Comprehensive performance of a low-cost spring-assisted mechanism for digital light processing

In additive manufacturing, separation is an important issue in constrained-surface digital light processing. A force higher than the force peak and a sharp increase in force increase the printing failure rate. This study comprehensively evaluated the performance of a low-cost spring-assisted separation mechanism. The Taguchi method was used to confirm the correlation between the inputs of the spring-assisted mechanism (number, coefficient, working height, free height of spring, and length of working arm) and obtain the parameters that minimize the separation force and time. Compared to the pulling-up and tilting mechanisms, the spring-assisted mechanism reduces the difference between the maximum and minimum separation forces for different geometric shapes and areas by 2.4 and 3 times, respectively. In addition, the spring-assisted mechanism solves the problems of the pulling-up mechanism, which has two separation force peaks, and the tilting mechanism, which has a sharp increase in force before the final separation. Finally, the separation force of specific geometric shapes and areas was predicted by the linear regression equation, and the error rate was maintained within 5%, which helped to significantly reduce the calculation costs and time.


Introduction
Additive layer manufacturing technology forms threedimensional (3D) models by stacking materials layer by layer. It can easily build high-quality models with complex structures while minimizing time and material costs. It has influenced industrial manufacturing to gradually shift from traditional to nonconventional processes [1]. Many incremental processes have been used, with the main differences among them being the stacking method and the materials used. Some processes layer by melting or softening the material, such as selective laser melting (SLM), direct metal laser sintering (DMLS), directed energy deposition (DED), and fused deposition modeling (FDM) [2][3][4].
Stereolithography (SLA) is another commonly used technique that uses a light source to irradiate a photosensitive liquid resin with a fixed thickness that is stacked layer by layer [5][6][7]. The key to successful manufacturing is that the light source must provide sufficient energy to cure the material. For example, SLA uses a laser, whereas digital light processing (DLP) uses a projector. DLP can be further divided according to the modeling direction of the build plate: constrained surface (i.e., bottom-up) [8] and free surface (i.e., top-down) [9]. Constrained-surface DLP has become the mainstream approach because of its good material filling rate, low amount of material waste, and short processing time [10]. However, a constrained-surface DLP has a separation failure problem. This is because the space between the cured layer and resin tank is close to the vacuum state; thus, they can only be separated by an external force [11]. An excessive separation force can easily be generated when large areas are printed, damaging the cured layer, or separating the cured layer from the build plate. This can result in printing failure, limiting the printing area.
There are many ways to reduce the separation force, such as optimizing the experimental parameters [12][13][14], changing the contact area between the bottom of the resin tank and the cured layer [15][16][17], or adding materials [18][19][20]. The development of an innovative separation mechanism is a practical approach that may provide additional benefits. Wang et al. [21] proposed an active separation bottom-up stereolithography method, which adds a layer of watercontaining Teflon film in the resin tank and pumps water to reduce the separation force on the cured layer. Another practical approach is to change the pulling-up mechanism, which fixes both sides of the resin tank during separation [22]. Wu et al. [23] found that the tilting mechanism improved the uniformity of photosensitive liquid resin. Changing the separation speed and using polydimethylsiloxane (PDMS) film can reduce the stress on a structure with a large separation force to avoid damaging the printed item. Jin et al. [24] and Xu et al. [25] proposed using vibrations to reduce the separation force without damaging the printed item or affecting the dimensional accuracy. They developed a vibrationassisted system and built a mechanical-analysis model. Lin et al. [26] built a spring-assisted mechanism to reduce the separation force by using the additional pre-stress provided by the compressed spring.
Another approach to varying the separation force is to change the printing geometry. Determining the relationship between the geometry and separation force is valuable for improving manufacturing efficiency. Pan et al. [12] found that a porous shape can increase the effective separation area of the cured layer and obtained an approximate polynomial relationship for predicting the separation force of a porous round. Khadilkar et al. [27] used deep learning to predict the separation stress distribution in cured layers. Their method can be used to determine the stress distribution of each layer and is more efficient than the finite element analysis. Yadegari et al. [28] changed the printing parameters to obtain the separation force-time curve of a resin tank containing a PDMS film. Their experimental results revealed that a fracture mechanics model can be used to predict the maximum separation force. Gritsenko et al. [29] used a fluid mechanics model to simulate the separation force of cylindrical parts, and concluded that optimizing the transient parameters can reduce the separation force. In addition, increasing the printing speed/rate and maintaining a constant height were found to reduce processing time. He et al. [30] used a Siamese neural network to predict the printing speed and performed physical model simulations to obtain the appropriate speed range and best speed for printed items. Wang et al. [31] proposed using a neural network to predict the separation force for molding five symmetric geometric shapes. They used the finite element method (FEM) to verify the prediction model of a neural network. However, their model generated relatively large errors when dealing with complex geometric shapes and could only predict reasonable trends.
The literature review above reveals that separation and mechanism costs are important issues in DLP machines. This study demonstrated the effectiveness of a low-cost spring-assisted mechanism for the separation of DLP. The Taguchi method was used to confirm the correlation between the inputs of the spring-assisted mechanism and obtain the parameters that minimize the separation force and time. Different geometric shapes and areas were printed to compare the manufacturing stability of the proposed method and those of the pulling-up and tilting mechanisms. In addition, the separation issue of more than one force peak and sharpness was also reviewed. Finally, a linear regression equation was established to predict the separation force in a specific geometric shape and area to significantly reduce the calculation cost and time.
The remainder of this paper is organized as follows. Section 2 presents the spring-assisted mechanism, separation force measurement equipment, Taguchi method, and linear regression. Section 3 presents experimental results verifying the effectiveness of the spring-assisted mechanism. Section 4 discusses the performance of the spring-assisted mechanism and its application. Finally, Section 5 presents the conclusions and possible future directions of research.

Spring-assisted mechanism
The schematic of the spring-assisted mechanism is shown in Fig. 1a. The right side is a fulcrum, and the left side is free to move up but subjected to an initial force (Fr) by a compressed spring. According to Hooke's law, Fr can be calculated based on the spring compression, spring constant, and number of springs. When a cured layer starts to separate, the build plate rises and generates a separation force Fp. Both Fp and Fr increase with the lifting distance of the build plate until the cured layer separates. After separation of the cured layer, Fr returns to its initial value until the next cycle. To implement the spring-assisted mechanism, this study uses Titan 2 (Kudo3D, Inc.) [32] to build the prototype, as illustrated in Fig. 1b. One side of the resin tank, which is close to the Z axis of Titan 2, is a fulcrum. The compressed spring mechanism is located on the other side. It is fixed by a stainless steel bar, two purple hollow plastic tubes, and two long screws that can be locked on Titan 2. Moreover, it is sandwiched between two purple plastic bars with holes in them. The upper one is buckled on the stainless steel bar, whereas the lower one is buckled on the resin tank.
According to Hooke's law and the moment theorem, parameters that may affect the separation force include the number of springs, spring coefficient, working height of the springs, free height of the springs, and length of the working arm. Table 1 presents the ranges of values of these five parameters obtained in a feasibility experiment. The springs required for the experiment were purchased from a Japanese company (Misumi) [33] and the material is SWP-A of JIS G 3522 (Japanese Industrial Standard piano wire). The printed items have geometric shapes, including a regular triangle, square, pentagon, hexahedron, round, and donut. The items were printed from an ABS-like resin (3DM Company) [34].

Separation force measurement system and separation force-time diagram for separating the cured layer
The separation force measurement system comprised an LC201 load cell, DMD4059 signal conditioner (OMEGA Engineering), and USB-6002 data acquisition card (DAQ Device, National Instruments) [35,36]. Because the load cell measured the voltage, the separation force was obtained using the following conversion: where x is the mass (g), and y is the voltage. Figure 2 shows the diagram of the separation force versus time for a single separation process. Points A and B represent the exposure and molding of photosensitive resin, respectively. At point B, the light source stopped projecting the light, and the separation process began. At points B (1) x = (y − 0.0291)∕ − 0.0004   and C, the build plate started to move upward and separate from the resin layer at point D, where the separation force was at its maximum. Therefore, the separation distance was from B to D, and the separation time was represented by t. At point E, the build plate returned to the position for printing the next layer after a waiting interval.

Taguchi method
The Taguchi method uses experimental planning and statistical techniques to reduce the overall number of experiments and determine the factors that affect manufacturing quality to stabilize the quality and reduce costs. The Taguchi method involves the following steps: (1) selecting the quality characteristics; (2) determining the ideal function of the quality characteristics; (3) listing all factors that affect the quality characteristics; (4) determining the levels of signal, control, and noise factors; (5) selecting the appropriate orthogonal array and plan the experiment; (6) conducting the experiment and collect data; (7) analyzing the data; and (8) verifying the experimental results. Quality characteristics have corresponding ideal target values, which can be divided into the following types: nominal best, smaller better (STB), and larger better. These have target values of zero, infinity, and threshold values. A control factor is a parameter set by the user to improve the robustness. The signal factor is a parameter that the user adjusts to change its quality characteristics. The noise factor is a parameter that affects the quality characteristics that cannot be controlled by the user. An experimental array is considered orthogonal if a direct intersecting relationship exists between any two rows. The Taguchi method provides many useful orthogonal arrays, the most significant advantages of which are simplified data analysis and reduced experimental costs. The signal-to-noise ratio (SNR) is a measurement of quality that considers the average value and standard deviation of a quality characteristic. A characteristic is considered to be of good quality when the average value is consistent with the target value and the standard deviation is small.
In this study, the STB was adopted to minimize the separation force. The SNR, mean value, and standard deviation are calculated as follows: where y is the average value, y i is the measured value of the quality, and n is the number of samples. Analysis of variance (ANOVA) was performed to determineobtain the influence and error degree of error of each experimental parameter on the entirewhole process. This required the calculationcalculating of the correction number (CF), sum of squares between groups (SSA), total sum of squares, mean square (MSA), and contribution percentage (P): where n is the number of calculated items, p is the number of levels of control factors, m is the number of levels used, and df is the number of levels of control factors minus one.
An L18 orthogonal array was used in this study. To avoid interaction between parameters, the number of springs, spring coefficient, working height of springs, free height of springs, and length of the working arm were set to rows 1, 3, 4, 5, and 6, respectively. An experimental plan was developed according to the upper, intermediate, and lower limits of the control ranges for each parameter in Table 1. The values are presented in Table 2.

Linear regression model
The Pearson correlation coefficient is typically used in data display and curve integration to measure the linear dependence between two variables. The degree to which this coefficient approaches 1 is related to the number of datasets. A smaller number of datasets increased the fluctuation of the correlation coefficient, and the absolute value of the correlation coefficient approached 1. Increasing the number of datasets decreased the absolute value of the correlation coefficient. Therefore, if the number of samples is relatively small, a large correlation coefficient is insufficient to indicate a close linear relationship between the variables X and Y. The Pearson's correlation coefficient of the samples is calculated as follows: where S x is the standard deviation of x, S y is the standard deviation of y, and C x,y is the covariance of the variables x and y.
To confirm a linear relationship, the significance of the sample correlation coefficient must be verified. The verification data is obtained using This value is compared with the value (degrees of freedom: n-2) as given in Appendix Table 10. The correlation coefficient is considered significant if the following condition is satisfied: This indicates that a linear relationship between query values can be explained (significance level a = 0.05). If all data meet the condition in Eq. (15), a linear correlation between x and y can be confirmed. The coefficients are calculated as follows: The linear regression model is given by Figure 3 shows a representative printed item: a 20 × 20 mm square. Table 3 presents the separation force data obtained in the experiments and the SNR calculated using Eqs. (1)-(3). Minimizing the separation force increased the SNR. Table 4 and Fig. 4 indicate that the optimal parameter combination for minimizing the separation force was one spring, a spring coefficient of 0.1 N/mm, a spring working height of 14.5 mm, a free height of the spring of 15 mm, and an axle base of 165 mm. As   Table 5, the ANOVA results indicate that the most important parameter affecting the separation force was the axle base, followed by the free height of the spring and spring coefficients. Figure 5 shows the 3D object produced according to the optimal parameters. This object demonstrates the manufacturing stability of the spring-assisted mechanism. To fully analyze the characteristics of the spring-assisted mechanism, the printing parameters with the minimum separation time were verified experimentally. The experimental data, SNR, factor response table, factor response diagram, and ANOVA results are presented in Appendix Tables 11, 12 and 13 and Fig. 12. The optimal parameter combination for minimizing the separation time was two springs, a spring coefficient of 0.3 N/mm, a spring working height of 13.0 mm, a free height of 25 mm in the spring, and an axle base of 165 mm. The ANOVA results revealed that the most important parameter affecting the separation time was the axle base, followed by the free height of the spring and the spring coefficients. Figure 6 summarizes the experimental results for the minimum separation force and time of the spring-assisted, pulling-up, and tilting mechanisms. By adjusting the printing parameters, the spring-assisted mechanism can be used to vary the separation force and time. Because the separation force is the key factor that affects printing quality, the subsequent experiments and performance comparisons in this study mainly focused on optimizing the separation force.

Comparison of separation mechanisms for printed items with different geometric shapes and areas
The separation characteristics of the spring-assisted, pulling-up, and tilting mechanisms were compared for different geometric shapes and areas. Figure 7 shows the geometric shapes of the printed items: square, regular triangle, pentagon, hexahedron, round, and donut. Each geometric shape had a printing area of 400 mm 2 . Figure 8 shows the measured separation forces for the three mechanisms. Table 6 lists the experimental results. For the different geometric shapes, the average separation force of the spring-assisted mechanism was 3.03 N with a standard deviation of 0.07. This was 33.3% lower than the separation force of the pullingup mechanism and only 5.2% higher than that of the tilting mechanism. The spring-assisted mechanism had the smallest standard deviation in the separation force, indicating that it provided the highest stability during printing. Figure 9 shows the separation forces of the three mechanisms for squares with printing areas in the range of 100-2500 mm 2 . Table 7 indicates that the separation force of the springassisted mechanism increases linearly with the printing area, with values between those of the pulling-up and tilting mechanisms.

Linear regression model for predicting the separation force according to the geometric shape
To confirm that linear regression could be used to predict the separation force of the spring-assisted mechanism, an equation was constructed, and the calculated values were compared with those of the printing experiments. First, the separation force equations were constructed based on square areas of 100, 400, 900, 1600, and 2500 mm 2 . The experimental data of the separation forces are presented in Appendix Tables 14, 15, 16, 17, 18, 19, 20 and 21.
The experimental data revealed that the separation force was clearly higher for the first 10 layers than for the last 15 layers, which can be attributed to the surface tension     between the build plate and photosensitive liquid resin [37]. To maintain the consistency of the samples, only data for the 11 th -25 th layers were used for statistical analysis. The difference between the average and median values of the separation force data was less than 10%, indicating a normal distribution. A statistical analysis was performed using Eqs. (10)- (13), and the resulting data are presented in Table 8. The Pearson correlation coefficient was 0.99, and all statistical values met the condition in Eq. (15), indicating that the correlation coefficient was significant. This implies that the linear regression equation for the separation force of the printed squares of different areas is meaningful. Figure 10 shows the linear regression trend line for the separation force of the printed square. This is expressed by where x is the area (mm 2 ). The prediction accuracy of the separation force was determined by the error rate between the predicted separation force and experimental data. Six squares with different areas were selected for verification. Table 9 lists the predicted separation force, experimental data, and error (19) y(x) = 1.433 + 0.003114x Fig. 9 Separation forces depending on the printing area: a spring-assisted mechanism, b pulling-up mechanism, and c tilting mechanism  Fig. 11. The equations are as follows: where x is the area (mm 2 ).

Discussion
The design concept of the spring-assisted mechanism was similar to that proposed by Wang et al. [21]. This provides a counteracting force during the separation process, which (20) y(x) = 1.09 + 0.005867x    reduces the separation force. However, it has a lower cost than introducing oxygen as an inhibitor [38] or using a water pumping mechanism [21]. Figure 6 shows that the curve of the minimum separation force or separation time of the spring-assisted mechanism was between those of the pulling-up and tilting mechanisms. This demonstrates the flexibility of the spring-assisted mechanism in adjusting the parameters to vary the separation force and time. An ANOVA was performed to determine the relationship and significance of each parameter considered in this study, following the methods of Zamheri et al. [39] and Putra et al. [40]. Comparing the optimal parameters for minimizing the separation force and separation time of the spring-assisted mechanism, both require the longest axle base. In addition, reducing the separation time required to apply a relatively large pre-stress before the object is separated based on Hooke's law requires an increase in the number of springs and a reduction in the free height of the spring. Meanwhile, minimizing the separation force requires a decrease in the spring coefficient and length of the working arm. Figure 8 shows that the spring-assisted mechanism reduced the separation force generated from printing triangles for a given printing area. Table 6 indicates that the spring-assisted mechanism printed different geometric shapes with the smallest standard deviation of the separation force and reduced the difference between the maximum and minimum forces by 2.4 and 3 times compared with the pulling-up and tilting mechanisms, respectively. This helped to reduce the probability of defects or failures on the printed items and control the printing quality. Pan et al. [12] and Yadegari et al. [41] proposed that porous geometric shapes would increase the effective separation area, which would increase the separation force. This characteristic was observed when the spring-assisted mechanism printed the donut, which had the maximum separation force.
For printing items with different areas, Fig. 9 shows that the spring-assisted mechanism eliminated the problems of the pulling-up mechanism, which had two separation force peaks, and the tilting mechanism, which had a sharp increase in the force before separation. This helped improve the manufacturing stability. Yadegari et al. [41] experimentally demonstrated that the separation force increased with the cross-sectional area of the printed item. The spring-assisted mechanism fits this trend and exhibits a linear relationship similar to that of the pulling-up mechanism. Therefore, linear regression was used to predict the separation force, which could provide a reference for large-area printing. The linear regression model accurately predicted the separation force of the printed squares with different areas, which supports the arguments of Yadegari et al. [41] and Gritsenko et al. [29] that mathematical models can be used to predict the separation force. Finally, if the standard deviation of  the separation force of the round shape is taken as a benchmark, the results indicate that the separation force increases with the complexity of the geometric shape. This result is the same as that of Wang et al. [31]. However, the linear regression model can still predict a reasonable trend for such shapes.

Conclusions
This study demonstrated the superior separation performance of a low-cost spring-assisted mechanism. The contributions of this study are summarized as follows.
1. The most important parameter affecting the separation force and separation time of the spring-assisted mechanism was the axle base, followed by the free height of the spring and spring coefficients. An axle base of 165 mm can minimize both the separation force and separation time. 2. The spring-assisted mechanism printed different geometric shapes with the smallest standard deviation of the separation force and reduced the difference between the maximum and minimum forces by 2.4 and 3 times compared to the pulling-up and tilting mechanisms, respectively. In addition, the spring-assisted mechanism solved the problems of the pulling-up mechanism, which has Fig. 11 Linear regression of separation force: a regular triangle, b pentagon, c hexahedron, d round, and e donut two separation force peaks, and the tilting mechanism, which exhibits a sharp increase in force before the final separation. This helped reduce the probability of defects or failures in the printed items and control the printing quality. 3. A linear regression trend was obtained between the separation force of the spring-assisted mechanism and printing area. In addition, equations were constructed to quickly predict the separation force with different geometric shapes and areas, which greatly reduced the calculation cost and time. The prediction error rate gen-erally remained less than 5%, except for an area of 676 mm 2 .
For future research, dimensional tolerance can be incorporated as an evaluation objective for multi-objective optimization. In addition, carbon emissions from energy consumption and the impact of volatile organic compounds produced during the manufacturing process on human health can also be considered. Finally, a fixture that enables the spring-assisted mechanism to be installed on a commercial printing mechanism of the printer is proposed to speed up commercialization.