Calibration Technique of Thermal Analysis Model for Metal Additive Manufacturing Process Simulation by Nonlinear Regression and Optimization
Round 1
Reviewer 1 Report
A very comprehensive research work for Additive Manufacturing Process Simulation.
Author Response
Thank you for appreciating our research. We expect this study to contribute to Additive Manufacturing Process Simulation technology.
Reviewer 2 Report
General comments
The manuscript presents a method for using non-linear regression for fitting model-parameters, and exemplifies this method by FEM-simulation of LPBF systems. This approach is interesting, and important due to the relative large uncertainty in the materials properties during LPBF conditions. And something which unfortunately is often neglected in published studies. The work also ties into the currently hot topic of creating digital twins for processes to be used with adaptive process control and machine learning applications.
I am however in no position to evaluate the novelty of the approach in regards to LPBF, as statistical models are not my field of expertise. The method seems to be rigorous and correct, and was an interesting read. This section could be improved by redoing the analysis for several different materials, and using and comparing the results other models for the thermal field (for example the models presented by Mirkoohi (DOI 10.3390/ma12132052). This would demonstrate a generality of the model, and in my opinion contribute to an increased impact potential of the paper. On a tangential note it would also be interesting to see predictions outside the training range.
The FEM model used for determining the fitted parameters however is questionable for predictions during LPBF processing as it is based on assumptions that not necessarily represent the conditions during LPBF well. These issues (see below) need to be addressed, either by
- Clearly discussing the limitations of the model, and placing the focus of the manuscript on the regression model. This would decrease the value of the manuscript for the LPBF community, and should be combined with more clearly discussing the merits of the regression model, and how it differs from earlier similar models.
or by
- Redoing the simulations using more realistic source terms and material properties.
The paper is well written and clearly explains the methodology.
In summary the manuscript has potential to become a good paper and is well written, but major revisions are necessary.
Background
The ability to predict the dimensions of the melt pool in a quick and cheap matter is important for the development of the field. This area of research has attracted much attention in the last years through CFD studies, FEM-modelling, and analytical models. The relationship of this paper to these studies is at present not made clear, and the paper is missing references and comparisons to:
- CFD studies, for example the ones carried out at LLNL (ex DOI:10.1179/1743284714Y.0000000728)
- Analytical models for predicting the melt pool sizes, for example the work of Mirkoohi (DOI 10.3390/ma12132052) and the concept of normalized enthalpy (explained in detail in Rubenchik et al DOI 10.1016/j.jmatprotec.2018.02.034).
Several analytical models exist which predict the size of the melt pool in terms of normalized enthalpy and the Peclet number. These relations are often linear, and it would be important to explain why one should use a regression model rather than these models.
Furthermore the paper would benefit from a deeper explanation of where and how regression models are currently used, and how this manuscript differs from previous work.
The regression model
- The fitted model parameters βij are not disclosed. Without these it is difficult to evaluate the model and validating it. This needs to be done, possibly in an appendix.
- The model does not account for scanning speed, which is well known to have a huge impact on the melt pool dimensions. This seems to significantly limit the usefulness of the model. The authors need to explain this decision.
FEM Model
The FEM-model has some assumptions which are not necessarily repressentative of LPBF conditions:
- The source term is modelled as a volumetric term. This would be appropriate in for example EPBF, but it is clear from CFD studies (see above) that the laser is shining on molten and coagulated material, not on the powder bed. There are situations where the laser can illuminate powder (see for example the thesis of Lindström (DOI 10.5075/epfl-thesis-9050) or for experimental data Ye et al (DOI 10.1002/adem.201900185 ) but this appears to be a minor effect only relevant at low power processing conditions. An interesting approach for how to deal with this is found in a recent article by Ghasemi-Tabasi (DOI https://doi.org/10.1016/j.addma.2020.101496).
This assumption gives rise to the unrealistic shape of the melt pools in figure 3. - The material properties are taken as the properties of a powder bed
Based on the same arguments as in 1, this is not a realistic assumption. - Convection and radiation is included, but not evaporative cooling. In most situations this would be the dominant of the three, as the surface temperature in LPBF reach (and sometimes exceed) the boiling point. How this can be easily implemented as a source term is shown in for example a paper by Le et al. (10.1016/j.ijthermalsci.2019.105992) and many other CFD papers. This becomes very important when a surface heat source is used instead of a volumetric source.
Addressing these points would significantly improve the relevance of the paper to the LPBF community.
Comparing the results to experiments (many experimental data points are published) would be a good way to build confidence in the modelling.
I would further suggest expanding the analysis to a wider range of processing parameters.
Finally I am not convinced that the mesh is fine enough. The authors should clarify if the solution is numerically converged (with respect to the mesh size), perhaps in the supplementary material.
Author Response
General comments
This section could be improved by redoing the analysis for several different materials, and using and comparing the results other models for the thermal field (for example the models presented by Mirkoohi (DOI 10.3390/ma12132052). This would demonstrate a generality of the model, and in my opinion contribute to an increased impact potential of the paper. On a tangential note it would also be interesting to see predictions outside the training range.
Answer>
According to the reviewer’s opinion, if various analyses are performed for several different materials and models, the generality and usefulness of the technique proposed in this paper will be verified better. However, for the analysis of various materials and models, a lot of research period and work are additionally required, and there is a limit to the amount of paper. Therefore, in this paper, we intended to consider and focus on only the minimum analysis models and examples required to verify the validity of the proposed technique. Therefore, a thermal analysis model judged to be the most efficient and valid among the various models investigated by our research team was selected and used to implement the proposed technique. The model introduced by the reviewer (Mirkoohi, DOI 10.3390/ma12132052) also can be considered as one of thermal analysis models for the proposed technique, so it is referred in the introduction.
(Page 3, Line 121 to 125 : ”Mirkoohi et al. [15] introduced five different heat source models (steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source) to predict the three-dimensional temperature field analytically. The proposed temperature field models were validated using experimental measurement of melt pool geometry.” )
An important purpose of this study is to estimate the analysis parameters that can produce the best results using a given thermal analysis model rather than suggesting a new analysis model. So, if a more advanced analysis model such as the one introduced by the reviewer is available, it can be selected and used to implement the proposed technique for improvement of the analysis results by estimation (or calibration) of analysis parameters.
Predicting the outside of the training range is not the scope of this study and the results cannot be guaranteed.
The FEM model used for determining the fitted parameters however is questionable for predictions during LPBF processing as it is based on assumptions that not necessarily represent the conditions during LPBF well. These issues (see below) need to be addressed, either by
- Clearly discussing the limitations of the model, and placing the focus of the manuscript on the regression model. This would decrease the value of the manuscript for the LPBF community, and should be combined with more clearly discussing the merits of the regression model, and how it differs from earlier similar models.
or by
- Redoing the simulations using more realistic source terms and material properties.
Answer>
As the reviewer pointed out, the thermal analysis model used in this paper did not have very high accuracy or reliability to represent all the aspects and conditions of the LPBF process in detail. However, the intention of this study is to show that even for low precision models, more reliable analysis results can be obtained by properly calibrating the analysis parameters. So, we have added comments to the introduction to make this intention more clear.
(Page 4, Line 147 to 152 : “The procedure proposed in this study can be applied to all kinds of analysis models based on FEM or CFD that include uncertain analysis parameters. Through this technique, optimal analysis parameters can be determined more efficiently, and more reliable analysis results even for models with relatively low fidelity can be obtained by applying the optimal analysis parameters. In this study, this technique is applied to a thermal analysis model using FEM.”)
Background
The ability to predict the dimensions of the melt pool in a quick and cheap matter is important for the development of the field. This area of research has attracted much attention in the last years through CFD studies, FEM-modelling, and analytical models. The relationship of this paper to these studies is at present not made clear, and the paper is missing references and comparisons to:
- CFD studies, for example the ones carried out at LLNL (ex DOI:10.1179/1743284714Y.0000000728)
- Analytical models for predicting the melt pool sizes, for example the work of Mirkoohi (DOI 10.3390/ma12132052) and the concept of normalized enthalpy (explained in detail in Rubenchik et al DOI 10.1016/j.jmatprotec.2018.02.034).
Several analytical models exist which predict the size of the melt pool in terms of normalized enthalpy and the Peclet number. These relations are often linear, and it would be important to explain why one should use a regression model rather than these models.
Furthermore the paper would benefit from a deeper explanation of where and how regression models are currently used, and how this manuscript differs from previous work.
Answer>
As the reviewer mentioned, the prediction of the melt pool dimension is a very important topic, and various studies have been conducted with CFD, analytical model, etc. as well as the FEM-modeling mainly mentioned in this paper. However, the studies in CFD, analytical model, etc. were not properly mentioned in the original manuscript, so they were supplemented in the Introduction. In addition, the relationship between the studies for the prediction of the melt pool dimension and this work were also described in the Introduction to clarify the subject of this paper.
(Line 111 to 128 : “In addition to methods using FEM, many studies also have been conducted using CFD and analytical models to propose accurate thermal analysis models for LPBF process simulation and prediction of the melt pool size. King et al. [13] described multiscale modeling strategy, including powder scale model that simulated single track/single multilayer builds, and provided powder bed and melt pool thermal data, and the modeling was tied to experiments through data mining. Cheng et al. [14] applied a CFD model to investigate the fluid dynamics in melt pools and resultant pore defects. To accurately capture the melting and solidification process, major process physics, such as the surface tension, evaporation as well as laser multi-reflection, have been considered in the model. The predicted melt pool dimensions were validated with experimental measurements. Mirkoohi et al. [15] introduced five different heat source models (steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source) to predict the three-dimensional temperature field analytically. The proposed temperature field models were validated using experimental measurement of melt pool geometry. Rubenchik et al.[16] evaluated that the temperature distribution in the simple thermal model of SLM was characterized by two dimensionless parameters (normalized enthalpy and the ratio of dwell time to the diffusion time).”)
As mentioned earlier, this study does not propose a new LPBF process simulation model, but rather a method of optimizing analysis parameters for better analysis results with existing models including CFD-based models, etc. by applying a regression model and an optimization technique. In this process, the FEM-based model was applied as the reference analysis model. Therefore, comparison of results with existing models is not meaningful for this study and is not the scope of this study. On the other hand, in addition to the FEM-based model used in this study, the proposed method can also be applied to calibrating the analysis parameters of other methods such as CFD for better analysis results. The Introduction has been modified to reveal these contents more clearly.
In addition, as commented by the reviewer, how the regression model is used and how this paper is differentiated from existing works were also described in the Introduction.
(Line 155 to 165 : “This procedure is based on a regression model, which has been utilized in various fields due to advantage in speed and optimization. To improve the accuracy of the vibration analysis model, a regression model was used[17], and stress was set as parameter to evaluate fatigue performance[18]. In addition, it was also used to optimize geometrical and engineering characteristic of building analysis such as Tunnel[19], but there was no case applied to the LPBF process simulation. The procedure proposed in this study can be applied to all kinds of analysis models based on FEM or CFD that include uncertain analysis parameters. Through this technique, optimal analysis parameters can be determined more efficiently, and more reliable analysis results even for models with relatively low fidelity can be obtained by applying the optimal analysis parameters. In this study, this technique is applied to a thermal analysis model using FEM.”)
The regression model
- The fitted model parameters βij are not disclosed. Without these it is difficult to evaluate the model and validating it. This needs to be done, possibly in an appendix.
Answer>
A description of βij has been added to Appendix A.
- The model does not account for scanning speed, which is well known to have a huge impact on the melt pool dimensions. This seems to significantly limit the usefulness of the model. The authors need to explain this decision.
Answer>
This paper describes how to estimate the optimal analysis parameters for given process parameters (power, speed, radius, hatch spacing). Although the correlation between the scan speed and the melt pool size was not directly explained, it is implicitly considered because analyses for various scan speeds are performed in the process of estimating the optimal analysis parameters. That is, in this study, in order to create a regression analysis model and estimate the optimal analysis parameters, thermal analyses on the process parameter cases including three different scan speeds (100, 150, 200 mm/s) as shown in Table 1 were performed, and the change of melt pool dimension with respect to each scan speed was reflected in the regression model and optimization process for this process.
FEM model
The FEM-model has some assumptions which are not necessarily representative of LPBF conditions:
- The source term is modelled as a volumetric term.
Answer>
We were not familiar with the volumetric source term, as EPBF and CFD are not the authors' field of expertise. However, in studies related to LPBF simulation using FEM, it was confirmed that various heat sources such as surface heat source and volumetric heat source were used, and the representative exponentially decaying equation method was applied in this study. In the future, we will conduct additional research on the source term and apply the method proposed in this study to a more advanced and precise model.
- The material properties are taken as the properties of a powder bed
Answer>
As stated in the Introduction, the powder bed is modeled as a continuum in FEM. Therefore, since each powder particle cannot be modeled, the material properties are regarded as the properties of the powder bed, and this FEM modeling does not represent the LPBF condition exactly. However, in this study, we propose an optimization technique to calibrate the analysis parameters so that a relatively simple FEM model can represent the LPBF process as accurately as possible and produce more reliable analysis results. The introduction has been modified to explain this intention more clearly.
(Line 149 to 152 : “Through this technique, optimal analysis parameters can be determined more efficiently, and more reliable analysis results even for models with relatively low fidelity can be obtained by applying the optimal analysis parameters. In this study, this technique is ap-plied to a thermal analysis model using FEM.”)
- Convection and radiation is included, but not evaporative cooling.
Answer>
Evaporative cooling is one of the microscopic level phenomena described in Page 2, Line 60. There is a limit to the implementation of the microscopic level phenomena in the thermal analysis model of mesoscopic scale conducted in this paper, so it is not the scope of this paper. In line 61 of Page 2, evaporative cooling was added as one of the microscopic level phenomena.
Finally I am not convinced that the mesh is fine enough. The authors should clarify if the solution is numerically converged (with respect to the mesh size), perhaps in the supplementary material.
Answer>
A previous study related to mesh size is referenced in Page 6, Line 182. This study stated that if the finite element mesh is one-fourth of the laser beam diameter, it is fine enough to accurately simulate steep temperature gradients. Since this preliminary study was conducted in the study of FEM modeling for LPBF simulation, it is judged to be reliable. therefore, it is not necessary to reproduce this study again in this paper.
Reviewer 3 Report
Well written document with very minor sentence construction issues which truth be told, do not hinder the reader. The effort to use regression (while being wary of overfitting) supplementing the standard FEM to improve the thermal analysis is appreciated.
Author Response
Thank you for appreciating our work. We tried to further enhance the quality of this paper.
Reviewer 4 Report
Summary:
The manuscript entitled “Calibration Technique of Thermal Analysis Model for Metal Additive Manufacturing Process Simulation by Nonlinear Regression and Optimization” focuses on the use of a regression model to obtain the optimal values of parameters to improve the thermal analysis model. In this manuscript, the authors described the thermal analysis model, proceed to apply the regression model on 6 analysis parameters, and optimized the 3 dominant parameters.
However, the authors compared the proposed model with the original thermal analysis model which had up to 13.7% errors from experimental results. The reviewer fails to see how the proposed model is better than the original thermal analysis model when both models are compared to experimental results
Below are some comments for the authors’ consideration.
Section 1
Page 1, Line 28: Spelling “par1ticular” to be corrected.
Page 1, Line 36: Authors mentioned “accurately predict the characteristics of parts with respect to process parameters such as scan pattern, scan speed, and laser power.” What about other factors such as powder properties?
Section 2
What are the values of the parameters (material properties, hatch spacing, laser scanning speed, laser spot size, laser power) used for the simulations?
Were the tracks scanned continuously or was there a pause after scanning each track? Pausing after each scan can allow the melt track to cool, affecting the size of the neighboring melt pool.
Can the authors verify the accuracy of this simulation result in Figure 3 with experimental results?
Page 5, Line 171: what is “?”?
Page 5, Line 179: Can the author provide more explanation on “?”? For example, “?” is the ratio of the volume of gas to the total volume of the cell. The value of “?” ranges from 0 to 1. “?=0” means the cell only contains gas and “?=1” means the cell only contains metal.
Page 7, Line 209: The authors have used powder particle size of 45 µm for the study. In reality, powders used have a distribution range. How will using the OPD range for 45 µm particle size affect the results for OPD sensitivity?
Page 7, Line 211: Why is the absorption coefficient set to “±10%”?
Page 7, Line 213: The authors are assuming Fe (iron) and AISI 316L have the same OPD. Can the authors clarify if it is true?
Page 7, Line 217: The authors are assuming it is a linear relationship between powder size and OPD and performing linear interpolation. Can the authors clarify if it is justifiable?
Section 4:
The authors are comparing their simulation results with the results of another numerical model. However, according to Foroozmehr et al. [4], the thermal analysis model has an error of up to 13.7% from experimental results. How can the authors justify validating the proposed model with another model with errors? The proposed model has errors up to 1.72% (for the optimized results) from the thermal analysis which might mean the proposed model results might not be better than the thermal analysis model when validating with experiments.
Authors can consider comparing their model with the experimental results from Foroozmehr et al. [4] and showing if their model yields a lower error than the original thermal analysis model.
Author Response
Summary
However, the authors compared the proposed model with the original thermal analysis model which had up to 13.7% errors from experimental results. The reviewer fails to see how the proposed model is better than the original thermal analysis model when both models are compared to experimental results
Answer>
Foroozmehr et al. were referred to obtain information on thermal modeling techniques and materials for LPBF process simulation. However, since the analysis model used for validation adopted a heat source model and analysis parameters different from Foroozmehr et al., it cannot be considered that the same analysis model which has errors from the experimental results was used in this paper. That is, our model is different from the model by Foroozmehr et al. Therefore, if accurate verification data, whether numerical model or experimental data, are given, the model can be calibrated to obtain more accurate analysis results through parameter optimization using the regression model proposed in this study.
Section 1
Page 1, Line 28 : Spelling “par1ticular” to be corrected.
Answer>
Corrected “par1ticular” to “particular”
Page 1, Line 36 : Authors mentioned “accurately predict the characteristics of parts with respect to process parameters such as scan pattern, scan speed, and laser power.” What about other factors such as powder properties?
Answer>
Prediction of powder properties is also necessary. It was modified to “it is necessary to accurately predict the characteristics of parts with respect to powder properties and process parameters such as scan pattern, scan speed, and laser power.”
Section 2
What are the values of the parameters (material properties, hatch spacing, laser scanning speed, laser spot size, laser power) used for the simulations?
Answer>
Parameter values are listed in Table 1.
Were the tracks scanned continuously or was there a pause after scanning each track? Pausing after each scan can allow the melt track to cool, affecting the size of the neighboring melt pool.
Answer>
Tracks were scanned continuously without pause after scanning each track. The sentence “and are continuously scanned without pause after scanning each track.” is added in Line 174 to 175.
Can the authors verify the accuracy of this simulation result in Figure 3 with experimental results?
Answer>
The reason for performing the analysis as shown in Figure 3 is to determine the appropriate FEM model size (number of tracks and length) for generating a regression analysis model using the analysis data. In other words, since it is simply an auxiliary analysis to understand the trend of the analysis results, the accuracy of the simulation results in Figure 3 cannot be verified, and there is no need to do so. (The purpose of this analysis was added to section 2, Line 167~169) However, it was confirmed that the melt pool width and depth become almost constant after the 5th track in the thermal analysis for LPBF simulation, and this trend was judged to be sufficiently reliable. Therefore, the melt pool size was measured at the 3mm point of the 6th track in the subsequent thermal analysis.
Page 5, Line 171 : what is “?”?
Answer>
The sentence “ is the coefficient multiplied by the conductivity of the solid to obtain the conductivity of the powder.” is added in Line 218 to 219.
Page 5, Line 179 : Can the author provide more explanation on “?”? For example, “?” is the ratio of the volume of gas to the total volume of the cell. The value of “?” ranges from 0 to 1. “?=0” means the cell only contains gas and “?=1” means the cell only contains metal.
Answer>
Detailed description of has been added in Line 226 to 229. (”which is the ratio of the volume of gas to the total volume of the cell, The value of the porosity() ranges from 0 to 1. “” means the cell only contains gas and “” means the cell only contains metal.”)
Page 7, Line 209 : The authors have used powder particle size of 45 µm for the study. In reality, powders used have a distribution range. How will using the OPD range for 45 µm particle size affect the results for OPD sensitivity?
Answer>
The powder size is not actually uniform and has a distribution. The OPD value used in this paper is defined for a given mean value and distribution of the powder size. A content for a distribution of powder particle size has been added to Line 258.
Page 7, Line 211 : Why is the absorption coefficient set to “±10%”?
Answer>
We predict that absorptivity will be determined in relation to scan speed, or powder characteristic, etc. However, it is difficult to specify the absorptivity as there has not been any research related to the absorptivity of the powder bed. Therefore, studies like this study are more needed because of these kinds of analysis parameters with uncertain values. In this study, the range of absorptivity was relatively widely set to ±10%, so that the range of the thermal analysis results with respect to the absorptivity was increased. By doing this, an appropriate absorptivity value can be estimated through regression and optimization.
Page 7, Line 213 : The authors are assuming Fe (iron) and AISI 316L have the same OPD. Can the authors clarify if it is true?
Answer>
We did not confirm studies on OPD of AISI316L and studies that verified that Fe and Aisi316L had the same OPD. We referred to the study of Foroozmehr et al., and they estimated the OPD of AISI316L using the same assumptions. Reference paper [4] was added to Line 263.
Page 7, Line 217 : The authors are assuming it is a linear relationship between powder size and OPD and performing linear interpolation. Can the authors clarify if it is justifiable?
Answer>
Since we did not find any studies that explain the relationship between powder size and OPD, we did not confirm that there is a linear relationship between powder size and OPD. However, we just needed to set the range of OPD instead of a single value, so powder size and OPD did not have to be in exact linear relationship. We thought the range of 102-170μm for OPD was wide enough to estimate the optimal value of OPD. In order to explain the procedure of determining the range of OPD, the following sentence was added to Line 265~267.
“If the OPD for powder size 50 μm is 170 μm, then the OPD for powder size 45 μm is calculated to be 170 μm, and If the OPD for powder size 75 μm is 170 μm, then OPD for powder size 45 μm is calculated to be 102 μm by linear interpolation.”
Section 4
The authors are comparing their simulation results with the results of another numerical model. However, according to Foroozmehr et al. [4], the thermal analysis model has an error of up to 13.7% from experimental results. How can the authors justify validating the proposed model with another model with errors? The proposed model has errors up to 1.72% (for the optimized results) from the thermal analysis which might mean the proposed model results might not be better than the thermal analysis model when validating with experiments.
Authors can consider comparing their model with the experimental results from Foroozmehr et al. [4] and showing if their model yields a lower error than the original thermal analysis model.
Answer>
The problem of verifying the proposed model with another model with errors (Foroozmehr et al.) was further explained so as not to cause misunderstanding as described in the Summary above. We tried to verify the validity of the proposed method by checking how well the method finds the originally given analysis parameter values for the reference thermal analysis model with given specific analysis parameter values. The error of 1.72% is not the error with the thermal analysis model proposed in other studies, but the difference between the originally assumed analysis parameter value and the estimated analysis parameter value when estimating the analysis parameter value using the method proposed in this study. Therefore, this result means that the regression model estimates the analysis parameter values ​​of the originally assumed thermal analysis model well enough. When applied to future experiments, if the original analysis model is modeled sufficiently well to simulate the complexity of the behavior of the real system, it will be possible to determine the value of the analysis parameter of the model that can produce the result closest to the actual behavior. The conclusion has been supplemented to better reveal these contents.
Round 2
Reviewer 4 Report
No further comments
