Multi-Objective Optimization for the Compressive Strength and Dimensional Accuracy of LCD Printed Parts Using Grey Relational Analysis

Additive Manufacturing (AM) is a revolutionary technique in modern manufacturing that can make complicated shapes with very little waste and tremendous material efficiency [1, 2]. Resin 3D printing techniques have gained popularity for their high-resolution 3D printing with fine details [3]. They are also known as photopolymerization techniques [4].

Stereolithography (SLA) and liquid crystal display (LCD)-based printing are two examples of vat photopolymerization processes that are highly recognized for their excellent precision and surface quality [5]. LCD 3D printing differs from DLP (Digital Light Processing) in that it utilizes a UV-light source that has been filtered via an LCD screen to cure photopolymer resins layer by layer, as shown in Figure 1 [6, 7]. More and more people have adopted this method for both prototyping and functioning applications because it is affordable and has a high feature resolution [8-10].

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Figure 1. Schematic diagram of LCD printing [10]

ABS-like photopolymers are a common type of resin used in LCD 3D printing. They try to mimic how traditional Acrylonitrile Butadiene Styrene (ABS) behaves mechanically in standard manufacturing. These materials were chosen because they are rigid, strong, with simple fabrication and post-processing [11]. The proper selection of the process variables, like layer thickness, exposure duration, lifting speeds, and others, can have a big effect on how well printed parts behave mechanically (e.g., their compressive strength) and how accurately they fit together [12]. Various investigations have shown that the mechanical strength is a significant aspect of the quality of the fabricated objects, according to the relevant publications.

Brighenti et al. [13] conducted experiments and constructed theoretical models to find out how the mechanical characteristics of LCD printed photopolymers rely on the printing process parameters, which include the duration the UV light is on and the thickness of the layers. Through LCD 3D printing, Ahmed and Mugendiran [14] observed the process conditions that affect the mechanical qualities of PLA resin. By making the layers thicker and shortening the time between cures, you can get the most strength.

Diab et al. [15] explored how different printing parameters affect the tensile strength, strain, and Young's modulus of the printed parts using a Stereolithography machine. Their result revealed that the layer height, post curing time, and orientation affected the mechanical behavior of fabricated parts. Magalhães et al. [16] assessed the influence of the printing in different angular positions using cost effective LCD printer. Also, the samples were tested with three types of UV light curing resin in five different places on the printing platform. Their results showed that printing with inclined position had a significant effect on the printed parts quality.

Recent advancements in vat-photopolymerization underscore the need of multi objective optimization. Chekkaramkodi et al. [9] reviewed the significance of photopolymerization in the production of functional devices. Dhanunjayarao and Naidu [17] presented experimental findings for the dimensional accuracy of post cured samples fabricated by MSLA technique. They have reached the conclusion that a layer thickness of 0.06 mm constantly shows minimal variance for all of their results measures.

Unlike most investigations that concentrated on single-response optimization (e.g., strength or accuracy) for the thermoplastic-based additive manufacturing processes, the current work introduces an innovative application of Grey Relational Analysis to concurrently optimize both compressive strength and dimensional accuracy in LCD-printed ABS-like resins. To our knowledge, no prior study has systematically examined the cumulative impact of exposure duration, lift velocity, and light-off delay on this material system. This shows the contribution to the field and the novelty of the current research.

This part illustrates and discusses the result of testing on the LCD-printed ABS-like parts’ compressive strength and dimensional accuracy. Table 2 shows the measured values of the responses. To keep the data presentation consistent, all of the numbers in the table were rounded to two decimal places.

The main focus of the examination is to clarify how the three main process parameters: exposure time, light-off delay, and lift speed affect the measured responses.

Main effects plot charts have been used to show how each parameter directly affects the compressive strength, the measured diameter, and the height. These charts show how particular levels of parameters affect specific performance measures and how the process reacts to changes in those levels. Also, the Analysis of Variance (ANOVA) on both the mechanical and dimensional responses to was used to figure out how important each of these factors is in relation to the others. This statistical method makes it possible to find the most important factors, showing which parameters have the biggest effect on the differences in compressive strength and accuracy that were seen. The combination of these graphs and statistics gives us a better understanding of the trade-offs between mechanical performance and dimensional fidelity. This is the basis for the multi-objective optimization technique provided in this paper.

Table 2. Experiments result of the compressive strength and dimensional accuracy

3.1 Compressive strength results

The main effect plots for the compressive strength illustrated in Figure 5 highlight that exposure time is the most important factor that affects how the printed samples behave mechanically. The compressive strength is raised when the exposure period goes from 1.8 seconds to 2.6 seconds. Longer UV exposure leads to increased photopolymerization and better interlayer adhesion, which makes the cross-linked polymer network denser and more cohesive. Light-off delay, on the other hand, had a small positive effect. By increasing the delay from 0.5 s to 1.5 s, the resin had more time to stabilise and level between layers. This made the surface less likely to have faults and made the compressive strength a little better. Lift speed had a relatively small effect compared to the other parameters. Very high lift speeds (80 mm/min) can cause too much peel force, which could lead to micro-defects or partial delamination between layers. However, the effect was not as strong as that of exposure time and light-off delay.

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Figure 5. Main effects plot for the printed parts compressive strengths

The ANOVA results clarified in Table 3 verified this tendency, showing that exposure duration was responsible for about 63% of the difference in compressive strength, light-off delay for 15%, and lift speed for just 11%.

Table 3. ANOVA result of compressive strength

Along with ANOVA, a regression analysis has been performed to ensure that exposure duration strongly affects compressive strength. The regression model validated that exposure time was the most significant, contributing to around 61-63% of the variation, which aligns with the ANOVA findings. It has been examined how the factors interacted with each other (Et × Ls, Et × Loff, Ls × Loff), whereas the results were not statistically significant. This shows that the primary effects are mostly responsible for the differences that have been observed, while interactions play only a little role.

3.2 Dimensional accuracy results

For the dimensional accuracy represented by the diameter and height error percentages, the influence of the parameters on the responses gave a considerably different from those for compressive strength, where light-off delay was the most important affecting parameter according to the ANOVA results shown in Table 4 and Table 5, with 43% and 25% for the diameter and height accuracy, respectively. As can be seen in the main effect plots illustrated in Figure 6, when the delay was increased from 0.5 s to 1.0 s, the dimensional accuracy improved. This was because the longer pause let the resin settle uniformly, which reduced undesired resin flow and made the layers more even. It's interesting that the accuracy went down a little as the delay went up to 1.5 s. This could be because the edges may have over-cured or the resin may have bled a little since it was exposed to ambient light for a longer period before the next layer was cured.

Table 4. ANOVA result of diameter accuracy

Table 5. ANOVA result of height accuracy

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Figure 6. Main effects plot for the dimensional accuracy: (a) diameter error percentage, (b) height error percentage

Exposure duration had a secondary but important effect; longer exposure times (2.6 s) caused the sections to be a little oversized because they were over-polymerized at the edges. On the other hand, lower exposure (1.8 s) relatively undershot the dimensions because the boundaries didn't fully cure. Lift speed caused around 19% of the size differences. Slower speeds (40 mm/min) let the resin drain better and the layers line up better, while faster speeds (80 mm/min) caused little errors because of suction and peel forces.

The ANOVA results indicated somewhat elevated error contributions. This diversity can be ascribed to uncontrollable reasons, including slight fluctuations in resin temperature, light scattering inside the vat, and the intrinsic heterogeneity of photopolymer curing. Even though these factors may not be completely removed, the consistent experimental technique made sure that their effect remained acceptable.

Overall, the combination of diameter and height accuracies shows that light-off delay is the most important factor for managing dimensional fidelity. On the other hand, exposure time needs to be optimised to find the right balance between accuracy and mechanical strength. The current study measured dimensional accuracy through weighing up the errors in height and diameter. Both dimensions have a direct effect on the validity of compression testing, hence they were given equal weight. A sensitivity analysis demonstrated that modifying the weighting between diameter and height affected the optimization result by less than 5%, validating the resilience of this methodology.

The results of the mechanical and dimensional assessments together show how important it is to use a multi-objective optimisation technique for LCD 3D printing of ABS-like photopolymers. Longer exposure times improve compressive strength much strongly by increasing cross-link density, but they also tend to make dimensional accuracy worse by over-curing and edge expansion. On the other hand, the light-off delay mostly controls dimensional fidelity. Lift speed wasn't as important as other factors, but it nevertheless plays a part in reducing flaws caused by peeling and increasing the quality of the surface. These results show that no one factor can improve both mechanical performance and accuracy on its own. Instead, the trade-off area is defined by the interaction between exposure time (which is more important for mechanical strength) and light-off delay (which is more important for dimensional accuracy). This is where both attributes can be optimized at the same time. This understanding is the basis for the multi-objective optimization method used in this study, which tries to find parameter settings that give high compressive strength without losing dimensional accuracy.

3.3 Grey relational optimization

For optimizing the multiple printing characteristics that have been explored in the presented work, the Grey Relational Analysis (GRA) method was adopted to improve these outcomes simultaneously. GRA is a common method for solving multi-objective optimization problems, especially when the interactions between the variables are complicated or not fully recognized. This method transforms multiple performance factors into one grey relational grade (GRG), which allows to rank experimental conditions based on their overall quality of performance [21]. There are a number of steps in the GRA process. Firstly, normalisation is applied to bring all of the obtained values into a range that can be compared, usually between 0 and 1, depending on whether the response is "larger-the-better," "smaller-the-better," or "nominal-the-best." for the compressive strength case, the chosen criteria were larger is better using following equation [22]:

$y_i(k)=\frac{x_i(k)-\min x_{i(k)}}{\max x_i(k)-\min x_{i(k)}}$     (1)

where, $y_i(k)$ is $i^{\text {th}}$ normalized response value and $x_i(k)$ is the observed value for the $i^{\text {th}}$ run of the $k^{\text {th}}$ response. $\max x_i(k)$ and $\min x_i(k)$ are the maximum and minimum values across all experiments.

For the dimensional accuracy of the sample’s diameter and the height the criteria were nominal-the-best which can be expressed as:

$y_i(k)=1-\frac{\left|x_i(k)-x_{o(k)}\right|}{\max \left(\left|\max x_i(k)-x_0\right|,\left|\min x_i(k)-x_0\right|\right)}$     (2)

Next, the Deviation Sequence is generated, which indicates how far each normalised value is from the ideal (reference) value. A smaller deviation means that the performance in that area is better. The normalization data as well as the deviations sequence of the outputs are clarified in Table 6.

After that, the Grey Relational Coefficient (GRC) is calculated for each output using Eq. (3).

$\zeta_i(k)=\frac{\Delta_{\min}+\zeta \Delta_{\max}}{\Delta_i(k)+\zeta \Delta_{\max}}$     (3)

where, $\Delta_{\min}$ and $\Delta_{\max}$ are the global minimum and maximum values in different data series, respectively, for the $k^{\text {th}}$ response. The $\zeta_i(k)$ is the grey relational coefficient. The $\zeta$ is the distinguishing factor. GRC shows how close each possible outcome is to the best solution based on the deviation sequence and a differentiating factor, that is usually set to 0.5 [23].

After all, the GRG (Grey Relational Grade) represents the average of the GRCs for all of the outputs in each trial. The experiment with the highest GRG is the best combination to meet all of the goals. Table 7 illustrates the result of the calculations of the aforementioned steps to find the optimal parameter combination.

Table 6. Normalization and deviation sequence values

As can be noted in Table 7, experiment No. 18 has the optimal combination of printing parameters, namely, exposure time of 2.2 s, lifting speed of 80mm/min, and light of delay 1.5 mm/min. This particular approach is effective and appropriate when it's required to find a balance between contending outcomes, like making the printed parts stronger while keeping their dimensions accurate. Grey Relational Analysis (GRA) has been used over other multi-objective methods like TOPSIS because it can handle complicated interactions with little experimental data and makes it easy to rank combinations of parameters. This is why GRA is so useful for studies of additive manufacturing, since it is possible to look at the trade-offs between strength and precision at the same time.

Table 7. Grey Relational coefficient, grade and rank of optimal parameters