Optimization of 3D Printing Parameters on Deformation by BP Neural Network Algorithm

Abstract

Traditional processing technology is not suitable for the requirements of advanced manufacturing due to the disadvantages of large repeated experiments, high cost, and low economic effect. As the latest additive technology, 3D printing technology has to deal with many issues such as process parameters and nonlinear mathematical models. A three-layer backpropagation (BP) artificial neural network with a Lavenberg–Marquardt algorithm was established to train the network and predict orthogonal experimental data. Additionally, the best combination of parameters of material deformations were predicted and verified by experiments. The results show that the predicted value obtained by the BP model is in good agreement with the experimental value curve, with a small relative error and a correlation coefficient of 0.99985. Moreover, the deformation errors of the printed model are not more than 3%. The incorporation of the BP neural network algorithm into the 3D printing process can, therefore, help cope with related problems, which is a future trend.

1. Introduction

As one of the representative technologies of the four industrial revolutions, 3D printing technology has drawn increasing attention from the industrial sector and the investor community [1,2,3]. 3D printing technology, going by the name of “additive manufacturing” in academic terms, is also known as additive manufacturing or incremental manufacturing. According to the definition published by the 3D Printing Technical Committee (F42 Committee) established by the American Society for Testing and Materials (ASTM) in 2009 [4], 3D printing, based on 3D Computer Aided Design (CAD) model data, is a way of manufacturing by adding materials layer by layer, which is diametrically opposed to traditional material processing methods. It adopts a manufacturing method of directly manufacturing a three-dimensional physical solid model that is completely consistent with the corresponding mathematical model [5]. The content of 3D printing technology covers all printing processes, technologies, equipment categories, and applications related to “rapid prototyping” at the front end of the product life cycle and “rapid manufacturing” at the full production cycle [6]. The technologies involved in 3D printing include the integration of CAD modeling, measurement, interface software, numerical control, precision machinery, lasers, materials, and other disciplines [7]. At present, the materials that have been developed mainly include plastics [8], resins [9], and metals [10]. However, for 3D printing technology to be applied in more fields, it is necessary to develop more printable materials. According to the characteristics of the materials, the relationship between processing, structure, and materials needs to be delved into in depth. Besides, efforts should be made to develop quality test procedures and methods, establish normative standards for material performance data, etc. [11]. Compared with traditional processes, the main advantages of additive manufacturing are (1) rapid manufacturing of complex structures [12]; (2) support personalized customization [13]; and (3) precise manufacturing processes [14]. Therefore, 3D printing technology is widely applied in stereo lithography apparatus, polymer, three-dimensional printing, gluing, and fused deposition modeling [15,16,17].

However, for the printing process, there is more than one printing parameter, such as printing speed (10–80 mm/s), printing temperature (100–300 °C), filling density (10–70%), scanning speed (10–70 mm/s), and initial layer thickness (0.1–0.5 mm), and it is necessary to continuously adjust and optimize the process parameters according to the expected plan. Following that, a large number of repeated experiments need to be carried out, which will result in the waste of printing materials and time costs, going against the goal of sustainable development. To handle the above-mentioned difficulties, the use of artificial neural networks (ANN) [18,19] to guide the experiment is expected to obtain excellent experimental parameters for experimental verification. The backpropagation (BP) neural network, one of the methods of the artificial neural network, plays a significant role in dealing with many problems that cannot be clearly defined in the mathematical model [20,21]. The test samples set were trained and adjusted by the self-learning function. The powerful mapping ability of BP neural network was then used to store the learned information in the weight under the self-organization performance through the learning of the samples [22]. The trained BP neural network displayed a strong, non-linear mapping ability with unconstrained output samples set when the training samples were input again [23]. The BP neural network, when applied to solve real-life problems, can bring huge benefits to people [24,25,26,27]. To sum up, it is found that there are few studies on the BP neural network optimization of 3D printing parameters, and there is also a lack of theoretical support. Therefore, combining BP with 3D printing technology to optimize the predicted deformation is a strong potential design concept, which opens up a new way for the combination of artificial intelligence and 3D printing technology.

Based on the analysis of the influence of the weight of the 3D printing material on the deformation amount, this paper employs the BP neural network to optimize the process parameters in the printing process by the orthogonal experiment and finally obtains the process parameter combination with the smallest amount of material deformation. Additionally, the 3D printing model prepared with the best combination of process parameters delivers the best functions.

2. Experimental Method

The experiment used a 3D printer assembled by parts produced by Zhongshan Rainbow Printer Consumables Co., Ltd. (Zhongshan, China), as shown in Figure 1. The printing material is polylactic acid (PLA) material with primary color 1.75 mm, produced by Dongguan Dezhijian Plastic Electronics Co., Ltd. (Dongguan, China).

2.1. Design of the Print Model

Material deposition characteristics are related to printing speed, filling density, printing temperature, printing layer thickness, and other parameters. In this experiment, the STL format was exported after UG modeling [28], and the data were imported into a 3D printer for model printing after processed with Cura slicing software (version 15.06, Ultimaker, Utrecht, The Netherlands), as shown in Figure 2.

2.2. Design of the Orthogonal Test

The orthogonal experiment was designed to reasonably classify the test data and factors, put them into a pre-set, neatly arranged table and conduct overall design, comprehensive comparison, and statistical analysis [29,30]. Under experimental conditions, the optimal process parameters are found through the comparison of the test results of each group and range analysis, and then the process products with better performance are obtained [31].

In this experiment, the amount of deformation S (mm/mm) of the printed material is used as an inspection index, while printing speed A (mm/s), printing temperature T (°C), filling density W (%), and initial layer thickness D (mm) are the same as the variable factors, as shown in

Table 1. The levels and factors of the orthogonal test.

Level	A (mm/s)	T (°C)	W (%)	D (mm)
1	40	200	30	0.1
2	45	210	40	0.2
3	50	220	50	0.3

. Moreover, the L9 (34) orthogonal experimental [32] results are shown in

Table 2. Results of the orthogonal test.

Sample	A (mm/s)	T (°C)	W (%)	D (mm)	S (mm/mm)
1	1 (40)	1 (200)	1 (30)	1 (0.1)	0.16
2	1 (40)	2 (210)	2 (40)	2 (0.2)	0.12
3	1 (40)	3 (220)	3 (50)	3 (0.3)	0.14
4	2 (45)	1 (200)	2 (40)	3 (0.30	0.15
5	2 (45)	2 (210)	3 (50)	1 (0.1)	0.17
6	2 (45)	3 (220)	1 (30)	2 (0.2)	0.09
7	3 (50)	1 (200)	3 (50)	2 (0.2)	0.25
8	3 (50)	2 (210)	1 (30)	3 (0.3)	0.30
9	3 (50)	3 (220)	2 (40)	1 (0.1)	0.11

. Levels 1, 2, and 3, respectively, indicate the influence of each factor (In terms of column), and the 9 test results are divided into 3 groups corresponding to each level of each factor (column). Moreover, we consider the average value of the deformation in the X/Y/Z direction. The calculation process of the deformation amount is as follows: the set length is a1 (mm), the actual printing length is b1 (mm), and the deformation amount is A = |b1 − a1|/a1. In the Y direction, the calculation process of the deformation amount is as follows: the set length is a2 (mm), the actual printing length is b2 (mm), and the deformation amount is B = |b2 − a2|/a2. In the Z direction, the calculation process of the deformation amount is as follows: the set length is a3 (mm), the actual printing length is b3 (mm), and the deformation amount is B = |b3 − a3|/a3. The average value of the deformation is S = (A + B + C)/3 (mm/mm).

According to the principle of orthogonal experiment, three levels of factors have three influencing values. For example, the A (mm/s) factor can be decomposed into test indicators A₁, A₂, and A₃. As shown in Table 1, tests 1, 2, and 3 are determined by the test indicator A₁; tests 4, 5, and 6 are determined by the test indicator A₂; and tests 7, 8, and 9 are determined by the test indicator A₃. The three index values K₁, K₂, and K₃ of factor A (mm/s) can be obtained by calculation, which are 0.42, 0.41, and 0.66, respectively. The experimental indicators T, W, and D can also be calculated by the above theory, as shown in

Table 3. Range analysis of orthogonal test results.

Level	A (mm/s)	T (°C)	W (%)	D (mm)
K1	0.42	0.56	0.55	0.44
K2	0.41	0.59	0.38	0.46
K3	0.66	0.34	0.56	0.59
Rj	0.083	0.084	0.061	0.050

.

If the influence of the factor on the index of the orthogonal test is 0, then K_j values (j = 1, 2 and 3) should be equal [33]. Calculations in Table 3 indicate that the values of K_j are different, and the result of the orthogonal test changes with the level of the factor. Therefore, based on the relative value of K_j, the influence of level factor A_j (j = 1, 2, and 3) on the index of orthogonal test can be judged. The verification index of the orthogonal experiment is the amount of deformation. The smaller the amount of deformation change, the better the performance. For example, as K₂ < K₁ < K₃ in factor A (mm/s), K₂ is the optimal factor level of factor A. Similarly, it can be calculated that T₃, W_2, and D₁ are the optimal levels of factors T, W, and D, respectively. From the analysis on the range R_j value (R_j = max{} − min{}) [32], it can be seen that factor T has the greatest influence, followed by factor A and factor W, and the smallest is factor D, that is, R_1T > R_1A > R_1W > R_1D.

To figure out the accuracy of the orthogonal test, an analysis of variance is carried out [34]. The analysis of variance can analyze the size of the test error and thereby test accuracy. It can not only present the order of the influence of each factor and the interaction on the test index but also identify which factors have significant effects and which ones are not significant. For significant factors, the optimal level is selected and strictly controlled in the experiment; for insignificant ones, the optimal level can be determined according to specific circumstances. The calculation formula is as follows [35]:

$$S{S}_T={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{t=1}^s{x}_{it}^2}}-\frac{T^2}{ns}$$

(1)

where n is the orthogonal test number; s is the number of test repetitions; $x_{it}$ is the t-th retest of the i-th test; and T is the sum of all test data. The degree of freedom is $d{f}_j=m-1$, and m is the number of factor levels.

It can be seen from

Table 4. Analysis of variance on amount of deformation S (mm/mm).

Level	Deviation Square Sum	Degree of Freedom	F Value	Significant Level
A	0.012	2	1.333	***
T	0.013	2	1.444	****
W	0.007	2	0.778	**
D	0.004	2	0.444	*
Error	0.04	8

The * stands for significant level, more * means more influence.

that the effects of the four factors are distinct, and the significance level is T > A > W > D. Through the comprehensive analysis on the range and variance of the orthogonal test, it can be concluded that the process conditions that affect the deformation S are better: A2T3W2D1. Since the process did not appear in the orthogonal test, the test needs to be verified.

2.3. Design of the BP Neural Network

According to the experimental conditions, a simple three layer BP neural network model consisting of input layer, hidden layer, and output layer was designed, as shown in Figure 3. The number of hidden layer nodes has a greater influence on the accuracy of the network. The number of hidden layer nodes can be calculated as follows [36]:

$$n1={(m+n)}^{1/2}+a$$

(2)

where m is the number of output neurons, n is the number of input neurons, and a is the constant values ranging from 1 to 10. The fastest convergence rate and higher-precision algorithm, Lavenberg–Marquardt (LM), which comprises the Gauss–Newton and the Steepest Descent method of algorithm [37,38], was adopted. The LM algorithm is a network training function that updates weight and bias values [39]. The relative error obtained from this algorithm is smaller than any other algorithm.

The input sample is 4, a figure constructed before the network training according to Table 2 (The orthogonal test data). Then Formula (3) was used to normalize the data, resulting in the value converges between 0 and 1, as shown in

Table 5. The normalized data.

Sample	A (mm/s)	T (°C)	W (%)	D (mm)	S (mm/mm)
1	0	0	0	0	0.33
2	0	0.5	0.5	0.5	0.14
3	0	1	1	1	0.23
4	0.5	0	0.5	1	0.28
5	0.5	0.5	1	0	0.38
6	0.5	1	0	0.5	0
7	1	0	1	0.5	0.76
8	1	0.5	0	1	1
9	1	1	1.5	0	0.09

. Similarly, the actual predicted output value of the network can be obtained after the network output value is denormalized by Formula (4).

$$x_n=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$$

(3)

$$x_n=x_{\min }-x_n\cdot (x_{\max }-x_{\min })$$

(4)

where $x_n$ is the standardized data, $x$ is the experimental data or the data after de-standard processing; and $x_{\min }$ and $x_{\max }$ are the minimum and maximum values of the experiment, respectively.

The setting of the parameters of the BP neural network is as follows: the neuron function uses tansig (S-tangent function), the output layer neuron function uses purelin, the training function uses trainlm, the learning rate is set to 0.05, and the expected error is 0.001. The normalization function uses premnmx to achieve the result between 0 and 1. After training and simulation [40], the data are denormalized (postmnmx) [41].

3. Results and Discussion

Figure 4 displays the error changes of the BP neural network for corrosion potential and wear rate during training. Figure 4 is the MSE change trend graph during BP neural network training. It can be seen that the network converges to the expected value after a limited number of steps. Therefore, in the 3D printing process, the process effect obtained by different process parameters can be predicted by the established BP neural network mathematical model.

Based on the experimental data in Table 2, the BP neural network model was trained. The experimental values and fitting values are shown in

Table 6. Comparison of experimental and fitting values of deformation in the BP neural network model.

Sample	Experimental Value	Fitting Value	Relative Error/×10−2
1	0.16	0.161	0.62
2	0.12	0.126	0.50
3	0.14	0.141	0.71
4	0.15	0.151	0.67
5	0.17	0.172	0.12
6	0.09	0.094	0.44
7	0.25	0.249	0.36
8	0.30	0.299	0.04
9	0.11	0.108	0.18

.

Figure 5 shows that the fitting value of the BP neural network model is highly consistent with the experimental value, and the correlation coefficient is 0.99985. Therefore, the BP neural network model established in the 3D printing process can predict the combined parameters of the smallest deformation [42].

According to the orthogonal experiment, all the combinations of technological level parameters are constructed, that is, 84 combinations. Input these combinations into the BP neural network model established previously for predictive analysis, and the results are shown in Figure 6.

It can be found that the predicted values are quite close to experimental values. The smallest amount of deformation is 0.0906, which corresponds to the 54th set of parameter combinations, which is A₂T₃W₃D₃ (A = 45 mm/s, T = 220 °C, W = 30%, and D = 0.3 mm).

Based on the optimization results of the BP neural network, the parameters A₂T₃W₃D₃ are used for corresponding experimental verification. The printed model diagram is shown in Figure 7a. Meanwhile, Figure 7b shows that the physical model printed under the optimization parameters (A₂T₃W₃D₃) has a small amount of deformation. Therefore, the BP neural network model plays a guiding role in the 3D printing process, effectively saving time and cost. Moreover, for further verifying the results of deformation, the nine deformation values in the ears, head, and limbs of the model were measured, as shown in

Table 7. Comparison of the set values and measured values of printed model.

Location	The Set Value (mm)	Measured Value (mm)	Error/×10−2
A	5	4.91	1.8
B	5	4.97	0.6
C	5	5.03	0.6
D	5	5.11	2.2
E	4	4.12	3.0
F	4.5	4.52	0.4
G	4.5	4.57	1.6
H	4	4.10	2.5
I	4	4.12	3.0

.

Through the analysis of the set and measured values of the nine parts (A–I, as marked in yellow solid line in Figure 7b), it can be seen that the deformation error value of the nine parts is less than 5%. It can be seen that it is feasible and reasonable to guide the 3D printing entity construction by using BP neural network to predict parameters.

4. Conclusions

In this manuscript, 3D printing technology, the BP neural network, and the orthogonal experiment are combined to build a model that can be used to predict the deformation of PLA materials in 3D printing technology. Compared with the traditional processing technology, this technology has obvious advantages. Through BP model construction, orthogonal data training, and print parameter optimization, the deformation is verified and predicted. Further, backed up by the principle of the orthogonal experiment, the main factors that affect deformation are obtained as follows: T (°C) > A (mm/s) > W (%) > D (mm). The constructed BP neural network structure delivers good reliability in learning training, simulation test, and numerical prediction. The optimal process parameters are A = 45 mm/s, T = 220 °C, W = 30%, and D = 0.3 mm, and the smallest amount of deformation is 0.0906 mm/mm. The predicted value obtained by the BP model is in good agreement with the experimental value curve, with a small relative error (the maximum value does not exceed 0.1%) and a correlation coefficient of 0.99985. Therefore, this research provides a new approach for studying the application of BP neural network in 3D printing.