Experimental Modeling and Process Optimization of Laser Transmission Welding with Fiber Optic Laser for Polymethyl Methacrylate in Zigzag Path

Experimental Modeling and Process Optimization of Laser Transmission Welding with Fiber Optic Laser for Polymethyl Methacrylate in Zigzag Path | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental Modeling and Process Optimization of Laser Transmission Welding with Fiber Optic Laser for Polymethyl Methacrylate in Zigzag Path Milad Rahmaninia, Majid Ghoreishi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5342698/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 This study experimentally evaluated Laser Transmission Welding (LTW) between two transparent and identical Polymethyl Methacrylate (PMMA) sheets using a fiber optic laser following a zigzag path. The research focused on the effects of laser power, welding speed, and distance between scan lines on lap-shear force, weld-seam width, and changes in weld morphology. Pyrometry was used to measure the welding temperature and determine input parameters. Analysis of Variance (ANOVA) and Response Surface Methodology (RSM) were employed to analyze and optimize the input parameters for maximum lap-shear force and minimal weld-seam width. The findings indicated that higher laser power, slower welding speed, and a reduced distance between scan lines increased heat input, leading to enhanced polymer melting and improved weld strength, reflected by higher lap-shear force and broader weld-seam width. Conversely, lower heat input decreased both lap-shear force and weld-seam width. Optimal values for lap-shear force and weld-seam width were determined to be 886.4 N and 26.37 mm, respectively, through multi-objective optimization. The zigzag welding path contributed to uniform heat distribution, even mixing of melted materials, and better structural integrity in the weld zone. Morphological analysis revealed that the weld strength was enhanced due to the presence of smaller, evenly distributed bubbles in the weld pool, attributed to the zigzag path. These findings highlight the significance of controlling welding parameters to optimize strength and seam quality in laser transmission welding of PMMA. Laser transmission welding Polymethyl Methacrylate Transparent polymer welding parameters Zigzag Path Optimization Morphological Analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1. Introduction Polymethyl Methacrylate (PMMA) is a transparent thermoplastic known commercially as Perspex and Plexiglass. Due to its properties such as high hardness and transparency, corrosion resistance, low weight, and 92% light transmission capability, it is used in many industries including automotive, aerospace, agriculture, construction, household appliances, optical instruments, and packaging industries [ 1 , 2 ]. Given the application of PMMA in various industries, the process of joining this material is of significant importance. Laser welding is one of the processes used for joining thermoplastics, which is utilized in both research and industry. Laser Transmission Welding (LTW) is a thermal technique that is used for the purpose of welding different types of thermoplastics together, as well as attaching thermoplastics to metals, ceramics, and composites [ 3 , 4 ]. Laser transmission welding has many advantages over other methods of combining thermoplastics, including flexibility, quick processing time, high processing speed, non-contact operation, cheap production cost, a small heat-affected zone (HAZ), and the ability to achieve high strength. These benefits have been shown in studies [ 5 , 6 ]. The LTW process is comprised of four distinct stages: laser transmission, heat production, melting, and solidification [ 7 , 8 ]. When the laser beam goes through the see-through polymer, it is absorbed by the absorbing polymer, resulting in a thermal zone at the boundary between the two polymers. Within this region, polymer components undergo a melting process. The molten materials then mix together due to the application of clamp pressure, resulting in the formation of a connection between the two parts. This bond solidifies when the materials cool down [ 9 ]. According to a research done by Wang et al., it was shown that the most effective force for combining PMMA polymer parts using the LTW technique to obtain sufficient strength is 20 N [ 10 ]. Line energy, together with clamp pressure, is a significant factor that influences the strength of a weld. The relationship between laser power and welding speed, expressed as the ratio of power to speed per unit length, is known as line energy [ 11 ]. Augmenting the strength of the laser has a direct impact on the amount of energy in each line, which in turn influences the density of the laser's energy. Intense power consumption during long-term welding (LTW) leads to a higher amount of heat being generated, which in turn causes the polymer to melt more extensively [ 12 ]. High levels of laser power may result in the combustion of polymers, an increase in the heat-affected zone (HAZ) region, and an expansion of the weld-seam width. On the other hand, using low power for welding might lead to inadequate melting of the polymer and result in poor weld strength [ 13 , 14 ]. The welding speed directly influences the duration of the laser beam's engagement with the base materials during the welding process. Reducing the pace at which welding is performed results in a longer duration of contact and higher amount of heat transferred. In contrast, a faster welding speed decreases the amount of time for contact and might result in insufficient bonding because of the decreased amount of heat input [ 15 , 16 ]. Nevertheless, it is crucial to ascertain the ideal laser power and welding speed for each material, taking into account its specific qualities and the kind of laser used, in order to generate a weld of suitable strength [ 17 ]. Response Surface Methodology (RSM) is a statistical technique used to construct experiments and create empirical models. It has been used in numerous research to investigate the effects of different factors on outputs such as laser power, weld-seam width, heat input, and the heat-affected zone (HAZ) [ 18 , 19 ]. Kumar et al. used Response Surface Methodology (RSM) to construct the experiments for optimizing the parameters of Laser Transmission Welding (LTW) in the bonding of two transparent polymers, polymethyl methacrylate and polycarbonate, using a pulsed Nd: YVO4 laser. The findings were enhanced by the use of Desirability Function analysis. This research examined the effects of many factors, including laser power, pulse frequency, scanning speed, wobble width, and wobbling frequency, on lap-shear force and weld-seam width. The analysis of variance findings indicates that the wobbling width parameter had the most significant influence on weld strength, while the scanning speed parameter had the largest impact on weld-seam width [ 20 ]. Acherjee et al. conducted research on the laser transmission welding of two polymers, PMMA and ABS, using RSM modeling. This study used a diode laser with a wavelength of 809.4 nm. The influence of four factors, including laser power, welding speed, stand-off distance, and clamp pressure, on both weld strength and weld-seam width was assessed. According to the analysis of variance data, it was determined that the stand-off distance had the greatest impact on both the strength and weld width [ 17 ]. The evaluation of weld quality relies heavily on the important criteria of weld strength [ 9 ]. The criterion used to assess the strength of welds in lap joint connections is the shear force exerted by the tensile testing equipment on the weld joint [ 21 , 22 ]. The mode of weld zone failure under shear stress is crucial in determining the appropriate range of factors that impact weld strength. Surface damage and substrate damage are prevalent problems in components that are connected using the LTW technique. If the weld joint itself sustains damage, it is classified as surface damage. Surface damage is indicative of lower weld strength in comparison to the underlying material. However, if the harm arises from the region next to the weld joint, it is referred to as substrate damage. The presence of substrate damage suggests that the weld connection has a greater strength than the base material [ 23 , 24 ]. Expanding the width of the weld-seam results in a wider weld pool, leading to an increased amount of polymer melting. This, in turn, enhances the strength of the weld. Nevertheless, an extreme augmentation in the weld-seam width has the potential to diminish the visual quality. Hence, it is important to contemplate an optimum combination of factors in order to get the highest possible weld strength while simultaneously maintaining satisfactory visual quality [ 25 , 26 ]. Controlling the LTW process not only optimizes it but also minimizes faults in the joint region and ensures that the parameters influencing weld strength and weld-seam width are within the proper range [ 27 , 28 ]. Temperature measurement throughout the LTW process yields data on the amount of heat applied to the weld zone, the extent of polymer melting, and the range of the heat-affected zone (HAZ) [ 29 ]. Pyrometry is a contactless technique used to measure the temperature in the LTW process. Due to the rapid heat transfer rate in LTW and the possibility of measurement inaccuracies when employing Pyrometry to determine the temperature in the weld zone, it is necessary for both the heat input temperature to the weld zone and the emitted temperature from this region to be quite high [ 30 , 31 ] . The current study presents a thorough analysis of the effects of a zigzag laser beam path and three adjustable parameters (laser power, welding speed and distance between scan lines) on the strength, width, and morphology of the weld between two transparent PMMA polymer pieces. This analysis was conducted through experimental investigation, empirical modeling, and process optimization. In order to connect the two transparent PMMA polymer pieces, a fiber optic laser was used. This laser has the ability to generate a laser beam that follows a zigzag path. Additionally, a black ink coating was applied at the junction of the two polymers to serve as an absorber. This research aimed to examine the impact of a zigzag laser beam path in LTW welding, using a fiber optic laser source, on the weldability, lap-shear force, weld-seam width, and weld morphology of two comparable and transparent PMMA polymers. Furthermore, another aim was to use the method of Pyrometry to ascertain the amounts of both variable and constant input factors. The RSM approach was used to organize experiments and develop mathematical models that can accurately forecast the impact, or lack thereof, of input factors on the intended outcome. Morphological study was conducted on the weld zone to ascertain the connection process and evaluate the impact of the zigzag laser beam route in this region. Desirability Function analysis was used to optimize the variable parameters. 2. Experimental methods and details 2.1. Material and process Transparent PMMA sheets with dimensions of 80 mm × 35 mm × 4 mm were prepared for this experimental study. The physical properties of this polymer are presented in Table 1 . For the LTW process, a Raycus_50QB fiber marking laser machine with a maximum power of 50 W, a wavelength of 1064 nm, adjustable speed up to 7000 mm/s, adjustable frequency range of 50–100 kHz, and a computer connected to the laser machine was used. Parameter settings for each welding stage were adjusted using the EZ-CAD software available on the computer connected to the laser machine. In this laser device, the laser beam is transmitted via an optical fiber cable from the laser source to the laser head. For welding, the laser beam with a pulse frequency of 50 kHz and a focal length of 120 mm was focused on the surface of the sample. To remove dust and other surface impurities, all sample surfaces were cleaned with ethyl alcohol. To absorb the laser beam, the surface of half of the workpieces was coated with ink. Before welding, the surfaces were dried with warm air to eliminate surface moisture. The welding process of PMMA samples is shown in Figs. 1 a, and a welded PMMA sample is shown in Fig. 1 b. Table 1 Physical and mechanical properties of Poly methyl methacrylate [ 32 ]. Property PMMA Density (g/cm 3 ) 1.18 Melting Point (℃) 220–240 Surface Hardness (Rockwell) M92, M90,M100 Glass Transition Temp (Tg) 110 to 120 Linear Thermal Expansion (× 10 − 5 mm/mm.k) 6.3 Thermal Conductivity at 20 ℃ (KW/mk) 0.12–0.17 Refractive index 1.49 Luminance transmission 92% Tensile Strength (MPa) 72 Tensile Modulus (GPa) 3.1 In order to secure the location of the components and prevent the ingress of air into the joint region, two identical clamps were used. In order to ensure a minimum force of 20 N exerted on the PMMA joint region [ 10 ], a piezoresistive sensor and an Arduino UNO board were used to monitor the force. Figure 2 illustrates the process of affixing the clamps to the workpieces and quantifying the force exerted by the clamps via the use of a piezoelectric sensor. 2.2 Testing process Inadequate bonding occurs due to inadequate fusion induced by low temperatures in the weld zone. Conversely, too high temperatures in the welding area lead to the combustion and degradation of the polymer. Pyrometry was used to control the temperature inside the welding zone. Due to the substantial heat transfer, accurately measuring the temperature of the weld zone in the Laser Transmission Welding (LTW) process is a challenge. Therefore, it is impractical to measure the temperature of the weld area using pyrometry precisely. Pyrometry, however, may be an appropriate technique for visually examining and determining the range of input parameters for research purposes. Therefore, a pyrometer with a temperature range from − 35 to 500 degrees Celsius and a precision of 0.1 degrees Celsius was used to estimate the temperature of the weld zone and determine the acceptable range of input parameters. Figure 3 shows the temperature measurement of the welding zone by pyrometry. A narrow weld-seam width leads to cleanliness and a visually pleasing look for the weld zone. Hence, the objective of measuring the width of the weld-seam is to get its minimum value. A microscope with optical capabilities was used to quantify the breadth of the weld-seam. Initially, photographs of the area where the weld was made were taken, and then, the measurements of the width of the weld-seam were determined using ImageJ software. The reported findings are derived from the mean of three measurements obtained from each sample. The strength of the welded PMMA pieces increases proportionally with the magnitude of the shear force they can endure. Consequently, a tensile test was used to evaluate the strength of the weld. The testing machine has a maximum capacity of 2.5 tons. As per the ASTM D 1002 standard, the upper and lower jaws of the tensile testing equipment held the welded sample, with 2.5 cm measured from each direction, identical to the illustration in Fig. 4 .a. The welded samples underwent a tensile test at a temperature of 25°C, with a speed of 0.5 mm/min. Analyzing the fracture morphology provides information on the quantities of thermal energy used, the quantity of molten material produced, the extent of their fusion, and the possibility of welding defects. After the fracture test, the scanning electron microscope (SEM) was set to a magnification of 2000x to capture images for the aim of analyzing the morphology of the place of the fracture. 2.3 Experimental design 2.3.1 OFAT Method Through initial studies employing the one factor at a time (OFAT) approach, three parameters—laser power, welding speed, and distance between scan lines —were determined to have a significant impact on lap-shear force, weld-seam width, and weld morphology in zigzag welding path. After evaluating the influence of these input parameters, the technique of calculating temperature using pyrometry based on one-factor-at-a-time (OFAT) approach was used to establish the parameter configurations. The study aimed to examine the effect of modifying a solitary parameter on the temperature of the weld zone. Fluctuations in heat input parameter values result in alterations in the temperature of the weld zone. Figure 4 .b illustrates a welded sample that was created using a zigzag path. b) Schematic of PMMA welded sample with zigzag beam path. 2.3.2 RSM Method Response Surface Methodology (RSM) is a collection of mathematical and statistical tools that are used to model and analyze issues in which the output of interest is affected by many input factors. The goal is to maximize the efficiency of the reaction. The outcome of this procedure yields a regression equation (Eq. 1 ) that precisely defines the connection between the input parameters (χ) and the response variable (y). The equation may be described as follows: y represents the response, χ represents the independent variables, β represents the regression coefficients, and ε represents the observed error [ 33 ]. $$y={\beta _0}+\sum\limits_{{i=1}}^{k} {{\beta _i}{x_i}+} \sum\limits_{{i=1}}^{k} {{\beta _{ii}}x_{i}^{2}+} \sum\limits_{i} {\sum\limits_{j} {{\beta _{ij}}{x_i}{x_j}+\varepsilon } }$$ 1 The study used Response Surface Methodology (RSM) and the face-centered central composite design (FCCD) to plan the experiments. The purpose of the experimental design was to investigate the influence of the independent variables (χ i , χ 2 i , χ i χ j ) on the response of the regression equation (y). The evaluated parameters consist of laser power, welding speed, and distance between scan lines, which are analyzed at three distinct levels. The levels of the input parameters are shown in Table 2 . Table 2 Process control parameters and their limits Input Parameters (Controllable) Unit Notations Level -1 0 + 1 Laser power (A) Watt P 20 25 30 Scan speed (B) \(\frac{{mm}}{s}\) V 400 425 450 distance between scan lines (C) mm LD 0.015 0.02 0.025 2.3.3 Optimization using examination of desirability functions. The Derringer and Suich optimization methodology is a viable method for simultaneously optimizing several outputs [ 34 ]. This approach relies on Desirability functions. Under this methodology, every output y i is first transformed into a desirability function di, which spans from zero to one (0 ≤ di ≤ 1). Within this function, when the output y i matches the desired value, the variable di is assigned a value of 1 Conversely, if the output falls beyond the allowed range, di is assigned a value of 0 The input variables are chosen in a manner that optimizes the total desirability D [ 33 ]. 3. Results and discussion 3.1 Development of mathematical models The Minitab Software was used to assess and generate an appropriate regression equation for fitting the collected data. Before the analysis of variance, to remove factor noise, tests were performed in the order of the results presented in Table 3 . The ANOVA approach was used to assess the significance or insignificance of the input parameters. The F-value and lack of fit were used to assess and examine the efficacy or ineffectiveness of the input parameters, as well as the correctness and sufficiency of the model, in this approach. 3.1.1 Analysis of lap-shear Force The purpose of the regression equation is to construct a coherent link between the response variable and the independent input factors. Eq. 2 is the regression equation that reflects the output shear force. Table 4 displays the R², corrected R², and anticipated R² values, as well as other indicators of adequacy for the shear force. The proximity of the R², adjusted R², and predicted R² values to one suggests that the model is efficient. Based on the data shown in the table, if the input parameters have a P-value lower than 0.05 (α = 0.05, or 95% confidence level), it signifies that they significantly affect the shear force with a confidence level above 95%. If any of the input parameters have a P-value that exceeds 0.05, it indicates that they lack significance. Furthermore, a model is deemed satisfactory if the lack-of-fit value exceeds 0.05. The ANOVA table indicates that the variables Laser power (P), welding speed (S), distance between scan lines (LD), the quadratic effect of laser power (P²), the quadratic effect of welding speed (S²), the interaction effect of laser power and welding speed (P×S), and the interaction effect of welding speed and distance between scan lines (S×LD) significantly influence the lap shear force. Out of all the input parameters, the one with the most influence on the lap shear force is laser power with an F-Value of 1598.31. On the other hand, the parameter with the least influence is the quadratic effect of welding speed (S²) with an F-Value of 5.36. The parameters (LD²) representing the quadratic effect of the distance between scan lines, and (P×LD) representing the interaction effect of laser power and distance between scan lines, were eliminated from the model since they have no impact on the shear force and their removal was done to enhance the model. Table 3. Design matrix and measured responses Results Experimental information Weld-seam width (mm) Lap-shear Force (N) Welding Parameters Std order Run order LD (mm) S P (watt) 38 1025 0.020 425 30 2 1 21 245 0.025 450 20 37 2 27 875 0.015 400 20 30 3 40 1044 0.015 450 30 25 4 37 936 0.025 400 30 3 5 37 664 0.020 425 25 35 6 38 792 0.020 400 25 32 7 35 655 0.020 425 25 8 8 24 585 0.025 400 20 9 9 35 670 0.020 425 25 38 10 33 542 0.025 425 25 1 11 31 472 0.015 450 20 40 12 44 1256 0.015 400 30 5 13 25 785 0.025 450 30 12 14 24 580 0.020 425 20 16 15 37 695 0.020 425 25 23 16 40 845 0.015 425 25 33 17 39 710 0.020 425 25 14 18 36 660 0.020 425 25 36 19 34 530 0.020 450 25 18 20 F Zigzag = 3691 − 351.8 P + 14.4S-80680 LD + 4.723 P×P-0.0375 S×S + 0.38 P×S + 124 S×LD (2) Table 4 ANOVA analysis for the lap-shear Force width model (after backward elimination) Source DF Sum of squares Mean squares F-value Prob > F Model 7 982624 140375 428.21 0.000 Significant Linear 3 906815 302272 922.08 0.000 P 1 523952 523952 1598.31 0.000 S 1 187142 187142 570.88 0.000 LD 1 195720 195720 597.04 0.000 Square 2 55838 27919 85.17 0.000 P*P 1 44604 44604 136.06 0.000 S*S 1 1758 1758 5.36 0.039 2-Way Interaction 2 19972 9986 30.46 0.000 P*S 1 18050 18050 55.06 0.000 S*LD 1 1922 1922 5.86 0.032 Error 12 3934 328 Lack-of-Fit 7 1540 220 0.46 0.830 Not Sigficant Pure Error 5 2393 479 Total 19 986558 R 2 = 99.60% Adjusted R 2 = 99.37% Peredict R 2 = 98.99% 3.1.2 Analysis of weld-seam width Equation 3 is the regression equation that describes the outcome of the weld-seam width. The equation has a parabolic nature as a result of the quadratic impact of laser power (P²) on the weld-seam width. Table 5 shows that the laser power (P), welding speed (S), and the distance between scan lines (LD) have a considerable impact on the output of weld-seam width. This impact is statistically significant with a confidence level above 95%. Furthermore, the quadratic impact of laser power (P²), together with the interaction effects of laser power with welding speed (P×S), laser power with distance between scan lines (P×LD), and welding speed with distance between scan lines (S×LD), are statistically significant for this output at a significance level of α = 0.05. The model's adequacy is shown by the near proximity of the R², adjusted R², and anticipated R² values to one, as well as a P-value of 0.884 for the Lack of Fit, as presented in Table 5 . The laser power, with an F-Value of 227.47, is the most significant input parameter on the output of weld-seam width. On the other hand, the interaction impact of laser power and distance between scan lines (P×LD), with an F-Value of 6.93, is the least influential parameter. The quadratic parameters LD² and S² were eliminated from the model since they do not have any effect on the output of weld-seam width. W Zigzag = -406.1 + 19.87 P + 0.649 S + 6660 LD - 0.2120 P×P - 0.01700 P×S - 45.0 P×LD - 15.00 S×LD (3) Table 5 ANOVA analysis for the weld-seam width model (after backward elimination) Source DF Sum of squares Mean squares F-value Prob > F Model 7 752.225 107.461 73.58 0.000 Significant Linear 3 537.400 179.133 122.66 0.000 P 1 324.900 324.900 222.47 0.000 S 1 36.100 36.100 24.72 0.000 LD 1 176.400 176.400 120.79 0.000 Square 1 140.450 140.450 96.17 0.000 P*P 1 140.450 140.450 96.17 0.000 2-Way Interaction 3 74.375 24.792 16.98 0.000 P×S 1 36.125 36.125 24.74 0.000 P×LD 1 10.125 10.125 6.93 0.022 S×LD 1 28.125 28.125 19.26 0.001 Error 12 17.525 1.460 Lack-of-Fit 7 6.025 0.861 0.37 0.884 Not Sigficant Pure Error 5 11.500 2.300 Total 19 769.750 R 2 = 97.72% Adjusted R 2 = 96.40% Peredict R 2 = 94.04% 3.2 Effects of process parameters on the responses 3.2.1. Lap-shear force The graphs shown in Fig. 5 provide the examination of the influence of each input parameter. Increasing the laser power (P) from 20 W to 30 W resulted in higher temperatures in the weld region and enhanced polymer melting. Upon reaching their critical temperatures, the absorbing and transparent polymers underwent melting, resulting in an expansion in the volume of the molten fluid. Consequently, there was an increased degree of intermingling and adhesion among the polymer molecules. Consequently, a stronger bond between the two polymers was established after they hardened. Increasing the welding speed (S) led to a decrease in the temperature of the weld zone, hence lowering the amount of polymer melt in that area. As a consequence, the weld strength decreased when the welding speed was increased from 400 mm/s to 450 mm/s. The distance between scan lines (LD) has a direct impact on the quantity of laser beam scans inside a certain area. Consequently, reducing the distance between scan lines of the beam resulted in an increased number of laser beam scans on the surface under examination. Increasing the number of laser beam scans on a surface resulted in higher temperatures in the weld zone, leading to an increase in the melting of the polymer in that particular area. Consequently, the weld strength decreased as the distance between scan lines rose from 0.015 mm to 0.025 mm. Concurrently augmenting laser intensity and reducing welding velocity results in a rise in line energy [ 15 ]. Inadequate fusion or weak weld strength occurs due to low line energy, while excessive line energy leads to polymer base materials being burned and degraded. Thus, it is necessary to determine the most favorable energy level for the line energy. In order to achieve uniform line energy across all levels of laser power and welding speed, one may either simultaneously raise both power and speed or reduce both simultaneously. Using this method, after the ideal line energy is attained, a uniform heat input is achieved in the welding area. Figure 6 displays the contour and planar graphs illustrating the changes in shear force as a result of the combined influence of laser power and welding speed (P×S). The beamline parameter distance in these photos is set to its center value of 0.02 mm. Figure 6 (a) demonstrates that the combination of increasing laser power and reducing welding speed led to an increase in weld strength. This is caused by the higher amount of heat being applied to the area where the weld is being made, which is influenced by the changing energy levels along the weld line. The maximum heat input to the weld zone was seen at a laser power of around 29–30 W, with a welding speed ranging from 400–435 mm/s. In contrast, diminishing the laser power and augmenting the welding speed resulted in a loss in line energy, which in turn led to a reduction in heat input to the weld zone, a decrease in polymer melting, and therefore, a decline in weld strength. The minimum shear force values were observed when the laser power ranged from around 20–23 W and the welding speed varied from around 448–450 mm/s. The planar graph in Fig. 6 (b) illustrates the correlation between line energy and heat input on weld strength. It demonstrates that shear pressures exceeding 1000 N were attained when the line energy reached its highest point. Figures 7 (a) and (b) show the contour and planar graphs illustrating the changes in shear force resulting from the interaction between welding speed and the distance between scan lines (S×LD). In this case, the laser power remains constant at its center value of 25 W. Figure 7 (a) demonstrates that reducing both the welding speed and the distance between scan lines at the same time resulted in an increase in the lap-shear force. Thus, it can be inferred that a decrease in the interaction effect of welding speed and the distance between scan lines (S×LD) results in an increase in the heat input to the weld zone. Enhanced thermal transfer, the generation of a suitable amount of molten material substance, integration of the base material, and eventually the creation of a robust connection in the welding area are further consequences of amplifying the interaction effect of welding speed and the distance between scan lines (S×LD). The optimal welding speed range for achieving the largest shear force in a zigzag route is around 400–410 mm/s, while the recommended distance between scan lines is around 0.015–0.016 mm. In contrast, the optimal values for minimizing lap-shear force are 435–450 mm/s and 0.023–0.025 mm. Based on the data shown in Fig. 7 (b), it was found that while using a laser power of 25 W, no welds were seen to have a shear strength of more than 1000 N. The laser power parameter has a stronger impact on the heat input to the weld zone compared to the welding speed, distance between scan lines, and their interaction effect. Consequently, shear strengths greater than 1000 N were observed when the laser power reached 30 W. 3.2.2. Weld-seam width According to the schematics shown in Fig. 8 , an escalation in laser power led to an expansion of the breadth of the weld seam. The increase of both laser power and heat input in the weld zone not only improved weld strength but also resulted in an enlargement of the weld seam width and an unfavorable aesthetic of the weld joint. Increasing the welding speed led to less time of laser beam exposure in the weld zone, resulting in a reduction in heat input and heat transfer to the weld zone. This resulted in a narrower weld seam width for the joint. Aside from the welding speed, the distance between scan lines also influenced the welding time. Minimizing this distance resulted in an increase in both the duration of the welding process and the amount of heat applied. Consequently, a drop in this parameter caused an augmentation in weld seam width, whilst an increase in the distance between scan lines led to a reduction in weld seam width. Therefore, the combination of higher laser power, lower welding speed, and shorter distances between scan lines resulted in a greater amount of heat input being applied, leading to an expansion in the weld-seam width. Based on Fig. 9 (a), the smallest measured width of the weld seam for the zigzag path was found to be between 20 and 21 W laser power and 400–450 mm/s welding speed. The highest documented width of the weld seam in this path was seen within the approximate range of 26–30 W laser power and 400–405 mm/s welding speed. According to the contour plot, higher laser power levels had a greater effect on the breadth of the weld seam when compared to differences in speed. The heat input was much more responsive at higher temperatures. Therefore, in high-power welding, even little adjustments in welding speed resulted in significant fluctuations in heat input and, subsequently, in the dimensions of the weld seam width. Figure 9 (b) demonstrates that a consistent rise in laser power, as a result of its stronger impact on line energy in comparison to welding speed, resulted in an expansion of the weld-seam width. Hence, in order to achieve uniform energy distribution throughout all levels of the interaction effect between laser power and welding speed (P×S), it is crucial to acknowledge that changes in laser power had a more pronounced impact on the width of the weld seam compared to changes in welding speed. The contour and surface plots in Fig. 10 depict the variations in the weld-seam width caused by the interaction effect of welding speed and distance between scan lines (S×LD), using a central laser power of 25 W, along a zigzag path. Figure 10 (a) illustrates a significant negative connection between the interaction effect of welding speed and distance between scan lines (S×LD) and the weld-seam width. The decrease in welding speed and the decrease in the distance between scan lines resulted in an increase in the heat input inside the welding zone, which consequently led to an enlargement in the weld-seam width. According to Fig. 10 (a), the most favorable the weld-seam width in the zigzag path was determined to be around 440–450 mm/s for welding speed and 0.0237–0.025 mm for the distance between scan lines. Conversely, the most extensive weld-seam width was seen when the welding speed ranged from around 400 to 450 mm/s and the distance between scan lines ranged from 0.015 to 0.016 mm. Based on the surface plot shown in Fig. 10 -b, it is evident that altering the distance between scan lines has a greater effect on the weld-seam width compared to adjusting the welding speed. This is done to maintain line energy balance across various levels of the interaction parameters. The contour and surface plots in Fig. 11 demonstrate that the variations in weld seam width exhibit significant curvature and well-defined boundaries. The figures indicate that the interaction effect of laser power and distance between scan lines (P×LD) has a substantial impact on the weld-seam width. Figure 11 (a) illustrates that the welding zone experienced the highest level of heat, leading to the widest weld seam, when the laser power was approximately in the range of 25–30 W and the distance between scan lines was about 0.015–0.0175 mm. On the contrary, the weld seam's smallest width was seen along the zigzag path when the laser power was between 20 and 21 W, and the distance between scan lines was from 0.021 to 0.025 mm. Also, in Fig. 11 -b, it is clear that the lowest value of the weld-seam width is obtained when the laser power is at the lowest value and the distance between scan lines is at the highest value. 4. Morphological analysis An examination of the microstructure in the weld zone is essential to study the bonding process in relation to the input parameters. Crystal structures, by their very nature, elongate the distance the beam travels in polymer structures, thereby increasing the probability of laser beam absorption and heat production in the area exposed to the laser [ 35 , 36 ]. As a result, crystalline and semi-crystalline structures have a greater potential to produce a melted fluid at the weld area compared to amorphous structures [ 37 ]. PMMA is a polymer characterized by its non-crystalline structure. The non-crystalline form of this polymer presents difficulties when examining its microstructure [ 20 ]. The post-weld polymer structure comprises a diverse array of bubbles, spherulites, and porosities. Factors such as heat input, line energy, cooling rate of molten material, laser beam scanning path, and Laser beam diameter are important parameters that have a considerable impact on the microstructure of the weld zone [ 9 ]. Raising the amount of heat applied to the weld area causes the moisture that remains and the polymer to evaporate. Bubble formation occurs as a consequence of the trapping of gases such as H 2 O, CO 2 , and CO, which is caused by moisture evaporation and molten material between the two polymers [ 38 ]. The existence of minute bubbles and their consistent dispersion throughout the welding zone improves the strength of the weld. The homogeneous distribution and flow of molten material in the welding region is impacted by the existence of tiny bubbles. Conversely, a higher quantity of bubbles in the welding zone signifies a more significant level of fusion of the underlying material, resulting in more amalgamation of molten substances. Poor fusing and mixing of molten materials occur as the size of the bubble in the weld zone increases. Consequently, the existence of sizable bubbles in the weld zone diminishes the strength of the weld [ 39 ]. An augmentation in line energy and a reduction in cooling time within the crystallization range result in an enlargement of spherulites in the molten pool. Moreover, the presence of bigger spherulites might lead to the development of fractures in their vicinity, leading to a decrease in the strength of the weld [ 40 ]. The trajectory of the laser beam inside the welding zone has an impact on the quantity and dimensions of voids and porosities. When the laser beam travels a greater distance during welding, the molten material will be distributed more evenly in the region where the weld is formed. This leads to a decrease in the quantity of empty spaces and air pockets in the weld [ 20 ]. Figure 12 shows enlarged images of the weld area for samples 13 and 2. Sample 13, with a tensile strength of 1256 N, had the highest weld strength, while sample 2, with a tensile strength of 245 N, showed the lowest weld strength. Figures Fig. 12 a, Fig. 12 c, and Fig. 12 e depict the microstructure of sample 13. The existence of bubbles, voids, and spherulites clearly indicates the impact of laser beam irradiation and the subsequent solidification of molten material. The presence of bubbles may be ascribed to the emission of gases from residual moisture in the polymer. The even distribution of small bubbles inside the weld pool resulted in improved weld strength. The laser beam's zigzag path promoted its dispersion throughout several regions, thereby limiting the formation of further voids and porosities in the weld pool. The presence of spherulites in the weld pool and the stratified composition of this area suggest a significant line energy during the welding process of this specimen. As a result, a greater shear force is necessary for the joint to fail. Nevertheless, the proliferation of spherulites inside the weld region hindered any improvement in the strength of the weld. Figures Fig. 12 b, Fig. 12 d, and Fig. 12 f depict the microstructure of sample 2. The photos indicate that the low energy level used during the welding process of this sample led to inadequate melting of the surface and negligible blending of the molten material. Inadequate bonding with low strength resulted from the existence of huge bubbles and the uneven distribution of smaller bubbles. The reduced quantity of spherulites in this region was a result of the limited thermal energy input during the welding process. As a result, the joint collapsed when subjected to a little amount of external strain. 5. Optimization of Lap shear force and Weld-seam width The process outputs were optimized by adjusting the parameters to achieve optimum weld strength and low weld-seam width. Figure 13 presents the process parameters arranged in columns, where each row represents different variations in the outputs. Every individual cell demonstrates the changes in the corresponding output when the input parameters are modified. The values shown at the top of each column represent the high, optimal and low settings for each parameter, respectively. The optimization findings indicate that the ideal parameter values are a laser power of 20 W, a welding speed of 400 mm/s, and a beam distance of 0.015 mm. The first cell of each row displays the forecasted output value and its corresponding probability of attainment. Based on the projected model, if welding is repeated using these ideal parameters, the welded samples will exhibit a maximum tensile strength of 886.41 N and a minimum width of the weld seam of 26.37 mm. The findings suggest that the given optimum values are satisfactory, as shown by a Desirability Function score of 70%. 6. Verification of results In order to verify the accuracy of the data generated from the Minitab program, a series of experimental tests were done three times, in accordance with the desirability function values. The tests were conducted using the following variable parameters: a laser power of 20 W, a welding speed of 400 mm/s, and a distance between scan lines of 0.015 mm. In addition, the predetermined parameters - focal distance, clamping force, and pulse frequency - were kept at 120 mm, 20 N, and 50 Hz, respectively, in line with prior examples. The findings from these three samples are shown in Table 6 . The modeling and optimization process yielded satisfactory results, as seen by the reported error percentages. The accuracy of the process may be deemed acceptable, with the Minitab program producing findings that closely align with the experimental data. Conclusion The findings presented in this research are derived from the range of input factors that were taken into account. The base material decline and inability to establish adequate bonding were caused by the excessive amplification of laser power and substantial reduction in welding speed. Insufficient welding power, when paired with high welding speed, led to the lack of a molten pool and unsatisfactory fusion. The relationship between laser power and welding speed is often known as line energy. In order to get a weld that is both strong and thin, it is necessary to perform the Laser-Transmission Welding (LTW) procedure using the ideal line energy value. The distance between scan lines is another parameter affecting weld strength and weld-seam width. Smaller distances between scan lines result in increased welding time and consequently higher heat input to the weld zone. As a result, reducing this parameter leads to an increase in both weld strength and weld-seam width. The distance between beam lines is an additional factor that impacts the strength of the weld and the weld-seam width. Reducing the distance between scan lines leads to longer welding time and, as a consequence, greater heat input to the weld zone. Consequently, decreasing this parameter results in an augmentation of both Lap-shear force and weld-seam width. The ANOVA analysis reveals that laser power is the most significant factor on both lab-shear force and weld-seam width. The most lap-shear force ever recorded is 1256 N, whereas the minimum width of a weld-seam ever recorded is 21 mm. An increased quantity of little bubbles has led to a rise in the lap-shear force. The lack of spherulites and layering in the microstructure of samples that fractured during tensile testing suggests that the connection created was weak, resulting in the deterioration of the weld with minimum external force. The multi-objective optimization determined that the ideal input parameters are a laser power of 20 W, a welding speed of 400 mm/s, and a distance between scan lines of 0.015 mm. The optimization analysis yielded a projected shear force output of 886.41N with a probability of 63.44%. Additionally, the expected result for the weld-seam width is 26.37 mm with a probability of 63.76%. Furthermore, the desirability function is set at a value of 70%. Declarations Funding No specific grant from funding agencies in the public, commercial, or not-for-profit sectors was received for this work. Competing Interests The authors have no relevant financial or non-financial interests to disclose. Authors' Contributions Milad Rahmaninia (Main Author): Conceptualization, Methodology, Writing - Original Draft, Investigation, Formal Analysis. Dr.Majid Ghoreishi (Supervisor): Supervision, Funding Acquisition, Project Administration, Writing - Review & Editing. Data Availibility All data generated or analyzed during this study are included in this published article. No additional datasets were used or required for the study. Acknowledgement The authors would like to thank the K. 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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-5342698","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":375368619,"identity":"47e8baee-189c-4339-af39-b066eb257b79","order_by":0,"name":"Milad 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11:41:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":167595,"visible":true,"origin":"","legend":"\u003cp\u003eMethod of measuring the clamping force.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/cc1366f8471c5f361ecb6772.png"},{"id":69444541,"identity":"4a6b425d-da6f-403b-bd70-43790cfbbcdb","added_by":"auto","created_at":"2024-11-20 11:41:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":117763,"visible":true,"origin":"","legend":"\u003cp\u003ePyrometry is used to measure the temperature of the weld zone.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/75b5ac5fb8c099ee1e73447a.png"},{"id":69445721,"identity":"ab5ae880-c5d5-4d8d-83ec-18baf7562eb0","added_by":"auto","created_at":"2024-11-20 11:57:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":124884,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic diagram of tensile testing of sample for the lap shear test.\u003c/p\u003e\n\u003cp\u003eb) Schematic of PMMA welded sample with zigzag beam path.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/77274b0703917828f30b51a6.png"},{"id":69444548,"identity":"169dcbd1-1469-499f-b163-0f8605abee89","added_by":"auto","created_at":"2024-11-20 11:41:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":94604,"visible":true,"origin":"","legend":"\u003cp\u003eMain Effects Plots for Lap-shear force.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/b047cb2d9f4c375b41a8b4c4.png"},{"id":69445723,"identity":"9a62aeaa-cd43-4016-95c2-28f4c759dedf","added_by":"auto","created_at":"2024-11-20 11:57:28","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":257747,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Contours plot and (b) response surface plot showing the effect of P and S on the lap-shear force that LD= 0.02 mm.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/b676e672c17c976a62623462.png"},{"id":69444542,"identity":"6cabc631-34da-44f5-a90e-1001fc22f315","added_by":"auto","created_at":"2024-11-20 11:41:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":215146,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Contours plot and (b) response surface plot showing the effect of S and LD on the lap-shear force that P= 25 W.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/4ecdaabdd89c86605d792dc9.png"},{"id":69446385,"identity":"855c7ea5-fc90-41bf-a865-d8fd6e6684a9","added_by":"auto","created_at":"2024-11-20 12:05:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":95480,"visible":true,"origin":"","legend":"\u003cp\u003eMain Effects Plots for Weld-seam with.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/3d88091eaaaf8c8c6150b7fb.png"},{"id":69444901,"identity":"af127a66-4024-4e36-ae04-b6ba61563976","added_by":"auto","created_at":"2024-11-20 11:49:28","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":205388,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Contours plot and (b) response surface plot showing the effect of P and S on the Weld-seam width that LD= 0.02 mm.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/c073493be68eb3e94a5ed32e.png"},{"id":69444903,"identity":"5ac6674f-627d-4c5e-bb5c-ad69cc36be35","added_by":"auto","created_at":"2024-11-20 11:49:29","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":215635,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Contours plot and (b) response surface plot showing the effect of S and LD on the Weld-seam width that P= 25 W.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/ec01e09327400642d8f24d25.png"},{"id":69444551,"identity":"412c7e25-3565-4ac0-830e-7073f1d54e13","added_by":"auto","created_at":"2024-11-20 11:41:29","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":181629,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Contours plot and (b) response surface plot showing the effect of P and LD on the Weld-seam width the S= 25 mm/s.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/645cfdfcd1ca6595569f9ea9.png"},{"id":69444552,"identity":"d6861fea-4e03-4497-ba18-89eedc95288a","added_by":"auto","created_at":"2024-11-20 11:41:29","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":1555191,"visible":true,"origin":"","legend":"\u003cp\u003eSEM micrograph of conventional LTW of PMMA/PMMA weld zone at a) 300× magnification for sample 1 b) 300×magnification for sample 35 c) 600× magnification for sample 1 d) 600× magnification for sample 35 e)1000× magnification for sample 1 f) 1000× magnification for sample 35\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/b80a2b72732ed024bfb992fc.png"},{"id":69444905,"identity":"1c8b141c-c2bd-44cd-a3bf-019fb38e2627","added_by":"auto","created_at":"2024-11-20 11:49:29","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":250756,"visible":true,"origin":"","legend":"\u003cp\u003eOptimization plot for Weld-seam width and weld lap shear force.\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/7a9589853216da309ffe7f58.png"},{"id":70966037,"identity":"86ea40e2-a84e-4b01-b518-fa39f4e947ec","added_by":"auto","created_at":"2024-12-09 16:21:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4461281,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5342698/v1/043f5942-707b-4b19-9c55-96627b1bd1ae.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experimental Modeling and Process Optimization of Laser Transmission Welding with Fiber Optic Laser for Polymethyl Methacrylate in Zigzag Path","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003ePolymethyl Methacrylate (PMMA) is a transparent thermoplastic known commercially as Perspex and Plexiglass. Due to its properties such as high hardness and transparency, corrosion resistance, low weight, and 92% light transmission capability, it is used in many industries including automotive, aerospace, agriculture, construction, household appliances, optical instruments, and packaging industries [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Given the application of PMMA in various industries, the process of joining this material is of significant importance. Laser welding is one of the processes used for joining thermoplastics, which is utilized in both research and industry.\u003c/p\u003e \u003cp\u003eLaser Transmission Welding (LTW) is a thermal technique that is used for the purpose of welding different types of thermoplastics together, as well as attaching thermoplastics to metals, ceramics, and composites [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Laser transmission welding has many advantages over other methods of combining thermoplastics, including flexibility, quick processing time, high processing speed, non-contact operation, cheap production cost, a small heat-affected zone (HAZ), and the ability to achieve high strength. These benefits have been shown in studies [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe LTW process is comprised of four distinct stages: laser transmission, heat production, melting, and solidification [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. When the laser beam goes through the see-through polymer, it is absorbed by the absorbing polymer, resulting in a thermal zone at the boundary between the two polymers. Within this region, polymer components undergo a melting process. The molten materials then mix together due to the application of clamp pressure, resulting in the formation of a connection between the two parts. This bond solidifies when the materials cool down [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. According to a research done by Wang et al., it was shown that the most effective force for combining PMMA polymer parts using the LTW technique to obtain sufficient strength is 20 N [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Line energy, together with clamp pressure, is a significant factor that influences the strength of a weld. The relationship between laser power and welding speed, expressed as the ratio of power to speed per unit length, is known as line energy [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Augmenting the strength of the laser has a direct impact on the amount of energy in each line, which in turn influences the density of the laser's energy. Intense power consumption during long-term welding (LTW) leads to a higher amount of heat being generated, which in turn causes the polymer to melt more extensively [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. High levels of laser power may result in the combustion of polymers, an increase in the heat-affected zone (HAZ) region, and an expansion of the weld-seam width. On the other hand, using low power for welding might lead to inadequate melting of the polymer and result in poor weld strength [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The welding speed directly influences the duration of the laser beam's engagement with the base materials during the welding process. Reducing the pace at which welding is performed results in a longer duration of contact and higher amount of heat transferred. In contrast, a faster welding speed decreases the amount of time for contact and might result in insufficient bonding because of the decreased amount of heat input [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Nevertheless, it is crucial to ascertain the ideal laser power and welding speed for each material, taking into account its specific qualities and the kind of laser used, in order to generate a weld of suitable strength [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eResponse Surface Methodology (RSM) is a statistical technique used to construct experiments and create empirical models. It has been used in numerous research to investigate the effects of different factors on outputs such as laser power, weld-seam width, heat input, and the heat-affected zone (HAZ) [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Kumar et al. used Response Surface Methodology (RSM) to construct the experiments for optimizing the parameters of Laser Transmission Welding (LTW) in the bonding of two transparent polymers, polymethyl methacrylate and polycarbonate, using a pulsed Nd: YVO4 laser. The findings were enhanced by the use of Desirability Function analysis. This research examined the effects of many factors, including laser power, pulse frequency, scanning speed, wobble width, and wobbling frequency, on lap-shear force and weld-seam width. The analysis of variance findings indicates that the wobbling width parameter had the most significant influence on weld strength, while the scanning speed parameter had the largest impact on weld-seam width [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Acherjee et al. conducted research on the laser transmission welding of two polymers, PMMA and ABS, using RSM modeling. This study used a diode laser with a wavelength of 809.4 nm. The influence of four factors, including laser power, welding speed, stand-off distance, and clamp pressure, on both weld strength and weld-seam width was assessed. According to the analysis of variance data, it was determined that the stand-off distance had the greatest impact on both the strength and weld width [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe evaluation of weld quality relies heavily on the important criteria of weld strength [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The criterion used to assess the strength of welds in lap joint connections is the shear force exerted by the tensile testing equipment on the weld joint [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The mode of weld zone failure under shear stress is crucial in determining the appropriate range of factors that impact weld strength. Surface damage and substrate damage are prevalent problems in components that are connected using the LTW technique. If the weld joint itself sustains damage, it is classified as surface damage. Surface damage is indicative of lower weld strength in comparison to the underlying material. However, if the harm arises from the region next to the weld joint, it is referred to as substrate damage. The presence of substrate damage suggests that the weld connection has a greater strength than the base material [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Expanding the width of the weld-seam results in a wider weld pool, leading to an increased amount of polymer melting. This, in turn, enhances the strength of the weld. Nevertheless, an extreme augmentation in the weld-seam width has the potential to diminish the visual quality. Hence, it is important to contemplate an optimum combination of factors in order to get the highest possible weld strength while simultaneously maintaining satisfactory visual quality [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Controlling the LTW process not only optimizes it but also minimizes faults in the joint region and ensures that the parameters influencing weld strength and weld-seam width are within the proper range [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Temperature measurement throughout the LTW process yields data on the amount of heat applied to the weld zone, the extent of polymer melting, and the range of the heat-affected zone (HAZ) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Pyrometry is a contactless technique used to measure the temperature in the LTW process. Due to the rapid heat transfer rate in LTW and the possibility of measurement inaccuracies when employing Pyrometry to determine the temperature in the weld zone, it is necessary for both the heat input temperature to the weld zone and the emitted temperature from this region to be quite high [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] .\u003c/p\u003e \u003cp\u003eThe current study presents a thorough analysis of the effects of a zigzag laser beam path and three adjustable parameters (laser power, welding speed and distance between scan lines) on the strength, width, and morphology of the weld between two transparent PMMA polymer pieces. This analysis was conducted through experimental investigation, empirical modeling, and process optimization. In order to connect the two transparent PMMA polymer pieces, a fiber optic laser was used. This laser has the ability to generate a laser beam that follows a zigzag path. Additionally, a black ink coating was applied at the junction of the two polymers to serve as an absorber. This research aimed to examine the impact of a zigzag laser beam path in LTW welding, using a fiber optic laser source, on the weldability, lap-shear force, weld-seam width, and weld morphology of two comparable and transparent PMMA polymers. Furthermore, another aim was to use the method of Pyrometry to ascertain the amounts of both variable and constant input factors. The RSM approach was used to organize experiments and develop mathematical models that can accurately forecast the impact, or lack thereof, of input factors on the intended outcome. Morphological study was conducted on the weld zone to ascertain the connection process and evaluate the impact of the zigzag laser beam route in this region. Desirability Function analysis was used to optimize the variable parameters.\u003c/p\u003e"},{"header":"2. Experimental methods and details","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Material and process\u003c/h2\u003e \u003cp\u003eTransparent PMMA sheets with dimensions of 80 mm \u0026times; 35 mm \u0026times; 4 mm were prepared for this experimental study. The physical properties of this polymer are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. For the LTW process, a Raycus_50QB fiber marking laser machine with a maximum power of 50 W, a wavelength of 1064 nm, adjustable speed up to 7000 mm/s, adjustable frequency range of 50\u0026ndash;100 kHz, and a computer connected to the laser machine was used. Parameter settings for each welding stage were adjusted using the EZ-CAD software available on the computer connected to the laser machine. In this laser device, the laser beam is transmitted via an optical fiber cable from the laser source to the laser head. For welding, the laser beam with a pulse frequency of 50 kHz and a focal length of 120 mm was focused on the surface of the sample. To remove dust and other surface impurities, all sample surfaces were cleaned with ethyl alcohol. To absorb the laser beam, the surface of half of the workpieces was coated with ink. Before welding, the surfaces were dried with warm air to eliminate surface moisture. The welding process of PMMA samples is shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, and a welded PMMA sample is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical and mechanical properties of Poly methyl methacrylate [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProperty\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePMMA\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity (g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMelting Point (℃)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e220\u0026ndash;240\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSurface Hardness (Rockwell)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM92, M90,M100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGlass Transition Temp (Tg)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e110 to 120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLinear Thermal Expansion (\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e mm/mm.k)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThermal Conductivity at 20 ℃ (KW/mk)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.12\u0026ndash;0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRefractive index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLuminance transmission\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e92%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTensile Strength (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTensile Modulus (GPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn order to secure the location of the components and prevent the ingress of air into the joint region, two identical clamps were used. In order to ensure a minimum force of 20 N exerted on the PMMA joint region [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], a piezoresistive sensor and an Arduino UNO board were used to monitor the force. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the process of affixing the clamps to the workpieces and quantifying the force exerted by the clamps via the use of a piezoelectric sensor.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Testing process\u003c/h2\u003e \u003cp\u003eInadequate bonding occurs due to inadequate fusion induced by low temperatures in the weld zone. Conversely, too high temperatures in the welding area lead to the combustion and degradation of the polymer. Pyrometry was used to control the temperature inside the welding zone. Due to the substantial heat transfer, accurately measuring the temperature of the weld zone in the Laser Transmission Welding (LTW) process is a challenge. Therefore, it is impractical to measure the temperature of the weld area using pyrometry precisely. Pyrometry, however, may be an appropriate technique for visually examining and determining the range of input parameters for research purposes. Therefore, a pyrometer with a temperature range from \u0026minus;\u0026thinsp;35 to 500 degrees Celsius and a precision of 0.1 degrees Celsius was used to estimate the temperature of the weld zone and determine the acceptable range of input parameters. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the temperature measurement of the welding zone by pyrometry.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA narrow weld-seam width leads to cleanliness and a visually pleasing look for the weld zone. Hence, the objective of measuring the width of the weld-seam is to get its minimum value. A microscope with optical capabilities was used to quantify the breadth of the weld-seam. Initially, photographs of the area where the weld was made were taken, and then, the measurements of the width of the weld-seam were determined using ImageJ software. The reported findings are derived from the mean of three measurements obtained from each sample.\u003c/p\u003e \u003cp\u003eThe strength of the welded PMMA pieces increases proportionally with the magnitude of the shear force they can endure. Consequently, a tensile test was used to evaluate the strength of the weld. The testing machine has a maximum capacity of 2.5 tons. As per the ASTM D 1002 standard, the upper and lower jaws of the tensile testing equipment held the welded sample, with 2.5 cm measured from each direction, identical to the illustration in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.a. The welded samples underwent a tensile test at a temperature of 25\u0026deg;C, with a speed of 0.5 mm/min.\u003c/p\u003e \u003cp\u003eAnalyzing the fracture morphology provides information on the quantities of thermal energy used, the quantity of molten material produced, the extent of their fusion, and the possibility of welding defects. After the fracture test, the scanning electron microscope (SEM) was set to a magnification of 2000x to capture images for the aim of analyzing the morphology of the place of the fracture.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Experimental design\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 OFAT Method\u003c/h2\u003e \u003cp\u003eThrough initial studies employing the one factor at a time (OFAT) approach, three parameters\u0026mdash;laser power, welding speed, and distance between scan lines \u0026mdash;were determined to have a significant impact on lap-shear force, weld-seam width, and weld morphology in zigzag welding path. After evaluating the influence of these input parameters, the technique of calculating temperature using pyrometry based on one-factor-at-a-time (OFAT) approach was used to establish the parameter configurations.\u003c/p\u003e \u003cp\u003eThe study aimed to examine the effect of modifying a solitary parameter on the temperature of the weld zone. Fluctuations in heat input parameter values result in alterations in the temperature of the weld zone. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.b illustrates a welded sample that was created using a zigzag path.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eb) Schematic of PMMA welded sample with zigzag beam path.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 RSM Method\u003c/h2\u003e \u003cp\u003eResponse Surface Methodology (RSM) is a collection of mathematical and statistical tools that are used to model and analyze issues in which the output of interest is affected by many input factors. The goal is to maximize the efficiency of the reaction. The outcome of this procedure yields a regression equation (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) that precisely defines the connection between the input parameters (χ) and the response variable (y). The equation may be described as follows: y represents the response, χ represents the independent variables, β represents the regression coefficients, and ε represents the observed error [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$y={\\beta _0}+\\sum\\limits_{{i=1}}^{k} {{\\beta _i}{x_i}+} \\sum\\limits_{{i=1}}^{k} {{\\beta _{ii}}x_{i}^{2}+} \\sum\\limits_{i} {\\sum\\limits_{j} {{\\beta _{ij}}{x_i}{x_j}+\\varepsilon } }$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe study used Response Surface Methodology (RSM) and the face-centered central composite design (FCCD) to plan the experiments. The purpose of the experimental design was to investigate the influence of the independent variables (χ\u003csub\u003ei\u003c/sub\u003e, χ\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ei\u003c/sub\u003e, χ\u003csub\u003ei\u003c/sub\u003e χ\u003csub\u003ej\u003c/sub\u003e) on the response of the regression equation (y). The evaluated parameters consist of laser power, welding speed, and distance between scan lines, which are analyzed at three distinct levels. The levels of the input parameters are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eProcess control parameters and their limits\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eInput Parameters\u003c/p\u003e \u003cp\u003e(Controllable)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNotations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLevel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e+\u0026thinsp;1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLaser power (A)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWatt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScan speed (B)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{{mm}}{s}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edistance between scan lines (C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.025\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3 Optimization using examination of desirability functions.\u003c/h2\u003e \u003cp\u003eThe Derringer and Suich optimization methodology is a viable method for simultaneously optimizing several outputs [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. This approach relies on Desirability functions. Under this methodology, every output y\u003csub\u003ei\u003c/sub\u003e is first transformed into a desirability function di, which spans from zero to one (0\u0026thinsp;\u0026le;\u0026thinsp;di\u0026thinsp;\u0026le;\u0026thinsp;1). Within this function, when the output y\u003csub\u003ei\u003c/sub\u003e matches the desired value, the variable di is assigned a value of 1 Conversely, if the output falls beyond the allowed range, di is assigned a value of 0 The input variables are chosen in a manner that optimizes the total desirability D [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003e3.1 Development of mathematical models\u003c/h2\u003e\n \u003cp\u003eThe Minitab Software was used to assess and generate an appropriate regression equation for fitting the collected data. Before the analysis of variance, to remove factor noise, tests were performed in the order of the results presented in Table\u0026nbsp;\u003cspan\u003e3\u003c/span\u003e. The ANOVA approach was used to assess the significance or insignificance of the input parameters. The F-value and lack of fit were used to assess and examine the efficacy or ineffectiveness of the input parameters, as well as the correctness and sufficiency of the model, in this approach.\u003c/p\u003e\n \u003cdiv id=\"Sec11\"\u003e\n \u003ch2\u003e3.1.1 Analysis of lap-shear Force\u003c/h2\u003e\n \u003cp\u003eThe purpose of the regression equation is to construct a coherent link between the response variable and the independent input factors. Eq.\u0026nbsp;2 is the regression equation that reflects the output shear force. Table\u0026nbsp;\u003cspan\u003e4\u003c/span\u003e displays the R\u0026sup2;, corrected R\u0026sup2;, and anticipated R\u0026sup2; values, as well as other indicators of adequacy for the shear force. The proximity of the R\u0026sup2;, adjusted R\u0026sup2;, and predicted R\u0026sup2; values to one suggests that the model is efficient. Based on the data shown in the table, if the input parameters have a P-value lower than 0.05 (\u0026alpha;\u0026thinsp;=\u0026thinsp;0.05, or 95% confidence level), it signifies that they significantly affect the shear force with a confidence level above 95%. If any of the input parameters have a P-value that exceeds 0.05, it indicates that they lack significance. Furthermore, a model is deemed satisfactory if the lack-of-fit value exceeds 0.05. The ANOVA table indicates that the variables Laser power (P), welding speed (S), distance between scan lines (LD), the quadratic effect of laser power (P\u0026sup2;), the quadratic effect of welding speed (S\u0026sup2;), the interaction effect of laser power and welding speed (P\u0026times;S), and the interaction effect of welding speed and distance between scan lines (S\u0026times;LD) significantly influence the lap shear force. Out of all the input parameters, the one with the most influence on the lap shear force is laser power with an F-Value of 1598.31. On the other hand, the parameter with the least influence is the quadratic effect of welding speed (S\u0026sup2;) with an F-Value of 5.36. The parameters (LD\u0026sup2;) representing the quadratic effect of the distance between scan lines, and (P\u0026times;LD) representing the interaction effect of laser power and distance between scan lines, were eliminated from the model since they have no impact on the shear force and their removal was done to enhance the model.\u003c/p\u003e\n \u003cp\u003eTable 3. Design matrix and measured responses\u003c/p\u003e\n \u003cdiv\u003e\n \u003cdiv\u003e\n \u003ctable dir=\"rtl\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"624\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e\u003cstrong\u003eResults\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e\u003cstrong\u003eExperimental information\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eWeld-seam width\u0026nbsp;(mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eLap-shear Force\u0026nbsp;\u0026nbsp;(N)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eWelding Parameters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eStd order\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eRun order\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eLD (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eS\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003eP (watt)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e38\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e1025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e21\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e245\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e450\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e20\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e37\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e27\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e875\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.015\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e400\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e20\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e40\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e1044\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.015\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e450\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e37\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e936\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e400\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e3\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e37\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e664\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e35\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e38\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e792\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e400\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e32\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e35\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e655\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e8\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e24\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e585\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e400\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e20\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e9\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e35\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e670\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e38\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e33\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e542\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e1\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e31\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e472\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.015\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e450\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e20\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e40\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e44\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e1256\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.015\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e400\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e5\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e785\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.025\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e450\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e30\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e12\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e24\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e580\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e20\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e16\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e37\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e695\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e23\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e40\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e845\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.015\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e33\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e39\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e710\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e14\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e36\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e660\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e425\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e36\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e34\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e530\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e0.020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e450\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e25\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e18\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\"\u003e\n \u003cp dir=\"LTR\"\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\u0026nbsp;\n \u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Taba\" border=\"1\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003csub\u003eZigzag\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e=\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3691\u0026thinsp;\u0026minus;\u0026thinsp;351.8 P\u0026thinsp;+\u0026thinsp;14.4S-80680 LD\u0026thinsp;+\u0026thinsp;4.723 P\u0026times;P-0.0375 S\u0026times;S\u0026thinsp;+\u0026thinsp;0.38 P\u0026times;S\u0026thinsp;+\u0026thinsp;124 S\u0026times;LD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 4\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eANOVA analysis for the lap-shear Force width model (after backward elimination)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSource\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eDF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSum of squares\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean squares\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eF-value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProb\u0026thinsp;\u0026gt;\u0026thinsp;F\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e982624\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140375\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e428.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSignificant\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eLinear\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e906815\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e302272\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e922.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eP\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e523952\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e523952\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1598.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e187142\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e187142\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e570.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eLD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e195720\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e195720\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e597.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eSquare\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55838\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e27919\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eP*P\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e44604\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e44604\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e136.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eS*S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.039\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e2-Way Interaction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19972\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9986\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eP*S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18050\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18050\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eS*LD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1922\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1922\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.032\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eError\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3934\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e328\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eLack-of-Fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1540\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e220\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.830\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNot Sigficant\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003ePure Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2393\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e986558\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;99.60%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eAdjusted R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;99.37%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003ePeredict R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;98.99%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec12\"\u003e\n \u003ch2\u003e3.1.2 Analysis of weld-seam width\u003c/h2\u003e\n \u003cp\u003eEquation 3 is the regression equation that describes the outcome of the weld-seam width. The equation has a parabolic nature as a result of the quadratic impact of laser power (P\u0026sup2;) on the weld-seam width. Table\u0026nbsp;\u003cspan\u003e5\u003c/span\u003e shows that the laser power (P), welding speed (S), and the distance between scan lines (LD) have a considerable impact on the output of weld-seam width. This impact is statistically significant with a confidence level above 95%. Furthermore, the quadratic impact of laser power (P\u0026sup2;), together with the interaction effects of laser power with welding speed (P\u0026times;S), laser power with distance between scan lines (P\u0026times;LD), and welding speed with distance between scan lines (S\u0026times;LD), are statistically significant for this output at a significance level of \u0026alpha;\u0026thinsp;=\u0026thinsp;0.05. The model\u0026apos;s adequacy is shown by the near proximity of the R\u0026sup2;, adjusted R\u0026sup2;, and anticipated R\u0026sup2; values to one, as well as a P-value of 0.884 for the Lack of Fit, as presented in Table\u0026nbsp;\u003cspan\u003e5\u003c/span\u003e. The laser power, with an F-Value of 227.47, is the most significant input parameter on the output of weld-seam width. On the other hand, the interaction impact of laser power and distance between scan lines (P\u0026times;LD), with an F-Value of 6.93, is the least influential parameter. The quadratic parameters LD\u0026sup2; and S\u0026sup2; were eliminated from the model since they do not have any effect on the output of weld-seam width.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tabb\" border=\"1\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003csub\u003eZigzag\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e=\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-406.1 +\u0026nbsp;19.87\u0026nbsp;P +\u0026nbsp;0.649\u0026nbsp;S +\u0026nbsp;6660\u0026nbsp;LD -\u0026nbsp;0.2120\u0026nbsp;P\u0026times;P -\u0026nbsp;0.01700\u0026nbsp;P\u0026times;S -\u0026nbsp;45.0\u0026nbsp;P\u0026times;LD -\u0026nbsp;15.00\u0026nbsp;S\u0026times;LD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 5\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eANOVA analysis for the weld-seam width model (after backward elimination)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSource\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSum of squares\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean squares\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eF-value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProb\u0026thinsp;\u0026gt;\u0026thinsp;F\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e752.225\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e107.461\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e73.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSignificant\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLinear\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e537.400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e179.133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e122.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e324.900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e324.900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e222.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e176.400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e176.400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e120.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSquare\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140.450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140.450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP*P\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140.450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140.450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2-Way Interaction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e74.375\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.792\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u0026times;S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP\u0026times;LD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.022\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS\u0026times;LD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eError\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.460\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLack-of-Fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.861\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.884\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNot Sigficant\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePure Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e769.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;97.72%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eAdjusted R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;96.40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003ePeredict R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;94.04%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\"\u003e\n \u003ch2\u003e3.2 Effects of process parameters on the responses\u003c/h2\u003e\n \u003cdiv id=\"Sec14\"\u003e\n \u003ch2\u003e3.2.1. Lap-shear force\u003c/h2\u003e\n \u003cp\u003eThe graphs shown in Fig.\u0026nbsp;\u003cspan\u003e5\u003c/span\u003e provide the examination of the influence of each input parameter. Increasing the laser power (P) from 20 W to 30 W resulted in higher temperatures in the weld region and enhanced polymer melting. Upon reaching their critical temperatures, the absorbing and transparent polymers underwent melting, resulting in an expansion in the volume of the molten fluid. Consequently, there was an increased degree of intermingling and adhesion among the polymer molecules. Consequently, a stronger bond between the two polymers was established after they hardened. Increasing the welding speed (S) led to a decrease in the temperature of the weld zone, hence lowering the amount of polymer melt in that area. As a consequence, the weld strength decreased when the welding speed was increased from 400 mm/s to 450 mm/s. The distance between scan lines (LD) has a direct impact on the quantity of laser beam scans inside a certain area. Consequently, reducing the distance between scan lines of the beam resulted in an increased number of laser beam scans on the surface under examination. Increasing the number of laser beam scans on a surface resulted in higher temperatures in the weld zone, leading to an increase in the melting of the polymer in that particular area. Consequently, the weld strength decreased as the distance between scan lines rose from 0.015 mm to 0.025 mm.\u003c/p\u003e\n \u003cp\u003eConcurrently augmenting laser intensity and reducing welding velocity results in a rise in line energy [\u003cspan\u003e15\u003c/span\u003e]. Inadequate fusion or weak weld strength occurs due to low line energy, while excessive line energy leads to polymer base materials being burned and degraded. Thus, it is necessary to determine the most favorable energy level for the line energy. In order to achieve uniform line energy across all levels of laser power and welding speed, one may either simultaneously raise both power and speed or reduce both simultaneously. Using this method, after the ideal line energy is attained, a uniform heat input is achieved in the welding area. Figure\u0026nbsp;\u003cspan\u003e6\u003c/span\u003e displays the contour and planar graphs illustrating the changes in shear force as a result of the combined influence of laser power and welding speed (P\u0026times;S). The beamline parameter distance in these photos is set to its center value of 0.02 mm. Figure\u0026nbsp;\u003cspan\u003e6\u003c/span\u003e(a) demonstrates that the combination of increasing laser power and reducing welding speed led to an increase in weld strength. This is caused by the higher amount of heat being applied to the area where the weld is being made, which is influenced by the changing energy levels along the weld line. The maximum heat input to the weld zone was seen at a laser power of around 29\u0026ndash;30 W, with a welding speed ranging from 400\u0026ndash;435 mm/s. In contrast, diminishing the laser power and augmenting the welding speed resulted in a loss in line energy, which in turn led to a reduction in heat input to the weld zone, a decrease in polymer melting, and therefore, a decline in weld strength. The minimum shear force values were observed when the laser power ranged from around 20\u0026ndash;23 W and the welding speed varied from around 448\u0026ndash;450 mm/s. The planar graph in Fig.\u0026nbsp;\u003cspan\u003e6\u003c/span\u003e(b) illustrates the correlation between line energy and heat input on weld strength. It demonstrates that shear pressures exceeding 1000 N were attained when the line energy reached its highest point. Figures\u0026nbsp;\u003cspan\u003e7\u003c/span\u003e(a) and (b) show the contour and planar graphs illustrating the changes in shear force resulting from the interaction between welding speed and the distance between scan lines (S\u0026times;LD). In this case, the laser power remains constant at its center value of 25 W. Figure\u0026nbsp;\u003cspan\u003e7\u003c/span\u003e(a) demonstrates that reducing both the welding speed and the distance between scan lines at the same time resulted in an increase in the lap-shear force. Thus, it can be inferred that a decrease in the interaction effect of welding speed and the distance between scan lines (S\u0026times;LD) results in an increase in the heat input to the weld zone. Enhanced thermal transfer, the generation of a suitable amount of molten material substance, integration of the base material, and eventually the creation of a robust connection in the welding area are further consequences of amplifying the interaction effect of welding speed and the distance between scan lines (S\u0026times;LD). The optimal welding speed range for achieving the largest shear force in a zigzag route is around 400\u0026ndash;410 mm/s, while the recommended distance between scan lines is around 0.015\u0026ndash;0.016 mm. In contrast, the optimal values for minimizing lap-shear force are 435\u0026ndash;450 mm/s and 0.023\u0026ndash;0.025 mm. Based on the data shown in Fig.\u0026nbsp;\u003cspan\u003e7\u003c/span\u003e(b), it was found that while using a laser power of 25 W, no welds were seen to have a shear strength of more than 1000 N. The laser power parameter has a stronger impact on the heat input to the weld zone compared to the welding speed, distance between scan lines, and their interaction effect. Consequently, shear strengths greater than 1000 N were observed when the laser power reached 30 W.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec15\"\u003e\n \u003ch2\u003e3.2.2. Weld-seam width\u003c/h2\u003e\n \u003cp\u003eAccording to the schematics shown in Fig.\u0026nbsp;\u003cspan\u003e8\u003c/span\u003e, an escalation in laser power led to an expansion of the breadth of the weld seam. The increase of both laser power and heat input in the weld zone not only improved weld strength but also resulted in an enlargement of the weld seam width and an unfavorable aesthetic of the weld joint. Increasing the welding speed led to less time of laser beam exposure in the weld zone, resulting in a reduction in heat input and heat transfer to the weld zone. This resulted in a narrower weld seam width for the joint. Aside from the welding speed, the distance between scan lines also influenced the welding time. Minimizing this distance resulted in an increase in both the duration of the welding process and the amount of heat applied. Consequently, a drop in this parameter caused an augmentation in weld seam width, whilst an increase in the distance between scan lines led to a reduction in weld seam width. Therefore, the combination of higher laser power, lower welding speed, and shorter distances between scan lines resulted in a greater amount of heat input being applied, leading to an expansion in the weld-seam width. Based on Fig.\u0026nbsp;\u003cspan\u003e9\u003c/span\u003e(a), the smallest measured width of the weld seam for the zigzag path was found to be between 20 and 21 W laser power and 400\u0026ndash;450 mm/s welding speed. The highest documented width of the weld seam in this path was seen within the approximate range of 26\u0026ndash;30 W laser power and 400\u0026ndash;405 mm/s welding speed. According to the contour plot, higher laser power levels had a greater effect on the breadth of the weld seam when compared to differences in speed. The heat input was much more responsive at higher temperatures. Therefore, in high-power welding, even little adjustments in welding speed resulted in significant fluctuations in heat input and, subsequently, in the dimensions of the weld seam width. Figure\u0026nbsp;\u003cspan\u003e9\u003c/span\u003e(b) demonstrates that a consistent rise in laser power, as a result of its stronger impact on line energy in comparison to welding speed, resulted in an expansion of the weld-seam width. Hence, in order to achieve uniform energy distribution throughout all levels of the interaction effect between laser power and welding speed (P\u0026times;S), it is crucial to acknowledge that changes in laser power had a more pronounced impact on the width of the weld seam compared to changes in welding speed. The contour and surface plots in Fig.\u0026nbsp;\u003cspan\u003e10\u003c/span\u003e depict the variations in the weld-seam width caused by the interaction effect of welding speed and distance between scan lines (S\u0026times;LD), using a central laser power of 25 W, along a zigzag path. Figure\u0026nbsp;\u003cspan\u003e10\u003c/span\u003e(a) illustrates a significant negative connection between the interaction effect of welding speed and distance between scan lines (S\u0026times;LD) and the weld-seam width. The decrease in welding speed and the decrease in the distance between scan lines resulted in an increase in the heat input inside the welding zone, which consequently led to an enlargement in the weld-seam width. According to Fig.\u0026nbsp;\u003cspan\u003e10\u003c/span\u003e(a), the most favorable the weld-seam width in the zigzag path was determined to be around 440\u0026ndash;450 mm/s for welding speed and 0.0237\u0026ndash;0.025 mm for the distance between scan lines. Conversely, the most extensive weld-seam width was seen when the welding speed ranged from around 400 to 450 mm/s and the distance between scan lines ranged from 0.015 to 0.016 mm. Based on the surface plot shown in Fig.\u0026nbsp;\u003cspan\u003e10\u003c/span\u003e-b, it is evident that altering the distance between scan lines has a greater effect on the weld-seam width compared to adjusting the welding speed. This is done to maintain line energy balance across various levels of the interaction parameters. The contour and surface plots in Fig.\u0026nbsp;\u003cspan\u003e11\u003c/span\u003e demonstrate that the variations in weld seam width exhibit significant curvature and well-defined boundaries. The figures indicate that the interaction effect of laser power and distance between scan lines (P\u0026times;LD) has a substantial impact on the weld-seam width. Figure\u0026nbsp;\u003cspan\u003e11\u003c/span\u003e(a) illustrates that the welding zone experienced the highest level of heat, leading to the widest weld seam, when the laser power was approximately in the range of 25\u0026ndash;30 W and the distance between scan lines was about 0.015\u0026ndash;0.0175 mm. On the contrary, the weld seam\u0026apos;s smallest width was seen along the zigzag path when the laser power was between 20 and 21 W, and the distance between scan lines was from 0.021 to 0.025 mm. Also, in Fig.\u0026nbsp;\u003cspan\u003e11\u003c/span\u003e-b, it is clear that the lowest value of the weld-seam width is obtained when the laser power is at the lowest value and the distance between scan lines is at the highest value.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4. Morphological analysis","content":"\u003cp\u003eAn examination of the microstructure in the weld zone is essential to study the bonding process in relation to the input parameters. Crystal structures, by their very nature, elongate the distance the beam travels in polymer structures, thereby increasing the probability of laser beam absorption and heat production in the area exposed to the laser [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. As a result, crystalline and semi-crystalline structures have a greater potential to produce a melted fluid at the weld area compared to amorphous structures [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. PMMA is a polymer characterized by its non-crystalline structure. The non-crystalline form of this polymer presents difficulties when examining its microstructure [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The post-weld polymer structure comprises a diverse array of bubbles, spherulites, and porosities. Factors such as heat input, line energy, cooling rate of molten material, laser beam scanning path, and Laser beam diameter are important parameters that have a considerable impact on the microstructure of the weld zone [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Raising the amount of heat applied to the weld area causes the moisture that remains and the polymer to evaporate. Bubble formation occurs as a consequence of the trapping of gases such as H\u003csub\u003e2\u003c/sub\u003eO, CO\u003csub\u003e2\u003c/sub\u003e, and CO, which is caused by moisture evaporation and molten material between the two polymers [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The existence of minute bubbles and their consistent dispersion throughout the welding zone improves the strength of the weld. The homogeneous distribution and flow of molten material in the welding region is impacted by the existence of tiny bubbles. Conversely, a higher quantity of bubbles in the welding zone signifies a more significant level of fusion of the underlying material, resulting in more amalgamation of molten substances. Poor fusing and mixing of molten materials occur as the size of the bubble in the weld zone increases. Consequently, the existence of sizable bubbles in the weld zone diminishes the strength of the weld [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. An augmentation in line energy and a reduction in cooling time within the crystallization range result in an enlargement of spherulites in the molten pool. Moreover, the presence of bigger spherulites might lead to the development of fractures in their vicinity, leading to a decrease in the strength of the weld [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. The trajectory of the laser beam inside the welding zone has an impact on the quantity and dimensions of voids and porosities. When the laser beam travels a greater distance during welding, the molten material will be distributed more evenly in the region where the weld is formed. This leads to a decrease in the quantity of empty spaces and air pockets in the weld [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows enlarged images of the weld area for samples 13 and 2. Sample 13, with a tensile strength of 1256 N, had the highest weld strength, while sample 2, with a tensile strength of 245 N, showed the lowest weld strength. Figures Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea, Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ec, and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ee depict the microstructure of sample 13. The existence of bubbles, voids, and spherulites clearly indicates the impact of laser beam irradiation and the subsequent solidification of molten material. The presence of bubbles may be ascribed to the emission of gases from residual moisture in the polymer. The even distribution of small bubbles inside the weld pool resulted in improved weld strength. The laser beam's zigzag path promoted its dispersion throughout several regions, thereby limiting the formation of further voids and porosities in the weld pool. The presence of spherulites in the weld pool and the stratified composition of this area suggest a significant line energy during the welding process of this specimen. As a result, a greater shear force is necessary for the joint to fail. Nevertheless, the proliferation of spherulites inside the weld region hindered any improvement in the strength of the weld. Figures Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eb, Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ed, and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ef depict the microstructure of sample 2. The photos indicate that the low energy level used during the welding process of this sample led to inadequate melting of the surface and negligible blending of the molten material. Inadequate bonding with low strength resulted from the existence of huge bubbles and the uneven distribution of smaller bubbles. The reduced quantity of spherulites in this region was a result of the limited thermal energy input during the welding process. As a result, the joint collapsed when subjected to a little amount of external strain.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Optimization of Lap shear force and Weld-seam width","content":"\u003cp\u003eThe process outputs were optimized by adjusting the parameters to achieve optimum weld strength and low weld-seam width. Figure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e presents the process parameters arranged in columns, where each row represents different variations in the outputs. Every individual cell demonstrates the changes in the corresponding output when the input parameters are modified. The values shown at the top of each column represent the high, optimal and low settings for each parameter, respectively. The optimization findings indicate that the ideal parameter values are a laser power of 20 W, a welding speed of 400 mm/s, and a beam distance of 0.015 mm. The first cell of each row displays the forecasted output value and its corresponding probability of attainment. Based on the projected model, if welding is repeated using these ideal parameters, the welded samples will exhibit a maximum tensile strength of 886.41 N and a minimum width of the weld seam of 26.37 mm. The findings suggest that the given optimum values are satisfactory, as shown by a Desirability Function score of 70%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6. Verification of results","content":"\u003cp\u003eIn order to verify the accuracy of the data generated from the Minitab program, a series of experimental tests were done three times, in accordance with the desirability function values. The tests were conducted using the following variable parameters: a laser power of 20 W, a welding speed of 400 mm/s, and a distance between scan lines of 0.015 mm. In addition, the predetermined parameters - focal distance, clamping force, and pulse frequency - were kept at 120 mm, 20 N, and 50 Hz, respectively, in line with prior examples. The findings from these three samples are shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. The modeling and optimization process yielded satisfactory results, as seen by the reported error percentages. The accuracy of the process may be deemed acceptable, with the Minitab program producing findings that closely align with the experimental data.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1731426620.png\"\u003e\u003cbr\u003e\u003c/p\u003e\n"},{"header":"Conclusion","content":"\u003cp\u003eThe findings presented in this research are derived from the range of input factors that were taken into account.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe base material decline and inability to establish adequate bonding were caused by the excessive amplification of laser power and substantial reduction in welding speed. Insufficient welding power, when paired with high welding speed, led to the lack of a molten pool and unsatisfactory fusion.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe relationship between laser power and welding speed is often known as line energy. In order to get a weld that is both strong and thin, it is necessary to perform the Laser-Transmission Welding (LTW) procedure using the ideal line energy value.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe distance between scan lines is another parameter affecting weld strength and weld-seam width. Smaller distances between scan lines result in increased welding time and consequently higher heat input to the weld zone. As a result, reducing this parameter leads to an increase in both weld strength and weld-seam width.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe distance between beam lines is an additional factor that impacts the strength of the weld and the weld-seam width. Reducing the distance between scan lines leads to longer welding time and, as a consequence, greater heat input to the weld zone. Consequently, decreasing this parameter results in an augmentation of both Lap-shear force and weld-seam width.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe ANOVA analysis reveals that laser power is the most significant factor on both lab-shear force and weld-seam width.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe most lap-shear force ever recorded is 1256 N, whereas the minimum width of a weld-seam ever recorded is 21 mm.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAn increased quantity of little bubbles has led to a rise in the lap-shear force. The lack of spherulites and layering in the microstructure of samples that fractured during tensile testing suggests that the connection created was weak, resulting in the deterioration of the weld with minimum external force.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe multi-objective optimization determined that the ideal input parameters are a laser power of 20 W, a welding speed of 400 mm/s, and a distance between scan lines of 0.015 mm.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe optimization analysis yielded a projected shear force output of 886.41N with a probability of 63.44%. Additionally, the expected result for the weld-seam width is 26.37 mm with a probability of 63.76%. Furthermore, the desirability function is set at a value of 70%.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;No specific grant from funding agencies in the public, commercial, or not-for-profit sectors was received for this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eInterests\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMilad Rahmaninia (Main Author): Conceptualization, Methodology, Writing - Original Draft, Investigation,\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eFormal\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eAnalysis.\u003cbr\u003e\u0026nbsp;Dr.Majid Ghoreishi (Supervisor): Supervision, Funding Acquisition, Project Administration, Writing - Review \u0026amp; Editing.\u003c/p\u003e\n\u003cp\u003e\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003e\u003cstrong\u003eData Availibility\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eAll data generated or analyzed during this study are included in this published article. No additional datasets were used or required for the study.\u003c/p\u003e\n\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank the K. N. Toosi University of Technology, Tehran, Iran, for the financial support and research facilities used in this research.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eS. Prakash and S. Kumar, Determining the suitable CO2 laser based technique for microchannel fabrication on PMMA, Optics \u0026amp; Laser Technology, vol. 139, p. 107017, (2021). https://doi.org/10.1016/j.optlastec.2021.107017\u003c/li\u003e\n \u003cli\u003eY. Huang, X. Gao, B. Ma and Y. Zhang, Interface formation and bonding mechanisms of laser welding of PMMA plastic and 304 austenitic stainless steel, Metals, vol. 11, p. 1495, (2021). https://doi.org/10.3390/met11091495\u003c/li\u003e\n \u003cli\u003eY. Luan, J. Liu and Y. 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Duval, Diode laser welding of polymers: microstructures of the welded zones for polypropylene, in International Congress on Applications of Lasers \u0026amp; Electro-Optics, pp. 1499-1507, (2001). https://doi.org/10.2351/1.5059820\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":"Laser transmission welding, Polymethyl Methacrylate, Transparent polymer welding parameters, Zigzag Path, Optimization, Morphological Analysis","lastPublishedDoi":"10.21203/rs.3.rs-5342698/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5342698/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study experimentally evaluated Laser Transmission Welding (LTW) between two transparent and identical Polymethyl Methacrylate (PMMA) sheets using a fiber optic laser following a zigzag path. The research focused on the effects of laser power, welding speed, and distance between scan lines on lap-shear force, weld-seam width, and changes in weld morphology. Pyrometry was used to measure the welding temperature and determine input parameters. Analysis of Variance (ANOVA) and Response Surface Methodology (RSM) were employed to analyze and optimize the input parameters for maximum lap-shear force and minimal weld-seam width. The findings indicated that higher laser power, slower welding speed, and a reduced distance between scan lines increased heat input, leading to enhanced polymer melting and improved weld strength, reflected by higher lap-shear force and broader weld-seam width. Conversely, lower heat input decreased both lap-shear force and weld-seam width. Optimal values for lap-shear force and weld-seam width were determined to be 886.4 N and 26.37 mm, respectively, through multi-objective optimization. The zigzag welding path contributed to uniform heat distribution, even mixing of melted materials, and better structural integrity in the weld zone. Morphological analysis revealed that the weld strength was enhanced due to the presence of smaller, evenly distributed bubbles in the weld pool, attributed to the zigzag path. These findings highlight the significance of controlling welding parameters to optimize strength and seam quality in laser transmission welding of PMMA.\u003c/p\u003e","manuscriptTitle":"Experimental Modeling and Process Optimization of Laser Transmission Welding with Fiber Optic Laser for Polymethyl Methacrylate in Zigzag Path","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-20 11:41:24","doi":"10.21203/rs.3.rs-5342698/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":"d9d3b9ef-454c-44bd-899d-55b4f4fb272a","owner":[],"postedDate":"November 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-09T16:20:35+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-20 11:41:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5342698","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5342698","identity":"rs-5342698","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}