Experimental optimization of the interlayer bonding of poly (methyl methacrylate) 3D printing substrates

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Kechagias, Dimitrios Chaidas, Stephanos Zaoutsos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6260832/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Filament 3D printing is a variant of the material extrusion process that has gained popularity for customized applications in various fields. Poly(methyl methacrylate) filaments have been utilized in 3D printing for the fabrication of bespoke biomedical devices and components without requiring post-treatment. This study introduces an experimental approach to optimize interlayer bonding. Therefore, using a second-order Box-Behnken design of experiments, an experimental window was investigated to optimize interlayer bonding quality by investigating the effects of infill density, printing speed, and nozzle temperature. With optimum parameter values, a bending strength of more than 48 MPa and an average surface roughness of less than 10 µm can be achieved. Poly(methyl methacrylate) filament material extrusion 3D-printing optimization experimental design bending Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1 Introduction Although 3D printing technology is often adopted for functional bespoke parts [1], when final dimensions and surface quality are of utmost importance, material removal processes are preferred as the primary or cooperative processes [1]. Infill porosity [2], production time, shell surface and infill body defects, strength [3, 4], and interlaminar bonding [5] should be improved to increase the number of 3D printing applications in the industry [6, 7]. In this context, parameter optimization [8], the development of new composite filaments [9–11], and hybrid manufacturing are crucial for increasing the number of 3D printing products on the market [8]. The molecular mass of the polymer matrix of the molecules and the bonding conditions between strands and layers [9], such as pressure, nozzle diameter, layer thickness, deposition rate, temperatures, and strand geometry, are extremely important to the strength of the outer shell of 3D-printed parts and the internal structural filling [10, 11]. In the literature, the issue of parameter effects of filament 3D printing onto manufactured quality has been studied by many researchers since the late 90s and still remains a hot issue mainly due to the following four causalities: (i) new materials being developed [12, 13], (ii) ironing conditions tuning [14], (iii) environmental conditions [15], and (iv) innovative new strand paths according to the demanded graded material deposition [16]. In Fig. 1, all processing parameters are summarized, demonstrating that optimizing the filament 3D printing process remains a challenge for researchers. This is mainly due to the new data that arise from new filament compositions (pure, blended, or composite filaments) and technological process innovations [17]. Therefore, the effects of the processing parameters are not generalized for all 3D printing filaments. A characteristic paradigm is the effect of layer thickness variation on part porosity, strength, and roughness, with very controversial results in the literature. On the other hand, experimental design aspires to explore process quality issues for parameter tuning and process optimization [18]. The experimental area under study is the primary concern, and the variable parameters and their corresponding levels should be initially screened. However, in screening designs such as Taguchi and Plackett-Burman [19, 20], the experimental combinatorial trials assume linear parameter effects and, therefore, can predict a good parameter combination but not the optimal parameter values. These trials are usually followed by validation experiments to confirm the goodness of the linearity assumption. Due to the highly complex and parameter-dependent filament 3D printing process, the screening experimental design cannot incorporate second-order or cross-interaction products and, therefore, fails to present optimum conditions for all studied parameters [21]. Therefore, a specific experimental window should be run in most cases to determine the optimal solution among the selected parameters (predictors) based on the optimization objectives (responses). In this case, the surface response methodology SRM is the most effective route for experimental design [22]. By typically choosing three variable parameters with three levels each, the selected experimental points (located at the center, faces, or edges of a cube wireframe) can support second-order predictive models with more prominent experimental power than the screening design of experiments DOE cases. Fig. 2 illustrates the route for optimizing the performance of the filament material extrusion process using pure poly(methyl methacrylate) (PMMA) filament. Following Fig. 2, this work builds upon the screening design of previous work in a broader experimental area for PLA 3D printed tensile specimens, testing six parameters: infill density, deposition angle, nozzle temperature, printing speed, layer thickness, and bed temperature, using the Taguchi experimental design [23]. Then, the bending type of loading was investigated to identify the interlayer bonding quality (which is not directly correlated with the tensile strength results) by varying three influential parameters in a smaller experimental window: infill density (90−95−100 %), printing temperature (250−255−260 °C), and printing speed (30−35−40 mm/s) utilizing a second-order design of experiments approach. Additionally, surface roughness measurements were performed for the same conditions to characterize upper surface texture. The results reveal significant interactions between predictors, even if the experimental area was significantly smaller. Multi-objective optimization is followed by the ANOVA and second-order models (desirability approach). To the authors' knowledge, the optimization of bonding conditions (bending strength and upper surface roughness) within the above experimental window for ±45 rectilinear infills (almost isotropic parts), a 0.2 mm layer thickness, and a 100 ºC bed temperature is achieved for the first time in filament 3D printing. 2 Materials and Methods The poly(methyl methacrylate) (PMMA) filament examined in this study was the 3Diakon by Mitsubishi Chemical (1.75 mm diameter, specific gravity 1.14 g/cm³). PMMA is lightweight and rigid, with high impact resistance while maintaining good abrasion resistance and high ultraviolet properties. The specimens were prepared for 3D printing using Cura software and then 3D-printed in a flat position on the platform of a Craftbot Plus 3D printer, utilizing a 0.4 mm nozzle diameter. Mechanical tests were conducted using an INSTRON 3382 universal testing machine with a 100 kN load capacity. Strain-stress outputs were recorded to calculate the bending strength. The flexural specimens were designed and prepared according to the standard ASTM D790 with a strain rate of 1 mm/min. Upper surface roughness parameters Ra (average surface roughness) and Rt (max height) were measured by a nose surface tester (Surftest RJ-210; ISO1997) with a sample line length of 4 mm (0.5 mm/s, Lc=0.8 mm). 2.1 Parameter screening A screening design with six parameters at five levels each (a broader experimental area) was conducted using the Taguchi L 25 (5 ^6 ) orthogonal array for tensile specimens, as presented in [23]. The ANOVA analysis was used to rank the significance of the six parameters. The conclusions were the following: The deposition angle is ranked first for tensile strength; however, it is observed that there are significant differences between 90º and 0º parallel lines. This means that if the loading is not in the direction of deposited lines, the strength is reduced considerably, resulting in high anisotropy. In literature, a ±45° angle (rectilinear infill) was suggested as an alternative to other infill styles to reduce anisotropy; thus, this selection was adopted for the bending tests [24]. The bed temperature was ranked fifth out of six parameters (4.4% error contribution; see Table 4 of [23]). Therefore, the bed temperature was set at 100 ºC, as suggested by the filament manufacturer (±100 ºC). This bed temperature is above the glass transition temperature of PMMA and is appropriate for low strain (1 mm/min here) in the linear viscoelastic regime, as proposed in the literature for similar infill structures (±45 rectilinear) [25]. Layer thickness was ranked sixth out of six parameters (4% error contribution; see Table 4 of [23]). Therefore, layer thickness and Z-offset are kept constant (0.2 mm of each one) to avoid the noise, which follows the literature findings (a rate of ½ for 0.4 mm nozzle diameter) [26]. Nozzle temperature, printing speed, and infill density were ranked second, third, and fourth out of the six critical parameters and were considered for further consideration. Additionally, printing speed and temperature showed complex interactions that need further consideration for the PMMA filament. 2.2 Box-Behnken design A Box-Behnken second-order design with fifteen experiments and three repetitions at the central point was employed in a smaller window experimental area to investigate the flexural strength (Flex-sb; MPa), flexural modulus (Flex-E; MPa), and upper surface roughness parameters (Ra and Rt; μm). The three tested parameters (predictors) were (i) infill density Di, (ii) nozzle temperature Nt, and (iii) printing speed Ps, as communicated in the previous section. Table 1 presents the minimum, center, and maximum levels and codes for each predictor. Table 1 Predictors and codes PMMA (Acrylic) Codes Predictors Abbreviations -1 0 1 Infill Density Di (%) 90 95 100 Nozzle Temperature Nt (ºC) 250 255 260 Printing Speed Ps (mm/s) 30 35 40 All specimens were printed according to the run number listed in Table 2, which presents the fifteen combinations of predictors (Di, Nt, and Ps) and the corresponding observed performance measurements (Flex-sb, Flex-E, Ra, and Rt). The order of the experimental trials was determined randomly to better account for process noise, as the SRM design of experiments suggests. The layer thickness, bed temperature, and Z-offset were kept constant at 0.2 mm, 100 ºC, and 0.2 mm, respectively, to avoid interactions between these parameters that were observed in the screening design [23]. Additionally, a ±45º rectilinear infill was selected to reduce the anisotropy of the printed parts, as recommended in the literature [24]. Material flow and fan speed were set to 95% and zero, respectively, as recommended by the filament manufacturer. Finally, two perimeters, zero roofs, and zero bottom layers were decided. Table 2 Box-Behnken design: three predictors, three codes, and three repetitions in the central point Predictors Responses No. Di (%) Nt (ºC) Ps (mm/s) Flex-sb (MPa) Flex-E (MPa) Ra (μm) Rt (μm) 1 95 260 40 34.49 689.80 6.18 51.33 2 90 250 35 36.62 996.90 21.02 117.65 3 90 255 40 34.14 910.01 23.08 119.38 4 100 250 35 49.55 1449.13 9.64 62.38 5 90 255 30 34.18 889.67 23.64 123.38 6 90 260 35 33.23 865.06 18.35 107.68 7 100 260 35 43.97 1250.84 14.72 86.31 8 95 250 40 41.86 1162.13 6.57 54.63 9 100 255 40 45.77 1284.56 14.41 84.56 10 95 255 35 36.93 990.91 17.83 100.68 11 100 255 30 45.83 1318.03 11.44 74.74 12 95 255 35 35.60 954.22 20.59 109.41 13 95 260 30 37.34 1026.22 21.21 115.53 14 95 255 35 36.83 982.55 19.41 111.30 15 95 250 30 34.66 837.59 14.51 88.76 After the specimens were 3D printed (Fig. 3a), their roughness parameters Ra and Rt were measured (Fig. 3b). Figs 3c and 3d show the broken specimens and dimensions before testing. Figs 3e and 3f show the fracture area section and a scanning electron microscopy photo. All fifteen bending experiments were performed under the same conditions and at the same time, and as shown in Figs 3c, all specimens failed appropriately. According to the second-order polynomial equation, predictors (Xi; here Di, Nt, and Ps) and performances (Yk; here Flex-sb, Flex-E, Ra, and Rt) are related to the following formula in the general form: According to the second-order polynomial equation, predictors (Xi; here Di, Nt, and Ps) and performances (Yk; here Flex-sb, Flex-E, Ra, and Rt) are related to the following formula in the general form: $$\:{Y}_{k}={b}_{0}+\sum\:_{i}^{}{b}_{i}{X}_{i}+\sum\:_{i\ne\:j}^{}{b}_{ij}{X}_{i}{X}_{j}+\sum\:_{i}^{}{b}_{ii}{X}_{i}^{2}\pm\:e$$ 1 where constant (b o ), linear (b i ), cross (b ij ), and quadratic (b ii ) products are assigned between Xi inputs and Yk outputs. 3 Results and Discussion After reviewing the literature [23], three parameters (Di, Nt, and Ps) were tested to meet the bending and surface roughness modeling needs utilizing the Box-Behnken design (BBD). BBD employs three repetitions of the central point to achieve better statistical stability. More specifically, run No. 10, 12, and 14, which use the same 95% Di, 255 ºC Nt and 35 mm/s Ps, show very close output values with a spread lower than 5% for Flex-sb, Flex-E, and Ra and lower than 10% for Rt (i.e., Flex-sb values measured 36.93, 35.60, and 36.83 MPa; Flex-E flex-sb values measured 990.91, 954.22, and 982.55 MPa; Ra values measured 17.83, 20.59, and 19.41 μm; and Rt values measured 100.68, 109.41, 111.30 μm), which in other words this means that no further experiments needed and that the experimental power is enough for all four responses, as proposed by the literature [27]. 3.1 Flexural strength The ANOVA analysis (Table 3), the residual normality test (Fig. 4), the perturbation plots of parameter variations (Fig. 5), and the interaction plots for Flex-sb and Flex-E (Fig. 6) are depicted. It is noteworthy that the regression values of the Flex-sb and Flex-E second-order models are suitable for predictions, with p-values lower than 0.05 and F-values greater than 4; therefore, they are considered accurate models, as both have R² values higher than 95%. Additionally, the Anderson–Darling residual test yields p-values greater than 0.05, which supports the assumption that the residuals follow a normal distribution stochastically (Fig. 4). Moreover, Table 3 and the interaction plots in Fig. 6 demonstrate the significant influence of the cross-product Nt × Ps on Flex-sb and Flex-E, which exhibit complex trend lines, with F-values exceeding 4 (21.47 and 469.46, respectively) and p-values less than 0.05 (0.006 and 0.000, respectively). The other two cross-products are not significant. Finally, in Fig. 7, the response surfaces for Di, Nt, and Ps are observed according to Flex-sb and Flex-E. Table 3 Regression Analysis: Flex-E and Flex-sb versus Di; Nt; Ps Flex-sb Flex-E Par. D.F. S.S. M.S. F− p− S.S. M.S. F− p− Reg. 9 378.011 42.0012 35.71 0.001 611526 67947 292.07 0 Di 1 10.369 10.3687 8.81 0.031 26075 26075 112.08 0 Nt 1 0.858 0.8577 0.73 0.432 1054 1054 4.53 0.087 Ps 1 21.411 21.4112 18.20 0.008 108684 108684 467.17 0.000 Di 2 1 48.944 48.9440 41.61 0.001 104349 104349 448.54 0.000 Nt 2 1 2.068 2.0677 1.76 0.242 46 46 0.2 0.676 Ps 2 1 0.048 0.0481 0.04 0.848 6966 6966 29.94 0.003 Di×Nt 1 1.199 1.1990 1.02 0.359 1104 1104 4.75 0.081 Di×Ps 1 0.000 0.0001 0.00 0.993 724 724 3.11 0.138 Nt×Ps 1 25.251 25.2506 21.47 0.006 109217 109217 469.46 0.000 Error 5 5.881 1.1763 1163 233 Lack-of-Fit 3 4.784 1.5947 2.91 0.266 424 141 0.38 0.78 Pure-Error 2 1.097 0.5486 740 370 Total 14 383.893 612689 S 1.08456 15.2526 R 2 98.47% 99.81% 3.2 Surface roughness Follow the ANOVA analysis (Table 4), the residual normality test (Fig. 8), and the perturbation plots of parameter variations (Fig. 9) for Ra and Rt. It is worth noting that the Ra and Rt second-order models' regression values are not suitable for predictions with p-values higher than 0.05 and F-values lower than 4; therefore, they are not considered accurate models but rather for illustrating the trend lines of parameter effects. The noise likely depends on the filament material flow during deposition, which is influenced by the filament diameter (1.75 ± 0.05 mm), feed rate, and deposition velocity. On the other hand, the Anderson–Darling residual test yields p-values greater than 0.05, which supports the assumption that the residuals follow a normal distribution well. Thus, we can generalize the results even if the noise is higher than 5%. Additionally, Table 4 shows that the Nt and Nt 2 terms have the most significant influence on Ra and Rt, yielding F-values close to 4, which is considered the threshold for determining a term's significance [20]. In the case of Ra and Rt, the interaction charts are not considered necessary after ANOVA analysis. Lastly, in Fig. 10, the response surfaces between the predictors and the Ra and Rt responses are shown. Table 4 Regression Analysis: Ra and Rt versus Di; Nt; Ps Ra Rt Par. D.F. S.S. M.S. F− p− S.S. M.S. F− p− Reg. 9 364.394 40.488 2.24 0.194 6778 753.11 2.62 0.151 Di 1 24.433 24.433 1.35 0.298 405.49 405.49 1.41 0.288 Nt 1 70.783 70.783 3.91 0.105 1062.58 1062.58 3.7 0.113 Ps 1 14.077 14.077 0.78 0.418 271.29 271.29 0.94 0.376 Di 2 1 6.648 6.648 0.37 0.571 80.3 80.3 0.28 0.62 Nt 2 1 81.075 81.075 4.48 0.088 1234.79 1234.79 4.3 0.093 Ps 2 1 22.557 22.557 1.25 0.315 469.74 469.74 1.63 0.257 Di×Nt 1 15.012 15.012 0.83 0.404 287.32 287.32 1 0.363 Di×Ps 1 3.115 3.115 0.17 0.695 47.8 47.8 0.17 0.7 Nt×Ps 1 12.578 12.578 0.69 0.442 226.02 226.02 0.79 0.416 Error 5 90.5 18.1 1437.45 287.49 Lack-of-Fit 3 86.68 28.893 15.13 0.063 1373.26 457.75 14.26 0.066 Pure-Error 2 3.82 1.91 64.19 32.09 Total 14 454.893 454.893 S 4.2544 16.9555 R 2 80.11% 82.50% 3.3 Optimization By adopting the above second-order models and setting the desirability function to minimize Flex-sb and Flex-E and minimize Ra and Rt, the optimum parameter values are 100% Di, 250 ºC Nt, and 40 mm/s Ps (Fig. 11a), as well as the Nt and Ps values that give Ra lower than 10 μm and Flex-sb higher than 48 MPa keeping Di at 100% (Fig. 11b). 4 Conclusions Each filament material extrusion process should have its parameters tuned to achieve the highest quality performance. In cases where multiple objectives, such as strength properties and surface quality, are of utmost importance, the optimization process is not a routine matter and is certainly not merely a statistical study. Therefore, in this work, an appropriate experimental design was developed and followed, after a previous screening design for evaluating the three ‘fractionally significant’ parameters. The proposed approach achieves improved flexural and surface properties for PMMA ± 45 rectilinear infill (showed non-significant anisotropy; see Birosz et al [ 24 ]), which are similar to Polyjet and SLS processes in X and Y directions as in the literature pointed out (see Reyes et al. (2022) [ 28 ]), but lower than milling pure PMMA specimens. In the literature, we have observed better PMMA filament material extrusion part flexural properties for parts with all lines aligned in the same direction (loading direction) and lower layer thickness [ 29 ]. However, in these cases, the mechanical properties are anisotropic. Therefore, although the nozzle temperatures and printing speeds differ for each material, it is straightforward to follow the proposed experimental procedure, and with a minimal experimental power of fifteen runs, to optimize the interlaminar bonding process. The above stochastic study can be extended to include more filaments and utilized further in all 3D printing processes for process optimization and planning, with minimal experimental effort, without compromising experimental power. Declarations Author contribution statement John D. Kechagias: conceptualization, methodology, writing, data curation, original draft, supervision; Dimitrios Chaidas: experimental data; Stephanos Zaoutsos: data curation, analysis, review Conflict of interest The author(s) declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article Data availability Data will be made available upon request References Zhong Z-W (2020) Advanced polishing, grinding and finishing processes for various manufacturing applications: a review. Mater Manuf Process 35:1279–1303. https://doi.org/10.1080/10426914.2020.1772481 Al-Maharma AY, Patil SP, Markert B (2020) Effects of porosity on the mechanical properties of additively manufactured components: a critical review. Mater Res Express 7:122001. https://doi.org/10.1088/2053-1591/abcc5d Wickramasinghe S, Do T, Tran P (2020) FDM-Based 3D Printing of Polymer and Associated Composite: A Review on Mechanical Properties, Defects and Treatments. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6260832","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":432779208,"identity":"73ed8988-d200-47eb-9601-443e73c6d991","order_by":0,"name":"John D. Kechagias","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBACxh4GBmYgLcfAwEOiFmMGNmK1gMwGaUlsIFoLc8/hg58LamrTN9zvPcD4dQ8xDuttS5aecex47oZjfAnMMs+I0dLPY8bMw3YMqIXHgFniAFFa+L8x8/w7lm5AvJbeHjZm3raaBJAWxg9Eaek5ZizN23fAcOaxHIPDDMRoMexJfviZ51udPN/hM4YPfxClpQFMHYaQREWNPISqg7jyBzFaRsEoGAWjYMQBALy8NnkOlutKAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-5768-4285","institution":"University of Thessaly: Panepistemio Thessalias","correspondingAuthor":true,"prefix":"","firstName":"John","middleName":"D.","lastName":"Kechagias","suffix":""},{"id":432779209,"identity":"ab772165-a0ec-45b0-ac2c-57330a0d0ead","order_by":1,"name":"Dimitrios Chaidas","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Dimitrios","middleName":"","lastName":"Chaidas","suffix":""},{"id":432779210,"identity":"e3eeecda-364f-445a-87bc-66f1cb62ee3c","order_by":2,"name":"Stephanos Zaoutsos","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Stephanos","middleName":"","lastName":"Zaoutsos","suffix":""}],"badges":[],"createdAt":"2025-03-19 10:54:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6260832/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6260832/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79672356,"identity":"f942ca49-5b42-4e59-8a4a-1e633e9dada4","added_by":"auto","created_at":"2025-04-01 11:28:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":112916,"visible":true,"origin":"","legend":"\u003cp\u003eParameter tuning for filament 3D printing process\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/c7c28f16b88cdee19039c4bd.png"},{"id":79671098,"identity":"9e5a7611-4c3c-4a04-afbc-125efcc8769e","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":52252,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental design steps and data processing\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/ae57b5c01f3f0b322bb07653.png"},{"id":79671110,"identity":"a0cb366f-43cd-47c2-be55-e9334d111d70","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1063177,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 3D printing process, (b) specimens’ Ra and Rt measurements, (c) PMMA broken parts, (d) width and thickness measurements before testing, (e) fracture surface, and (f) SEM image of the fracture surface\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/c14f6b1ef974b000a7bf5e5a.png"},{"id":79671106,"identity":"41d0f067-a886-4bc3-91bb-8961d7d42205","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":144783,"visible":true,"origin":"","legend":"\u003cp\u003eResidual normality test for Flex-sb and Flex-E\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/01c50a1555359d145b6361ca.png"},{"id":79671100,"identity":"6108fa56-4498-4e2a-b19d-efdf0b0e2703","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":75268,"visible":true,"origin":"","legend":"\u003cp\u003ePerturbation plots according to the 2\u003csup\u003end\u003c/sup\u003e-order models for Flex-sb and Flex-E\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/5b3b0bf8d46abe2cfad3ce93.png"},{"id":79672535,"identity":"28cf46b9-a49f-4c39-856f-f777dcf460f3","added_by":"auto","created_at":"2025-04-01 11:36:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":160840,"visible":true,"origin":"","legend":"\u003cp\u003eInteraction plots for Flex-sb and Flex-E\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/ee29c388f9b997a9a7886583.png"},{"id":79671403,"identity":"b25cc4d7-7b59-4f66-8e7d-a457ca8d258f","added_by":"auto","created_at":"2025-04-01 11:20:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":210743,"visible":true,"origin":"","legend":"\u003cp\u003eSurface response fitting of the second-order equation for Flex-sb and Flex-E\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/bd28e44e6673c326a341c4c7.png"},{"id":79671103,"identity":"d56a06d2-59c7-4bca-94ec-ea62b279e62b","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":141581,"visible":true,"origin":"","legend":"\u003cp\u003eResidual normality test for Ra and Rt\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/508a7c7b7b15266892a41a47.png"},{"id":79671408,"identity":"6c2a61bc-b86b-40ff-bbdb-5975d18d909b","added_by":"auto","created_at":"2025-04-01 11:20:06","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":76999,"visible":true,"origin":"","legend":"\u003cp\u003ePerturbation plots according to the 2\u003csup\u003end\u003c/sup\u003e-order models for Ra and Rt\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/12d16ea6c1c34d586cb6e4a8.png"},{"id":79671117,"identity":"a3f4ec82-ae5e-431f-8eb3-50b4d4e76f0f","added_by":"auto","created_at":"2025-04-01 11:12:06","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":249613,"visible":true,"origin":"","legend":"\u003cp\u003eSurface response fitting of the second-order equation for Ra and Rt\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/540a9740dea5fc5c4beb4849.png"},{"id":79672360,"identity":"7263616f-4c83-49ee-8f1c-e7294dbf8175","added_by":"auto","created_at":"2025-04-01 11:28:06","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":439030,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Optimized values, and (b) Experimental area of Flex-sb\u0026gt;48MPa and Ra\u0026lt;10μm (100% Di)\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/c976a440653b41fe01224ce5.png"},{"id":82253022,"identity":"18437385-14e3-404e-98cb-b4d0b50e3987","added_by":"auto","created_at":"2025-05-08 10:29:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3764680,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6260832/v1/3f11e54b-db3e-45da-8b4e-aa77b66cf96c.pdf"}],"financialInterests":"","formattedTitle":"Experimental optimization of the interlayer bonding of poly (methyl methacrylate) 3D printing substrates","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eAlthough 3D printing technology is often adopted for functional bespoke parts [1], when final dimensions and surface quality are of utmost importance, material removal processes are preferred as the primary or cooperative processes [1]. Infill porosity [2], production time, shell surface and infill body defects, strength [3, 4], and interlaminar bonding [5] should be improved to increase the number of 3D printing applications in the industry [6, 7]. In this context, parameter optimization [8], the development of new composite filaments [9\u0026ndash;11], and hybrid manufacturing are crucial for increasing the number of 3D printing products on the market [8]. The molecular mass of the polymer matrix of the molecules and the bonding conditions between strands and layers [9], such as pressure, nozzle diameter, layer thickness, deposition rate, temperatures, and strand geometry, are extremely important to the strength of the outer shell of 3D-printed parts and the internal structural filling [10, 11].\u003c/p\u003e\n\u003cp\u003eIn the literature, the issue of parameter effects of filament 3D printing onto manufactured quality has been studied by many researchers since the late 90s and still remains a hot issue mainly due to the following four causalities: (i) new materials being developed [12, 13], (ii) ironing conditions tuning [14], (iii) environmental conditions [15], and (iv) innovative new strand paths according to the demanded graded material deposition [16].\u003c/p\u003e\n\u003cp\u003eIn Fig. 1, all processing parameters are summarized, demonstrating that optimizing the filament 3D printing process remains a challenge for researchers. This is mainly due to the new data that arise from new filament compositions (pure, blended, or composite filaments) and technological process innovations [17]. Therefore, the effects of the processing parameters are not generalized for all 3D printing filaments. A characteristic paradigm is the effect of layer thickness variation on part porosity, strength, and roughness, with very controversial results in the literature.\u003c/p\u003e\n\u003cp\u003eOn the other hand, experimental design aspires to explore process quality issues for parameter tuning and process optimization [18]. The experimental area under study is the primary concern, and the variable parameters and their corresponding levels should be initially screened. However, in screening designs such as Taguchi and Plackett-Burman [19, 20], the experimental combinatorial trials assume linear parameter effects and, therefore, can predict a good parameter combination but not the optimal parameter values. These trials are usually followed by validation experiments to confirm the goodness of the linearity assumption.\u003c/p\u003e\n\u003cp\u003eDue to the highly complex and parameter-dependent filament 3D printing process, the screening experimental design cannot incorporate second-order or cross-interaction products and, therefore, fails to present optimum conditions for all studied parameters [21]. Therefore, a specific experimental window should be run in most cases to determine the optimal solution among the selected parameters (predictors) based on the optimization objectives (responses). In this case, the surface response methodology SRM is the most effective route for experimental design [22]. By typically choosing three variable parameters with three levels each, the selected experimental points (located at the center, faces, or edges of a cube wireframe) can support second-order predictive models with more prominent experimental power than the screening design of experiments DOE cases.\u003c/p\u003e\n\u003cp\u003eFig. 2 illustrates the route for optimizing the performance of the filament material extrusion process using pure poly(methyl methacrylate) (PMMA) filament.\u003c/p\u003e\n\u003cp\u003eFollowing Fig. 2, this work builds upon the screening design of previous work in a broader experimental area for PLA 3D printed tensile specimens, testing six parameters: infill density, deposition angle, nozzle temperature, printing speed, layer thickness, and bed temperature, using the Taguchi experimental design [23]. Then, the bending type of loading was investigated to identify the interlayer bonding quality (which is not directly correlated with the tensile strength results) by varying three influential parameters in a smaller experimental window: infill density (90\u0026minus;95\u0026minus;100 %), printing temperature (250\u0026minus;255\u0026minus;260 \u0026deg;C), and printing speed (30\u0026minus;35\u0026minus;40 mm/s) utilizing a second-order design of experiments approach. Additionally, surface roughness measurements were performed for the same conditions to characterize upper surface texture.\u003c/p\u003e\n\u003cp\u003eThe results reveal significant interactions between predictors, even if the experimental area was significantly smaller. Multi-objective optimization is followed by the ANOVA and second-order models (desirability approach).\u003c/p\u003e\n\u003cp\u003eTo the authors\u0026apos; knowledge, the optimization of bonding conditions (bending strength and upper surface roughness) within the above experimental window for \u0026plusmn;45 rectilinear infills (almost isotropic parts), a 0.2 mm layer thickness, and a 100 \u0026ordm;C bed temperature is achieved for the first time in filament 3D printing.\u003c/p\u003e"},{"header":"2 Materials and Methods","content":"\u003cp\u003eThe poly(methyl methacrylate) (PMMA) filament examined in this study was the 3Diakon by Mitsubishi Chemical (1.75 mm diameter, specific gravity 1.14 g/cm\u0026sup3;). PMMA is lightweight and rigid, with high impact resistance while maintaining good abrasion resistance and high ultraviolet properties. The specimens were prepared for 3D printing using Cura software and then 3D-printed in a flat position on the platform of a Craftbot Plus 3D printer, utilizing a 0.4 mm nozzle diameter.\u003c/p\u003e\n\u003cp\u003eMechanical tests were conducted using an INSTRON 3382 universal testing machine with a 100 kN load capacity. Strain-stress outputs were recorded to calculate the bending strength. The flexural specimens were designed and prepared according to the standard ASTM D790 with a strain rate of 1 mm/min.\u003c/p\u003e\n\u003cp\u003eUpper surface roughness parameters Ra (average surface roughness) and Rt (max height) were measured by a nose surface tester (Surftest RJ-210; ISO1997) with a sample line length of 4 mm (0.5 mm/s, Lc=0.8 mm).\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e\u003cem\u003e2.1 Parameter screening\u003c/em\u003e\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eA screening design with six parameters at five levels each (a broader experimental area) was conducted using the Taguchi L\u003csub\u003e25\u003c/sub\u003e (5\u003csup\u003e^6\u003c/sup\u003e) orthogonal array for tensile specimens, as presented in [23]. The ANOVA analysis was used to rank the significance of the six parameters. The conclusions were the following:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eThe deposition angle is ranked first for tensile strength; however, it is observed that there are significant differences between 90\u0026ordm; and 0\u0026ordm; parallel lines. This means that if the loading is not in the direction of deposited lines, the strength is reduced considerably, resulting in high anisotropy. In literature, a \u0026plusmn;45\u0026deg; angle (rectilinear infill) was suggested as an alternative to other infill styles to reduce anisotropy; thus, this selection was adopted for the bending tests [24].\u003c/li\u003e\n \u003cli\u003eThe bed temperature was ranked fifth out of six parameters (4.4% error contribution; see Table 4 of [23]). Therefore, the bed temperature was set at 100 \u0026ordm;C, as suggested by the filament manufacturer (\u0026plusmn;100 \u0026ordm;C). This bed temperature is above the glass transition temperature of PMMA and is appropriate for low strain (1 mm/min here) in the linear viscoelastic regime, as proposed in the literature for similar infill structures (\u0026plusmn;45 rectilinear) [25].\u003c/li\u003e\n \u003cli\u003eLayer thickness was ranked sixth out of six parameters (4% error contribution; see Table 4 of [23]). Therefore, layer thickness and Z-offset are kept constant (0.2 mm of each one) to avoid the noise, which follows the literature findings (a rate of \u0026frac12; for 0.4 mm nozzle diameter) [26].\u003c/li\u003e\n \u003cli\u003eNozzle temperature, printing speed, and infill density were ranked second, third, and fourth out of the six critical parameters and were considered for further consideration. Additionally, printing speed and temperature showed complex interactions that need further consideration for the PMMA filament.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2\u003e\u003cstrong\u003e\u003cem\u003e2.2 Box-Behnken design\u003c/em\u003e\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eA Box-Behnken second-order design with fifteen experiments and three repetitions at the central point was employed in a smaller window experimental area to investigate the flexural strength (Flex-sb; MPa), flexural modulus (Flex-E; MPa), and upper surface roughness parameters (Ra and Rt; \u0026mu;m). The three tested parameters (predictors) were (i) infill density Di, (ii) nozzle temperature Nt, and (iii) printing speed Ps, as communicated in the previous section. Table 1 presents the minimum, center, and maximum levels and codes for each predictor.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Predictors and codes\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003ePMMA (Acrylic)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 298px;\"\u003e\n \u003cp\u003eCodes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 151px;\"\u003e\n \u003cp\u003ePredictors\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eAbbreviations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 90px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 151px;\"\u003e\n \u003cp\u003eInfill Density\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eDi (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 90px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 151px;\"\u003e\n \u003cp\u003eNozzle Temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eNt (\u0026ordm;C)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 90px;\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 151px;\"\u003e\n \u003cp\u003ePrinting Speed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003ePs (mm/s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 90px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAll specimens were printed according to the run number listed in Table 2, which presents the fifteen combinations of predictors (Di, Nt, and Ps) and the corresponding observed performance measurements (Flex-sb, Flex-E, Ra, and Rt). The order of the experimental trials was determined randomly to better account for process noise, as the SRM design of experiments suggests.\u003c/p\u003e\n\u003cp\u003eThe layer thickness, bed temperature, and Z-offset were kept constant at 0.2 mm, 100 \u0026ordm;C, and 0.2 mm, respectively, to avoid interactions between these parameters that were observed in the screening design [23]. Additionally, a \u0026plusmn;45\u0026ordm; rectilinear infill was selected to reduce the anisotropy of the printed parts, as recommended in the literature\u0026nbsp;[24].\u0026nbsp;Material flow and fan speed were set to 95% and zero, respectively, as recommended by the filament manufacturer. Finally, two perimeters, zero roofs, and zero bottom layers were decided.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e Box-Behnken design: three predictors, three codes, and three repetitions in the central point\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"557\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 170px;\"\u003e\n \u003cp\u003ePredictors\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 331px;\"\u003e\n \u003cp\u003eResponses\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eNo.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eDi\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eNt\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(\u0026ordm;C)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003ePs\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(mm/s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003eFlex-sb\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eFlex-E\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003eRa\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(\u0026mu;m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003eRt\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(\u0026mu;m)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e34.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e689.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e6.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e51.33\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e36.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e996.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e21.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e117.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e34.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e910.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e23.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e119.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e49.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1449.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e9.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e62.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e34.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e889.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e23.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e123.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e33.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e865.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e18.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e107.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e43.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1250.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e14.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e86.31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e41.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1162.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e6.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e54.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e45.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1284.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e14.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e84.56\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e10\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e95\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e255\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e35\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e36.93\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e990.91\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e17.83\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e100.68\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e45.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1318.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e11.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e74.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e12\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e95\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e255\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e35\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e35.60\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e954.22\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e20.59\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e109.41\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e37.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e1026.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e21.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e115.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e14\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e95\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e255\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e35\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e36.83\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e982.55\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e19.41\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e111.30\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 95px;\"\u003e\n \u003cp\u003e34.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e837.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e14.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e88.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAfter the specimens were 3D printed (Fig. 3a), their roughness parameters Ra and Rt were measured (Fig. 3b). Figs 3c and 3d show the broken specimens and dimensions before testing. Figs 3e and 3f show the fracture area section and a scanning electron microscopy photo. All fifteen bending experiments were performed under the same conditions and at the same time, and as shown in Figs 3c, all specimens failed appropriately.\u003c/p\u003e\n\u003cp\u003eAccording to the second-order polynomial equation, predictors (Xi; here Di, Nt, and Ps) and performances (Yk; here Flex-sb, Flex-E, Ra, and Rt) are related to the following formula in the general form:\u003c/p\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003cp\u003eAccording to the second-order polynomial equation, predictors (Xi; here Di, Nt, and Ps) and performances (Yk; here Flex-sb, Flex-E, Ra, and Rt) are related to the following formula in the general form:\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$$\\:{Y}_{k}={b}_{0}+\\sum\\:_{i}^{}{b}_{i}{X}_{i}+\\sum\\:_{i\\ne\\:j}^{}{b}_{ij}{X}_{i}{X}_{j}+\\sum\\:_{i}^{}{b}_{ii}{X}_{i}^{2}\\pm\\:e$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere constant (b\u003csub\u003eo\u003c/sub\u003e), linear (b\u003csub\u003ei\u003c/sub\u003e), cross (b\u003csub\u003eij\u003c/sub\u003e), and quadratic (b\u003csub\u003eii\u003c/sub\u003e) products are assigned between Xi inputs and Yk outputs.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3 Results and Discussion","content":"\u003cp\u003eAfter reviewing the literature [23], three parameters (Di, Nt, and Ps) were tested to meet the bending and surface roughness modeling needs utilizing the Box-Behnken design (BBD).\u003c/p\u003e\n\u003cp\u003eBBD employs three repetitions of the central point to achieve better statistical stability. More specifically, run No. 10, 12, and 14, which use the same 95% Di, 255 \u0026ordm;C Nt and 35 mm/s Ps, show very close output values with a spread lower than 5% for Flex-sb, Flex-E, and Ra and lower than 10% for Rt (i.e., Flex-sb values measured 36.93, 35.60, and 36.83 MPa; Flex-E flex-sb values measured 990.91, 954.22, and 982.55 MPa; Ra values measured 17.83, 20.59, and 19.41 \u0026mu;m; and Rt values measured 100.68, 109.41, 111.30 \u0026mu;m), which in other words this means that no further experiments needed and that the experimental power is enough for all four responses, as proposed by the literature [27].\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e\u003cem\u003e3.1 Flexural strength\u003c/em\u003e\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eThe ANOVA analysis (Table 3), the residual normality test (Fig. 4), the perturbation plots of parameter variations (Fig. 5), and the interaction plots for Flex-sb and Flex-E (Fig. 6) are depicted.\u003c/p\u003e\n\u003cp\u003eIt is noteworthy that the regression values of the Flex-sb and Flex-E second-order models are suitable for predictions, with p-values lower than 0.05 and F-values greater than 4; therefore, they are considered accurate models, as both have R\u0026sup2; values higher than 95%. Additionally, the Anderson\u0026ndash;Darling residual test yields p-values greater than 0.05, which supports the assumption that the residuals follow a normal distribution stochastically (Fig. 4).\u003c/p\u003e\n\u003cp\u003eMoreover, Table 3 and the interaction plots in Fig. 6 demonstrate the significant influence of the cross-product Nt \u0026times; Ps on Flex-sb and Flex-E, which exhibit complex trend lines, with F-values exceeding 4 (21.47 and 469.46, respectively) and p-values less than 0.05 (0.006 and 0.000, respectively). The other two cross-products are not significant.\u003c/p\u003e\n\u003cp\u003eFinally, in Fig. 7, the response surfaces for Di, Nt, and Ps are observed according to Flex-sb and Flex-E.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3\u003c/strong\u003e Regression Analysis: Flex-E and Flex-sb versus Di; Nt; Ps\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"565\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eFlex-sb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eFlex-E\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003ePar.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003eD.F.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eS.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eM.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003eF\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003ep\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eS.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eM.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eF\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003ep\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eReg.\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e9\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e378.011\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e42.0012\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e35.71\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.001\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e611526\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e67947\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e292.07\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDi\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e10.369\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e10.3687\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e8.81\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.031\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e26075\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e26075\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e112.08\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eNt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.858\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.8577\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.432\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e1054\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e1054\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e4.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.087\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePs\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e21.411\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e21.4112\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e18.20\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.008\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e108684\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e108684\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e467.17\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.000\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDi\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e48.944\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e48.9440\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e41.61\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.001\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e104349\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e104349\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e448.54\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.000\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eNt\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e2.068\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e2.0677\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.242\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.676\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003ePs\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.048\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.0481\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.848\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e6966\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e6966\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e29.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eDi\u0026times;Nt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1.199\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1.1990\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.359\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e1104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e1104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e4.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.081\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eDi\u0026times;Ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.993\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e724\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e724\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.138\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eNt\u0026times;Ps\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e25.251\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e25.2506\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e21.47\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.006\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e109217\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e109217\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e469.46\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.000\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eError\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e5.881\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1.1763\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e1163\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eLack-of-Fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e4.784\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1.5947\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.266\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e424\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003ePure-Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1.097\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e0.5486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e740\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e370\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e383.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e612689\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\" style=\"width: 275px;\"\u003e\n \u003cp\u003e1.08456\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003e15.2526\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\" style=\"width: 275px;\"\u003e\n \u003cp\u003e98.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003e99.81%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003ch2\u003e\u003cstrong\u003e\u003cem\u003e3.2 Surface roughness\u003c/em\u003e\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eFollow the ANOVA analysis (Table 4), the residual normality test (Fig. 8), and the perturbation plots of parameter variations (Fig. 9) for Ra and Rt. It is worth noting that the Ra and Rt second-order models\u0026apos; regression values are not suitable for predictions with p-values higher than 0.05 and F-values lower than 4; therefore, they are not considered accurate models but rather for illustrating the trend lines of parameter effects. The noise likely depends on the filament material flow during deposition, which is influenced by the filament diameter (1.75 \u0026plusmn; 0.05 mm), feed rate, and deposition velocity. On the other hand, the Anderson\u0026ndash;Darling residual test yields p-values greater than 0.05, which supports the assumption that the residuals follow a normal distribution well. Thus, we can generalize the results even if the noise is higher than 5%. Additionally, Table 4 shows that the Nt and Nt\u003csup\u003e2\u003c/sup\u003e terms have the most significant influence on Ra and Rt, yielding F-values close to 4, which is considered the threshold for determining a term\u0026apos;s significance [20].\u003c/p\u003e\n\u003cp\u003eIn the case of Ra and Rt, the interaction charts are not considered necessary after ANOVA analysis. Lastly, in Fig. 10, the response surfaces between the predictors and the Ra and Rt responses are shown.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e Regression Analysis: Ra and Rt versus Di; Nt; Ps\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 226px;\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eRt\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003ePar.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003eD.F.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eS.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eM.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003eF\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003ep\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eS.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eM.S.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003eF\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003ep\u0026minus;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eReg.\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e9\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e364.394\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e40.488\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.24\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.194\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e6778\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e753.11\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.62\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.151\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eDi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e24.433\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e24.433\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.298\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e405.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e405.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.288\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eNt\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e70.783\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e70.783\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.91\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.105\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1062.58\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1062.58\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.7\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.113\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003ePs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e14.077\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e14.077\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.418\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e271.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e271.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.376\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eDi\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e6.648\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e6.648\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.571\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e80.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e80.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eNt\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e81.075\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e81.075\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.48\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.088\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1234.79\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1234.79\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.3\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e0.093\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003ePs\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e22.557\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e22.557\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.315\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e469.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e469.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.257\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eDi\u0026times;Nt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e15.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e15.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.404\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e287.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e287.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.363\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eDi\u0026times;Ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e3.115\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e3.115\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.695\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e47.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e47.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eNt\u0026times;Ps\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e12.578\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e12.578\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.442\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e226.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e226.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.416\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eError\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e90.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e18.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1437.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e287.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eLack-of-Fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e86.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e28.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e15.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.063\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e1373.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e457.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e14.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e0.066\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003ePure-Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e3.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e64.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e32.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 42px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e454.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e454.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\" style=\"width: 267px;\"\u003e\n \u003cp\u003e4.2544\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003e16.9555\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 62px;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\" style=\"width: 267px;\"\u003e\n \u003cp\u003e80.11%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003e82.50%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e\u003cem\u003e3.3 Optimization\u003c/em\u003e\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eBy adopting the above second-order models and setting the desirability function to minimize Flex-sb and Flex-E and minimize Ra and Rt, the optimum parameter values are 100% Di, 250 \u0026ordm;C Nt, and 40 mm/s Ps (Fig. 11a), as well as the Nt and Ps values that give Ra lower than 10 \u0026mu;m and Flex-sb higher than 48 MPa keeping Di at 100% (Fig. 11b).\u003c/p\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eEach filament material extrusion process should have its parameters tuned to achieve the highest quality performance. In cases where multiple objectives, such as strength properties and surface quality, are of utmost importance, the optimization process is not a routine matter and is certainly not merely a statistical study. Therefore, in this work, an appropriate experimental design was developed and followed, after a previous screening design for evaluating the three \u0026lsquo;fractionally significant\u0026rsquo; parameters.\u003c/p\u003e \u003cp\u003eThe proposed approach achieves improved flexural and surface properties for PMMA\u0026thinsp;\u0026plusmn;\u0026thinsp;45 rectilinear infill (showed non-significant anisotropy; see Birosz et al [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]), which are similar to Polyjet and SLS processes in X and Y directions as in the literature pointed out (see Reyes et al. (2022) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]), but lower than milling pure PMMA specimens. In the literature, we have observed better PMMA filament material extrusion part flexural properties for parts with all lines aligned in the same direction (loading direction) and lower layer thickness [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. However, in these cases, the mechanical properties are anisotropic.\u003c/p\u003e \u003cp\u003eTherefore, although the nozzle temperatures and printing speeds differ for each material, it is straightforward to follow the proposed experimental procedure, and with a minimal experimental power of fifteen runs, to optimize the interlaminar bonding process.\u003c/p\u003e \u003cp\u003eThe above stochastic study can be extended to include more filaments and utilized further in all 3D printing processes for process optimization and planning, with minimal experimental effort, without compromising experimental power.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contribution statement\u003c/strong\u003e John D. Kechagias: conceptualization, methodology, writing, data curation, original draft, supervision; Dimitrios Chaidas: experimental data; Stephanos Zaoutsos: data curation, analysis, review\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e The author(s) declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e Data will be made available upon request\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eZhong Z-W (2020) Advanced polishing, grinding and finishing processes for various manufacturing applications: a review. Mater Manuf Process 35:1279\u0026ndash;1303. https://doi.org/10.1080/10426914.2020.1772481\u003c/li\u003e\n\u003cli\u003eAl-Maharma AY, Patil SP, Markert B (2020) Effects of porosity on the mechanical properties of additively manufactured components: a critical review. 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Rapid Prototyp J 27:562\u0026ndash;582. https://doi.org/10.1108/RPJ-08-2019-0230\u003c/li\u003e\n\u003cli\u003eBianchi I, Forcellese A, Mancia T, et al (2022) Process parameters effect on environmental sustainability of composites FFF technology. Mater Manuf Process 37:591\u0026ndash;601. https://doi.org/10.1080/10426914.2022.2049300\u003c/li\u003e\n\u003cli\u003eKristiawan RB, Imaduddin F, Ariawan D, et al (2021) A review on the fused deposition modeling (FDM) 3D printing: Filament processing, materials, and printing parameters. Open Eng 11:639\u0026ndash;649. https://doi.org/10.1515/eng-2021-0063\u003c/li\u003e\n\u003cli\u003eBlaj M, Oancea G (2021) Fused deposition modelling process: a literature review. IOP Conf Ser Mater Sci Eng 1009:012006. https://doi.org/10.1088/1757-899X/1009/1/012006\u003c/li\u003e\n\u003cli\u003eCarlyle WM, Montgomery DC, Runger GC (2000) Optimization Problems and Methods in Quality Control and Improvement. J Qual Technol 32:1\u0026ndash;17. https://doi.org/10.1080/00224065.2000.11979963\u003c/li\u003e\n\u003cli\u003eVanaja K, Shobha Rani RH (2007) Design of Experiments: Concept and Applications of Plackett Burman Design. Clin Res Regul Aff 24:1\u0026ndash;23. https://doi.org/10.1080/10601330701220520\u003c/li\u003e\n\u003cli\u003ePhadke MS (1989) Quality engineering using robust design. Prentice Hall PTR, Englewood Cliffs, New Jersey 07632\u003c/li\u003e\n\u003cli\u003eCosta N (2019) Design of experiments \u0026ndash; overcome hindrances and bad practices. TQM J 31:772\u0026ndash;789. https://doi.org/10.1108/TQM-02-2019-0035\u003c/li\u003e\n\u003cli\u003eMontgomery DC (2012) Design and Analysis of Experiments, eighth ed. Wiley, Hoboken, NJ, USA\u003c/li\u003e\n\u003cli\u003eKechagias JD, Vidakis N, Petousis M, Mountakis N (2023) A multi-parametric process evaluation of the mechanical response of PLA in FFF 3D printing. Mater Manuf Process 38:941\u0026ndash;953. https://doi.org/10.1080/10426914.2022.2089895\u003c/li\u003e\n\u003cli\u003eBirosz MT, Ledeny\u0026aacute;k D, And\u0026oacute; M (2022) Effect of FDM infill patterns on mechanical properties. Polym Test 113:107654. https://doi.org/10.1016/j.polymertesting.2022.107654\u003c/li\u003e\n\u003cli\u003eStreet DP, Ledford WK, Allison AA, et al (2019) Self-Complementary Multiple Hydrogen-Bonding Additives Enhance Thermomechanical Properties of 3D-Printed PMMA Structures. Macromolecules 52:5574\u0026ndash;5582. https://doi.org/10.1021/acs.macromol.9b00546\u003c/li\u003e\n\u003cli\u003eLiu Y, Bai W, Cheng X, et al (2021) Effects of printing layer thickness on mechanical properties of 3D-printed custom trays. J Prosthet Dent 126:671.e1-671.e7. https://doi.org/10.1016/j.prosdent.2020.08.025\u003c/li\u003e\n\u003cli\u003eMontgomery DC, Lynch C (2023) Optimal Experimental Designs for Hypothesis Testing with Multiple Factors: Maximizing Power for the Biological Sciences. Int J Exp Des Proc Opt 1:. https://doi.org/10.1504/IJEDPO.2023.10061657\u003c/li\u003e\n\u003cli\u003eGarc\u0026iacute;a Reyes M, Bataller Torras A, Cabrera Carrillo JA, et al (2022) A study of tensile and bending properties of 3D-printed biocompatible materials used in dental appliances. J Mater Sci 57:2953\u0026ndash;2968. https://doi.org/10.1007/s10853-021-06811-3\u003c/li\u003e\n\u003cli\u003eObaeed NH, Hamdan W (2024) Optimizing Fused Deposition Modelling Process Parameters for Medical Grade Polymethylmethacrylate Flexural Strength. Adv Sc Techn Research J 18:349\u0026ndash;359. https://doi.org/10.12913/22998624/182876\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Poly(methyl methacrylate), filament material extrusion, 3D-printing, optimization, experimental design, bending","lastPublishedDoi":"10.21203/rs.3.rs-6260832/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6260832/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFilament 3D printing is a variant of the material extrusion process that has gained popularity for customized applications in various fields. Poly(methyl methacrylate) filaments have been utilized in 3D printing for the fabrication of bespoke biomedical devices and components without requiring post-treatment. This study introduces an experimental approach to optimize interlayer bonding. Therefore, using a second-order Box-Behnken design of experiments, an experimental window was investigated to optimize interlayer bonding quality by investigating the effects of infill density, printing speed, and nozzle temperature. With optimum parameter values, a bending strength of more than 48 MPa and an average surface roughness of less than 10 µm can be achieved.\u003c/p\u003e","manuscriptTitle":"Experimental optimization of the interlayer bonding of poly (methyl methacrylate) 3D printing substrates","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-01 11:12:01","doi":"10.21203/rs.3.rs-6260832/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"93017176-1c4c-4602-8af8-01fd74f1e463","owner":[],"postedDate":"April 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-08T10:21:07+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-01 11:12:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6260832","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6260832","identity":"rs-6260832","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}