	0.039	0.292	0.125
排序	4	5	2	6	1	3

Tab.5. Range analysis of grey relational degree

Fig.6. Trend chart of grey relational degree

Fig.7. Optimized result

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