Optimization of PLA 4D printing parameters using box⁃behnken response surface method

doi:10.19491/j.issn.1001-9278.2025.11.012

Abstract

Abstract:

The response surface method was used to investigate the effect of FDM parameters on the shape memory performance of PLA materials. These parameters include the number of top and bottom layers， filling rate， sample thickness， sample bending degree， sample printing direction， and deformation temperature. The shape memory performance is considered through two response variables： shape recovery rate and shape recovery time. Using the Box⁃Behnken design， high⁃order models were developed to calculate the optimum parameter combination with high accuracy compared to the experimental results. According to the results， the relative errors between the shape recovery rate of the sample and the shape recovery time with respect to the experimental results and model prediction results were 1.526 09 % and 2.390 3 %， respectively. The accuracy of the prediction model is good， which has certain reference significance for future research on 4D printing.

Key words: polylactic acid, shape recovery rate, shape recovery time, response surface methodolog

CLC Number:

TQ321

LIU Shaogang, QIU Dandan, ZHANG Xianchao, WANG Xinyue. Optimization of PLA 4D printing parameters using box⁃behnken response surface method[J]. China Plastics, 2025, 39(11): 72-78.

Figures/Tables 18

References 16

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顺序	顶层与底层数	填充率/%	厚度/mm	弯曲程度/°	模型打印方向	赋形温度/℃		形状恢复时间/s
1	2	20	5	90	2	75	86.7	29.1
2	8	20	5	90	2	75	96.4	35
3	2	80	5	90	2	75	94.13	37.99
4	8	80	5	90	2	75	98.92	46.1
5	2	20	5	180	2	75	84.37	25.75
6	8	20	5	180	2	75	97.69	36.75
7	2	80	5	180	2	75	93.102	43.75
8	8	80	5	180	2	75	98.4	50.24
9	5	20	4	130	1	75	78.22	19.1
10	5	80	4	130	1	75	85.59	36
11	5	20	6	130	1	75	81.14	30.35
12	5	80	6	130	1	75	87.75	48.2
13	5	20	4	130	3	75	88.24	34.5
14	5	80	4	130	3	75	88.37	47.04
15	5	20	6	130	3	75	89.03	40
16	5	80	6	130	3	75	94.2	64
17	5	50	4	90	2	65	91.23	26.9
18	5	50	6	90	2	65	95.1	33.8
19	5	50	4	180	2	65	93.37	29.15
20	5	50	6	180	2	65	95.01	42.15
21	5	50	4	90	2	85	92.059	25
22	5	50	6	90	2	85	91.73	39.2
23	5	50	4	180	2	85	84.49	36.15
24	5	50	6	180	2	85	88.91	48.16
25	2	50	5	90	1	75	75.52	25.4
26	8	50	5	90	1	75	90.74	28.2
27	2	50	5	180	1	75	71.51	34.25
28	8	50	5	180	1	75	83.75	39.25
29	2	50	5	90	3	75	85.93	42.1
30	8	50	5	90	3	75	93.79	52.1
31	2	50	5	180	3	75	82.78	41.75
32	8	50	5	180	3	75	91.846	51.75
33	5	20	5	130	1	65	84.43	20.5
34	5	80	5	130	1	65	90.8	39.04
35	5	20	5	130	3	65	94.62	41.4
36	5	80	5	130	3	65	96.06	56.4
37	5	20	5	130	1	85	81.17	27.4
38	5	80	5	130	1	85	90.1	46.67
39	5	20	5	130	3	85	87.72	38.57
40	5	80	5	130	3	85	95.47	58.8
41	2	50	4	130	2	65	85.74	29.5
42	8	50	4	130	2	65	96.55	32.61
43	2	50	6	130	2	65	87.65	41.4
44	8	50	6	130	2	65	96.46	44.4
45	2	50	4	130	2	85	81.05	32.4
46	8	50	4	130	2	85	94.1	35.61
47	2	50	6	130	2	85	88.011	48.88
48	8	50	6	130	2	85	92.68	52.7
49	5	50	5	130	2	75	98.68	38
50	5	50	5	130	2	75	95.61	37
51	5	50	5	130	2	75	94.84	36
52	5	50	5	130	2	75	94.84	34
53	5	50	5	130	2	75	95.493	35
54	5	50	5	130	2	75	97.15	34

顺序	顶层与底层数	填充率/%	厚度/mm	弯曲程度/°	模型打印方向	赋形温度/℃		形状恢复时间/s
1	2	20	5	90	2	75	86.7	29.1
2	8	20	5	90	2	75	96.4	35
3	2	80	5	90	2	75	94.13	37.99
4	8	80	5	90	2	75	98.92	46.1
5	2	20	5	180	2	75	84.37	25.75
6	8	20	5	180	2	75	97.69	36.75
7	2	80	5	180	2	75	93.102	43.75
8	8	80	5	180	2	75	98.4	50.24
9	5	20	4	130	1	75	78.22	19.1
10	5	80	4	130	1	75	85.59	36
11	5	20	6	130	1	75	81.14	30.35
12	5	80	6	130	1	75	87.75	48.2
13	5	20	4	130	3	75	88.24	34.5
14	5	80	4	130	3	75	88.37	47.04
15	5	20	6	130	3	75	89.03	40
16	5	80	6	130	3	75	94.2	64
17	5	50	4	90	2	65	91.23	26.9
18	5	50	6	90	2	65	95.1	33.8
19	5	50	4	180	2	65	93.37	29.15
20	5	50	6	180	2	65	95.01	42.15
21	5	50	4	90	2	85	92.059	25
22	5	50	6	90	2	85	91.73	39.2
23	5	50	4	180	2	85	84.49	36.15
24	5	50	6	180	2	85	88.91	48.16
25	2	50	5	90	1	75	75.52	25.4
26	8	50	5	90	1	75	90.74	28.2
27	2	50	5	180	1	75	71.51	34.25
28	8	50	5	180	1	75	83.75	39.25
29	2	50	5	90	3	75	85.93	42.1
30	8	50	5	90	3	75	93.79	52.1
31	2	50	5	180	3	75	82.78	41.75
32	8	50	5	180	3	75	91.846	51.75
33	5	20	5	130	1	65	84.43	20.5
34	5	80	5	130	1	65	90.8	39.04
35	5	20	5	130	3	65	94.62	41.4
36	5	80	5	130	3	65	96.06	56.4
37	5	20	5	130	1	85	81.17	27.4
38	5	80	5	130	1	85	90.1	46.67
39	5	20	5	130	3	85	87.72	38.57
40	5	80	5	130	3	85	95.47	58.8
41	2	50	4	130	2	65	85.74	29.5
42	8	50	4	130	2	65	96.55	32.61
43	2	50	6	130	2	65	87.65	41.4
44	8	50	6	130	2	65	96.46	44.4
45	2	50	4	130	2	85	81.05	32.4
46	8	50	4	130	2	85	94.1	35.61
47	2	50	6	130	2	85	88.011	48.88
48	8	50	6	130	2	85	92.68	52.7
49	5	50	5	130	2	75	98.68	38
50	5	50	5	130	2	75	95.61	37
51	5	50	5	130	2	75	94.84	36
52	5	50	5	130	2	75	94.84	34
53	5	50	5	130	2	75	95.493	35
54	5	50	5	130	2	75	97.15	34

变异来源	平方和	自由度	均方	F值	P值
模型	1 943.84	17	114.34	55.09	<0.000 1	S
A	549.44	1	549.44	264.73	<0.000 1
B	166.23	1	166.23	80.09	<0.000 1
C	34.23	1	34.23	16.49	0.000 3
D	30.42	1	30.42	14.66	0.000 5
E	317.82	1	317.82	153.13	<0.000 1
F	73.63	1	73.63	35.47	<0.000 1
AB	20.9	1	20.9	10.07	0.003 1
AC	13.47	1	13.47	6.49	0.015 3
AE	13.87	1	13.87	6.68	0.013 9
BE	13.67	1	13.67	6.59	0.014 6
BF	9.83	1	9.83	4.74	0.036 1
DF	20.7	1	20.7	9.97	0.003 2
A²	69.87	1	69.87	33.66	<0.000 1
B²	24.15	1	24.15	11.63	0.001 6
C²	124.72	1	124.72	60.09	<0.000 1
D²	16.25	1	16.25	7.83	0.008 2
E²	624.85	1	624.85	301.06	<0.000 1
残差	74.72	36	2.08
失拟项	63.18	31	2.04	0.882 8	0.636 1	NS
纯误差	11.54	5	2.31
总和	2 018.56	53

变异来源	平方和	自由度	均方	F值	P值
模型	1 943.84	17	114.34	55.09	<0.000 1	S
A	549.44	1	549.44	264.73	<0.000 1
B	166.23	1	166.23	80.09	<0.000 1
C	34.23	1	34.23	16.49	0.000 3
D	30.42	1	30.42	14.66	0.000 5
E	317.82	1	317.82	153.13	<0.000 1
F	73.63	1	73.63	35.47	<0.000 1
AB	20.9	1	20.9	10.07	0.003 1
AC	13.47	1	13.47	6.49	0.015 3
AE	13.87	1	13.87	6.68	0.013 9
BE	13.67	1	13.67	6.59	0.014 6
BF	9.83	1	9.83	4.74	0.036 1
DF	20.7	1	20.7	9.97	0.003 2
A²	69.87	1	69.87	33.66	<0.000 1
B²	24.15	1	24.15	11.63	0.001 6
C²	124.72	1	124.72	60.09	<0.000 1
D²	16.25	1	16.25	7.83	0.008 2
E²	624.85	1	624.85	301.06	<0.000 1
残差	74.72	36	2.08
失拟项	63.18	31	2.04	0.882 8	0.636 1	NS
纯误差	11.54	5	2.31
总和	2 018.56	53

变异来源	平方和	自由度	均方	F值	P值
模型	4 551.03	12	379.25	56.95	<0.000 1	S
A	218.65	1	218.65	32.83	<0.000 1
B	1 607.37	1	1 607.37	241.38	<0.000 1
C	928.52	1	928.52	139.43	<0.000 1
D	141.18	1	141.18	21.2	<0.000 1
E	1 178.88	1	1 178.88	177.03	<0.000 1
F	113.93	1	113.93	17.11	0.000 2
BD	12.32	1	12.32	1.85	0.181 2
DE	51.16	1	51.16	7.68	0.008 3
EF	27.98	1	27.98	4.2	0.046 8
A²	64.69	1	64.69	9.72	0.003 3
D²	66.63	1	66.63	10.01	0.002 9
E²	108.49	1	108.49	16.29	0.000 2
残差	273.03	41	6.66
失拟项	259.69	36	7.21	2.71	0.134	NS
纯误差	13.33	5	2.67
总和	4 824.06	53