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Figure 16. Error convergence according to the tree number selection in the Random Forest routine execution. MSR = Mean of Squared Residuals, VE = Variation Explained (%), MSE = Mean Squared Error: A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction.

Figure 16 Error convergence according to the tree number selection in the Random Forest routine execution. MSR = Mean of Squared Residuals, VE = Variation Explained (%), MSE = Mean Squared Error: A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction.

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Table 1. Control factors and their associated settings. As stated earlier, fast recipe-making is imperative when concocting industrial trials. The standard Taguchi-type L9(3*) OA [43] accommodates as many as four controlling factors by requiring nine specific experimental recipes to be executed. The four factors are accommodated in a saturated scheme. Saturated experimental plans may also be deemed ‘lean-and-green’, because they promote the maximization of the investigated influences. Each factor participates in the experimental plan at three operating settings through the preset configuration of the OA sampler. The promoted ‘lean-and-green’ engineering aspect is evident at this point, since the total work volume is reduced by a ratio of 1/9; a full- factorial arrangement of the four 3-level factors would otherwise demand a total of 81 (=34) trials. In Table 2, we list the scheduled factorial combinations according to the Lo(3*) OA arrangement. The nine-run OA set-up was makeshift replicated twice. This is another minimal (lean-and-green) replication practice. Finally, the tolerance limits for both the clearance and the groove depth were decided to be restricted within +0.02 mm.
Table 1. Control factors and their associated settings. As stated earlier, fast recipe-making is imperative when concocting industrial trials. The standard Taguchi-type L9(3*) OA [43] accommodates as many as four controlling factors by requiring nine specific experimental recipes to be executed. The four factors are accommodated in a saturated scheme. Saturated experimental plans may also be deemed ‘lean-and-green’, because they promote the maximization of the investigated influences. Each factor participates in the experimental plan at three operating settings through the preset configuration of the OA sampler. The promoted ‘lean-and-green’ engineering aspect is evident at this point, since the total work volume is reduced by a ratio of 1/9; a full- factorial arrangement of the four 3-level factors would otherwise demand a total of 81 (=34) trials. In Table 2, we list the scheduled factorial combinations according to the Lo(3*) OA arrangement. The nine-run OA set-up was makeshift replicated twice. This is another minimal (lean-and-green) replication practice. Finally, the tolerance limits for both the clearance and the groove depth were decided to be restricted within +0.02 mm.
Table 3. Chemical composition % and mechanical properties of steel P265GH.
Table 3. Chemical composition % and mechanical properties of steel P265GH.
Table 2. Four-factor experimental arrangement Lo (34) OA for testing joint strength.
Table 2. Four-factor experimental arrangement Lo (34) OA for testing joint strength.
Next, using a CAD/CAM mechanical design software (Fusion 360, Autodesk, San Francisco, CA, USA), 3D solid models were designed in order to generate the required G-code programs for the CNC milling treatment of the test tubesheet specimens (Figure 3). For the machining of the test tubesheet specimens, a 3-axis vertical milling CNC center (Genos M560-V-e, Okuma, Oguchi, Aichi, Japan) was employed which was also integrated with an OSP-P300MA-e (Okuma, Oguchi, Aichi, Japan) controller as depicted in Figure 5. Table 4. Chemical composition % and mechanical properties of steel P215NL.
Next, using a CAD/CAM mechanical design software (Fusion 360, Autodesk, San Francisco, CA, USA), 3D solid models were designed in order to generate the required G-code programs for the CNC milling treatment of the test tubesheet specimens (Figure 3). For the machining of the test tubesheet specimens, a 3-axis vertical milling CNC center (Genos M560-V-e, Okuma, Oguchi, Aichi, Japan) was employed which was also integrated with an OSP-P300MA-e (Okuma, Oguchi, Aichi, Japan) controller as depicted in Figure 5. Table 4. Chemical composition % and mechanical properties of steel P215NL.
Figure 5. The CNC machining center with the integrated controller. Figure 4. (a) Drill inserts and drill-body tool-holder; (b) drill inserts, boring tool-holder, and finish boring head adapter; (c) T-slot milling cutters; (d) tubesheet specimens after exiting the machin- ing process.
Figure 5. The CNC machining center with the integrated controller. Figure 4. (a) Drill inserts and drill-body tool-holder; (b) drill inserts, boring tool-holder, and finish boring head adapter; (c) T-slot milling cutters; (d) tubesheet specimens after exiting the machin- ing process.
Figure 6. (a) Tube expanding machine; (b) three-roller tube expander.
Figure 6. (a) Tube expanding machine; (b) three-roller tube expander.
Because of the criticality of a proper specimens’ preparation in ensuring trustworthy test-joint strength measurements, the grooves on the tubesheet-hole walls, along with the tube inner and outer surfaces, were pre-treated to rid of any surface blemishes, such as burrs, grease, oil residue, rust, or dirt. The finalized torque settings which were applied during the tube-rolling process and their expected tube wall thickness reduction percentage are listed in Table 6. Before conducting the tube expansion process (Figure 7d), the required tube wal reduction percentage for each experiment was pre-evaluated to select suitable trial setting: for the OA scheme. The relative tabulations from refs. [51,52] were adopted to complet the ensuing detailed calculations. Equation (1) from ref. [7] was used to allow a realistic pre-estimation of the tube inner diameters for the tube-rolling process (Table 5). Moreove! the tubesheet hole diameter, as well as the tube inner and outer diameters, were measurec thrice each (Figure 7), for every replicated nine-run set of experiments, and their mear values were recorded. The tolerance limits of individual experiment were determined to be the expanded tube inner diameters for eact within +£0.05 mm.
Because of the criticality of a proper specimens’ preparation in ensuring trustworthy test-joint strength measurements, the grooves on the tubesheet-hole walls, along with the tube inner and outer surfaces, were pre-treated to rid of any surface blemishes, such as burrs, grease, oil residue, rust, or dirt. The finalized torque settings which were applied during the tube-rolling process and their expected tube wall thickness reduction percentage are listed in Table 6. Before conducting the tube expansion process (Figure 7d), the required tube wal reduction percentage for each experiment was pre-evaluated to select suitable trial setting: for the OA scheme. The relative tabulations from refs. [51,52] were adopted to complet the ensuing detailed calculations. Equation (1) from ref. [7] was used to allow a realistic pre-estimation of the tube inner diameters for the tube-rolling process (Table 5). Moreove! the tubesheet hole diameter, as well as the tube inner and outer diameters, were measurec thrice each (Figure 7), for every replicated nine-run set of experiments, and their mear values were recorded. The tolerance limits of individual experiment were determined to be the expanded tube inner diameters for eact within +£0.05 mm.
Table 6. Torque values used for tube rolling. 2.5. Joint Strength Measurements
Table 6. Torque values used for tube rolling. 2.5. Joint Strength Measurements
Before commencing the tube push-out testing procedure, the tube ends of the tube spec- imens were sealed with welded plugs as depicted in Figure 8a. A tensile/compressive test- ing machine (CTM/50, Galdabini, Cardano al Campo, Varese, Italy) was utilized (Figure 8b) to perform the tube push-out tests. The testing machine was integrated with GraphWork 5.0 test software which recorded the applied loads on the tubes during the push-out testing process. Moreover, a round steel bar of material S355 (Figure 8c), with nominal diameter and length dimensions of 14 mm and 295 mm, respectively, was inserted into the tube end to direct the axial load transmission (Figure 8d); it forced the tube out of the tubesheet hole to the point of mechanical failure of the joint or the tube (Figure 8e,f). The push-out tests were carried out at a constant crosshead speed of 5 mm/min. After the axial tube- displacement process was initiated, the applied load was monitored and recorded by the esting equipment. The maximum load was applied at the start of the displacement cycle and then it was gradually decreased. The terminal condition of the tube-to-tubesheet speci- mens exiting the push-out testing is demonstrated in Figure 8g. Duplicate joint strength measurements were obtained for the nine-run tube-to-tubesheet specimens.
Before commencing the tube push-out testing procedure, the tube ends of the tube spec- imens were sealed with welded plugs as depicted in Figure 8a. A tensile/compressive test- ing machine (CTM/50, Galdabini, Cardano al Campo, Varese, Italy) was utilized (Figure 8b) to perform the tube push-out tests. The testing machine was integrated with GraphWork 5.0 test software which recorded the applied loads on the tubes during the push-out testing process. Moreover, a round steel bar of material S355 (Figure 8c), with nominal diameter and length dimensions of 14 mm and 295 mm, respectively, was inserted into the tube end to direct the axial load transmission (Figure 8d); it forced the tube out of the tubesheet hole to the point of mechanical failure of the joint or the tube (Figure 8e,f). The push-out tests were carried out at a constant crosshead speed of 5 mm/min. After the axial tube- displacement process was initiated, the applied load was monitored and recorded by the esting equipment. The maximum load was applied at the start of the displacement cycle and then it was gradually decreased. The terminal condition of the tube-to-tubesheet speci- mens exiting the push-out testing is demonstrated in Figure 8g. Duplicate joint strength measurements were obtained for the nine-run tube-to-tubesheet specimens.
Figure 8. (a) Tube end sealing; (b) push-out testing machine; (c) round S355 steel bar; (d) preparation for push-out testing; (e) before tube displacement; (f) after tube displacement; (g) tested tube-to- tubesheet specimens after tube push-out testing completed.
Figure 8. (a) Tube end sealing; (b) push-out testing machine; (c) round S355 steel bar; (d) preparation for push-out testing; (e) before tube displacement; (f) after tube displacement; (g) tested tube-to- tubesheet specimens after tube push-out testing completed.
Figure 9. The input-output saturated L9(3*) OA arrangement for duplicated response data.
Figure 9. The input-output saturated L9(3*) OA arrangement for duplicated response data.
Figure 10. The two separate data reduction steps to generate the mean (M) and SNR responses, respectively.
Figure 10. The two separate data reduction steps to generate the mean (M) and SNR responses, respectively.
Table 7. Duplicated dataset, mean, and SNR estimations of the joint strength.
Table 7. Duplicated dataset, mean, and SNR estimations of the joint strength.
Table 8. Response table for joint strength mean (N). The remaining two factors, the clearance and the groove depth, are behaving as of a lesser importance—at a similar effect magnitude between them. According to the response graph for the joint strength mean, the optimal setting of the tube wall thickness reduction is 12% and the respective optimal setting of the number of grooves is three. Similar observations may be drawn from the response table (Table 9) for the joint strength SNR. However, the discrepancies between settings are relatively smaller for the SNR estimations. The tube wall thickness reduction and the number of the grooves elicit a maximum difference in the joint strength mean SNR values of 6.53 dB and 4.55 dB, respectively. Overall, it may be remarked that both factors cause minor disturbance on the mean SNR response of the joint strength. Similarly, the main effects plot for the joint strength mean SNR shows that the corresponding optimal settings are exhibiting the same pattern as in the main effects for the means plot, i.e., optimally set at 12% for the former and three for the latter.
Table 8. Response table for joint strength mean (N). The remaining two factors, the clearance and the groove depth, are behaving as of a lesser importance—at a similar effect magnitude between them. According to the response graph for the joint strength mean, the optimal setting of the tube wall thickness reduction is 12% and the respective optimal setting of the number of grooves is three. Similar observations may be drawn from the response table (Table 9) for the joint strength SNR. However, the discrepancies between settings are relatively smaller for the SNR estimations. The tube wall thickness reduction and the number of the grooves elicit a maximum difference in the joint strength mean SNR values of 6.53 dB and 4.55 dB, respectively. Overall, it may be remarked that both factors cause minor disturbance on the mean SNR response of the joint strength. Similarly, the main effects plot for the joint strength mean SNR shows that the corresponding optimal settings are exhibiting the same pattern as in the main effects for the means plot, i.e., optimally set at 12% for the former and three for the latter.
Table 9. Response table for the joint strength SNR (dB). Tt o proceed with the analysis part, the statistical significance of the outcomes is obtained the ANOVA treatment. As expected, the two data reduction steps have each separately sized the duplicated form of the original datasets—mean and SNR estimations—to a ‘unreplicated response’ form. Additionally, the experimental OA-plan was decided fully loaded with controlling factors (‘saturated’ condition). Hence, the usefulness of the ANOVA is restricted to offering only a relative strength evaluation among the factoria butions. This is because in the saturated-unreplicated form, an OA sampler does not permit significance estimations in the absence of a residual error. This is observed for means and SNR estimations (Tables 10 and 11). Despite that, till worthwhile to contemplate the leading contributions, in terms of mean sum of from down virtua to be contri in bot. itis s h ANOVA tables, squares calculations. Ac sum of the mean sums of squares for both estimator treatments—mean and SNR joint strength response. Simi sums of squares of the Even though there is no the goodness-of-fit computations to assess the status of the predictions, nevertheless, a qualitative comparison between the data-reduced (mean and SNR) joint strength variable with the simplistic response graph and response table results seems to lead to an agreement. tually, the tube wall thickness contributes about 55% to the tota arly, the number of grooves contributes to the mean and SNR joint strength response about 30.57% and 25.74%, respectively. available information from either the statistical significance or
Table 9. Response table for the joint strength SNR (dB). Tt o proceed with the analysis part, the statistical significance of the outcomes is obtained the ANOVA treatment. As expected, the two data reduction steps have each separately sized the duplicated form of the original datasets—mean and SNR estimations—to a ‘unreplicated response’ form. Additionally, the experimental OA-plan was decided fully loaded with controlling factors (‘saturated’ condition). Hence, the usefulness of the ANOVA is restricted to offering only a relative strength evaluation among the factoria butions. This is because in the saturated-unreplicated form, an OA sampler does not permit significance estimations in the absence of a residual error. This is observed for means and SNR estimations (Tables 10 and 11). Despite that, till worthwhile to contemplate the leading contributions, in terms of mean sum of from down virtua to be contri in bot. itis s h ANOVA tables, squares calculations. Ac sum of the mean sums of squares for both estimator treatments—mean and SNR joint strength response. Simi sums of squares of the Even though there is no the goodness-of-fit computations to assess the status of the predictions, nevertheless, a qualitative comparison between the data-reduced (mean and SNR) joint strength variable with the simplistic response graph and response table results seems to lead to an agreement. tually, the tube wall thickness contributes about 55% to the tota arly, the number of grooves contributes to the mean and SNR joint strength response about 30.57% and 25.74%, respectively. available information from either the statistical significance or
Table 10. ANOVA treatment for the response means of the joint strength.
Table 10. ANOVA treatment for the response means of the joint strength.
Table 11. ANOVA treatment for the response SNR estimations of the joint strength. *: no value available.
Table 11. ANOVA treatment for the response SNR estimations of the joint strength. *: no value available.
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 12. Stepwise ANOVA results for unprocessed response joint strength dataset.
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 12. Stepwise ANOVA results for unprocessed response joint strength dataset.
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 13. Stepwise regression coefficients for the joint strength response dataset.
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 13. Stepwise regression coefficients for the joint strength response dataset.
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 14. Best subsets regression (B and D participate in all models).
A = Clearance, B = Number of Grooves, C = Groove Depth, D = Tube Wall Thickness Reduction. Table 14. Best subsets regression (B and D participate in all models).
Figure 11. (a) Response graph for joint strength SNR; (b) response graph for joint strength mean
Figure 11. (a) Response graph for joint strength SNR; (b) response graph for joint strength mean
Table 15. Predicted values for the maximum performance of the joint strength. 3.3. Confirmation Run for the Optimal Parameter Settings
Table 15. Predicted values for the maximum performance of the joint strength. 3.3. Confirmation Run for the Optimal Parameter Settings
The optimal layout of the specimens (the 10th factorial recipe), which is prepared on the suggested parameter adjustments from the previous subsection, is re-drawn and is shown in Figure 12. The confirmation run was comprised of five pairs of machined tubes and tubesheets, which are shown in Figure 13. Thus, the confirmation run was replicated five times. The collected measurements from the confirmation experiment are listed in Table 16. Figure 12. Drawing of the optimal tube-to-tubesheet specimens to be used for the confirmation runs.
The optimal layout of the specimens (the 10th factorial recipe), which is prepared on the suggested parameter adjustments from the previous subsection, is re-drawn and is shown in Figure 12. The confirmation run was comprised of five pairs of machined tubes and tubesheets, which are shown in Figure 13. Thus, the confirmation run was replicated five times. The collected measurements from the confirmation experiment are listed in Table 16. Figure 12. Drawing of the optimal tube-to-tubesheet specimens to be used for the confirmation runs.
Table 16. Joint strength observations from the confirmation trial runs. Even though only five confirmation runs were programmed to constitute an initial test sample, the tapered 95%-confidence-interval estimation (Table 16) hinted that no additional confirmation-run samples would be meaningful at this stage. The notion of lean thinking also extends to minimizing the confirmation trials, if the trends are already practically explainable and there is a firm grasp on how joint strength variability is distributed among its accounted sources. Moreover, this was attested because of the accompanying very low value of the coefficient of variation of the confirmed joint strength performance (0.0098). However, the discrepancy between the predictions due to the Taguchi method and the stepwise regression analysis, on one hand, and the confirmation-run joint strength mean response values, on the other, was calculated at a relative percentage of about 14%. While he complexity of the physical phenomena behind this mechanical process is known to be high, and in part, it could justify such realistic deviation, particularly under the espoused condition of the ‘lean-green-driven’ (miniaturized) experimentation, in the Discussion section there will be further exploration about the cause of such discrepancies. Conversely, the confirmation-run joint strength performance matches fairly close to the maximum observable joint strength measurement in the OA trials which was found to be 45,371.25 N Table 7). Thus, their difference may be viewed now more tolerable at the relative percentage of 3.3%. It is concluded that this study might have produced useful empirical relationships, but an alternative non-statistical treatment might provide insight from a different angle. This last issue will be discussed in the next section.
Table 16. Joint strength observations from the confirmation trial runs. Even though only five confirmation runs were programmed to constitute an initial test sample, the tapered 95%-confidence-interval estimation (Table 16) hinted that no additional confirmation-run samples would be meaningful at this stage. The notion of lean thinking also extends to minimizing the confirmation trials, if the trends are already practically explainable and there is a firm grasp on how joint strength variability is distributed among its accounted sources. Moreover, this was attested because of the accompanying very low value of the coefficient of variation of the confirmed joint strength performance (0.0098). However, the discrepancy between the predictions due to the Taguchi method and the stepwise regression analysis, on one hand, and the confirmation-run joint strength mean response values, on the other, was calculated at a relative percentage of about 14%. While he complexity of the physical phenomena behind this mechanical process is known to be high, and in part, it could justify such realistic deviation, particularly under the espoused condition of the ‘lean-green-driven’ (miniaturized) experimentation, in the Discussion section there will be further exploration about the cause of such discrepancies. Conversely, the confirmation-run joint strength performance matches fairly close to the maximum observable joint strength measurement in the OA trials which was found to be 45,371.25 N Table 7). Thus, their difference may be viewed now more tolerable at the relative percentage of 3.3%. It is concluded that this study might have produced useful empirical relationships, but an alternative non-statistical treatment might provide insight from a different angle. This last issue will be discussed in the next section.
Figure 13. Tubes and tubesheet specimens machined for the confirmation run.
Figure 13. Tubes and tubesheet specimens machined for the confirmation run.
Figure 14. Cont. A post-screening assessment could be initiated by depicting the four controlling factors in boxplots for each individual controlling factor to emphasize the visual aspect of their variability owing to different settings. In Figure 14, the corresponding four boxplots have been prepared (MINITAB 19.0, State College, PA, USA). It is immediately discerned that only the tube wall thickness reduction could amass distinguishable variation across settings. A linear dependence emerges which is solely framed by the two operating endpoints of this factor. The second (middle) setting merely overlaps across both end settings. The rest of the controlling factors do not pass the test of visual evidence. Perhaps, their influence on the joint strength response is dubious; their confidence intervals for their medians are overlapping across all settings. Equally striking is the asymmetric location tendencies in the data sample median values as exposed by individual settings.
Figure 14. Cont. A post-screening assessment could be initiated by depicting the four controlling factors in boxplots for each individual controlling factor to emphasize the visual aspect of their variability owing to different settings. In Figure 14, the corresponding four boxplots have been prepared (MINITAB 19.0, State College, PA, USA). It is immediately discerned that only the tube wall thickness reduction could amass distinguishable variation across settings. A linear dependence emerges which is solely framed by the two operating endpoints of this factor. The second (middle) setting merely overlaps across both end settings. The rest of the controlling factors do not pass the test of visual evidence. Perhaps, their influence on the joint strength response is dubious; their confidence intervals for their medians are overlapping across all settings. Equally striking is the asymmetric location tendencies in the data sample median values as exposed by individual settings.
Figure 14. Boxplots for the joint strength (JS in N) due to: (A) clearance (A in mm), (B) number of grooves (B), (C) groove depth (C in mm), and (D) tube wall thickness reduction (D in %).
Figure 14. Boxplots for the joint strength (JS in N) due to: (A) clearance (A in mm), (B) number of grooves (B), (C) groove depth (C in mm), and (D) tube wall thickness reduction (D in %).
No particular side is favored in the numerical accumulation of the observations; t hey are predominantly asymmetric across all four factors. A plausible question would be whether any additional trial runs would refine more the precision around the magnitude estimation of the effects and, hence, would assist to expediting the practical aspect of the profiling process. To check consistency in the duplicated trials of the joint strength experiments, the two replicates are regressed against each other (Figure 15). It results in a symmetrical line fitting—the fitted line slope is 1.03—and the adjusted coefficient of determination is estimated at 98.7%. It is inferred that there is no immediate concern to conduct more replications or selectively augment the volume of observations. It is useful to also obtain an alternative prediction from a classic algorithmic solver such as the Random Forest. The trial outcomes from running the Random Forest module 10 times are summarized and tabulated in Table 17 (IBM SPSS v.29, Armonk, NY, USA). The precision of the predictions is deemed adequate. This was determined by evaluating the descriptive statistics for a start-up sample. The Random Forest quantities of statistical interest were the mean of squared residuals (MSR), the percentage of the explained variation (VE), and the mean squared error (MSE) for the four controlling factors. Then, the descriptive statistics were re-evaluated by adding in the final sample (n = 10), an additional batch of five prediction runs from executing the Random Forest module. The mean difference estimates between the two sampling phases were found to converge to the listed precision with an experimental test power of 0.95. Thus, no further Random Forest solver runs were deemed necessary.
No particular side is favored in the numerical accumulation of the observations; t hey are predominantly asymmetric across all four factors. A plausible question would be whether any additional trial runs would refine more the precision around the magnitude estimation of the effects and, hence, would assist to expediting the practical aspect of the profiling process. To check consistency in the duplicated trials of the joint strength experiments, the two replicates are regressed against each other (Figure 15). It results in a symmetrical line fitting—the fitted line slope is 1.03—and the adjusted coefficient of determination is estimated at 98.7%. It is inferred that there is no immediate concern to conduct more replications or selectively augment the volume of observations. It is useful to also obtain an alternative prediction from a classic algorithmic solver such as the Random Forest. The trial outcomes from running the Random Forest module 10 times are summarized and tabulated in Table 17 (IBM SPSS v.29, Armonk, NY, USA). The precision of the predictions is deemed adequate. This was determined by evaluating the descriptive statistics for a start-up sample. The Random Forest quantities of statistical interest were the mean of squared residuals (MSR), the percentage of the explained variation (VE), and the mean squared error (MSE) for the four controlling factors. Then, the descriptive statistics were re-evaluated by adding in the final sample (n = 10), an additional batch of five prediction runs from executing the Random Forest module. The mean difference estimates between the two sampling phases were found to converge to the listed precision with an experimental test power of 0.95. Thus, no further Random Forest solver runs were deemed necessary.
Table 17. Random Forest trial statistics to fit the saturated Lo(3*) OA joint strength dataset.
Table 17. Random Forest trial statistics to fit the saturated Lo(3*) OA joint strength dataset.
Figure 17. Minimization of the out-of-bag error (OOB) due to number of variables randomly samplec as candidates at each split (mtry) in the Random Forest solver. sampling tactic, keeping replication to a minimum and finally performing confirmation runs to a restricted number. Nevertheless, a conceived factor such as the surface finish of the tubesheet holes may induce a detectable effect on joint strength [7,9]. This factor was not examined in the present research. According to the TEMA standards [7], it is stated: “a smooth tubesheet hole can provide a pressure tight joint at a lower level of wall reduction, but a rough tubesheet hole provides more mechanical strength than a smooth tubesheet hole” (pp. 10-31). Since rough tubesheet holes and strong joints may be related, extending his research would uncover valuable links to enhancing the joint integrity on the particular production materials as used in this study.
Figure 17. Minimization of the out-of-bag error (OOB) due to number of variables randomly samplec as candidates at each split (mtry) in the Random Forest solver. sampling tactic, keeping replication to a minimum and finally performing confirmation runs to a restricted number. Nevertheless, a conceived factor such as the surface finish of the tubesheet holes may induce a detectable effect on joint strength [7,9]. This factor was not examined in the present research. According to the TEMA standards [7], it is stated: “a smooth tubesheet hole can provide a pressure tight joint at a lower level of wall reduction, but a rough tubesheet hole provides more mechanical strength than a smooth tubesheet hole” (pp. 10-31). Since rough tubesheet holes and strong joints may be related, extending his research would uncover valuable links to enhancing the joint integrity on the particular production materials as used in this study.
Figure 18. Factorial profiling using the Random Forest solver to evaluate the partial dependence of: (1) Clearance (A), (2) Number of Grooves (B), (3) Groove Depth (C), and (4) Tube Wall Thickness Reduction (D).
Figure 18. Factorial profiling using the Random Forest solver to evaluate the partial dependence of: (1) Clearance (A), (2) Number of Grooves (B), (3) Groove Depth (C), and (4) Tube Wall Thickness Reduction (D).
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