<figure><img src="image_2153.png" /><figcaption>Fig. 2. An example of a forging stroke ($\alpha_0=1.4$, $x_b=0.75$, $\epsilon_h=17\%$) and resulting displacements of nodes in y and z-direction respectively.</figcaption></figure>

Several neural network architectures are suitable for this type of problem. However, a simple feed-forward artificial neural network was used for this study. This type of network has a fixed number of inputs and outputs and is well suited to approximate non-linearity in the functions. Other commonly used image-based alternatives limit the inputs to a fixed square grid of pixels. But in the case of this problem, restricting workpieces of different lengths to a fixed image size will make it resolution dependent.

In this study, MATLAB is used to program the neural networks. The input, output and the structure of the neural network is determined by defining reference configuration and deformed configuration at $t=t_0$ and $t$ respectively. This is similar to the formulation of non-linear problems in continuum mechanics. In this case, deformed configuration is the workpiece after the force is applied and the material is deformed for the given stroke, whereas the reference configuration is the workpiece before the application of the force. Let $P$ be a position vector to an arbitrary point in the workpiece such that in point $P(x_0, y_0)$ becomes $P_1(x_1, y_1)$ in the deformed configuration. The displacement of any point between the two configurations can be calculated as,

$$u = P_1 - P_0 \qquad (4)$$

Let $f$ be any function that maps any point in the deformed configuration to its displacement. Additionally, this function depends on the process parameters that determine the deformation and therefore the displacement of any point in the given configuration. Thus, this gives the position of the point in the deformed configuration:

$$P_1 = P - f(P, \alpha_0, x_b, \epsilon_h) \qquad (5)$$

The function $f$ is replaced by a neural network (final adaption consists of 16 layers with a total of 4800 neurons), as shown in Fig. 3. It can predict the coordinates in the deformed configuration from the process parameters and a given coordinate in the reference configuration. The output vector is the two components of the displacement which is then used to calculate the corresponding nodes in the deformed configuration. This network can run multiple times for each node in the single geometry to thus create a result for the complete body, since the input vector is only defined
for a single node. Finally, the resulting model can be trained and tested to predict the deformed part geometry after the forging stroke, independent of the mesh size used.

<figure><img src="image_2163.png" /><figcaption>Fig. 3. Flowchart of the model used for predicting displacement using neural networks.</figcaption></figure>

## Results and Discussion

The process of training neural networks involves calculating the loss by comparing the model results with the training data, in this case FEA results. The loss is then used to modify the *learnables* or *weights and biases* in the neurons. The training is performed in small batches of data. These batches are shuffled after every epoch, which is a complete iteration through the whole dataset. The training was performed on the 200 simulation results in the training dataset, which consisted of a total of 806,821 nodes or input vectors. It took around 20 epochs or 42,500 iterations on the 16 layer neural network with 4800 weights and biases (approximately 70 min training time).

The test data, which is collected separately, is a full factorial sampling of the variable space resulting in 54 simulations that are not a part of the training data. Testing the neural networks is essential not just to evaluate the network on unseen data but also to see how the model performs. Firstly, the error in the predicted coordinates and the actual coordinates from the FEA results is analyzed in the deformation zone. Secondly, this error is analyzed for the surface nodes separately since they form the boundary of the geometry, and hence define the workpiece volume that needs to obey the volume constancy. Finally, the root mean square error (RMSE) is analyzed for the complete geometry and analyzed for each process in the test dataset. Additionally, the time required for the simulation is also analyzed.

Fig. 4 shows the model output for an exemplary process from the test dataset corresponding to a large height reduction and a large bite ratio. The input to the model (Fig. 4 a) is the configuration before the third stroke. Here, the workpiece is aligned to the origin based on the bite length. With around 4000 nodes in the geometry, the model predicts the deformed configuration after the third stroke. The output (Fig. 4 b) of the model is the position of each node as predicted by the model, then overlaid with the error in position as compared with the FEA results. The predictions in the regions outside the deformation zone are predicted with a higher accuracy. A systematic error is visible in the deformation zone in the region corresponding to a large deformation. However, the overall RMSE for this geometry is 0.16 mm with all the nodes under 2 mm error.

Additionally, the errors in the longitudinal surface are plotted in Fig. 4 c). In the deformation zone, the error is relatively high with peaks in certain nodes. These nodes are consistently present in the region with large deformation, especially in the region under the radius of the
for a single node. Finally, the resulting model can be trained and tested to predict the deformed part geometry after the forging stroke, independent of the mesh size used.

<figure><img src="image_2154.png" /><figcaption>Fig. 3. Flowchart of the model used for predicting displacement using neural networks.</figcaption></figure>

## Results and Discussion

The process of training neural networks involves calculating the loss by comparing the model results with the training data, in this case FEA results. The loss is then used to modify the *learnables* or *weights and biases* in the neurons. The training is performed in small batches of data. These batches are shuffled after every epoch, which is a complete iteration through the whole dataset. The training was performed on the 200 simulation results in the training dataset, which consisted of a total of 806,821 nodes or input vectors. It took around 20 epochs or 42,500 iterations on the 16 layer neural network with 4800 weights and biases (approximately 70 min training time).

The test data, which is collected separately, is a full factorial sampling of the variable space resulting in 54 simulations that are not a part of the training data. Testing the neural networks is essential not just to evaluate the network on unseen data but also to see how the model performs. Firstly, the error in the predicted coordinates and the actual coordinates from the FEA results is analyzed in the deformation zone. Secondly, this error is analyzed for the surface nodes separately since they form the boundary of the geometry, and hence define the workpiece volume that needs to obey the volume constancy. Finally, the root mean square error (RMSE) is analyzed for the complete geometry and analyzed for each process in the test dataset. Additionally, the time required for the simulation is also analyzed.

Fig. 4 shows the model output for an exemplary process from the test dataset corresponding to a large height reduction and a large bite ratio. The input to the model (Fig. 4 a) is the configuration before the third stroke. Here, the workpiece is aligned to the origin based on the bite length. With around 4000 nodes in the geometry, the model predicts the deformed configuration after the third stroke. The output (Fig. 4 b) of the model is the position of each node as predicted by the model, then overlaid with the error in position as compared with the FEA results. The predictions in the regions outside the deformation zone are predicted with a higher accuracy. A systematic error is visible in the deformation zone in the region corresponding to a large deformation. However, the overall RMSE for this geometry is 0.16 mm with all the nodes under 2 mm error.

Additionally, the errors in the longitudinal surface are plotted in Fig. 4 c). In the deformation zone, the error is relatively high with peaks in certain nodes. These nodes are consistently present in the region with large deformation, especially in the region under the radius of the
<figure><img src="image_2164.png" /><figcaption>Fig. 4. Prediction of third stroke of forging (b) and its comparison with FEA result for an example process in the test dataset ($\alpha_0=1$, $x_b=0.75$, $\epsilon_h=21\%$).</figcaption></figure>

Fig. 5 shows the results for the different predictions in the test dataset corresponding to aspect ratio 1. Fig. 5 a) is a heat map of RMSE between the predicted and actual position for all the nodes of geometry in the given simulation. The maximum error in each of these simulations is shown in Fig. 5 b). The results presented here correspond to the third stroke, similar to the previous results. The maximum errors can be weakly correlated to the RMSE. Overall, RMSE for the complete test dataset is 0.486 mm. Predicting a single stroke for around 4000 nodes takes approximately 0.06 seconds (Intel Xeon E-2286G, NVIDIA Quadro P400).

It can be seen in Fig. 5 that the simulations with a smaller height reduction show consistently higher errors. This was also seen for other aspect ratios and it is mainly due to the smaller overall displacement values as compared to the size of the workpiece in these combinations. In addition, there are certain combinations with comparatively higher errors, which was also seen in the previous adaptions. For some of these outliers, no systematic explanation from the forging process can be found, except for the reasons explained earlier. It is challenging to control certain behaviors of the model due to a variety of factors that affect the prediction, such as the distribution of the data, randomness during the training process, hyperparameter values like learning rate and number of training epochs. The large number of neurons that form the neural network and their corresponding weights and biases make them less explainable (so-called "black box") and require thorough testing. Furthermore, due to the multidimensional input and output relationships, it is not possible to test the model for all possible combinations of variables. These challenges apply to such solutions.
<figure><img src="image_2155.png" /><figcaption>Fig. 4. Prediction of third stroke of forging (b) and its comparison with FEA result for an example process in the test dataset ($\alpha_0=1$, $x_b=0.75$, $\epsilon_h=21\%$).</figcaption></figure>

Fig. 5 shows the results for the different predictions in the test dataset corresponding to aspect ratio 1. Fig. 5 a) is a heat map of RMSE between the predicted and actual position for all the nodes of geometry in the given simulation. The maximum error in each of these simulations is shown in Fig. 5 b). The results presented here correspond to the third stroke, similar to the previous results. The maximum errors can be weakly correlated to the RMSE. Overall, RMSE for the complete test dataset is 0.486 mm. Predicting a single stroke for around 4000 nodes takes approximately 0.06 seconds (Intel Xeon E-2286G, NVIDIA Quadro P400).

It can be seen in Fig. 5 that the simulations with a smaller height reduction show consistently higher errors. This was also seen for other aspect ratios and it is mainly due to the smaller overall displacement values as compared to the size of the workpiece in these combinations. In addition, there are certain combinations with comparatively higher errors, which was also seen in the previous adaptions. For some of these outliers, no systematic explanation from the forging process can be found, except for the reasons explained earlier. It is challenging to control certain behaviors of the model due to a variety of factors that affect the prediction, such as the distribution of the data, randomness during the training process, hyperparameter values like learning rate and number of training epochs. The large number of neurons that form the neural network and their corresponding weights and biases make them less explainable (so-called "black box") and require thorough testing. Furthermore, due to the multidimensional input and output relationships, it is not possible to test the model for all possible combinations of variables. These challenges apply to such solutions.
<figure><img src="image_2165.png" /><figcaption>Fig. 5. Evaluation of the model over various processes corresponding to aspect ratio 1.</figcaption></figure>

Overall, the model successfully predicts the displacement and thus the deformed configuration of the forging stroke. The average error is well under 1% relative to the height of the workpiece. The majority of the data (around 70%) in any given simulation is outside the deformation zone and does not show any complex deformation patterns. In spite of this bias in the data, the model is able to predict deformation zone with a fair accuracy. The z-coordinates of the nodes that are undergoing deformation always lie in the same region, the positive z-direction and closer to the origin, making the corresponding features distinguishable from the remaining data.

The model has shown an excellent generalization in the variable space and the 2D space. It predicts good accuracy on the test data which belongs to the processes in variable space that are not a part of the training data. Additionally, the nodes that are tested also do not completely coincide with the training data. Any point in this 2D space can be predicted successfully using this model thus making it spatially independent. The spatial independence can be further demonstrated by using the same model, trained on a coarse mesh, to predict a geometry with finer mesh. A randomly selected process ($α_0=1, x_b=0.66, ε_h=23\%$) is simulated for a coarse and a finer mesh. A corresponding coarse mesh results in 3851 data points as compared to 10834 data points in the finer mesh. The results indicate a similar accuracy with the maximum error increasing from 2.28 mm to 2.50 mm. The overall RMSE for coarse mesh is 0.173 mm whereas for the fine mesh is 0.163 mm. This indicates spatial generalization as the nodes that are not part of the training data (which had coarse mesh) are still predicted with a comparable accuracy by the neural networks. The node-by-node design of the neural networks make it independent of the number of nodes in input model and the network learns the underlying patterns in the 2D space.

Finally, even though the model is trained on the third forging stroke, the repositioning of the training data makes the model virtually independent of the stroke number. That is, the model can predict any stroke, as long as the reference configuration of the geometry is correctly aligned to the press (similar to Fig. 1) in regards to the bite length of the next stroke. This can be demonstrated by taking an arbitrary set of points that form a rectangular geometry before the first stroke of forging. The model predicts the deformed configuration corresponding to the first stroke. This geometry can be translated in the z-direction to align to the press as mentioned before. The resulting geometry is the reference configuration of the second stroke. In this way, a geometry can be incrementally deformed using the same model for predicting each stroke.

Fig. 6 shows the incremental simulation of forging strokes using the developed 2D displacement model as described above for a randomly selected process from the test data ($α_0=1, x_b=0.55, ε_h=17\%$). Each predicted stroke is compared with the FEA result in order to evaluate the accuracy.
<figure><img src="image_2156.png" /><figcaption>Fig. 5. Evaluation of the model over various processes corresponding to aspect ratio 1.</figcaption></figure>

Overall, the model successfully predicts the displacement and thus the deformed configuration of the forging stroke. The average error is well under 1% relative to the height of the workpiece. The majority of the data (around 70%) in any given simulation is outside the deformation zone and does not show any complex deformation patterns. In spite of this bias in the data, the model is able to predict deformation zone with a fair accuracy. The z-coordinates of the nodes that are undergoing deformation always lie in the same region, the positive z-direction and closer to the origin, making the corresponding features distinguishable from the remaining data.

The model has shown an excellent generalization in the variable space and the 2D space. It predicts good accuracy on the test data which belongs to the processes in variable space that are not a part of the training data. Additionally, the nodes that are tested also do not completely coincide with the training data. Any point in this 2D space can be predicted successfully using this model thus making it spatially independent. The spatial independence can be further demonstrated by using the same model, trained on a coarse mesh, to predict a geometry with finer mesh. A randomly selected process ($α_0=1, x_b=0.66, ε_h=23\%$) is simulated for a coarse and a finer mesh. A corresponding coarse mesh results in 3851 data points as compared to 10834 data points in the finer mesh. The results indicate a similar accuracy with the maximum error increasing from 2.28 mm to 2.50 mm. The overall RMSE for coarse mesh is 0.173 mm whereas for the fine mesh is 0.163 mm. This indicates spatial generalization as the nodes that are not part of the training data (which had coarse mesh) are still predicted with a comparable accuracy by the neural networks. The node-by-node design of the neural networks make it independent of the number of nodes in input model and the network learns the underlying patterns in the 2D space.

Finally, even though the model is trained on the third forging stroke, the repositioning of the training data makes the model virtually independent of the stroke number. That is, the model can predict any stroke, as long as the reference configuration of the geometry is correctly aligned to the press (similar to Fig. 1) in regards to the bite length of the next stroke. This can be demonstrated by taking an arbitrary set of points that form a rectangular geometry before the first stroke of forging. The model predicts the deformed configuration corresponding to the first stroke. This geometry can be translated in the z-direction to align to the press as mentioned before. The resulting geometry is the reference configuration of the second stroke. In this way, a geometry can be incrementally deformed using the same model for predicting each stroke.

Fig. 6 shows the incremental simulation of forging strokes using the developed 2D displacement model as described above for a randomly selected process from the test data ($α_0=1, x_b=0.55, ε_h=17\%$). Each predicted stroke is compared with the FEA result in order to evaluate the accuracy.
<figure><img src="image_2166.png" /><figcaption>Fig. 5. An example process that is predicted incrementally to simulate a pass. The results are compared to a corresponding FEA result and the error in the position is overlaid on the prediction.</figcaption></figure>

After three strokes, the RMSE of the entire prediction is 0.61 mm thus showing a good generalization of the strokes and ability to simulate passes without a finite element model. The maximum error in position is however 3 mm. The first stroke has relatively poor accuracy since it deforms non-homogeneously and is not a part of the training data. However, the remaining strokes exhibit a closer prediction as the 90% of all the nodes have error in position lower than 1.16 mm. This ability of the model to generalize the different strokes does not directly arise from the neural network architecture but from the feature study and the preprocessing of the data.

## Conclusion and Outlook

The neural network model presented in this paper can predict the 2D local displacement in the geometry for any open die forging process in the applied variable space with an overall RMSE of 0.486 mm for a workpiece with around 100 mm in height. This approach predicts a single node at a time and shows a good spatial generalization thus making it resolution independent. Along with its capability to generalize the patterns in the variable space, the model is also able to predict the 2D material flow of any stroke for the given pass. Although the model is data driven, the application of known physics in collecting the data, studying the features, building the neural network architecture and evaluating the model, has been beneficial in achieving the found generalization. Finally, the ability of the model to predict the 2D displacement accurately in milli seconds makes it suitable for the use in a digital material shadow and related applications.

In the future it is planned to improve the existing 2D model e.g. by incorporating the effects of other variables like friction and temperature. Furthermore, an extension of the 2D model to predict 3D material flow seems possible. This extension enables tracing the workpiece geometry throughout complete forging processes including e.g. intermediate workpiece rotations. Finally, the model can be made more explainable and robust by embedding boundary conditions and the underlying physical conditions into the neural networks using custom loss functions and concepts like physics informed neural networks.

## Acknowledgement

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2023 Internet of Production – 390621612
<figure><img src="image_2157.png" /><figcaption>Fig. 5. An example process that is predicted incrementally to simulate a pass. The results are compared to a corresponding FEA result and the error in the position is overlaid on the prediction.</figcaption></figure>

After three strokes, the RMSE of the entire prediction is 0.61 mm thus showing a good generalization of the strokes and ability to simulate passes without a finite element model. The maximum error in position is however 3 mm. The first stroke has relatively poor accuracy since it deforms non-homogeneously and is not a part of the training data. However, the remaining strokes exhibit a closer prediction as the 90% of all the nodes have error in position lower than 1.16 mm. This ability of the model to generalize the different strokes does not directly arise from the neural network architecture but from the feature study and the preprocessing of the data.

## Conclusion and Outlook

The neural network model presented in this paper can predict the 2D local displacement in the geometry for any open die forging process in the applied variable space with an overall RMSE of 0.486 mm for a workpiece with around 100 mm in height. This approach predicts a single node at a time and shows a good spatial generalization thus making it resolution independent. Along with its capability to generalize the patterns in the variable space, the model is also able to predict the 2D material flow of any stroke for the given pass. Although the model is data driven, the application of known physics in collecting the data, studying the features, building the neural network architecture and evaluating the model, has been beneficial in achieving the found generalization. Finally, the ability of the model to predict the 2D displacement accurately in milli seconds makes it suitable for the use in a digital material shadow and related applications.

In the future it is planned to improve the existing 2D model e.g. by incorporating the effects of other variables like friction and temperature. Furthermore, an extension of the 2D model to predict 3D material flow seems possible. This extension enables tracing the workpiece geometry throughout complete forging processes including e.g. intermediate workpiece rotations. Finally, the model can be made more explainable and robust by embedding boundary conditions and the underlying physical conditions into the neural networks using custom loss functions and concepts like physics informed neural networks.

## Acknowledgement

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2023 Internet of Production - 390621612
## References

[1] F. Becker, P. Bibow, M. Dalibor, A. Gannouni, V. Hahn, C. Hopmann, M. Jarke, I. Koren, M. Kröger, J. Lipp, J. Maibaum, J. Michael, B. Rumpe, P. Sapel, N. Schäfer, G. J. Schmitz, G. Schuh, and A. Wortmann, "A Conceptual Model for Digital Shadows in Industry and Its Application," in Conceptual Modeling: 40th International Conference, ER 2021, Virtual Event, October 18–21, 2021, Proceedings, 2021, pp. 271–281.

[2] J. Yanagimoto, D. Banabic, M. Banu, and L. Madej, "Simulation of metal forming – Visualization of invisible phenomena in the digital era," CIRP Annals, vol. 71, no. 2, pp. 599–622, 2022, https://doi.org/10.1016/j.cirp.2022.05.007

[3] D. Recker, M. Franzke, and G. Hirt, "Fast models for online-optimization during open die forging," CIRP Annals, vol. 60, no. 1, pp. 295–298, 2011, https://doi.org/10.1016/j.cirp.2011.03.142.

[4] E. Siemer, "Qualitätsoptimierende Prozeßsteuerung des Reckschmiedens," 1987.

[5] C. M. Sellars, "Modelling microstructural development during hot rolling," Materials Science and Technology, vol. 6, no. 11, pp. 1072–1081, 1990, https://doi.org/10.1179/mst.1990.6.11.1072

[6] A. Tomlinson, and J. Stringer, "Spread and elongation in flat tool forging," Journal of the Iron and Steel Institute, 1959.

[7] D. Rosenstock, D. Recker, G. Hirt, K. J. Steingießer, R. Rech, B. Gehrmann, and R. Lamm, "Application of a Fast Calculation Model for the Process Monitoring of Open Die Forging Processes," KEM, 554-557, pp. 248-263, 2013, https://doi.org/10.4028/www.scientific.net/KEM.554-557.248

[8] K. Mehrotra, Elements of artificial neural networks. Cambridge, Mass: MIT Press, 1997.

[9] K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, vol. 2, no. 5, pp. 359–366, 1989, https://doi.org/10.1016/0893-6080(89)90020-8

[10] M. Knap, G. Kugler, H. Palkowski, and R. Turk, "Prediction of Material Spreading in Hot Open-Die Forging," steel research international, vol. 75, no. 6, pp. 405–410, 2004, https://doi.org/10.1002/srin.200405787

[11] S. Lee, K. Kim, and N. Kim, "A Preform Design Approach for Uniform Strain Distribution in Forging Processes Based on Convolutional Neural Network," J. Manuf. Sci. Eng, vol. 144, no. 12, 2022, https://doi.org/10.1115/1.4054904

[12] W. L. Chan, M. W. Fu, and J. Lu, "An integrated FEM and ANN methodology for metal-formed product design," Engineering Applications of Artificial Intelligence, vol. 21, no. 8, pp. 1170–1181, 2008, https://doi.org/10.1016/j.engappai.2008.04.001

[13] M. Mozaffar, S. Liao, X. Xie, S. Saha, C. Park, J. Cao, W. K. Liu, and Z. Gan, "Mechanistic artificial intelligence (mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives," Journal of Materials Processing Technology, vol. 302, p. 117485, 2022, https://doi.org/10.1016/j.jmatprotec.2021.117485
## References

[1] F. Becker, P. Bibow, M. Dalibor, A. Gannouni, V. Hahn, C. Hopmann, M. Jarke, I. Koren, M. Kröger, J. Lipp, J. Maibaum, J. Michael, B. Rumpe, P. Sapel, N. Schäfer, G. J. Schmitz, G. Schuh, and A. Wortmann, "A Conceptual Model for Digital Shadows in Industry and Its Application," in Conceptual Modeling: 40th International Conference, ER 2021, Virtual Event, October 18–21, 2021, Proceedings, 2021, pp. 271–281.

[2] J. Yanagimoto, D. Banabic, M. Banu, and L. Madej, "Simulation of metal forming – Visualization of invisible phenomena in the digital era," CIRP Annals, vol. 71, no. 2, pp. 599–622, 2022, https://doi.org/10.1016/j.cirp.2022.05.007

[3] D. Recker, M. Franzke, and G. Hirt, "Fast models for online-optimization during open die forging," CIRP Annals, vol. 60, no. 1, pp. 295–298, 2011, https://doi.org/10.1016/j.cirp.2011.03.142.

[4] E. Siemer, "Qualitätsoptimierende Prozeßsteuerung des Reckschmiedens," 1987.

[5] C. M. Sellars, "Modelling microstructural development during hot rolling," Materials Science and Technology, vol. 6, no. 11, pp. 1072–1081, 1990, https://doi.org/10.1179/mst.1990.6.11.1072

[6] A. Tomlinson, and J. Stringer, "Spread and elongation in flat tool forging," Journal of the Iron and Steel Institute, 1959.

[7] D. Rosenstock, D. Recker, G. Hirt, K. J. Steingießer, R. Rech, B. Gehrmann, and R. Lamm, "Application of a Fast Calculation Model for the Process Monitoring of Open Die Forging Processes," KEM, 554-557, pp. 248-263, 2013, https://doi.org/10.4028/www.scientific.net/KEM.554-557.248

[8] K. Mehrotra, Elements of artificial neural networks. Cambridge, Mass: MIT Press, 1997.

[9] K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, vol. 2, no. 5, pp. 359–366, 1989, https://doi.org/10.1016/0893-6080(89)90020-8

[10] M. Knap, G. Kugler, H. Palkowski, and R. Turk, "Prediction of Material Spreading in Hot Open-Die Forging," steel research international, vol. 75, no. 6, pp. 405–410, 2004, https://doi.org/10.1002/srin.200405787

[11] S. Lee, K. Kim, and N. Kim, "A Preform Design Approach for Uniform Strain Distribution in Forging Processes Based on Convolutional Neural Network," J. Manuf. Sci. Eng, vol. 144, no. 12, 2022, https://doi.org/10.1115/1.4054904

[12] W. L. Chan, M. W. Fu, and J. Lu, "An integrated FEM and ANN methodology for metal-formed product design," Engineering Applications of Artificial Intelligence, vol. 21, no. 8, pp. 1170–1181, 2008, https://doi.org/10.1016/j.engappai.2008.04.001

[13] M. Mozaffar, S. Liao, X. Xie, S. Saha, C. Park, J. Cao, W. K. Liu, and Z. Gan, "Mechanistic artificial intelligence (mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives," Journal of Materials Processing Technology, vol. 302, p. 117485, 2022, https://doi.org/10.1016/j.jmatprotec.2021.117485
# Enhancing metal-forming predictions with VR-infused digital twin models

URIBE David¹,ª*, BAUDOUIN Cyrille¹,ᵇ*, LOCARD Yoan²,ᶜ,
DURAND Camille¹,ᵈ, and BIGOT Régis¹,ᵉ

¹HESAM Université, Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, F-57070, Metz, France

²HESAM Université, Arts et Métiers Institute of Technology, LAMPA, F-53810, Changé, France

**Keywords:** Digital Twin, Virtual Reality, Forging Process, Surrogate Model, Numerical Simulation

**Abstract.** This article presents a two-step method to enhance metal-forming predictions by integrating Virtual Reality (VR) into Digital Twin models, focusing on single-blow cold copper upsetting operations. The process begins with developing a real-time predictive surrogate model that considers actual process parameters, acting as a crucial link between conventional numerical simulations and immediate decision-making. Subsequently, the surrogate model is integrated into a realistic VR environment, aligned with the experimental forging setup. The study underscores the need and potential advantages of real-time digital twins in the forging field, emphasizing the bridging capability between numerical simulations and instant decision-making through predictive modeling and immersive virtual environments.

## Introduction

In forging processes, numerical simulations are crucial for predicting outcomes without physical experimentation. They excel in estimating challenging-to-measure variables like deformation fields and temperature distributions. While effective for accurate predictions and exploring diverse scenarios, their time-consuming nature limits real-time application.

In recent times, thanks to technological advancements, the concept of digital twins has emerged. In the *JENII project* spearheaded by the Arts et Métiers Institute of Technology, immersive and interactive digital twins are developed to provide new training tools to students in specialized fields, such as the construction sector [1]. In this context, a digital twin of the VULCAIN laboratory's platform for forging is in progress. Immersion in a virtual environment allows students, among other things, to represent an industrial environment on real dimensions even if they do not have the machines, to see normally invisible things like the inside of a machine to understand its functioning or like a deformation field in a billet, to test several configurations in a trial-and-error approach at lower cost and in complete safety for men and machines. Moreover, this new educational tool will be accessible at any time, everywhere, for students, to prepare a practical work or to review their lessons for example.

There are several definitions of the digital twin, from the basic model (a physical and a digital environment with a data flow to update the digital environment) [2] to more expert models (also integrating a permanent connection between the two environments, prediction services by simulations or deductions via AI tools, human interactions or product life cycle concepts) [3]. We consider here that a digital twin includes five elementary building blocks: 1) a physical environment, 2) a digital environment, 3) a sensor data acquisition to update the digital

<figure><img src="image_2167.png" /></figure>

<footnote>ªdavid_santiago.uribe_espitia@ensam.eu, ᵇcyrille.baudouin@ensam.eu,</footnote>

<footnote>ᶜyoan.locard@ensam.eu, ᵈcamille.durand@ensam.eu, ᶜregis.bigot@ensam.eu</footnote>
# Enhancing metal-forming predictions with VR-infused digital twin models

URIBE David¹,ª*, BAUDOUIN Cyrille¹,ᵇ*, LOCARD Yoan²,ᶜ,
DURAND Camille¹,ᵈ, and BIGOT Régis¹,ᵉ

¹HESAM Université, Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, F-57070, Metz, France

²HESAM Université, Arts et Métiers Institute of Technology, LAMPA, F-53810, Changé, France

ᵃdavid_santiago.uribe_espitia@ensam.eu, ᵇcyrille.baudouin@ensam.eu,

ᶜyoan.locard@ensam.eu, ᵈcamille.durand@ensam.eu, ᶜregis.bigot@ensam.eu

**Keywords:** Digital Twin, Virtual Reality, Forging Process, Surrogate Model, Numerical Simulation

**Abstract.** This article presents a two-step method to enhance metal-forming predictions by integrating Virtual Reality (VR) into Digital Twin models, focusing on single-blow cold copper upsetting operations. The process begins with developing a real-time predictive surrogate model that considers actual process parameters, acting as a crucial link between conventional numerical simulations and immediate decision-making. Subsequently, the surrogate model is integrated into a realistic VR environment, aligned with the experimental forging setup. The study underscores the need and potential advantages of real-time digital twins in the forging field, emphasizing the bridging capability between numerical simulations and instant decision-making through predictive modeling and immersive virtual environments.

## Introduction

In forging processes, numerical simulations are crucial for predicting outcomes without physical experimentation. They excel in estimating challenging-to-measure variables like deformation fields and temperature distributions. While effective for accurate predictions and exploring diverse scenarios, their time-consuming nature limits real-time application.

In recent times, thanks to technological advancements, the concept of digital twins has emerged. In the *JENII project* spearheaded by the Arts et Métiers Institute of Technology, immersive and interactive digital twins are developed to provide new training tools to students in specialized fields, such as the construction sector [1]. In this context, a digital twin of the VULCAIN laboratory's platform for forging is in progress. Immersion in a virtual environment allows students, among other things, to represent an industrial environment on real dimensions even if they do not have the machines, to see normally invisible things like the inside of a machine to understand its functioning or like a deformation field in a billet, to test several configurations in a trial-and-error approach at lower cost and in complete safety for men and machines. Moreover, this new educational tool will be accessible at any time, everywhere, for students, to prepare a practical work or to review their lessons for example.

There are several definitions of the digital twin, from the basic model (a physical and a digital environment with a data flow to update the digital environment) [2] to more expert models (also integrating a permanent connection between the two environments, prediction services by simulations or deductions via AI tools, human interactions or product life cycle concepts) [3]. We consider here that a digital twin includes five elementary building blocks: 1) a physical environment, 2) a digital environment, 3) a sensor data acquisition to update the digital

<figure><img src="image_2158.png" /></figure>
environment, 4) advanced models to update the digital environment in real-time and predict future behavior, 5) a data flow from advanced models to control the physical system (Fig. 1).

<figure><img src="image_2168.png" /><figcaption>Fig. 1. Digital Twin Overview in a Cyber-Physical System.</figcaption></figure>

In this paper, we are particularly interested in blocks 4) and 2) described previously for a single-blow cold copper upsetting operation. Digital twins aim to offer capabilities similar to numerical simulations (e.g., piloting, control, simulation, optimization), with real-time capability as a key differentiator [4]. To achieve real-time functionality, digital twins require highly predictive and responsive models of real-world processes [5], along with an accurate and realistic virtual representation.

To address these challenges, we propose a two-step approach. First, a surrogate model is developed. This model considers the actual process parameters and can make real-time predictions about the final operation's outcome [6]. Secondly, the surrogate is incorporated into a well-defined and realistic Virtual Reality (VR) environment, designed specifically from the experimental forging setup.

## Experimental and Numerical Setup

The studied forging operation involves the cold one-blow upsetting of a cylindrical pure copper billet using a screw press.

The screw press employed in this experiment is a LASCO® SPR400, capable of delivering a maximum forging energy of 28.9 kJ at a ram speed of 680 mm/s (see Fig. 2a). Press control is achieved by setting the energy level between 1% and 100% of the maximum forging energy. The tools used in the press consist of flat surface dies located in both the press ram and the press table (see Fig. 2b).
environment, 4) advanced models to update the digital environment in real-time and predict future behavior, 5) a data flow from advanced models to control the physical system (Fig. 1).

<figure><img src="image_2159.png" /><figcaption>Fig. 1. Digital Twin Overview in a Cyber-Physical System.</figcaption></figure>

In this paper, we are particularly interested in blocks 4) and 2) described previously for a single-blow cold copper upsetting operation. Digital twins aim to offer capabilities similar to numerical simulations (e.g., piloting, control, simulation, optimization), with real-time capability as a key differentiator [4]. To achieve real-time functionality, digital twins require highly predictive and responsive models of real-world processes [5], along with an accurate and realistic virtual representation.

To address these challenges, we propose a two-step approach. First, a surrogate model is developed. This model considers the actual process parameters and can make real-time predictions about the final operation's outcome [6]. Secondly, the surrogate is incorporated into a well-defined and realistic Virtual Reality (VR) environment, designed specifically from the experimental forging setup.

## Experimental and Numerical Setup

The studied forging operation involves the cold one-blow upsetting of a cylindrical pure copper billet using a screw press.

The screw press employed in this experiment is a LASCO® SPR400, capable of delivering a maximum forging energy of 28.9 kJ at a ram speed of 680 mm/s (see Fig. 2a). Press control is achieved by setting the energy level between 1% and 100% of the maximum forging energy. The tools used in the press consist of flat surface dies located in both the press ram and the press table (see Fig. 2b).
<figure><img src="image_2169.png" /><figcaption>Fig. 2. Experimental setup. a) Screw Press b) Upsetting tooling and billet.</figcaption></figure>

The upsetting operation is modeled using a finite element method (FEM) software (FORGE®). A 2D model was made, as the billet was supposed to be axisymmetric (see Fig. 3). A Hansel-Spittel constitutive equation was used to represent the billet’s rheology:

$$ \sigma_s = A \cdot e^{m1 \cdot T} \cdot \varepsilon^{m2} \cdot \dot{\varepsilon}^{m3} \cdot e^{\frac{m4}{\varepsilon}}. \qquad (1) $$

where $\varepsilon$ and $\dot{\varepsilon}$ are strain and strain rate respectively; T is the temperature; A, m1, m2, m3, m4 are material constants, with specific values of 411.19, -0.00121, 0.13, 0.01472, and 0.002 respectively. The tools consisted of flat rigid surfaces in both the upper and lower dies. A Coulomb-Tresca friction law was used with $\mu = 0.1$ and $\bar{m} = 0.2$ and low thermal exchanges were assumed (2000 W/m²K).

<figure><img src="image_2170.png" /><figcaption>Fig. 3. Copper Upsetting: a) Experimental setup, b) Numerical setup.</figcaption></figure>

## Surrogate Model: Setting the Model’s Architecture

Surrogate models, integral to this study, rely on constructing a training database, commonly from experimental trials or numerical simulations.

Numerical simulations, preferred for cost-effectiveness and flexibility, are advantageous over experiments. They enable exploring various process parameter combinations and excel in predicting multiple forging aspects, such as temperature gradients and stress distributions, crucial for comprehensive model training.
<figure><img src="image_2160.png" /><figcaption>Fig. 2. Experimental setup. a) Screw Press b) Upsetting tooling and billet.</figcaption></figure>

The upsetting operation is modeled using a finite element method (FEM) software (FORGE®). A 2D model was made, as the billet was supposed to be axisymmetric (see Fig. 3). A Hansel-Spittel constitutive equation was used to represent the billet’s rheology:

$$ \sigma_s = A \cdot e^{m1 \cdot T} \cdot \varepsilon^{m2} \cdot \dot{\varepsilon}^{m3} \cdot e^{\frac{m4}{\varepsilon}}. \quad (1) $$

where $\varepsilon$ and $\dot{\varepsilon}$ are strain and strain rate respectively; $T$ is the temperature; $A, m1, m2, m3, m4$ are material constants, with specific values of 411.19, -0.00121, 0.13, 0.01472, and 0.002 respectively. The tools consisted of flat rigid surfaces in both the upper and lower dies. A Coulomb-Tresca friction law was used with $\mu = 0.1$ and $\bar{m} = 0.2$ and low thermal exchanges were assumed (2000 $W/m^2K$).

<figure><img src="image_2161.png" /><figcaption>Fig. 3. Copper Upsetting: a) Experimental setup, b) Numerical setup.</figcaption></figure>

## Surrogate Model: Setting the Model’s Architecture

Surrogate models, integral to this study, rely on constructing a training database, commonly from experimental trials or numerical simulations.

Numerical simulations, preferred for cost-effectiveness and flexibility, are advantageous over experiments. They enable exploring various process parameter combinations and excel in predicting multiple forging aspects, such as temperature gradients and stress distributions, crucial for comprehensive model training.
Reduced-order models, like surrogates, prioritize influential parameters for predicting desired outputs, omitting less impactful ones. Identifying these key input parameters is a pivotal step in surrogate model development.

In the final VR application for 'what-if' scenarios, defining primary outputs is crucial. These outputs, represented in VR through metaphoric visualizations, play a central role in exploring and understanding process variations.

In the current upsetting process, the aim is to predict the final shape of the copper billet and its deformation field after a single forging blow. A local sensitivity analysis around the billet's final height was performed, as detailed in [6]. The input variables selected for the desired predictions are the billet's initial height, initial diameter, and the setpoint for forging energy, collectively contributing to over 80% of the cumulative sensitivity. For a visual representation of the surrogate model's inputs and outputs, please refer to Fig. 4.

<figure><img src="image_2171.png" /><figcaption>Fig. 4. Surrogate model's Inputs and Outputs.</figcaption></figure>

For the model's training algorithm, the multilayer perceptron artificial neural network (MLP-ANN) was selected due to its effectiveness in applications within the field of metal forming [6-7]. However, these models are typically designed for regression or classification tasks where scalar inputs are used to forecast scalar outputs, while the outputs in this upsetting case are not exclusively scalar values (see Final Geometry and Deformation field in Fig. 4).

To address this data diversity challenge, model reduction techniques are employed. These techniques transform the non-scalar parameters into scalar variables. This reduction in complexity and dimensionality ensures the smooth integration of the geometry and field predictions with the neural network.

## Managing Complexity: Model Reduction Techniques

Model Reduction Techniques serve as the essential bridge that allows to adapt the surrogate model to handle the non-scalar nature of the data effectively. Within the scope of this study, two distinct approaches are employed to reduce the complexity of the data: the Bézier curves for billet's geometry representation and the Proper Orthogonal Decomposition (POD) for deformation fields representation.

**Simplifying Geometry Representation with Bézier Curves.** The upsetting geometry is modeled in numerical simulation as 2D profiles, assuming an axisymmetric condition. This means that the overall geometry can be represented as a single cutting profile, specifically a scatter of 2D points (x, y) on the billet's external surface (see Fig. 5a).

However, this representation is not suitable for a surrogate model, as accurately representing a profile requires between 15 and 30 coordinates, resulting in 30 to 60 data points. To address this, a parametric representation of these profiles is necessary. In this regard, Bézier curves have been employed [5].

Bézier curves are a mathematical tool that enables the creation of a smooth profile connecting an initial and a final point via a set of strategically positioned Control Points (CPs). The adjustment of these CPs precisely defines the curve's shape. Consequently, the parametric representation of the geometries becomes a more concise set of 2D coordinates. The number of CPs required depends on the complexity of the shape being represented and the desired level of accuracy. For
Reduced-order models, like surrogates, prioritize influential parameters for predicting desired outputs, omitting less impactful ones. Identifying these key input parameters is a pivotal step in surrogate model development.

In the final VR application for 'what-if' scenarios, defining primary outputs is crucial. These outputs, represented in VR through metaphoric visualizations, play a central role in exploring and understanding process variations.

In the current upsetting process, the aim is to predict the final shape of the copper billet and its deformation field after a single forging blow. A local sensitivity analysis around the billet's final height was performed, as detailed in [6]. The input variables selected for the desired predictions are the billet's initial height, initial diameter, and the setpoint for forging energy, collectively contributing to over 80% of the cumulative sensitivity. For a visual representation of the surrogate model's inputs and outputs, please refer to Fig. 4.

<figure><img src="image_2162.png" /><figcaption>Fig. 4. Surrogate model's Inputs and Outputs.</figcaption></figure>

For the model's training algorithm, the multilayer perceptron artificial neural network (MLP-ANN) was selected due to its effectiveness in applications within the field of metal forming [6-7]. However, these models are typically designed for regression or classification tasks where scalar inputs are used to forecast scalar outputs, while the outputs in this upsetting case are not exclusively scalar values (see Final Geometry and Deformation field in Fig. 4).

To address this data diversity challenge, model reduction techniques are employed. These techniques transform the non-scalar parameters into scalar variables. This reduction in complexity and dimensionality ensures the smooth integration of the geometry and field predictions with the neural network.

## Managing Complexity: Model Reduction Techniques

Model Reduction Techniques serve as the essential bridge that allows to adapt the surrogate model to handle the non-scalar nature of the data effectively. Within the scope of this study, two distinct approaches are employed to reduce the complexity of the data: the Bézier curves for billet's geometry representation and the Proper Orthogonal Decomposition (POD) for deformation fields representation.

**Simplifying Geometry Representation with Bézier Curves.** The upsetting geometry is modeled in numerical simulation as 2D profiles, assuming an axisymmetric condition. This means that the overall geometry can be represented as a single cutting profile, specifically a scatter of 2D points (x, y) on the billet's external surface (see Fig. 5a).

However, this representation is not suitable for a surrogate model, as accurately representing a profile requires between 15 and 30 coordinates, resulting in 30 to 60 data points. To address this, a parametric representation of these profiles is necessary. In this regard, Bézier curves have been employed [5].

Bézier curves are a mathematical tool that enables the creation of a smooth profile connecting an initial and a final point via a set of strategically positioned Control Points (CPs). The adjustment of these CPs precisely defines the curve's shape. Consequently, the parametric representation of the geometries becomes a more concise set of 2D coordinates. The number of CPs required depends on the complexity of the shape being represented and the desired level of accuracy. For
this case, with five CPs, the root-mean-squared error between the original FEM profiles and the
Bézier-reconstructed bulging profiles is below 0.03mm and does not significantly decrease with
the addition of more CPs. Consequently, five CPs were chosen for the parametric representation
(see Fig. 5b).

<figure><img src="image_2172.png" /><figcaption>Fig. 5. Billet's Geometry representation: a) 2D Scatter, b) Initial Bézier's CPs, c) Reduced representation of the Bézier's CPs.</figcaption></figure>

Additionally, considering the symmetry of the billet in its upper and lower portions, certain relationships were established: $x_1 = x_4, y_2 = H - y_4$, and $y_3 = y_5/2$. As a result, a new set of point conventions was adopted, introducing $r_{min}$ and $H$ as new variables, as illustrated in Fig. 5b. This new convention allows for the representation of the entire billet geometry using only five parameters $r_{min}, H, x_2, y_2$, and $x_3$ (see Fig. 5c).

Choosing the fourth-order Bézier curve strikes a balance between computational efficiency and accurately representing complex bulge patterns in upsetting geometry. This order provides flexibility in capturing curvature variations across different deformation states, friction conditions, and upsetting ratios.

Parametrizing deformation field data with Proper Orthogonal Decomposition (POD). The deformation fields of the billets are extracted from numerical simulations and are expressed as a 3D point cloud, encompassing two spatial dimensions ($x, y$) and a third dimension indicating deformation ($\varepsilon$), as illustrated in Fig. 6a. The point cloud's coordinates correspond to the nodes of the FEM simulation. To represent the deformation fields in the different upsetting cases under study, between 4000 and 15000 nodes are required, varying with the billet's size. This 3D point cloud poses challenges for integration into a surrogate model due to its size and variable node count because of re-meshing during simulations. Therefore, parametric reduction and representation are accomplished using POD techniques.

POD is a dimensionality reduction method that identifies dominant modes within the deformation field data. These modes, represented as a set of basis functions, capture the essential information while reducing the dimensionality. For the application of POD, an essential preliminary step is to discretize the deformation fields.

The discretization process involves performing linear interpolation to transform any deformation field into a 100x100 matrix, as depicted in Fig. 6. The choice of a 100x100 grid size was determined through gradient analysis of the deformation fields while varying the grid size, considering both the field quality and computer storage constraints.
this case, with five CPs, the root-mean-squared error between the original FEM profiles and the
Bézier-reconstructed bulging profiles is below 0.03mm and does not significantly decrease with
the addition of more CPs. Consequently, five CPs were chosen for the parametric representation
(see Fig. 5b).

<figure><img src="image_2163.png" /><figcaption>Fig. 5. Billet's Geometry representation: a) 2D Scatter, b) Initial Bézier's CPs, c) Reduced representation of the Bézier's CPs.</figcaption></figure>

Additionally, considering the symmetry of the billet in its upper and lower portions, certain relationships were established: $x_1 = x_4, y_2 = H - y_4$, and $y_3 = y_5/2$. As a result, a new set of point conventions was adopted, introducing $r_{min}$ and $H$ as new variables, as illustrated in Fig. 5b. This new convention allows for the representation of the entire billet geometry using only five parameters $r_{min}, H, x_2, y_2$, and $x_3$ (see Fig. 5c).

Choosing the fourth-order Bézier curve strikes a balance between computational efficiency and accurately representing complex bulge patterns in upsetting geometry. This order provides flexibility in capturing curvature variations across different deformation states, friction conditions, and upsetting ratios.

Parametrizing deformation field data with Proper Orthogonal Decomposition (POD). The deformation fields of the billets are extracted from numerical simulations and are expressed as a 3D point cloud, encompassing two spatial dimensions ($x, y$) and a third dimension indicating deformation ($\varepsilon$), as illustrated in Fig. 6a. The point cloud's coordinates correspond to the nodes of the FEM simulation. To represent the deformation fields in the different upsetting cases under study, between 4000 and 15000 nodes are required, varying with the billet's size. This 3D point cloud poses challenges for integration into a surrogate model due to its size and variable node count because of re-meshing during simulations. Therefore, parametric reduction and representation are accomplished using POD techniques.

POD is a dimensionality reduction method that identifies dominant modes within the deformation field data. These modes, represented as a set of basis functions, capture the essential information while reducing the dimensionality. For the application of POD, an essential preliminary step is to discretize the deformation fields.

The discretization process involves performing linear interpolation to transform any deformation field into a 100x100 matrix, as depicted in Fig. 6. The choice of a 100x100 grid size was determined through gradient analysis of the deformation fields while varying the grid size, considering both the field quality and computer storage constraints.
<figure><img src="image_2173.png" /><figcaption>Fig. 6. Discretization Process of the Deformation Fields: a) Original Scatter, b) Discretized Field.</figcaption></figure>

After defining the discretization process, a reduced Design of Experiments (DoE) is carried out using the Latin Hypercube Sampling (LHS) technique. In this approach, the three input parameters shown in Fig. 4 are varied within defined ranges:

* Initial Diameter= 15-50 [mm]

* Initial Height/Initial Diameter= 1.5-2

* Energy= 0-60 [%] of maximum energy

* Compression ratio (1-Final Height/Initial Height) = 0-50 [%]

Following the guideline of including a minimum of 10 combinations per active variable [8], 50 combinations were generated using Latin Hypercube Sampling (LHS). Each simulation produced around 660 data points, contributing to a total database size of 33,000 combinations. This database served for both applying the POD and training the surrogate model. The matrix for the POD was a 10,000x33,000 matrix, considering the number of discretized points and combinations. The deformation values span from ε = 0 to ε = 1.5.

The outcomes of the POD analysis revealed that the first basis function (mode) captured 75% of the energy in the dataset, while the inclusion of the second and third modes increased the energy capture to 79% and 82%, respectively. This implies that the first three basis functions (modes) collectively captured a substantial portion of the overall deformation variability in the dataset, enabling the reconstruction of a deformation field with only three basis functions associated with three single parameters:

$$DF_{100x100} \approx \overline{DF}_{100x100} + \sum_{i=1}^{n=3} b_i \cdot \Phi_i = \overline{DF}_{100x100} + (b_1 \cdot \Phi_1 + b_2 \cdot \Phi_2 + b_3 \cdot \Phi_3). \quad (2)$$

Here, $DF_{100x100}$ represents the discretized deformation field; $\overline{DF}_{100x100}$ is the mean deformation field obtained from the POD database; $\Phi_i$ is the $i_{th}$ basis function or mode obtained from the POD; and, $b_i$ is the coefficient associated with the $i_{th}$ mode.

Using three modes, the Mean Absolute Error and Mean Absolute Percentage Error were 0.012 and 0.16%, respectively, when comparing reconstructed and initial fields. No significant error reduction occurred beyond three modes, leading to their selection. This parametrized representation, using $b_1, b_2$, and $b_3$ as coefficients, enables field reconstruction with minimal error, streamlining the upsetting operation analysis. This parametrized representation, using $b_1, b_2$, and $b_3$ as coefficients, enables field reconstruction with minimal error, streamlining the upsetting operation analysis.

## Surrogate Model: Training, Validation, and Testing

The MLP-ANN featured a two-layer architecture with 20 neurons each, constructed using Keras API in TensorFlow with ADAM optimizer for backpropagation. A dropout of 0.2 was applied, and ReLU activation was used for hidden layers and linear activation for the output layer. Loss function: Mean Squared Error. The 33,000-combination database was split 80-20 for training and
<figure><img src="image_2164.png" /><figcaption>Fig. 6. Discretization Process of the Deformation Fields: a) Original Scatter, b) Discretized Field.</figcaption></figure>

After defining the discretization process, a reduced Design of Experiments (DoE) is carried out using the Latin Hypercube Sampling (LHS) technique. In this approach, the three input parameters shown in Fig. 4 are varied within defined ranges:

* Initial Diameter= 15-50 [mm]

* Initial Height/Initial Diameter= 1.5-2

* Energy= 0-60 [%] of maximum energy

* Compression ratio (1-Final Height/Initial Height) = 0-50 [%]

Following the guideline of including a minimum of 10 combinations per active variable [8], 50 combinations were generated using Latin Hypercube Sampling (LHS). Each simulation produced around 660 data points, contributing to a total database size of 33,000 combinations. This database served for both applying the POD and training the surrogate model. The matrix for the POD was a 10,000x33,000 matrix, considering the number of discretized points and combinations. The deformation values span from $\epsilon = 0$ to $\epsilon = 1.5$.

The outcomes of the POD analysis revealed that the first basis function (mode) captured 75% of the energy in the dataset, while the inclusion of the second and third modes increased the energy capture to 79% and 82%, respectively. This implies that the first three basis functions (modes) collectively captured a substantial portion of the overall deformation variability in the dataset, enabling the reconstruction of a deformation field with only three basis functions associated with three single parameters:

$$DF_{100x100} \approx \overline{DF}_{100x100} + \sum_{i=1}^{n=3} b_i \cdot \Phi_i = \overline{DF}_{100x100} + (b_1 \cdot \Phi_1 + b_2 \cdot \Phi_2 + b_3 \cdot \Phi_3). \quad (2)$$

Here, $DF_{100x100}$ represents the discretized deformation field; $\overline{DF}_{100x100}$ is the mean deformation field obtained from the POD database; $\Phi_i$ is the $i_{th}$ basis function or mode obtained from the POD; and, $b_i$ is the coefficient associated with the $i_{th}$ mode.

Using three modes, the Mean Absolute Error and Mean Absolute Percentage Error were 0.012 and 0.16%, respectively, when comparing reconstructed and initial fields. No significant error reduction occurred beyond three modes, leading to their selection. This parametrized representation, using $b_1, b_2$, and $b_3$ as coefficients, enables field reconstruction with minimal error, streamlining the upsetting operation analysis. This parametrized representation, using $b_1, b_2$, and $b_3$ as coefficients, enables field reconstruction with minimal error, streamlining the upsetting operation analysis.

## Surrogate Model: Training, Validation, and Testing

The MLP-ANN featured a two-layer architecture with 20 neurons each, constructed using Keras API in TensorFlow with ADAM optimizer for backpropagation. A dropout of 0.2 was applied, and ReLU activation was used for hidden layers and linear activation for the output layer. Loss function: Mean Squared Error. The 33,000-combination database was split 80-20 for training and
validation. Standardization addressed unit differences. Training metrics boasted an R2 of around 0.99 and a Mean Absolute Percentage Error below 1%. The model's computation time is under 500 milliseconds.

To evaluate the model's overall performance, an entirely independent subset, referred to as the testing subset, was examined. Within this subset, a comparison was made between the FEM geometries and deformation fields with those predicted by the Surrogate Model (refer to Table 1). The selected energies adhered to specific criteria, ensuring a compression ratio below 50% and deformation levels under 1.0. These criteria were crucial considerations, particularly for cold copper, aiming to prevent cracking and to remain within the domain defined by the rheology's law, used for the database.

<table><caption>Table 1. Billet Indexing: Testing Subset.</caption><thead><tr><th>Billet</th><th>Initial Diameter (ID)</th><th>Initial Height (IH)</th><th>Energy Setpoint: Experimental</th><th>Final Height (FH): Experimental</th><th>Compression ratio: (1-FH/IH)</th></tr></thead><tbody><tr><td>I</td><td>32 [mm]</td><td>44.30 [mm]</td><td>4.05 [kJ]</td><td>32.15 [mm]</td><td>27.42 [%]</td></tr><tr><td>II</td><td></td><td>56.85 [mm]</td><td>8.67 [kJ]</td><td>33.00 [mm]</td><td>41.95 [%]</td></tr><tr><td>III</td><td>24 [mm]</td><td>33.20 [mm]</td><td>2.31 [kJ]</td><td>25.80 [mm]</td><td>22.22 [%]</td></tr><tr><td>IV</td><td></td><td>37.75 [mm]</td><td>1.16 [kJ]</td><td>24.40 [mm]</td><td>35.36 [%]</td></tr></tbody></table>

The results indicate nearly overlapping geometries with a root-mean-squared error of 0.062 mm, a mean absolute error of 0.050 mm, and a mean absolute percentage error of 0.30% between every FEM bulging profile and every surrogate model's bulging profile prediction (see Fig. 7).

<figure><img src="image_2174.png" /><figcaption>Fig. 7. FEM vs Surrogate Model Geometry Predictions for Billet "I" (see Table 1 for Billet Indexing).</figcaption></figure>

The results of the deformation fields are presented in Fig. 8. Both the FEM and the Surrogate Model show similar forecasts, with a mean absolute error below 0.0040 and a mean absolute percentage error below 1.20% between them.
validation. Standardization addressed unit differences. Training metrics boasted an R2 of around 0.99 and a Mean Absolute Percentage Error below 1%. The model's computation time is under 500 milliseconds.

To evaluate the model's overall performance, an entirely independent subset, referred to as the testing subset, was examined. Within this subset, a comparison was made between the FEM geometries and deformation fields with those predicted by the Surrogate Model (refer to Table 1). The selected energies adhered to specific criteria, ensuring a compression ratio below 50% and deformation levels under 1.0. These criteria were crucial considerations, particularly for cold copper, aiming to prevent cracking and to remain within the domain defined by the rheology's law, used for the database.

<table><caption>Table 1. Billet Indexing: Testing Subset.</caption><thead><tr><th>Billet</th><th>Initial Diameter (ID)</th><th>Initial Height (IH)</th><th>Energy Setpoint: Experimental</th><th>Final Height (FH): Experimental</th><th>Compression ratio: (1-FH/IH)</th></tr></thead><tbody><tr><td>I</td><td>32 [mm]</td><td>44.30 [mm]</td><td>4.05 [kJ]</td><td>32.15 [mm]</td><td>27.42 [%]</td></tr><tr><td>II</td><td></td><td>56.85 [mm]</td><td>8.67 [kJ]</td><td>33.00 [mm]</td><td>41.95 [%]</td></tr><tr><td>III</td><td>24 [mm]</td><td>33.20 [mm]</td><td>2.31 [kJ]</td><td>25.80 [mm]</td><td>22.22 [%]</td></tr><tr><td>IV</td><td></td><td>37.75 [mm]</td><td>1.16 [kJ]</td><td>24.40 [mm]</td><td>35.36 [%]</td></tr></tbody></table>

The results indicate nearly overlapping geometries with a root-mean-squared error of 0.062 mm, a mean absolute error of 0.050 mm, and a mean absolute percentage error of 0.30% between every FEM bulging profile and every surrogate model's bulging profile prediction (see Fig. 7).

<figure><img src="image_2165.png" /><figcaption>Fig. 7. FEM vs Surrogate Model Geometry Predictions for Billet "I" (see Table 1 for Billet Indexing).</figcaption></figure>

The results of the deformation fields are presented in Fig. 8. Both the FEM and the Surrogate Model show similar forecasts, with a mean absolute error below 0.0040 and a mean absolute percentage error below 1.20% between them.
<figure><img src="image_2175.png" /><figcaption>Fig. 8. FEM vs Surrogate Model Deformation Field Predictions for billet "II" (see Table 1 for billet Indexing).</figcaption></figure>

## Virtual Reality Integration

Digital VR-environment creation. VR-environment is made according to a classic process [9]. First, all the machines are designed by CAD software. Secondly, the models are incorporated into Unity® and textures are applied from real environment photos for a realistic rendering. Then rigid body mobilities and other interactions between the components are managed by Unity built-in 3D physics (Nvidia PhysX) and by the XDE interactive physics engine developed by our partner CEA-LIST [10] (Fig. 11b).

### Surrogate Model Integration
The dynamic incorporation of the surrogate model is presented in Fig. 9. The Keras neural network is converted to the ONNX format using tf2onnx, serving as the import format for Unity Sentis [11]. POD matrices are converted to .csv files and read at runtime for deformation field reconstruction. The model is deployed through the creation of the inference engine (GPU worker). The output tensor (1, 8) includes 5 geometric parameters and 3 coefficients of POD modes. A half-cylinder is constructed through a triangulated 3D geometric mesh and a corresponding UV-map is assigned (see Fig. 10b). Vertex positions are dynamically updated based on the geometric parameters (see Fig. 10c). Two-dimensional textures (100x100) are generated using POD for the deformation fields, enhancing visual representation with a color gradient. A standard material applies these textures to the constructed mesh using the corresponding UV map (see Fig. 10c).

<figure><img src="image_2176.png" /><figcaption>Fig. 9. Integration of the surrogate model in VR-environment: 1) Inputs defined in the VR-environment, 2) Real-time Predictive Model, 3) Visualization of the results back in the VR-environment.</figcaption></figure>
<figure><img src="image_2166.png" /><figcaption>Fig. 8. FEM vs Surrogate Model Deformation Field Predictions for billet "II" (see Table 1 for billet Indexing).</figcaption></figure>

## Virtual Reality Integration

Digital VR-environment creation. VR-environment is made according to a classic process [9]. First, all the machines are designed by CAD software. Secondly, the models are incorporated into Unity® and textures are applied from real environment photos for a realistic rendering. Then rigid body mobilities and other interactions between the components are managed by Unity built-in 3D physics (Nvidia PhysX) and by the XDE interactive physics engine developed by our partner CEA-LIST [10] (Fig. 11b).

### Surrogate Model Integration
The dynamic incorporation of the surrogate model is presented in Fig. 9. The Keras neural network is converted to the ONNX format using tf2onnx, serving as the import format for Unity Sentis [11]. POD matrices are converted to .csv files and read at runtime for deformation field reconstruction. The model is deployed through the creation of the inference engine (GPU worker). The output tensor (1, 8) includes 5 geometric parameters and 3 coefficients of POD modes. A half-cylinder is constructed through a triangulated 3D geometric mesh and a corresponding UV-map is assigned (see Fig. 10b). Vertex positions are dynamically updated based on the geometric parameters (see Fig. 10c). Two-dimensional textures (100x100) are generated using POD for the deformation fields, enhancing visual representation with a color gradient. A standard material applies these textures to the constructed mesh using the corresponding UV map (see Fig. 10c).

<figure><img src="image_2167.png" /><figcaption>Fig. 9. Integration of the surrogate model in VR-environment: 1) Inputs defined in the VR-environment, 2) Real-time Predictive Model, 3) Visualization of the results back in the VR-environment.</figcaption></figure>
<figure><img src="image_2177.png" /><figcaption>Fig. 10. Real-time billet generation: a) Initial Billet b) Triangulated 3D geometric mesh and Initial UV-map (U=red, V=green). c) Dynamic representation of the forged billet (geometry and deformation field).</figcaption></figure>

**Interactive Experience.** The learner in the VR-environment can carry out its single-blow cold copper upsetting operation by adjusting the parameters as desired. In real time during the forging operation, he can visualize the internal workings of the machine and the deformation field (Fig. 11).

<figure><img src="image_2178.png" /><figcaption>Fig. 11. Real-time Prediction of Upsetting Operations 'What-If' Scenarios within a VR-environment.</figcaption></figure>

a) learner in VR-environment, b) screw press in VR-environment,

c) visualization of the internal working of the screw press, d) visualization of the deformation field of the billet.

Discussion

The surrogate model's assessment emphasizes geometry predictions, deformation field accuracy, and its potential extension for forecasting additional parameters in metal-forming processes.

Achieving precision comparable to Finite Element Method (FEM) simulations, the model excels in predicting geometry and deformation fields during cold copper upsetting, boasting a rapid
<figure><img src="image_2168.png" /><figcaption>Fig. 10. Real-time billet generation: a) Initial Billet b) Triangulated 3D geometric mesh and Initial UV-map (U=red, V=green). c) Dynamic representation of the forged billet (geometry and deformation field).</figcaption></figure>

**Interactive Experience.** The learner in the VR-environment can carry out its single-blow cold copper upsetting operation by adjusting the parameters as desired. In real time during the forging operation, he can visualize the internal workings of the machine and the deformation field (Fig. 11).

<figure><img src="image_2169.png" /><figcaption>Fig. 11. Real-time Prediction of Upsetting Operations 'What-If' Scenarios within a VR-environment.</figcaption></figure>

a) learner in VR-environment, b) screw press in VR-environment, c) visualization of the internal working of the screw press, d) visualization of the deformation field of the billet.

**Discussion**

The surrogate model's assessment emphasizes geometry predictions, deformation field accuracy, and its potential extension for forecasting additional parameters in metal-forming processes.

Achieving precision comparable to Finite Element Method (FEM) simulations, the model excels in predicting geometry and deformation fields during cold copper upsetting, boasting a rapid
computation time of 500 milliseconds for real-time decision-making. Its adaptability goes beyond, hinting at future applications like temperature and damage predictions.

The focus on predicting scalar outputs, facilitated by dimensionality reduction techniques, balances simplicity and interpretability. Emphasizing scalar predictions streamlines the modeling process and prioritizes interpretability. However, alternative approaches like Deep Neural Networks (DNN) could handle more complexity, depending on data nature, computational resources, and specific objectives.

Tailored criteria for energy selection, compression ratio, and deformation levels address unique considerations of working with cold copper. However, the methodology can be extended and applied to other materials, such as steels, and adapted for varying deformation levels.

## Conclusions

This study introduces a two-step approach integrating Virtual Reality (VR) into Digital Twin models to enhance metal-forming predictions. Focusing on cold one-blow upsetting of a pure copper billet, the methodology combines surrogate models, model reduction techniques, and VR for real-time exploration of process parameters. It proves feasible, accurate, and cost-effective, with transformative potential in manufacturing efficiency and cost reduction. The research sets the foundation for refining the methodology, exploring new applications, and integrating advanced technologies for enhanced real-time decision-making in metal-forming processes.

## Acknowledgments

We would like to sincerely thank the Technical Center for Mechanical Industry (CETIM) for their financial support in this research project. Also, we would like to thank Sébastien Burgun and Daniel Boehm for their technical support during the various tests conducted.

## References

[1] J. Goulding, W. Nadim, P. Petridis, et M. Alshawi, « Construction industry offsite production: A virtual reality interactive training environment prototype », Advanced Engineering Informatics, vol. 26, no 1, p. 103-116, janv. 2012. https://doi.org/10.1016/j.aei.2011.09.004

[2] M. Grieves et J. Vickers, « Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems », in Transdisciplinary Perspectives on Complex Systems: New Findings and Approaches, F.-J. Kahlen, S. Flumerfelt, et A. Alves, Éd. Cham: Springer International Publishing, 2017, p. 85-113. doi: 10.1007/978-3-319-38756-7_4

[3] R. Stark, C. Fresemann, et K. L window, « Development and operation of Digital Twins for technical systems and services », CIRP Annals, vol. 68, no 1, p. 129-132, 2019. https://doi.org/10.1016/j.cirp.2019.04.024

[4] K.-J. Wang, Y.-H. Lee, et S. Angelica, « Digital twin design for real-time monitoring – a case study of die cutting machine », International Journal of Production Research, vol. 59, no 21, p. 6471-6485, nov. 2021. https://doi.org/10.1080/00207543.2020.1817999

[5] D. Uribe, C. Baudouin, C. Durand, et R. Bigot, « Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin », Int J Mater Form, vol. 17, no 1, p. 7, déc. 2023. https://doi.org/10.1007/s12289-023-01803-x

[6] D. Uribe, C. Durand, C. Baudouin, P. Krumpipe, et R. Bigot, « Towards the Real-Time Piloting of a Forging Process: Development of a Surrogate Model for a Multiple Blow Operation », in Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity, Cham, 2023, p. 377-388. doi: 10.1007/978-3-031-41341-4_39
computation time of 500 milliseconds for real-time decision-making. Its adaptability goes beyond, hinting at future applications like temperature and damage predictions.

The focus on predicting scalar outputs, facilitated by dimensionality reduction techniques, balances simplicity and interpretability. Emphasizing scalar predictions streamlines the modeling process and prioritizes interpretability. However, alternative approaches like Deep Neural Networks (DNN) could handle more complexity, depending on data nature, computational resources, and specific objectives.

Tailored criteria for energy selection, compression ratio, and deformation levels address unique considerations of working with cold copper. However, the methodology can be extended and applied to other materials, such as steels, and adapted for varying deformation levels.

## Conclusions

This study introduces a two-step approach integrating Virtual Reality (VR) into Digital Twin models to enhance metal-forming predictions. Focusing on cold one-blow upsetting of a pure copper billet, the methodology combines surrogate models, model reduction techniques, and VR for real-time exploration of process parameters. It proves feasible, accurate, and cost-effective, with transformative potential in manufacturing efficiency and cost reduction. The research sets the foundation for refining the methodology, exploring new applications, and integrating advanced technologies for enhanced real-time decision-making in metal-forming processes.

## Acknowledgments

We would like to sincerely thank the Technical Center for Mechanical Industry (CETIM) for their financial support in this research project. Also, we would like to thank Sébastien Burgun and Daniel Boehm for their technical support during the various tests conducted.

## References

[1] J. Goulding, W. Nadim, P. Petridis, et M. Alshawi, « Construction industry offsite production: A virtual reality interactive training environment prototype », Advanced Engineering Informatics, vol. 26, no 1, p. 103-116, janv. 2012. https://doi.org/10.1016/j.aei.2011.09.004

[2] M. Grieves et J. Vickers, « Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems », in Transdisciplinary Perspectives on Complex Systems: New Findings and Approaches, F.-J. Kahlen, S. Flumerfelt, et A. Alves, Éd. Cham: Springer International Publishing, 2017, p. 85-113. doi: 10.1007/978-3-319-38756-7_4

[3] R. Stark, C. Fresemann, et K. L window, « Development and operation of Digital Twins for technical systems and services », CIRP Annals, vol. 68, no 1, p. 129-132, 2019. https://doi.org/10.1016/j.cirp.2019.04.024

[4] K.-J. Wang, Y.-H. Lee, et S. Angelica, « Digital twin design for real-time monitoring – a case study of die cutting machine », International Journal of Production Research, vol. 59, no 21, p. 6471-6485, nov. 2021. https://doi.org/10.1080/00207543.2020.1817999

[5] D. Uribe, C. Baudouin, C. Durand, et R. Bigot, « Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin », Int J Mater Form, vol. 17, no 1, p. 7, déc. 2023. https://doi.org/10.1007/s12289-023-01803-x

[6] D. Uribe, C. Durand, C. Baudouin, P. Krumpipe, et R. Bigot, « Towards the Real-Time Piloting of a Forging Process: Development of a Surrogate Model for a Multiple Blow Operation », in Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity, Cham, 2023, p. 377-388. doi: 10.1007/978-3-031-41341-4_39
[7] K. Slimani, M. Zaaf, et T. Balan, « Accurate surrogate models for the flat rolling process », International Journal of Material Forming, vol. 16, mars 2023. https://doi.org/10.1007/s12289-023-01744-5

[8] M. Schonlau, « Computer experiments and global optimization », Doctoral Thesis, University of Waterloo, 1997. Consulté le: 15 mai 2023. [En ligne]. Disponible sur: https://uwspace.uwaterloo.ca/handle/10012/190

[9] L. Dammacco, R. Carli, V. Lazazzera, M. Fiorentino, et M. Dotoli, « Designing complex manufacturing systems by virtual reality: A novel approach and its application to the virtual commissioning of a production line », Computers in Industry, vol. 143, p. 103761, déc. 2022. https://doi.org/10.1016/j.compind.2022.103761

[10] V. Weistroffer, F. Keith, A. Bisiaux, C. Andriot, et A. Lasnier, « Using Physics-based Digital Twins and Extended Reality for the Safety and Ergonomics Evaluation of Cobotic workstations », Frontiers in Virtual Reality, vol. 3, p. https://doi.org/10.3389/frvir.2022.781830, 2022. https://doi.org/10.3389/frvir.2022.781830

[11] onnx/tensorflow-onnx. Open Neural Network Exchange, 2024. Consulté le: 5 février 2024. [online]. Available on: https://github.com/onnx/tensorflow-onnx
[7] K. Slimani, M. Zaaf, et T. Balan, « Accurate surrogate models for the flat rolling process », International Journal of Material Forming, vol. 16, mars 2023. https://doi.org/10.1007/s12289-023-01744-5

[8] M. Schonlau, « Computer experiments and global optimization », Doctoral Thesis, University of Waterloo, 1997. Consulté le: 15 mai 2023. [En ligne]. Disponible sur: https://uwspace.uwaterloo.ca/handle/10012/190

[9] L. Dammacco, R. Carli, V. Lazazzera, M. Fiorentino, et M. Dotoli, « Designing complex manufacturing systems by virtual reality: A novel approach and its application to the virtual commissioning of a production line », Computers in Industry, vol. 143, p. 103761, déc. 2022. https://doi.org/10.1016/j.compind.2022.103761

[10] V. Weistroffer, F. Keith, A. Bisiaux, C. Andriot, et A. Lasnier, « Using Physics-based Digital Twins and Extended Reality for the Safety and Ergonomics Evaluation of Cobotic workstations », Frontiers in Virtual Reality, vol. 3, p. https://doi.org/10.3389/frvir.2022.781830, 2022. https://doi.org/10.3389/frvir.2022.781830

[11] onnx/tensorflow-onnx. Open Neural Network Exchange, 2024. Consulté le: 5 février 2024. [online]. Available on: https://github.com/onnx/tensorflow-onnx
# Effectiveness of machining equipment user guides:
A comparative study of augmented reality and traditional media

GHOBRIAL Mina¹,³,a*, SEITIER Philippe¹,b, LAGARRIGUE Pierre³,c,
GALAUP Michel²,d, and GILLES Patrick¹,de

¹ICA, Institut National des Sciences Appliquées de Toulouse, 135 Av. de Rangueil, 31400 Toulouse, France

²EFTS, Institut National Universitaire Champollion, Pl. de Verdun, 81000 Albi, France

³ICA, Institut National Universitaire Champollion, Pl. de Verdun, 81000 Albi, France

ªghobrial@insa-toulouse.fr, ᵇseitier@insa-toulouse.fr, ᶜpierre.lagarrigue@univ-jfc.fr,

d'michel.galaup@univ-jfc.fr, e'gilles@insa-toulouse.fr

**Keywords:** Augmented Reality, Instructions, Workload, Acceptability

**Abstract.** In the rapidly evolving landscape of manufacturing and material forming, innovative strategies are imperative for maintaining a competitive edge. Augmented Reality (AR) has emerged as a groundbreaking technology, offering new dimensions in how information is displayed and interacted with. It holds particular promise in the panel of instructional guides for complex machinery, potentially enhance traditional methods of knowledge transfer and operator training. Material forming, a key discipline within mechanical engineering, requires high-precision and skill, making it an ideal candidate for the integration of advanced instructional technologies like AR. This study aims to explore the efficiency of three distinct types of user manuals—video, paper, and augmented reality (AR)—on performance and acceptability in a material forming workshop environment. The focus will be on how AR can be specifically applied to improve task execution and understanding in material forming operations. Participants are mechanical engineering students specializing in material forming. They will engage in a series of standardized tasks related to machining processes. Performance will be gauged by metrics like task completion time and error rates, while task load will be assessed via the NASA Task Load Index (NASA-TLX) [1]. Acceptability of each manual type will be evaluated using the System Usability Scale (SUS) [2]. By comparing these various instructional formats, this research seeks to shed light on the most effective mediums for enhancing both operator performance and experience.

**Introduction**

The intersection of instructional technology and industrial training, particularly in the context of material forming, is an area of increasing interest for the industry and educational institutions. Immersive technologies—Augmented Reality (AR), Virtual Reality (VR), and Mixed Reality (MR)—particularly when applied to material forming and mechanical engineering, offer distinct advantages in enhancing traditional teaching methods. AR overlays digital information onto the real world, VR creates a fully immersive digital environment, and MR combines elements of both AR and VR, enabling interaction between virtual and real objects, based on Gandolfi's definition [3]. This study examines various types of instructional media to aid operators in efficiently using CNC machining equipment. There is a rich history of employing instructional media in industrial environments, but the emergence of immersive technologies like AR has altered the field. These advancements present unique opportunities for enhancing traditional teaching methods, especially in precision-demanding sectors like material forming in mechanical engineering. This paper seeks to explore these dynamics further, using MR (Fig. 2-a). Existing literature suggests that the adoption of immersive technologies like Augmented Reality and Mixed Reality in industrial and

<figure><img src="image_2179.png" /></figure>
# Effectiveness of machining equipment user guides: A comparative study of augmented reality and traditional media

GHOBRIAL Mina¹,³,a*, SEITIER Philippe¹,b, LAGARRIGUE Pierre³,c, GALAUP Michel²,d, and GILLES Patrick¹,de

¹ICA, Institut National des Sciences Appliquées de Toulouse, 135 Av. de Rangueil, 31400 Toulouse, France

²EFTS, Institut National Universitaire Champollion, Pl. de Verdun, 81000 Albi, France

³ICA, Institut National Universitaire Champollion, Pl. de Verdun, 81000 Albi, France

ªghobrial@insa-toulouse.fr, ᵇseitier@insa-toulouse.fr, ᶜpierre.lagarrigue@univ-jfc.fr,

d'michel.galaup@univ-jfc.fr, e'gilles@insa-toulouse.fr

**Keywords:** Augmented Reality, Instructions, Workload, Acceptability

**Abstract.** In the rapidly evolving landscape of manufacturing and material forming, innovative strategies are imperative for maintaining a competitive edge. Augmented Reality (AR) has emerged as a groundbreaking technology, offering new dimensions in how information is displayed and interacted with. It holds particular promise in the panel of instructional guides for complex machinery, potentially enhance traditional methods of knowledge transfer and operator training. Material forming, a key discipline within mechanical engineering, requires high-precision and skill, making it an ideal candidate for the integration of advanced instructional technologies like AR. This study aims to explore the efficiency of three distinct types of user manuals—video, paper, and augmented reality (AR)—on performance and acceptability in a material forming workshop environment. The focus will be on how AR can be specifically applied to improve task execution and understanding in material forming operations. Participants are mechanical engineering students specializing in material forming. They will engage in a series of standardized tasks related to machining processes. Performance will be gauged by metrics like task completion time and error rates, while task load will be assessed via the NASA Task Load Index (NASA-TLX) [1]. Acceptability of each manual type will be evaluated using the System Usability Scale (SUS) [2]. By comparing these various instructional formats, this research seeks to shed light on the most effective mediums for enhancing both operator performance and experience.

**Introduction**

The intersection of instructional technology and industrial training, particularly in the context of material forming, is an area of increasing interest for the industry and educational institutions. Immersive technologies—Augmented Reality (AR), Virtual Reality (VR), and Mixed Reality (MR)—particularly when applied to material forming and mechanical engineering, offer distinct advantages in enhancing traditional teaching methods. AR overlays digital information onto the real world, VR creates a fully immersive digital environment, and MR combines elements of both AR and VR, enabling interaction between virtual and real objects, based on Gandolfi's definition [3]. This study examines various types of instructional media to aid operators in efficiently using CNC machining equipment. There is a rich history of employing instructional media in industrial environments, but the emergence of immersive technologies like AR has altered the field. These advancements present unique opportunities for enhancing traditional teaching methods, especially in precision-demanding sectors like material forming in mechanical engineering. This paper seeks to explore these dynamics further, using MR (Fig. 2-a). Existing literature suggests that the adoption of immersive technologies like Augmented Reality and Mixed Reality in industrial and

<figure><img src="image_2170.png" /></figure>
educational settings offers substantial benefits in terms of enhancing learning experiences and operational efficiencies. These technologies have been found to improve visualization, control, and understanding of complex manufacturing systems, contributing to more effective training and skill development. AR, in particular, enables a more efficient execution of instructions by attaching virtual objects to real-world objects, streamlining the learning process. This feature is especially beneficial in fields such as material forming and CNC machining, where the integration of instructions with the physical workspace can significantly enhance the clarity and speed of task completion, leading to a more intuitive and effective training experience. This study begins with a comprehensive review of the existing literature, shedding light on the integration and efficacy of AR and other conventional instructional media in both industrial and educational settings. The experimental approach is then detailed, which involves mechanical engineering students undertaking a task on a CNC milling machine, guided by three distinct types of instructional media. The performance of these tools is assessed through various metrics.

## Literature Review

J. Butt [4] discusses the evolution and integration of additive manufacturing and Augmented Reality technologies. Stereolithography in the 1980s, focused on rapid prototyping using various materials. Over time, it expanded towards mass-scale production. AR technology, evolving since the 1960s, superimposes computer-generated images in real environments, enhancing user interaction. AR and additive manufacturing have increasingly intersected for AR's capability to superimpose virtual instructions onto physical workspaces, which significantly enhances task clarity and execution speed especially for complex material forming machines. Gonzalez-Franco et al. [5] explore the effectiveness of AR in complex manufacturing training, specifically in aircraft maintenance. Their study, involving 20 participants, compares immersive AR training with conventional face-to-face training methods. The research, utilizing a Mixed Reality setup with Head-Mounted Displays, found no significant difference in performance levels between the two training methods. This study underscores the potential of AR as a viable alternative to traditional training, offering insights into the application of collaborative Mixed Reality in transmitting procedural knowledge. In the context of additive manufacturing, the research by Ostrander et al. [6] explores the use of VR as an instructional tool. They investigate the effectiveness of VR in teaching introductory additive manufacturing concepts, comparing interactive and passive VR lessons. Their findings indicate that both forms of VR instruction can effectively convey technical concepts, with interactive VR showing advantages in enhancing self-efficacy. This study highlights the versatility of VR in educational settings and its potential in overcoming the limitations of traditional industrial training methods. Additionally, Mogessie et al. [7] address the demand for training in metals additive manufacturing machines, focusing on the EOS M290. Their approach involves an interactive VR training system, the 'AM Training Tutor', which demonstrates the utility of VR in specialized training scenarios. The ongoing development of a modular and generic version of this system suggests a future where VR training can be easily adapted for various machines, highlighting the scalability and customization potential of VR-based instructional technologies. A study by Botto et al. [8] focuses on the impact of AR on manual assembly operations in the manufacturing industry. Their research shows that AR-based assembly assistants can support key activities such as identification, handling, alignment, joining, adjustment, and inspection. They developed a tablet-based AR tool that integrates these activities and compared its effectiveness against traditional paper-based instructions. The study reveals that the AR tool generally reduces errors but increases the time needed for assembly, suggesting a trade-off between accuracy and efficiency [8]. The article by Sitko et al. [9] adds a new dimension to the existing literature by focusing specifically on the forging industry. It provides a comparative perspective between VR and AR, highlighting AR's practical applications and benefits in an industrial setting that faces unique challenges. This broadens the scope of this review by linking
educational settings offers substantial benefits in terms of enhancing learning experiences and operational efficiencies. These technologies have been found to improve visualization, control, and understanding of complex manufacturing systems, contributing to more effective training and skill development. AR, in particular, enables a more efficient execution of instructions by attaching virtual objects to real-world objects, streamlining the learning process. This feature is especially beneficial in fields such as material forming and CNC machining, where the integration of instructions with the physical workspace can significantly enhance the clarity and speed of task completion, leading to a more intuitive and effective training experience. This study begins with a comprehensive review of the existing literature, shedding light on the integration and efficacy of AR and other conventional instructional media in both industrial and educational settings. The experimental approach is then detailed, which involves mechanical engineering students undertaking a task on a CNC milling machine, guided by three distinct types of instructional media. The performance of these tools is assessed through various metrics.

## Literature Review

J. Butt [4] discusses the evolution and integration of additive manufacturing and Augmented Reality technologies. Stereolithography in the 1980s, focused on rapid prototyping using various materials. Over time, it expanded towards mass-scale production. AR technology, evolving since the 1960s, superimposes computer-generated images in real environments, enhancing user interaction. AR and additive manufacturing have increasingly intersected for AR's capability to superimpose virtual instructions onto physical workspaces, which significantly enhances task clarity and execution speed especially for complex material forming machines. Gonzalez-Franco et al. [5] explore the effectiveness of AR in complex manufacturing training, specifically in aircraft maintenance. Their study, involving 20 participants, compares immersive AR training with conventional face-to-face training methods. The research, utilizing a Mixed Reality setup with Head-Mounted Displays, found no significant difference in performance levels between the two training methods. This study underscores the potential of AR as a viable alternative to traditional training, offering insights into the application of collaborative Mixed Reality in transmitting procedural knowledge. In the context of additive manufacturing, the research by Ostrander et al. [6] explores the use of VR as an instructional tool. They investigate the effectiveness of VR in teaching introductory additive manufacturing concepts, comparing interactive and passive VR lessons. Their findings indicate that both forms of VR instruction can effectively convey technical concepts, with interactive VR showing advantages in enhancing self-efficacy. This study highlights the versatility of VR in educational settings and its potential in overcoming the limitations of traditional industrial training methods. Additionally, Mogessie et al. [7] address the demand for training in metals additive manufacturing machines, focusing on the EOS M290. Their approach involves an interactive VR training system, the 'AM Training Tutor', which demonstrates the utility of VR in specialized training scenarios. The ongoing development of a modular and generic version of this system suggests a future where VR training can be easily adapted for various machines, highlighting the scalability and customization potential of VR-based instructional technologies. A study by Botto et al. [8] focuses on the impact of AR on manual assembly operations in the manufacturing industry. Their research shows that AR-based assembly assistants can support key activities such as identification, handling, alignment, joining, adjustment, and inspection. They developed a tablet-based AR tool that integrates these activities and compared its effectiveness against traditional paper-based instructions. The study reveals that the AR tool generally reduces errors but increases the time needed for assembly, suggesting a trade-off between accuracy and efficiency [8]. The article by Sitko et al. [9] adds a new dimension to the existing literature by focusing specifically on the forging industry. It provides a comparative perspective between VR and AR, highlighting AR's practical applications and benefits in an industrial setting that faces unique challenges. This broadens the scope of this review by linking
AR not only to training and manufacturing but also to maintenance and operational efficiency in heavy industries. The work of Seitier et al. [10] focused onto the implementation of AR in mechanical engineering education, exploring its potential to enhance learning experiences. Meanwhile, Ghobrial et al. [11] conducted a specific study on the use of AR with a 3D printer as a simplified Additive Manufacturing machine, assessing its acceptability and success rate in an industrial context. This study builds upon previous works by adding a new dimension to the use of AR in mechanical engineering for both industrial and educational purposes. It conducts a comparative analysis throughout various study axes, offering an in-depth evaluation of how AR improves training performance. This contributes considerably to the existing knowledge on instructional technology in industrial and educational training.

## Experimental Setup

In this comparative study, the chosen procedure involves loading a new tool into a HURON VX8 machining center (Fig. 1). This process consists of three main stages, each involving a series of elementary actions (text entry, button pressing, door opening, etc.). The three main stages are the creation of the tool file, its allocation to a slot in the tool magazine, and the loading of the tool into the machine's tool slot. This is a procedure where students often make mistakes, leading to machine blockages. Therefore, developing an effective instructional support, meaning one that minimizes handling errors, is important. The experimental setup was carefully designed to evaluate the effectiveness of different educational supports (paper, video and Augmented Reality) to guide students during the loading of a new tool. Mechanical engineering students participated in this study. The setup involved the following key elements: (i) Participants were arbitrarily assigned to one of three stations, each one receiving a different type of instructional media: paper manual, video guide, or a AR headset equipped with an interactive scenario, (ii) before beginning the task, students completed a preliminary form providing general information such as their name, age, year in their mechanical engineering program, previous experience with CNC machines, and any prior experience with Head-Mounted Displays such as Virtual Reality headsets, (iii) the task assigned to each student was a tool load operation on a VX8 3-axis CNC machine. This procedure was chosen for its relevance to the usage of a typical CNC machine that is common in mechanical engineering discipline and has a specific protocol to each machine, (iv) a specific indication was given to the students, instructing them to seek the supervisor's help only if they were completely blocked at any step of the procedure. The supervisor was also responsible for intervening if a student was engaged in any action that could be dangerous or potentially damaging to the equipment. The frequency of such interventions was recorded for each participant, (v) the timing for each student's task was recorded. The clock started as soon as the participant finished filling out the initial form and stopped upon the completion of the tool load procedure.

A total of 96 mechanical engineering students, aged between 18 and 24 years old, participated in the experiment. These students represented various stages of their academic journey, ranging from the first year to the fourth year of their program. Students were evenly distributed across the different instructional media. This diverse and balanced participation ensured a comprehensive assessment of each instructional medium's effectiveness. Additionally, to ensure the integrity of the study's results, each student participated in the experiment only once, using one type of instructional media. This approach prevented any learning or familiarity effects from repeated exposure to the task, thus maintaining the validity of the comparative analysis between the different instructional media.

## Instructional media

The three instructional media used in this study were carefully selected and designed to offer a diverse range of learning experiences: (i) The paper guide consisted of the official constructor's user guide for executing the tool load task. The guide provided step-by-step instructions, along
AR not only to training and manufacturing but also to maintenance and operational efficiency in heavy industries. The work of Seitier et al. [10] focused onto the implementation of AR in mechanical engineering education, exploring its potential to enhance learning experiences. Meanwhile, Ghobrial et al. [11] conducted a specific study on the use of AR with a 3D printer as a simplified Additive Manufacturing machine, assessing its acceptability and success rate in an industrial context. This study builds upon previous works by adding a new dimension to the use of AR in mechanical engineering for both industrial and educational purposes. It conducts a comparative analysis throughout various study axes, offering an in-depth evaluation of how AR improves training performance. This contributes considerably to the existing knowledge on instructional technology in industrial and educational training.

## Experimental Setup

In this comparative study, the chosen procedure involves loading a new tool into a HURON VX8 machining center (Fig. 1). This process consists of three main stages, each involving a series of elementary actions (text entry, button pressing, door opening, etc.). The three main stages are the creation of the tool file, its allocation to a slot in the tool magazine, and the loading of the tool into the machine's tool slot. This is a procedure where students often make mistakes, leading to machine blockages. Therefore, developing an effective instructional support, meaning one that minimizes handling errors, is important. The experimental setup was carefully designed to evaluate the effectiveness of different educational supports (paper, video and Augmented Reality) to guide students during the loading of a new tool. Mechanical engineering students participated in this study. The setup involved the following key elements: (i) Participants were arbitrarily assigned to one of three stations, each one receiving a different type of instructional media: paper manual, video guide, or a AR headset equipped with an interactive scenario, (ii) before beginning the task, students completed a preliminary form providing general information such as their name, age, year in their mechanical engineering program, previous experience with CNC machines, and any prior experience with Head-Mounted Displays such as Virtual Reality headsets, (iii) the task assigned to each student was a tool load operation on a VX8 3-axis CNC machine. This procedure was chosen for its relevance to the usage of a typical CNC machine that is common in mechanical engineering discipline and has a specific protocol to each machine, (iv) a specific indication was given to the students, instructing them to seek the supervisor's help only if they were completely blocked at any step of the procedure. The supervisor was also responsible for intervening if a student was engaged in any action that could be dangerous or potentially damaging to the equipment. The frequency of such interventions was recorded for each participant, (v) the timing for each student's task was recorded. The clock started as soon as the participant finished filling out the initial form and stopped upon the completion of the tool load procedure.

A total of 96 mechanical engineering students, aged between 18 and 24 years old, participated in the experiment. These students represented various stages of their academic journey, ranging from the first year to the fourth year of their program. Students were evenly distributed across the different instructional media. This diverse and balanced participation ensured a comprehensive assessment of each instructional medium's effectiveness. Additionally, to ensure the integrity of the study's results, each student participated in the experiment only once, using one type of instructional media. This approach prevented any learning or familiarity effects from repeated exposure to the task, thus maintaining the validity of the comparative analysis between the different instructional media.

## Instructional media

The three instructional media used in this study were carefully selected and designed to offer a diverse range of learning experiences: (i) The paper guide consisted of the official constructor's user guide for executing the tool load task. The guide provided step-by-step instructions, along
with diagrams and safety precautions. It was intended to replicate a traditional learning method, where students rely on written documentation to understand and perform the procedure, (ii) the video guide consists of a comprehensive video was prepared by the shop's teachers and technicians, demonstrating the same tool load procedure as outlined in the paper manual. This video, displayed on a tablet at the respective station (Fig. 1), allowed students to visually follow the process in a sequential manner. The video aimed to provide a more dynamic and engaging learning experience compared to the static paper guide, potentially catering to students who learn better through visual demonstrations.

<figure><img src="image_2180.png" /><figcaption>Figure 1 - Student using video support</figcaption></figure>

(ii) For the Augmented Reality guide, a Microsoft Hololens 2 headset was used (Fig. 2-a), the integrated application was developed using Unity, a development platform. The AR guide creation process does not solely depend on Unity, some alternatives such as Unreal Engine could serve as a development solution. Vuforia Studio is another alternative that provides an off-the-shelf solution for AR development. Diota is an additional option that could be explored, offering AR tools for industrial sectors. The AR guide featured virtual objects that were superimposed onto the real-world environment of the CNC machine (Fig. 2-b) and a hand-attached menu (Fig. 2-c), in each step of the procedure. Some 3D models were integrated into the virtual scene. While pointing arrows were sourced from the Unity Asset Store, which offers a wide range of ready-made models and prefabs, other models were obtained directly from the makers, such as the Huron VX8 CNC machine's digital model. The tool holder, was custom-modeled using 3DExperience software to match the used tool holders. The hand-attached menu and hand coaches, which are interactive tools designed to facilitate user interaction within the AR environment, utilized Mixed Reality Toolkit (MRTK) prefabs. MRTK is a collection of scripts and components intended to accelerate the development of mixed reality applications. This interactive scenario was designed to guide students through the tool load process in an immersive way. Additionally, voice instructions were integrated to assist students who might have difficulty reading or following written instructions, due to the current state of the art of the AR hardware.
with diagrams and safety precautions. It was intended to replicate a traditional learning method, where students rely on written documentation to understand and perform the procedure, (ii) the video guide consists of a comprehensive video was prepared by the shop's teachers and technicians, demonstrating the same tool load procedure as outlined in the paper manual. This video, displayed on a tablet at the respective station (Fig. 1), allowed students to visually follow the process in a sequential manner. The video aimed to provide a more dynamic and engaging learning experience compared to the static paper guide, potentially catering to students who learn better through visual demonstrations.

<figure><img src="image_2171.png" /><figcaption>Figure 1 - Student using video support</figcaption></figure>

(ii) For the Augmented Reality guide, a Microsoft Hololens 2 headset was used (Fig. 2-a), the integrated application was developed using Unity, a development platform. The AR guide creation process does not solely depend on Unity, some alternatives such as Unreal Engine could serve as a development solution. Vuforia Studio is another alternative that provides an off-the-shelf solution for AR development. Diota is an additional option that could be explored, offering AR tools for industrial sectors. The AR guide featured virtual objects that were superimposed onto the real-world environment of the CNC machine (Fig. 2-b) and a hand-attached menu (Fig. 2-c), in each step of the procedure. Some 3D models were integrated into the virtual scene. While pointing arrows were sourced from the Unity Asset Store, which offers a wide range of ready-made models and prefabs, other models were obtained directly from the makers, such as the Huron VX8 CNC machine's digital model. The tool holder, was custom-modeled using 3DExperience software to match the used tool holders. The hand-attached menu and hand coaches, which are interactive tools designed to facilitate user interaction within the AR environment, utilized Mixed Reality Toolkit (MRTK) prefabs. MRTK is a collection of scripts and components intended to accelerate the development of mixed reality applications. This interactive scenario was designed to guide students through the tool load process in an immersive way. Additionally, voice instructions were integrated to assist students who might have difficulty reading or following written instructions, due to the current state of the art of the AR hardware.
<figure><img src="image_2181.png" /><figcaption>Figure 2 - Student using AR support</figcaption></figure>

Each of these instructional media was designed to cater to different learning tools and to evaluate the effectiveness of traditional media versus Augmented Reality in a mechanical engineering setting. The comparative study aims to assess not only the students' acceptability of each medium but also the students' efficiency, autonomy and comfort levels with each type of learning resource.

## Results and discussion

The performance outcomes of the three instructional tools is analyzed, emphasizing their impact on user engagement and productivity. A range of established metrics is utilized to assess aspects such as usability, task load, dependence, and task execution time. These metrics serve as a quantitative basis for comparison and shed light on the subjective user experiences. The examination of these results provides insights into the advantages and drawbacks of each tool. The following part details the methodologies behind each metric and the interpretation of the data: (i) System Usability Scale (SUS): The SUS is a simple, ten-item scale giving a global view of subjective assessments of usability. Each item is scored on a scale of 1 to 5, where 1 represents the lowest usability and 5 represents the highest, with alternating positive and negative connotations for the questions in order to keep the users' attention throughout the questions. The scores are converted to a 0-100 scale for easier interpretation, with 100 representing the best possible usability. Thus, a higher SUS score indicates better usability, (ii) NASA Task Load Index (NASA-TLX): The NASA-TLX is a widely-used, subjective workload assessment tool that rates perceived workload in order to assess a task, system, or team's effectiveness or other aspects of performance. It measures workload on a scale from 1 to 20, where 1 indicates no workload and 20 indicates an extremely high workload. Contrary to SUS, a higher score on the NASA-TLX indicates a higher load and, typically, a more negative impact on performance, (iii) dependence in this context is measured by the number of times a supervisor intervened. Fewer interventions indicate that the user can work more independently, which is considered better, (iv) task execution time is measured in order to evaluate efficiency, the lower the time required to execute the task, the more efficient the process. The paper guide demonstrates the highest dispersion in usability (Fig. 3-a) and task execution time (Fig. 3-b), suggesting inconsistent performance among users. Its lower peak in all
<figure><img src="image_2172.png" /><figcaption>Figure 2 - Student using AR support</figcaption></figure>

Each of these instructional media was designed to cater to different learning tools and to evaluate the effectiveness of traditional media versus Augmented Reality in a mechanical engineering setting. The comparative study aims to assess not only the students' acceptability of each medium but also the students' efficiency, autonomy and comfort levels with each type of learning resource.

## Results and discussion

The performance outcomes of the three instructional tools is analyzed, emphasizing their impact on user engagement and productivity. A range of established metrics is utilized to assess aspects such as usability, task load, dependence, and task execution time. These metrics serve as a quantitative basis for comparison and shed light on the subjective user experiences. The examination of these results provides insights into the advantages and drawbacks of each tool. The following part details the methodologies behind each metric and the interpretation of the data: (i) System Usability Scale (SUS): The SUS is a simple, ten-item scale giving a global view of subjective assessments of usability. Each item is scored on a scale of 1 to 5, where 1 represents the lowest usability and 5 represents the highest, with alternating positive and negative connotations for the questions in order to keep the users' attention throughout the questions. The scores are converted to a 0-100 scale for easier interpretation, with 100 representing the best possible usability. Thus, a higher SUS score indicates better usability, (ii) NASA Task Load Index (NASA-TLX): The NASA-TLX is a widely-used, subjective workload assessment tool that rates perceived workload in order to assess a task, system, or team's effectiveness or other aspects of performance. It measures workload on a scale from 1 to 20, where 1 indicates no workload and 20 indicates an extremely high workload. Contrary to SUS, a higher score on the NASA-TLX indicates a higher load and, typically, a more negative impact on performance, (iii) dependence in this context is measured by the number of times a supervisor intervened. Fewer interventions indicate that the user can work more independently, which is considered better, (iv) task execution time is measured in order to evaluate efficiency, the lower the time required to execute the task, the more efficient the process. The paper guide demonstrates the highest dispersion in usability (Fig. 3-a) and task execution time (Fig. 3-b), suggesting inconsistent performance among users. Its lower peak in all
metrics may indicate technological limitations, such as the lack of interactivity and real-time support, which could impede user performance and learning. The video guide shows a narrower dispersion, particularly in usability (Fig. 3-a) and dependence (Fig. 3-d), indicating more consistent performance. Its higher peaks suggest that video is more user-friendly and supports greater independence, possibly due to clear visual instructions and the ability to replay content. AR presents a significant time efficiency advantage with a peak similar to video, but with wider dispersion. This could imply that while AR can be highly effective, its performance fluctuates considerably among users, potentially due to ergonomic challenges or inconsistent technological maturity of AR devices. Its higher peak in dependence, relative to video, suggests that the used AR device may require more user effort or support to complete tasks independently.

<figure><img src="image_2182.png" /><figcaption>Figure 3 – Usability (a), Task Load (b), Task Execution Time (c) and Dependence (d) normal distributions</figcaption></figure>

In order to establish a basis for comparison, all metrics but SUS scores were recalculated as percentages, with higher values indicating more positive tool performance. Here's an explanation of how each of these indicators are calculated: (i) System Usability Scale (SUS): The scores are converted to a 0-100 scale for easier interpretation, with 100 representing the best possible usability. Thus, a higher SUS score indicates better usability. Similarly, other indicators have been recalibrated to the same 0-100 scale to ensure uniformity and ease of comparison, (ii) NASA Task Load Index (NASA-TLX): For this indicator, the scores have been inverted and converted to a 0-100 scale for consistency in presentation, the metric will be called Task Ease (Eq. 1).

$$Task\ Ease\ % = (1 - \frac{\text{NASA-TLX score} - 1}{19}) \times 100 \qquad (1)$$

(iii) This indicator was calculated by normalizing the actual number of times the supervisor intervened (dependence) against the range of observed number of times, with the lowest recorded number of times set as a reference point for 100% autonomy and the highest recorded number of times set as a reference point for 0% autonomy (Eq. 2).
metrics may indicate technological limitations, such as the lack of interactivity and real-time support, which could impede user performance and learning. The video guide shows a narrower dispersion, particularly in usability (Fig. 3-a) and dependence (Fig. 3-d), indicating more consistent performance. Its higher peaks suggest that video is more user-friendly and supports greater independence, possibly due to clear visual instructions and the ability to replay content. AR presents a significant time efficiency advantage with a peak similar to video, but with wider dispersion. This could imply that while AR can be highly effective, its performance fluctuates considerably among users, potentially due to ergonomic challenges or inconsistent technological maturity of AR devices. Its higher peak in dependence, relative to video, suggests that the used AR device may require more user effort or support to complete tasks independently.

<figure><img src="image_2173.png" /><figcaption>Figure 3 – Usability (a), Task Load (b), Task Execution Time (c) and Dependence (d) normal distributions</figcaption></figure>

In order to establish a basis for comparison, all metrics but SUS scores were recalculated as percentages, with higher values indicating more positive tool performance. Here's an explanation of how each of these indicators are calculated: (i) System Usability Scale (SUS): The scores are converted to a 0-100 scale for easier interpretation, with 100 representing the best possible usability. Thus, a higher SUS score indicates better usability. Similarly, other indicators have been recalibrated to the same 0-100 scale to ensure uniformity and ease of comparison, (ii) NASA Task Load Index (NASA-TLX): For this indicator, the scores have been inverted and converted to a 0-100 scale for consistency in presentation, the metric will be called Task Ease (Eq. 1).

$$Task\ Ease\ % = (1 - \frac{\text{NASA-TLX score} - 1}{19}) \times 100 \qquad (1)$$

(iii) This indicator was calculated by normalizing the actual number of times the supervisor intervened (dependence) against the range of observed number of times, with the lowest recorded number of times set as a reference point for 100% autonomy and the highest recorded number of times set as a reference point for 0% autonomy (Eq. 2).
$$Autonomy \% = \left(1 - \frac{\text{Number of times of intervention}}{\text{Highest Number} - \text{Lowest Number}}\right) \times 100 \qquad (2)$$

(iv) To create a consistent indicator, task execution time will also be converted to a positive percentage metric, with 100% being the most efficient. This percentage was also calculated by normalizing the actual task times against the range of observed times, with the lowest recorded task time set as a reference point for 100% efficiency and the highest recorded time set as a reference point for 0% efficiency (Eq. 3).

$$Efficiency \% = \left(1 - \frac{\text{Task Time} - \text{Best Time}}{\text{Worst Time} - \text{Best Time}}\right) \times 100 \qquad (3)$$

By inverting Task Load scale and normalizing the others, the study presents all the metrics on a consistent scale where a higher percentage always indicates a better outcome. This approach simplifies the comparison of different instructional tools across various performance metrics. The radar chart (Fig. 4) visually encapsulates the reported findings, plotting the performance of paper, video, and AR tools along axes that represent key metrics: Usability (as measured by the System Usability Scale), Task Ease (derived from the NASA-TLX score), Efficiency, and Autonomy. On the chart, video appears to offer a balanced performance across all metrics, scoring particularly high in usability and autonomy, indicating it is user-friendly and supports independent learning. Augmented Reality shows a notable efficiency advantage, potentially due to its interactive and engaging nature. However, it does not reach the same level of performance in autonomy, which may reflect the current ergonomic and technological maturity issues previously discussed. Paper scores the lowest across most metrics, particularly in efficiency and usability, suggesting that it is the least effective tool among the three for this application.

<figure><img src="image_2183.png" /><figcaption>Figure 4 - Tool Performance Radar Representation</figcaption></figure>

The findings suggest that Augmented Reality has the potential to enhance efficiency in learning environments. However, students that were assigned the AR headset reported several issues that may affect its practicality. These included difficulty with visibility due to lighting conditions and challenges with focus and accommodation, making reading instructions problematic for some. Additionally, the physical weight of the headset was noticeable to some users. The most common
$$Autonomy \% = \left(1 - \frac{\text{Number of times of intervention}}{\text{Highest Number} - \text{Lowest Number}}\right) \times 100 \qquad (2)$$

(iv) To create a consistent indicator, task execution time will also be converted to a positive percentage metric, with 100% being the most efficient. This percentage was also calculated by normalizing the actual task times against the range of observed times, with the lowest recorded task time set as a reference point for 100% efficiency and the highest recorded time set as a reference point for 0% efficiency (Eq. 3).

$$Efficiency \% = \left(1 - \frac{\text{Task Time} - \text{Best Time}}{\text{Worst Time} - \text{Best Time}}\right) \times 100 \qquad (3)$$

By inverting Task Load scale and normalizing the others, the study presents all the metrics on a consistent scale where a higher percentage always indicates a better outcome. This approach simplifies the comparison of different instructional tools across various performance metrics. The radar chart (Fig. 4) visually encapsulates the reported findings, plotting the performance of paper, video, and AR tools along axes that represent key metrics: Usability (as measured by the System Usability Scale), Task Ease (derived from the NASA-TLX score), Efficiency, and Autonomy. On the chart, video appears to offer a balanced performance across all metrics, scoring particularly high in usability and autonomy, indicating it is user-friendly and supports independent learning. Augmented Reality shows a notable efficiency advantage, potentially due to its interactive and engaging nature. However, it does not reach the same level of performance in autonomy, which may reflect the current ergonomic and technological maturity issues previously discussed. Paper scores the lowest across most metrics, particularly in efficiency and usability, suggesting that it is the least effective tool among the three for this application.

<figure><img src="image_2174.png" /><figcaption>Figure 4 - Tool Performance Radar Representation</figcaption></figure>

The findings suggest that Augmented Reality has the potential to enhance efficiency in learning environments. However, students that were assigned the AR headset reported several issues that may affect its practicality. These included difficulty with visibility due to lighting conditions and challenges with focus and accommodation, making reading instructions problematic for some. Additionally, the physical weight of the headset was noticeable to some users. The most common
feedback related to hand tracking and interaction with the system's buttons; students familiar with VR or who adapted quickly experienced fewer issues, highlighting a learning curve and adaptation factor in the effective use of AR for educational purposes. These interpretations align with the discussed results, indicating that while AR is promising for efficiency, video guides currently offer a more user-friendly and autonomous experience, and paper guides lag behind in these metrics, likely due to their static nature and lack of interactive features.

## Conclusion

The results further emphasize that the Augmented Reality technology, while promising, may still be facing challenges due to its current level of technological maturity. The efficiency advantage of AR as indicated in the graphs suggests it has significant potential for instructional use. However, the higher number of supervisor interventions required as compared to video guides could be indicative of ergonomics-related problems with the current state-of-the-art AR hardware in this application. These ergonomic challenges could stem from issues like user discomfort due to the weight or fit of the AR headset, interface complexity, or limitations in the user interaction design, which can hinder the learning process and require additional external guidance. Moreover, the lack of technological maturity might manifest in the form of less intuitive user experiences or technical reliability issues, which could explain why AR did not score as well as video in terms of autonomy. To summarize, the results suggest that while AR is an efficient medium, it may not yet provide the seamless and independent learning experience that more mature technologies like video can offer due to ergonomic and maturity-related limitations. These findings would likely be in line with discussions in the article's literature review, which have touched upon the current technological and ergonomic barriers that AR needs to overcome to achieve broader adoption and effectiveness in educational settings. It's important to note that AR technology, while showing promise, must undergo further exploration and testing using diverse mediums and devices. Further applications of AR in mechanical engineering training will be tested. This includes, on one hand, the creation of new applications for other types of machinery such as tool measurement benches, and on the other hand, the transposition of existing AR applications into tablet-based AR. In particular, the integration of AR in tablet mediums may effectively blend the advantages of video and AR, potentially offering an optimized balance of user-friendliness and interactive efficiency. This approach aims to harness the strengths of each medium to enhance the overall learning experience.

## References

[1] S. G. Hart and L. E. Staveland, "Development of NASA-TLX (Task Load Index): Results of Empirical and Theoretical Research," in Advances in Psychology, vol. 52, Elsevier, 1988, pp. 139-183. doi: 10.1016/S0166-4115(08)62386-9

[2] A. Bangor, P. Kortum, and J. Miller, "Determining What Individual SUS Scores Mean: Adding an Adjective Rating Scale," J. Usability Studies, vol. 4, no. 3, pp. 114-123, May 2009.

[3] E. Gandolfi, "Virtual Reality and Augmented Reality," 2018, pp. 545-561.

[4] J. Butt, "Exploring the Interrelationship between Additive Manufacturing and Industry 4.0," Designs, vol. 4, no. 2, p. 13, Jun. 2020. https://doi.org/10.3390/designs4020013

[5] M. Gonzalez-Franco, R. Pizzaro, J. Cermeron, K. Li, J. Thorn, W. Hutabarat, A. Tiwari, and P. Bermell-Garcia, "Immersive Mixed Reality for Manufacturing Training," Front. Robot. AI, vol. 4, Feb. 2017. https://doi.org/10.3389/frobt.2017.00003

[6] J. K. Ostrander, C. S. Tucker, T. W. Simpson, and N. A. Meisel, "Evaluating the Use of Virtual Reality to Teach Introductory Concepts of Additive Manufacturing," Journal of Mechanical Design, vol. 142, no. 5, p. 051702, May 2020. https://doi.org/10.1115/1.4044006
feedback related to hand tracking and interaction with the system's buttons; students familiar with VR or who adapted quickly experienced fewer issues, highlighting a learning curve and adaptation factor in the effective use of AR for educational purposes. These interpretations align with the discussed results, indicating that while AR is promising for efficiency, video guides currently offer a more user-friendly and autonomous experience, and paper guides lag behind in these metrics, likely due to their static nature and lack of interactive features.

## Conclusion

The results further emphasize that the Augmented Reality technology, while promising, may still be facing challenges due to its current level of technological maturity. The efficiency advantage of AR as indicated in the graphs suggests it has significant potential for instructional use. However, the higher number of supervisor interventions required as compared to video guides could be indicative of ergonomics-related problems with the current state-of-the-art AR hardware in this application. These ergonomic challenges could stem from issues like user discomfort due to the weight or fit of the AR headset, interface complexity, or limitations in the user interaction design, which can hinder the learning process and require additional external guidance. Moreover, the lack of technological maturity might manifest in the form of less intuitive user experiences or technical reliability issues, which could explain why AR did not score as well as video in terms of autonomy. To summarize, the results suggest that while AR is an efficient medium, it may not yet provide the seamless and independent learning experience that more mature technologies like video can offer due to ergonomic and maturity-related limitations. These findings would likely be in line with discussions in the article's literature review, which have touched upon the current technological and ergonomic barriers that AR needs to overcome to achieve broader adoption and effectiveness in educational settings. It's important to note that AR technology, while showing promise, must undergo further exploration and testing using diverse mediums and devices. Further applications of AR in mechanical engineering training will be tested. This includes, on one hand, the creation of new applications for other types of machinery such as tool measurement benches, and on the other hand, the transposition of existing AR applications into tablet-based AR. In particular, the integration of AR in tablet mediums may effectively blend the advantages of video and AR, potentially offering an optimized balance of user-friendliness and interactive efficiency. This approach aims to harness the strengths of each medium to enhance the overall learning experience.

## References

[1] S. G. Hart and L. E. Staveland, "Development of NASA-TLX (Task Load Index): Results of Empirical and Theoretical Research," in Advances in Psychology, vol. 52, Elsevier, 1988, pp. 139-183. doi: 10.1016/S0166-4115(08)62386-9

[2] A. Bangor, P. Kortum, and J. Miller, "Determining What Individual SUS Scores Mean: Adding an Adjective Rating Scale," J. Usability Studies, vol. 4, no. 3, pp. 114-123, May 2009.

[3] E. Gandolfi, "Virtual Reality and Augmented Reality," 2018, pp. 545-561.

[4] J. Butt, "Exploring the Interrelationship between Additive Manufacturing and Industry 4.0," Designs, vol. 4, no. 2, p. 13, Jun. 2020. https://doi.org/10.3390/designs4020013

[5] M. Gonzalez-Franco, R. Pizzaro, J. Cermeron, K. Li, J. Thorn, W. Hutabarat, A. Tiwari, and P. Bermell-Garcia, "Immersive Mixed Reality for Manufacturing Training," Front. Robot. AI, vol. 4, Feb. 2017. https://doi.org/10.3389/frobt.2017.00003

[6] J. K. Ostrander, C. S. Tucker, T. W. Simpson, and N. A. Meisel, "Evaluating the Use of Virtual Reality to Teach Introductory Concepts of Additive Manufacturing," Journal of Mechanical Design, vol. 142, no. 5, p. 051702, May 2020. https://doi.org/10.1115/1.4044006
[7] M. Mogessie, S. D. Wolf, M. Barbosa, N. Jones, and B. M. McLaren, “Work-in-Progress—A Generalizable Virtual Reality Training and Intelligent Tutor for Additive Manufacturing,” in 2020 6th International Conference of the Immersive Learning Research Network (iLRN), San Luis Obispo, CA, USA: IEEE, Jun. 2020, pp. 355–358. doi: 10.23919/iLRN47897.2020.9155119

[8] C. Botto, A. Cannavo, D. Cappuccio, G. Morat, A. N. Sarvestani, P. Ricci, V. Demarchi, and A. Saturnino, “Augmented Reality for the Manufacturing Industry: The Case of an Assembly Assistant,” in 2020 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), Atlanta, GA, USA: IEEE, Mar. 2020, pp. 299–304. doi: 10.1109/VRW50115.2020.00068

[9] M. Sitko, B. Wesołowski, J. Adamus, Ł. Lisiecki, K. Piotrowska-Madej, and L. Madej, “Perceptive review of augmented reality applications and their outlooks in the forging industry,” cmms, vol. 20, no. 2, p. 72, 2020. https://doi.org/10.7494/cmms.2020.2.0656

[10] P. Seitier, P. Gilles, V. Boudier, M. Galaup, and P. Lagarrigue, “Getting started procedure of a NC machine simplified by the use of a mixed-reality training scenario,” MATEC Web Conf., vol. 368, p. 01018, 2022. https://doi.org/10.1051/matecconf/202236801018

[11] M. Ghobrial, P. Seitier, M. Galaup, P. Lagarrigue, and P. Gilles, “Simplification of an Additive Manufacturing Machine Implementation Using Its CAD Model and Mixed-Reality,” in Advances in Additive Manufacturing: Materials, Processes and Applications, T. Mabrouki, H. Sahlaoui, H. Sallem, F. Ghanem, and N. Benyahya, Eds., in Lecture Notes in Mechanical Engineering., Cham: Springer Nature Switzerland, 2024, pp. 100–106. doi: 10.1007/978-3-031-47784-3_13
[7] M. Mogessie, S. D. Wolf, M. Barbosa, N. Jones, and B. M. McLaren, “Work-in-Progress—A Generalizable Virtual Reality Training and Intelligent Tutor for Additive Manufacturing,” in 2020 6th International Conference of the Immersive Learning Research Network (iLRN), San Luis Obispo, CA, USA: IEEE, Jun. 2020, pp. 355–358. doi: 10.23919/iLRN47897.2020.9155119

[8] C. Botto, A. Cannavo, D. Cappuccio, G. Morat, A. N. Sarvestani, P. Ricci, V. Demarchi, and A. Saturnino, “Augmented Reality for the Manufacturing Industry: The Case of an Assembly Assistant,” in 2020 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), Atlanta, GA, USA: IEEE, Mar. 2020, pp. 299–304. doi: 10.1109/VRW50115.2020.00068

[9] M. Sitko, B. Wesołowski, J. Adamus, Ł. Lisiecki, K. Piotrowska-Madej, and L. Madej, “Perceptive review of augmented reality applications and their outlooks in the forging industry,” cmms, vol. 20, no. 2, p. 72, 2020. https://doi.org/10.7494/cmms.2020.2.0656

[10] P. Seitier, P. Gilles, V. Boudier, M. Galaup, and P. Lagarrigue, “Getting started procedure of a NC machine simplified by the use of a mixed-reality training scenario,” MATEC Web Conf., vol. 368, p. 01018, 2022. https://doi.org/10.1051/matecconf/202236801018

[11] M. Ghobrial, P. Seitier, M. Galaup, P. Lagarrigue, and P. Gilles, “Simplification of an Additive Manufacturing Machine Implementation Using Its CAD Model and Mixed-Reality,” in Advances in Additive Manufacturing: Materials, Processes and Applications, T. Mabrouki, H. Sahlaoui, H. Sallem, F. Ghanem, and N. Benyahya, Eds., in Lecture Notes in Mechanical Engineering., Cham: Springer Nature Switzerland, 2024, pp. 100–106. doi: 10.1007/978-3-031-47784-3_13
# Accurate 3D modeling of laser-matter interaction in the AFP process by a conductive-radiative FEM approach

STORTI Bruno A.¹,ᵃ*, LE REUN Adrien¹,ᵇ, LE CORRE Steven¹,ᶜ

¹ Nantes Université, CNRS, LTEN, UMR 6607, La Chantrerie, Rue Christian Pauc, Nantes, 44200, Pays de la Loire, France

ᵃbruno.storti@univ-nantes.fr, ᵇadrien.le-reun@univ-nantes.fr, ᶜsteven.lecorre@univ-nantes.fr

**Keywords:** AFP, Conductive-Radiative Heat Transfer, Finite Elements

**Abstract.** Mainly driven by aeronautical demands, the Automated Fiber Placement (AFP) process has become pivotal in the in-situ manufacturing of intricate, high-performance composite components. AFP relies on robotic systems to meticulously lay continuous fiber-reinforced materials, employing controlled pressure and precise laser heating. Accurate thermal modeling is imperative to predict thermal effects impacting contact, adhesion, crystallinity, and residual constraints. This work introduces a novel numerical approach for efficient modeling the transient heat transfers in the AFP process using a coupled conductive-radiative finite element method (FEM) scheme. Radiative density from the laser-matter interaction is determined through an in-house parallelized FreeFEM++ code. Heat transfer at the micro-scale is assessed by using an artificial computational geometry based on fiber distributions obtained from tape micrograph. A parametric study with varying absorption coefficients of the carbon fibers is performed to accurately compute the radiative volumetric heat source. The proposed approach investigates various 2D and 3D scenarios involving different laser parameters. Results exhibit strong agreement with experimentally obtained data, showing a maximum temperature difference of 5-6°C at the end of the heating phase. Furthermore, a 3D case demonstrates the potential of this approach for modeling complex micro-scale geometries.

**Introduction**

The Automated Fiber Placement (AFP) is an established manufacturing process to efficiently produce large and complex high-performance composite parts featuring high strength-to-weight ratios, a characteristic which is highly demanded by the aeronautic industry, among others. The AFP is a layer-by-layer in-situ manufacturing technique which mainly consists in rapidly heating both the new layer of the tape and the substrate composite materials with a laser source to reach temperatures above the thermoplastic matrix melting point. This heating stage is followed by a rapid cooling stage where a controlled pressure is applied between the already deposed tape and the substrate to achieve a proper material consolidation.

Among the multiple physics involved during such a complex manufacturing procedure, the numerical modelling of the heat transfer is the most crucial and challenging one, since an accurate prediction of the thermal history is necessary for the proper modelling of factors such as intimate contact, autohesion, residual stress, and crystallinity during consolidation [1,2]. Several numerical approaches have been proposed in the literature for heat transfer modelling in the AFP context. For instance, in the work of [3] a surface-to-surface heat transfer radiation model was developed in Matlab for 3D surfaces where the laser diode and tape were discretized in a finite number of differential areas, and the energy exchanged was computed depending on their sizes, separation distance, and orientation angle. Consequently, the computed heat flux is applied as a boundary condition at the tape surface in a 2D transient heat conduction model. In the thesis work of [4], a comprehensive 2D transient heat conduction model was developed in COMSOL accounting for the roller, the laying tape, the substrate, and the tool, while the laser beam was modeled by a heat

<figure><img src="image_2184.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
# Accurate 3D modeling of laser-matter interaction in the AFP process by a conductive-radiative FEM approach

STORTI Bruno A.¹,ᵃ*, LE REUN Adrien¹,ᵇ, LE CORRE Steven¹,ᶜ

¹ Nantes Université, CNRS, LTEN, UMR 6607, La Chantrerie, Rue Christian Pauc, Nantes, 44200, Pays de la Loire, France

ᵃbruno.storti@univ-nantes.fr, ᵇadrien.le-reun@univ-nantes.fr, ᶜsteven.lecorre@univ-nantes.fr

**Keywords:** AFP, Conductive-Radiative Heat Transfer, Finite Elements

**Abstract.** Mainly driven by aeronautical demands, the Automated Fiber Placement (AFP) process has become pivotal in the in-situ manufacturing of intricate, high-performance composite components. AFP relies on robotic systems to meticulously lay continuous fiber-reinforced materials, employing controlled pressure and precise laser heating. Accurate thermal modeling is imperative to predict thermal effects impacting contact, adhesion, crystallinity, and residual constraints. This work introduces a novel numerical approach for efficient modeling the transient heat transfers in the AFP process using a coupled conductive-radiative finite element method (FEM) scheme. Radiative density from the laser-matter interaction is determined through an in-house parallelized FreeFEM++ code. Heat transfer at the micro-scale is assessed by using an artificial computational geometry based on fiber distributions obtained from tape micrograph. A parametric study with varying absorption coefficients of the carbon fibers is performed to accurately compute the radiative volumetric heat source. The proposed approach investigates various 2D and 3D scenarios involving different laser parameters. Results exhibit strong agreement with experimentally obtained data, showing a maximum temperature difference of 5-6°C at the end of the heating phase. Furthermore, a 3D case demonstrates the potential of this approach for modeling complex micro-scale geometries.

**Introduction**

The Automated Fiber Placement (AFP) is an established manufacturing process to efficiently produce large and complex high-performance composite parts featuring high strength-to-weight ratios, a characteristic which is highly demanded by the aeronautic industry, among others. The AFP is a layer-by-layer in-situ manufacturing technique which mainly consists in rapidly heating both the new layer of the tape and the substrate composite materials with a laser source to reach temperatures above the thermoplastic matrix melting point. This heating stage is followed by a rapid cooling stage where a controlled pressure is applied between the already deposed tape and the substrate to achieve a proper material consolidation.

Among the multiple physics involved during such a complex manufacturing procedure, the numerical modelling of the heat transfer is the most crucial and challenging one, since an accurate prediction of the thermal history is necessary for the proper modelling of factors such as intimate contact, autohesion, residual stress, and crystallinity during consolidation [1,2]. Several numerical approaches have been proposed in the literature for heat transfer modelling in the AFP context. For instance, in the work of [3] a surface-to-surface heat transfer radiation model was developed in Matlab for 3D surfaces where the laser diode and tape were discretized in a finite number of differential areas, and the energy exchanged was computed depending on their sizes, separation distance, and orientation angle. Consequently, the computed heat flux is applied as a boundary condition at the tape surface in a 2D transient heat conduction model. In the thesis work of [4], a comprehensive 2D transient heat conduction model was developed in COMSOL accounting for the roller, the laying tape, the substrate, and the tool, while the laser beam was modeled by a heat

<figure><img src="image_2175.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
flux boundary condition obtained via a ray-tracing (RT) approach. In [5] a Matlab RT implementation was coupled to a 2D transient thermal model developed in ABAQUS for tape consolidation studies in the AFP process. The heat flux distributions in the tape and substrate were characterized in terms of the laser incidence angle, wavelength, head tilt, and the contact width of the roller. Subsequently, a heat flux boundary condition was imposed in the thermal model at both the surfaces of the incoming tape and substrate obtained from RT.

A shared characteristic among the aforementioned methodologies is their exclusive reliance on angular decomposition between the laser beam and idealized smooth substrate/tape surfaces to estimate heat flux, neglecting the composite's micro-structure and/or surface irregularities. Recent investigations [6,7,8] highlight the importance of accounting for the micro-structural topology of fibers within the thermoplastic matrix when modeling laser-matter interactions. This emphasis is driven by the notable contrast in thermal properties within the composite, where the laser predominantly penetrates the semi-transparent thermoplastic matrix with minimal interaction, and which is primarily absorbed/reflected by the fibers. In [8], the fibers' geometry is depicted as a structured array of evenly spaced 10µm half cylinders across the composite surface, utilizing the RT method to analyze the composite's scattering behavior. A notable advancement in micro-structure thermo-optical modeling is detailed in [6,7], where authors utilized an artificially generated representative geometry. Employing the RT approach, they identified the laser impact zone on fiber surfaces and enforced a heat flux boundary condition on these surfaces. A significant finding from [6] indicates that precise determination of radiative volumetric heat sources may notably improve temperature prediction accuracy when employing homogenized composite structures in comparison with a standard surface heat flux condition.

In this work a novel numerical approach for thermal modelling at the micro-scale of a composite tape during AFP manufacturing conditions is proposed. The scheme is based on employing an efficient RTE solver developed in FreeFEM++ [9] as part of the thesis work of [10,11] to obtain the radiative heat source within the composite, and then coupling the solution to transient 2D and 3D heat conduction simulations. The RTE-FEM solver is based on the Discrete Ordinates Method (DOM) where an angular discretization is required in addition to the spatial FEM mesh. Being an accurate although memory demanding approach, the solution is obtained in parallel by using the PETSc libraries on a High-Performance Computer cluster.

## Study Case at the Composite Micro-scale

The radiative-conductive coupling scheme is to be applied at the micro-scale of a single tape which is considered to be stationary. To be able to compare the radiative-conductive solution with respect to both a numerical thermo-optical model and experimental results, the micro-structure of the tape analyzed here is identically to the one presented [7], where the composite material is made of a matrix of the high-performance polymer PEKK7002 reinforced with carbon fiber of the AS7 type. A micrograph of the composite micro-structure is depicted Fig. 1a. A comprehensive imaging analysis was developed in [6,7] to accurately represent the real micro-structure by an artificial computational one (see Fig. 1b) which is able to reproduce the fiber volume fraction (FVF) in the thickness of the composite tape. Hence, the geometry depicted in Fig. 1b is employed throughout this work. We refer the readers to the previously mentioned article for more insights regarding the micro-structure generation procedure.
flux boundary condition obtained via a ray-tracing (RT) approach. In [5] a Matlab RT implementation was coupled to a 2D transient thermal model developed in ABAQUS for tape consolidation studies in the AFP process. The heat flux distributions in the tape and substrate were characterized in terms of the laser incidence angle, wavelength, head tilt, and the contact width of the roller. Subsequently, a heat flux boundary condition was imposed in the thermal model at both the surfaces of the incoming tape and substrate obtained from RT.

A shared characteristic among the aforementioned methodologies is their exclusive reliance on angular decomposition between the laser beam and idealized smooth substrate/tape surfaces to estimate heat flux, neglecting the composite's micro-structure and/or surface irregularities. Recent investigations [6,7,8] highlight the importance of accounting for the micro-structural topology of fibers within the thermoplastic matrix when modeling laser-matter interactions. This emphasis is driven by the notable contrast in thermal properties within the composite, where the laser predominantly penetrates the semi-transparent thermoplastic matrix with minimal interaction, and which is primarily absorbed/reflected by the fibers. In [8], the fibers' geometry is depicted as a structured array of evenly spaced 10µm half cylinders across the composite surface, utilizing the RT method to analyze the composite's scattering behavior. A notable advancement in micro-structure thermo-optical modeling is detailed in [6,7], where authors utilized an artificially generated representative geometry. Employing the RT approach, they identified the laser impact zone on fiber surfaces and enforced a heat flux boundary condition on these surfaces. A significant finding from [6] indicates that precise determination of radiative volumetric heat sources may notably improve temperature prediction accuracy when employing homogenized composite structures in comparison with a standard surface heat flux condition.

In this work a novel numerical approach for thermal modelling at the micro-scale of a composite tape during AFP manufacturing conditions is proposed. The scheme is based on employing an efficient RTE solver developed in FreeFEM++ [9] as part of the thesis work of [10,11] to obtain the radiative heat source within the composite, and then coupling the solution to transient 2D and 3D heat conduction simulations. The RTE-FEM solver is based on the Discrete Ordinates Method (DOM) where an angular discretization is required in addition to the spatial FEM mesh. Being an accurate although memory demanding approach, the solution is obtained in parallel by using the PETSc libraries on a High-Performance Computer cluster.

## Study Case at the Composite Micro-scale

The radiative-conductive coupling scheme is to be applied at the micro-scale of a single tape which is considered to be stationary. To be able to compare the radiative-conductive solution with respect to both a numerical thermo-optical model and experimental results, the micro-structure of the tape analyzed here is identically to the one presented [7], where the composite material is made of a matrix of the high-performance polymer PEKK7002 reinforced with carbon fiber of the AS7 type. A micrograph of the composite micro-structure is depicted Fig. 1a. A comprehensive imaging analysis was developed in [6,7] to accurately represent the real micro-structure by an artificial computational one (see Fig. 1b) which is able to reproduce the fiber volume fraction (FVF) in the thickness of the composite tape. Hence, the geometry depicted in Fig. 1b is employed throughout this work. We refer the readers to the previously mentioned article for more insights regarding the micro-structure generation procedure.
<figure><img src="image_2185.png" /><figcaption>Figure 1: Micro-structure of the composite tape taken from [7]: (a) optical micrograph, (b) micro-structure generated artificially, (c) FEM mesh, (d) the distribution of the FVF.</figcaption></figure>

The representative geometry of the tape is 100µm width and 240µm height, and the fibers are 6.9µm diameter. The average FVF is 50%, where, as observed in Fig. 1d, the distribution is denser near the surfaces, achieving roughly 60%, and less dense in the center, where the FVF reduces to 40%. This is particularly important since, as will be developed later, the intensity of the laser is mostly absorbed by the first's fiber layers of the tape. In addition, Fig. 1c showcases the unstructured mesh of the micro-structure to be used by the FEM solvers, and which will be further explained in the following sections.

## Governing Equations and Numerical Model

The numerical modelling of the laser-matter interaction during the AFP process is developed in two stages throughout this work: first, the modelling of the radiative heat transfer between the laser beam and the composite micro-structure, and second, the modelling of the transient conductive heat transfer within the matrix and the fibers. Next, the governing equations are addressed.

The Discrete Ordinates Model (DOM) in Radiative Heat Transfer. The RTE is that of the monochromatic steady state defined as follows:

$$ (s \cdot \nabla + \beta(x))I_{\lambda}(x, s) = \frac{\sigma_s}{4\pi} \oint_{s'=4\pi} I_{\lambda}(x, s')\Phi(s, s')ds' + \kappa(x)I_b(T, \lambda) \quad \forall \mathbf{x} \in \Omega, s \in S, \quad (1) $$

where $\mathbf{x} = (x, y, z)$ and $s = (\phi, \theta)$ are the spatial and direction vectors, respectively, $I_\lambda$ is the radiative intensity at a given wavelength $\lambda$, $\kappa$ and $\sigma_s$ the absorption and scattering coefficients, $\Phi$ the scattering phase function, which defines the probability of a photon traveling in the $\mathbf{s}$ direction to be redirected to some other direction $\mathbf{s}'$, and $\beta = (\sigma_s + \kappa)$ stands for the extinction coefficient. To solve the RTE, a FEM formulation is employed here by employing a parallelized code developed in FreeFEM++[10] and compiled with PETSc. The FEM-RTE model is based on the DOM for radiation which solves the RTE for a finite number of discrete solid angles. Thus, after the discretization of the angular space $S$ by a set of $N_d$ discrete directions ($s_1, s_2, ..., s^{Nd}$) $\in S^{Nd}$ the equation of the RTE yields:

$$ (s_m \cdot \nabla + \beta(x))I_{m\lambda}(x, s) = \sigma_s \sum_{n=1}^{Nd} \omega_n I_{n\lambda}(x)\Phi_{m,n} + \kappa(x)I_b(T, \lambda) \quad \forall m = 1, ..., N_d \quad (2) $$

where $s_m$ represents the discrete directions vector obtained by the successive discretization of an unit circle, for a 2D case, or a unit sphere, for a 3D one, and $\omega_n$ is the quadrature weight. Following previous works of radiation in heterogeneous materials with inclusions and high contrast radiative properties [10], the in-scattering effects are modeled using the Henyey-Greenstein phase function $\Phi$ [10], with an anisotropic coefficient $g = 0.8$. Following the angular discretization, a standard
<figure><img src="image_2176.png" /><figcaption>Figure 1: Micro-structure of the composite tape taken from [7]: (a) optical micrograph, (b) micro-structure generated artificially, (c) FEM mesh, (d) the distribution of the FVF.</figcaption></figure>

The representative geometry of the tape is 100µm width and 240µm height, and the fibers are 6.9µm diameter. The average FVF is 50%, where, as observed in Fig. 1d, the distribution is denser near the surfaces, achieving roughly 60%, and less dense in the center, where the FVF reduces to 40%. This is particularly important since, as will be developed later, the intensity of the laser is mostly absorbed by the first's fiber layers of the tape. In addition, Fig. 1c showcases the unstructured mesh of the micro-structure to be used by the FEM solvers, and which will be further explained in the following sections.

## Governing Equations and Numerical Model

The numerical modelling of the laser-matter interaction during the AFP process is developed in two stages throughout this work: first, the modelling of the radiative heat transfer between the laser beam and the composite micro-structure, and second, the modelling of the transient conductive heat transfer within the matrix and the fibers. Next, the governing equations are addressed.

The Discrete Ordinates Model (DOM) in Radiative Heat Transfer. The RTE is that of the monochromatic steady state defined as follows:

$$ (s \cdot \nabla + \beta(x))I_{\lambda}(x, s) = \frac{\sigma_s}{4\pi} \oint_{s'=4\pi} I_{\lambda}(x, s')\Phi(s, s')ds' + \kappa(x)I_b(T, \lambda) \quad \forall \mathbf{x} \in \Omega, s \in S, \quad (1) $$

where $\mathbf{x} = (x, y, z)$ and $s = (\phi, \theta)$ are the spatial and direction vectors, respectively, $I_\lambda$ is the radiative intensity at a given wavelength $\lambda$, $\kappa$ and $\sigma_s$ the absorption and scattering coefficients, $\Phi$ the scattering phase function, which defines the probability of a photon traveling in the $\mathbf{s}$ direction to be redirected to some other direction $\mathbf{s}'$, and $\beta = (\sigma_s + \kappa)$ stands for the extinction coefficient. To solve the RTE, a FEM formulation is employed here by employing a parallelized code developed in FreeFEM++[10] and compiled with PETSc. The FEM-RTE model is based on the DOM for radiation which solves the RTE for a finite number of discrete solid angles. Thus, after the discretization of the angular space $S$ by a set of $N_d$ discrete directions $(s_1, s_2, ..., s^{Nd}) \in S^{Nd}$ the equation of the RTE yields:

$$ (s_m \cdot \nabla + \beta(x))I_{m\lambda}(x, s) = \sigma_s \sum_{n=1}^{Nd} \omega_n I_{n\lambda}(x)\Phi_{m,n} + \kappa(x)I_b(T, \lambda) \quad \forall m = 1, ..., N_d \quad (2) $$

where $s_m$ represents the discrete directions vector obtained by the successive discretization of an unit circle, for a 2D case, or a unit sphere, for a 3D one, and $\omega_n$ is the quadrature weight. Following previous works of radiation in heterogeneous materials with inclusions and high contrast radiative properties [10], the in-scattering effects are modeled using the Henyey-Greenstein phase function $\Phi$ [10], with an anisotropic coefficient $g = 0.8$. Following the angular discretization, a standard
space discretization with unstructured triangles/tetrahedral elements is performed and a vectorized FEM formulation is employed in this work [10,11]. Due to the advective-dominant nature of the RTE, the FEM equations are stabilized by the Streamlined-Upwind Petrov-Galerkin (SUPG) stabilization term [10,12].

Boundary Conditions in the RTE. To model the laser radiation applied to the top surface of the composite tape $\Gamma_t$ (see Fig. 1b), the following collimated boundary condition is considered:

$$ I_{\text{collimated}} = I_w(x_w, s) = \begin{cases} I_0, & \forall x_w \in \Gamma_t \quad \text{if } s = s_c, \\ 0, & \forall x_w \in \Gamma_t \quad \text{if } s \neq s_c, \end{cases} \qquad (3) $$

where $I_0$ is the radiative intensity strength of the diode laser beam. Following the experimental works reported in [7], two boundary conditions are considered for the laser beam: a near-normal incidence angle $\theta = 15^\circ$ with $I_0 = 1.47\text{Wmm}^{-2}$, and a grazing incidence angle with $\theta = 60^\circ$ and $I_0 = 2.793\text{Wmm}^{-2}$. Moreover, $\Gamma_p$ is treated as periodic.

Transient Conductive-Radiative Heat Transfer Equation. The transient heat transfer

Form including the radiation and conduction yields:

$$ \rho C_p \left( \frac{\partial T(t, \mathbf{x})}{\partial t} \right) = -\nabla \cdot \left( Q_r(T, \lambda, \mathbf{x}) + Q_c(t, \mathbf{x}) \right) \quad \forall \mathbf{x} \in \Omega, \forall t > 0, \qquad (4) $$

where $\rho$ and $C_p$ stand for the material density and specific heat capacity, respectively, and $\nabla \cdot Q_r(T, \lambda, \mathbf{x})$ and $\nabla \cdot Q_c(t, \mathbf{x})$ are the radiative and conductive volumetric sources, respectively. The later is defined from the Fourier's law as $\nabla \cdot Q_c(t, \mathbf{x}) = -k\nabla T(t, \mathbf{x})$, being $k$ the thermal conductivity of the material, and the radiative source term is as:

$$ \nabla \cdot Q_r(T, \lambda, \mathbf{x}) = \kappa 4\pi I_b(T, \lambda) - \kappa G(\mathbf{x}), \qquad (5) $$

where $G(\mathbf{x})$ is the radiative density obtained by the RTE solver, which is computed at a given point $\mathbf{x}$ in a participating medium as $G(\mathbf{x}) \approx \sum_{n=1}^{Nd} I_n(\mathbf{x})\omega_n$, and $I_b$ stands for the black body source term. For the present study case where temperatures are expected to reach $\approx 200^\circ\text{C}$, the $I_b$ term can be neglected, since it results of orders of magnitude lower than that of $\kappa G(\mathbf{x})$. In this way, the radiative and conductive heat transfer equations can be weakly coupled, i.e., the RTE is solved once for a given incidence angle and intensity of the laser, and its solution is coupled to the transient conductive equation via the volumetric source term.

## Parametric Analysis and RTE vs. RT Comparison

Parametric Study of Varying Absorption Coefficients. To characterize the properties of the matrix ($\Omega_1$) and fiber ($\Omega_2$) materials, proper values of the $\sigma_s$ and $\kappa$ coefficients must be used in the RTE solver. Given their unavailability, a parametric study has been conducted. Its purpose is to ascertain a more fitting collection of parameters that effectively characterize the laser-matter interaction. The composite sample can be modeled as a combination of a highly absorbing medium for the carbon fibers, and a semi-transparent one for the polymer matrix [10]. Then, the adopted parameters to perform the parametric study are depicted in Table 1, being $\kappa_2$ recognized as the most relevant one.

<table><caption>Table 1: Boundary conditions and thermal properties used for the radiative parametric study. $I_0$ is given in [Wmm$^{-2}$], $\theta$ in [$^\circ$], and $\sigma_s$ and $\kappa$ in [mm$^{-1}$].</caption><thead><tr><th></th><th><i>I</i><sub>0</sub></th><th><i>θ</i></th><th><i>σ</i><sub>s1</sub></th><th><i>σ</i><sub>s2</sub></th><th><i>κ</i><sub>1</sub></th><th><i>κ</i><sub>2</sub></th></tr></thead><tbody><tr><td>Near-normal incidence</td><td>1.47</td><td>15</td><td>0.01</td><td>0.01</td><td>0.01</td><td>200,400,600,800,1000</td></tr><tr><td>Grazing incidence</td><td>2.793</td><td>60</td><td>0.01</td><td>0.01</td><td>0.01</td><td>200,400,600,800,1000</td></tr></tbody></table>
space discretization with unstructured triangles/tetrahedral elements is performed and a vectorized FEM formulation is employed in this work [10,11]. Due to the advective-dominant nature of the RTE, the FEM equations are stabilized by the Streamlined-Upwind Petrov-Galerkin (SUPG) stabilization term [10,12].

Boundary Conditions in the RTE. To model the laser radiation applied to the top surface of the composite tape $\Gamma_t$ (see Fig. 1b), the following collimated boundary condition is considered:

$$I_{\text{collimated}} = I_w(x_w, s) = \begin{cases} I_0, & \forall x_w \in \Gamma_t \quad \text{if } s = s_c, \\ 0, & \forall x_w \in \Gamma_t \quad \text{if } s \neq s_c, \end{cases} \qquad (3)$$

where $I_0$ is the radiative intensity strength of the diode laser beam. Following the experimental works reported in [7], two boundary conditions are considered for the laser beam: a near-normal incidence angle $\theta = 15^\circ$ with $I_0 = 1.47\text{Wmm}^{-2}$, and a grazing incidence angle with $\theta = 60^\circ$ and $I_0 = 2.793\text{Wmm}^{-2}$. Moreover, $\Gamma_p$ is treated as periodic.

Transient Conductive-Radiative Heat Transfer Equation. The transient heat transfer

Form including the radiation and conduction yields:

$$\rho C_p \left( \frac{\partial T(t, \mathbf{x})}{\partial t} \right) = -\nabla \cdot \left( Q_r(T, \lambda, \mathbf{x}) + Q_c(t, \mathbf{x}) \right) \quad \forall \mathbf{x} \in \Omega, \forall t > 0, \qquad (4)$$

where $\rho$ and $C_p$ stand for the material density and specific heat capacity, respectively, and $\nabla \cdot Q_r(T, \lambda, \mathbf{x})$ and $\nabla \cdot Q_c(t, \mathbf{x})$ are the radiative and conductive volumetric sources, respectively. The later is defined from the Fourier's law as $\nabla \cdot Q_c(t, \mathbf{x}) = -k\nabla T(t, \mathbf{x})$, being $k$ the thermal conductivity of the material, and the radiative source term is as:

$$\nabla \cdot Q_r(T, \lambda, \mathbf{x}) = \kappa 4\pi I_b(T, \lambda) - \kappa G(\mathbf{x}), \qquad (5)$$

where $G(\mathbf{x})$ is the radiative density obtained by the RTE solver, which is computed at a given point $\mathbf{x}$ in a participating medium as $G(\mathbf{x}) \approx \sum_{n=1}^{Nd} I_n(\mathbf{x})\omega_n$, and $I_b$ stands for the black body source term. For the present study case where temperatures are expected to reach $\approx 200^\circ\text{C}$, the $I_b$ term can be neglected, since it results of orders of magnitude lower than that of $\kappa G(\mathbf{x})$. In this way, the radiative and conductive heat transfer equations can be weakly coupled, i.e., the RTE is solved once for a given incidence angle and intensity of the laser, and its solution is coupled to the transient conductive equation via the volumetric source term.

## Parametric Analysis and RTE vs. RT Comparison

Parametric Study of Varying Absorption Coefficients. To characterize the properties of the matrix ($\Omega_1$) and fiber ($\Omega_2$) materials, proper values of the $\sigma_s$ and $\kappa$ coefficients must be used in the RTE solver. Given their unavailability, a parametric study has been conducted. Its purpose is to ascertain a more fitting collection of parameters that effectively characterize the laser-matter interaction. The composite sample can be modeled as a combination of a highly absorbing medium for the carbon fibers, and a semi-transparent one for the polymer matrix [10]. Then, the adopted parameters to perform the parametric study are depicted in Table 1, being $\kappa_2$ recognized as the most relevant one.

<table><caption>Table 1: Boundary conditions and thermal properties used for the radiative parametric study. $I_0$ is given in [Wmm$^{-2}$], $\theta$ in [$^\circ$], and $\sigma_s$ and $\kappa$ in [mm$^{-1}$].</caption><thead><tr><th></th><th>I<sub>0</sub></th><th>θ</th><th>σ<sub>s1</sub></th><th>σ<sub>s2</sub></th><th>κ<sub>1</sub></th><th>κ<sub>2</sub></th></tr></thead><tbody><tr><td>Near-normal incidence</td><td>1.47</td><td>15</td><td>0.01</td><td>0.01</td><td>0.01</td><td>200,400,600,800,1000</td></tr><tr><td>Grazing incidence</td><td>2.793</td><td>60</td><td>0.01</td><td>0.01</td><td>0.01</td><td>200,400,600,800,1000</td></tr></tbody></table>
Furthermore, the radiative volumetric source $\nabla \cdot Q_r(y)$ is computed by Eqn. (5) along the tape y-axis from the FEM solution as follows:

$$ \nabla \cdot Q_r(y) = \frac{1}{\Delta y} \int_{y-\Delta y/2}^{y+\Delta y/2} \kappa(x) G(x) dy \approx \frac{1}{\Delta y} \left( \sum_{i=1}^{2} \sum_{j=1}^{n_e} \kappa_i G_i(e^j) A^j \right), \quad (6) $$

where $G_i(e^j)$ corresponds to the radiative density solution at the element $e^j$ of the $\Omega_i$ domain, $A_j$ stands for the element area/volume, $\Delta y$ are discretized thicknesses of 0.2µm, and $n_e$ the number of elements located at such thickness.

For solving the RTE the mesh shown in Fig. 1c was employed with 147.475 non-structured triangular elements refined towards the top surface of the domain. A total of $N_d = 80$ directions was employed for the angular discretization. Each simulation took roughly 4 minutes solving with GMRES and running in 80 cores of the cluster CCIPL located at Le centre de calcul intensif des Pays de la Loire, in France. The results of the radiative volumetric source for the near-normal incidence case obtained at 20µm thickness of the composite is observed in Fig. 2a. It is to notice that for $\kappa_2 = 200\text{mm}^{-1}$, the radiative density increases into the thickness of the composite tape, achieving a maximum peak at a roughly 3.75µm from the surface. As $\kappa_2$ increases, the maximum peak is given closer to the tape surface at thickness of roughly 2.5µm. This become evident from the RTE solution for three reprensative cases in Fig. 2b, where it is shown that as $\kappa_2$ increases, the radiative density is further concentrated at the top surface of the first layers of the carbon fibers. Furthermore, it is worth noticing that the main peak of the volumetric heat source increases of approximately 87% when $\kappa_2$ increases from 200mm$^{-1}$ to 600mm$^{-1}$. This is of importance since, as will be shown later, a proper representation of such a term will impact in the accuracy at the moment of predicting the tape surface temperature during the AFP process.

<figure><img src="image_2186.png" /><figcaption>Figure 2: Parametric results of the RTE for the near-normal incidence case: (a) the heat source distribution at the near surface of the composite, and (b) the radiative density field.</figcaption></figure>

In Fig. 3 are presented the results obtained from the RTE solver for the grazing laser beam case. Similar conclusions can be obtained as compared to the results obtained for $\theta = 15^\circ$. Nevertheless, it should be noticed that for $\theta = 60^\circ$ the distribution of the volumetric heat source is further concentrated at the surface of the tape, where the laser energy is almost totally absorbed at the 10µm thickness for $\kappa_2 > 200\text{mm}^{-1}$ (see Fig. 3a).
Furthermore, the radiative volumetric source $\nabla \cdot Q_r(y)$ is computed by Eqn. (5) along the tape y-axis from the FEM solution as follows:

$$ \nabla \cdot Q_r(y) = \frac{1}{\Delta y} \int_{y-\Delta y/2}^{y+\Delta y/2} \kappa(x) G(x) dy \approx \frac{1}{\Delta y} \left( \sum_{i=1}^{n_1} \sum_{j=1}^{n_e} \kappa_i G_i(e^j) A^j \right), \quad (6) $$

where $G_i(e^j)$ corresponds to the radiative density solution at the element $e^j$ of the $\Omega_i$ domain, $A_j$ stands for the element area/volume, $\Delta y$ are discretized thicknesses of 0.2µm, and $n_e$ the number of elements located at such thickness.

For solving the RTE the mesh shown in Fig. 1c was employed with 147.475 non-structured triangular elements refined towards the top surface of the domain. A total of $N_d = 80$ directions was employed for the angular discretization. Each simulation took roughly 4 minutes solving with GMRES and running in 80 cores of the cluster CCIPL located at Le centre de calcul intensif des Pays de la Loire, in France. The results of the radiative volumetric source for the near-normal incidence case obtained at 20µm thickness of the composite is observed in Fig. 2a. It is to notice that for $\kappa_2 = 200\text{mm}^{-1}$, the radiative density increases into the thickness of the composite tape, achieving a maximum peak at a roughly 3.75µm from the surface. As $\kappa_2$ increases, the maximum peak is given closer to the tape surface at thickness of roughly 2.5µm. This become evident from the RTE solution for three reprensative cases in Fig. 2b, where it is shown that as $\kappa_2$ increases, the radiative density is further concentrated at the top surface of the first layers of the carbon fibers. Furthermore, it is worth noticing that the main peak of the volumetric heat source increases of approximately 87% when $\kappa_2$ increases from 200mm$^{-1}$ to 600mm$^{-1}$. This is of importance since, as will be shown later, a proper representation of such a term will impact in the accuracy at the moment of predicting the tape surface temperature during the AFP process.

<figure><img src="image_2177.png" /><figcaption>Figure 2: Parametric results of the RTE for the near-normal incidence case: (a) the heat source distribution at the near surface of the composite, and (b) the radiative density field.</figcaption></figure>

In Fig. 3 are presented the results obtained from the RTE solver for the grazing laser beam case. Similar conclusions can be obtained as compared to the results obtained for $\theta = 15^\circ$. Nevertheless, it should be noticed that for $\theta = 60^\circ$ the distribution of the volumetric heat source is further concentrated at the surface of the tape, where the laser energy is almost totally absorbed at the 10µm thickness for $\kappa_2 > 200\text{mm}^{-1}$ (see Fig. 3a).
<figure><img src="image_2187.png" /><figcaption>Figure 3: Parametric results of the RTE for the grazing incidence case: (a) the heat source distribution at the near surface of the composite, and (b) the radiative density field.</figcaption></figure>

RTE vs RT Comparison. As a part of a previous work [6] the volumetric heat source distribution was obtained by the RT approach using a home-made Matlab code which considered the matrix as a full transparent material, and where the laser absorption is only given at the fiber surfaces by a purely geometrical approach. In Fig. 4 are compared the solutions obtained by the RTE with respect to that of RT, and to a double-beta fit function [6]. When using $κ_2 = 600\text{mm}^{-1}$, a well-matched volumetric heat source distribution is observed for a near-normal incidence (see Fig. 4a), resembling the double-beta function, accurately reproducing the closest-to-surface peak. Additionally, under grazing laser incidence (see Fig. 4b), the RTE solution replicates the volumetric heat source feature noted in [6], displaying a single dominant peak.

<figure><img src="image_2188.png" /><figcaption>Figure 4: Radiative source distribution across a 20µm composite depth alongside a comparative assessment against a previously published RT-based approach.</figcaption></figure>

## Results of RTE-Conductive Coupling on Composite Micro-structure

Experimental Setup Description. The thermophysical properties of the composite material to be used by the radiative-conductive coupling are the same as those reported in [6] and are recalled here in Table 2. The experimental reproduction of the AFP process and the temperature measurements were performed on an ad-hoc bench, which possess a rotating 2kW laser diode of the type LDM 200-6000 with adjusting incidence angle and distance to the tape surface. The laser diode was set to irradiate the composite at $λ = 980\text{nm}$ with controlled time and power. The temperature at the tape surface was measured by an infrared camera FLIR XC609. We refer the readers to the Refs. [6, 7] for further details regarding the experimental setup. For the transient
<figure><img src="image_2178.png" /><figcaption>Figure 3: Parametric results of the RTE for the grazing incidence case: (a) the heat source distribution at the near surface of the composite, and (b) the radiative density field.</figcaption></figure>

RTE vs RT Comparison. As a part of a previous work [6] the volumetric heat source distribution was obtained by the RT approach using a home-made Matlab code which considered the matrix as a full transparent material, and where the laser absorption is only given at the fiber surfaces by a purely geometrical approach. In Fig. 4 are compared the solutions obtained by the RTE with respect to that of RT, and to a double-beta fit function [6]. When using $κ_2 = 600\text{mm}^{-1}$, a well-matched volumetric heat source distribution is observed for a near-normal incidence (see Fig. 4a), resembling the double-beta function, accurately reproducing the closest-to-surface peak. Additionally, under grazing laser incidence (see Fig. 4b), the RTE solution replicates the volumetric heat source feature noted in [6], displaying a single dominant peak.

<figure><img src="image_2179.png" /><figcaption>Figure 4: Radiative source distribution across a 20µm composite depth alongside a comparative assessment against a previously published RT-based approach.</figcaption></figure>

## Results of RTE-Conductive Coupling on Composite Micro-structure

Experimental Setup Description. The thermophysical properties of the composite material to be used by the radiative-conductive coupling are the same as those reported in [6] and are recalled here in Table 2. The experimental reproduction of the AFP process and the temperature measurements were performed on an ad-hoc bench, which possess a rotating 2kW laser diode of the type LDM 200-6000 with adjusting incidence angle and distance to the tape surface. The laser diode was set to irradiate the composite at $λ = 980\text{nm}$ with controlled time and power. The temperature at the tape surface was measured by an infrared camera FLIR XC609. We refer the readers to the Refs. [6, 7] for further details regarding the experimental setup. For the transient
heat transfer problem, the heating time of the laser is set to $t_c = 20$ms, which corresponds to the exposure time in an AFP manufacturing process where the laying speed is 500ms with a 12mm laser beam width. The experience lasted a total of $t_t = 40$ms.

<table><caption>Table 2: Thermal properties of the matrix and the carbon fibers. $k$ is given in [$Wm^{-1}K^{-1}$], $\rho$ in [kg m$^{-3}$], $C_p$ in [$Jkg^{-1}K^{-1}$], and $\sigma_s$ and $\kappa$ in [mm$^{-1}$].</caption><thead><tr><th></th><th>k</th><th>ρ</th><th>Cp</th><th>σs</th><th>κ</th></tr></thead><tbody><tr><td>PEKK7002</td><td>0.27</td><td>1290</td><td>T ≤ T<sub>g</sub>, 3.35T[°C] + 1017.0<br>T<sub>g</sub> < T < T<sub>m</sub>, 3.45T[°C] + 1137.6</td><td>0.01</td><td>0.01</td></tr><tr><td>Carbon fibre AS7</td><td>2.2</td><td>1790</td><td>-0.00295T[°C]<sup>2</sup> + 3.493T[°C] + 578</td><td>0.01</td><td>600</td></tr></tbody></table>

Radiative-Conductive Coupling Algorithm and 2D Case Results. The Algorithm 1 is used to solve the radiative-conductive equations in the artificially generated composite micro-structure under AFP conditions, where $\delta_t$ is the time-step discretization employed by the Crank-Nicolson scheme ($\delta_t = 0.5$s), and $\{X_c, d\}$ are the fiber coordinates and diameter, respectively. The boundary conditions for the coupled radiative-conductive problem are: a third type boundary condition at the top composite surface $\Gamma_t$ (see Fig. 1b) defined as $-k(\partial T/\partial n) = h_c(T - T_{amb})$, being n the outward normal vector, $T_{amb}$ the ambient temperature considered at 20°C, and $h_c$ a convective exchange coefficient with the surrounding air of $5Wm^{-2}K^{-1}$; isolated boundaries at $\Gamma_p$ modeled as $-k(\partial T/\partial n) = 0$; and a perfect contact at the composite-tool interface $\Gamma_b$, with an imposed temperature of $T = T_{tool}$, considering the tool to be at $T_{amb}$.

<caption>**Algorithm 1:** RTE-conduction of AFP process on composite microstructure</caption>

Input: $\{X_c, d\}$, $\{I, \theta\}$, $\{t_t, t_c, \delta t\}$, $\{\rho, k, C_p, \kappa, \sigma\}_{1,2}$, $\{h_c, T_{amb}, T_{tool}\}$

**Define:** $T_N, T_{N+1}, T_i$

1. $\Omega_1^h \cup \Omega_2^h \leftarrow$ Generation of artificial micro-structure from $\{X_c, d\}$, and meshing;
2. $G(\mathbf{x}) \leftarrow$ solve the RTE on $\Omega_1^h \cup \Omega_2^h$ with $\{I, \theta\}$, and $\{\kappa_1, \sigma_1, \kappa_2, \sigma_2\}$;
3. $\nabla \cdot Q_r \leftarrow$ compute radiative heat source term with $G(\mathbf{x})$ and $\{\kappa_1, \kappa_2\}$;
4. $T_N = T_i$
5. **for** $t < t_{t_c}$: $t = t + \delta t$; **do**
6. &nbsp;&nbsp;&nbsp;&nbsp;**if** $t \le t_c$ **then**
7. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**then** $T_{N+1} \leftarrow$ solve conduction eq. using $\nabla \cdot Q_r, T_N, \{\rho, k, C_p\}_{1,2}$, and $\{h_c, T_{amb}, T_{tool}\}$
8. &nbsp;&nbsp;&nbsp;&nbsp;**else**
9. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**else** $T_{N+1} \leftarrow$ solve conduction eq. using $\nabla \cdot Q_r = 0, T_N, \{\rho, k, C_p\}_{1,2}$, and $\{h_c, T_{amb}, T_{tool}\}$
10. **return** $T(t)$

The results obtained by the RTE-conduction for near-normal and grazing laser incidences are presented in Figs. 5a and 5b, respectively. Notably, a very good agreement with the experimental results of [6] can be observed during the heating and cooling phases. The results are in accordance with those obtained by the thermo-optical model using the RT approach as well. The temperature differences between the experimental and the numerical approaches proposed here at the most critical point (end of the heating phase) were 4.6°C and 5.8°C for the near-normal and grazing incidence scenarios, respectively. Nevertheless, these results fall within the uncertainty range of the experimental measurements, where the maximum uncertainties were estimated at ±10.5°C (±5.05% of $\bar{T}_{max}$=208.0°C) for the near-normal case and ±6.8°C (±3.25% of $\bar{T}_{max}$=211.5°C) for the grazing scenario. It is worth clarifying that these uncertainties were computed by repeating the experiment on five different samples in each case, and averaging the temperatures obtained in a
limited region of the heated area [6]. The main sources of these measurement uncertainties were: i) the thermal camera resolution, ii) tape surface heterogeneities, iii) within-batch tape variations, and iv) fluctuations linked to the setup conditions and operator manipulation. According to the camera manufacturer, the uncertainties resulting from the thermal measurements were estimated at ±2% and are comprised in the previously reported values.

<figure><img src="image_2189.png" /><figcaption>Figure 5: Transient temperature evolution of the composite surface obtained through the RTE-conduction approach. (*) Experimental and numerical research conducted by Le Reun et al [6].</figcaption></figure>

RTE-Conduction on a 3D Case. To assess the feasibility of addressing complex geometries with the RTE-conductive approach, let us assume a 3D case where the fibers and the matrix domains are extruded in the z-axis direction by 100µm. The mesh used for the conductive heat transfer within the composite is obtained by extruding the elements of the 2D mesh of Fig. 1b, resulting in 3.451.200 tetrahedral elements. To solve the RTE, a reduced domain was employed accounting for the first's four fiber layers (see Fig. 6a) prioritizing an accurate solution in such a region and considering the large memory requirements of the RTE solver in 3D cases [10]. Then, the RTE mesh is conformed by a total of 3.879.000 tetrahedral elements (see Fig. 6b). A linear interpolation is performed to transfer the results obtained in the reduced 3D RTE domain to the full 3D conductive one. The RTE boundary conditions are those of the near-normal case depicted on Table 1, and the boundary conditions for the conductive heat transfer are identically to the ones presented in the previous subsection. The RTE solution took in total 24 minutes on 160 cores with $N_d = 160$ directions by using the GMRES solver, and it is presented in Fig. 6c. The results obtained at four different times by performing the RTE-conduction coupling is presented in Fig. 7, taking an additionally of 18 minutes. During the heating phase, which is the most critical one, the temperature delta at the top surface of the composite is of roughly 6°C. This is strictly linked to the laser orientation and microfibers arrangement, emphasizing the necessity for accurately modeling the radiative heat source.
limited region of the heated area [6]. The main sources of these measurement uncertainties were: i) the thermal camera resolution, ii) tape surface heterogeneities, iii) within-batch tape variations, and iv) fluctuations linked to the setup conditions and operator manipulation. According to the camera manufacturer, the uncertainties resulting from the thermal measurements were estimated at ±2% and are comprised in the previously reported values.

<figure><img src="image_2180.png" /><figcaption>Figure 5: Transient temperature evolution of the composite surface obtained through the RTE-conduction approach. (*) Experimental and numerical research conducted by Le Reun et al [6].</figcaption></figure>

RTE-Conduction on a 3D Case. To assess the feasibility of addressing complex geometries with the RTE-conductive approach, let us assume a 3D case where the fibers and the matrix domains are extruded in the z-axis direction by 100µm. The mesh used for the conductive heat transfer within the composite is obtained by extruding the elements of the 2D mesh of Fig. 1b, resulting in 3.451.200 tetrahedral elements. To solve the RTE, a reduced domain was employed accounting for the first's four fiber layers (see Fig. 6a) prioritizing an accurate solution in such a region and considering the large memory requirements of the RTE solver in 3D cases [10]. Then, the RTE mesh is conformed by a total of 3.879.000 tetrahedral elements (see Fig. 6b). A linear interpolation is performed to transfer the results obtained in the reduced 3D RTE domain to the full 3D conductive one. The RTE boundary conditions are those of the near-normal case depicted on Table 1, and the boundary conditions for the conductive heat transfer are identically to the ones presented in the previous subsection. The RTE solution took in total 24 minutes on 160 cores with $N_d = 160$ directions by using the GMRES solver, and it is presented in Fig. 6c. The results obtained at four different times by performing the RTE-conduction coupling is presented in Fig. 7, taking an additionally of 18 minutes. During the heating phase, which is the most critical one, the temperature delta at the top surface of the composite is of roughly 6°C. This is strictly linked to the laser orientation and microfibers arrangement, emphasizing the necessity for accurately modeling the radiative heat source.
<figure><img src="image_2190.png" /><figcaption>Figure 6: 3D radiative heat transfer on composite micro-structure: (a) reduced computational domain, (b) unstructured mesh of tetrahedral elements, and (c) the resulting radiative density field.</figcaption></figure>

In contrast, during the cooling phase, such delta temperature diminishes to less than 1°C. It can further be noticed from Fig. 7 that, as expected, the heat flux is much higher within the fibers than within the matrix. This is mainly due to the higher fiber thermal conductivity, which is of roughly one order of magnitude superior compared to the one of the matrix.

<figure><img src="image_2191.png" /><figcaption>Figure 7: Result of the 3D RTE-conductive coupling 3D on the composite micro-structure showcasing the temperature field at the irradiated surface, and the heat flux within the composite.</figcaption></figure>

## Conclusions and future work

A numerical methodology based on a one-way coupling of the finite element radiative-conductive heat transfer equations specifically conceived for accurate modeling of the temperature evolution within a composite micro-structure facing typical AFP process conditions with varying laser beam incidence and intensity was presented in this work. The scheme allows addressing materials with high contrast thermal properties encountered within the composite material for the matrix and fibers such as the absorption coefficient and the thermal conductivity. A parametric study allowed the proper identification of the absorption coefficient of the carbon fibers, a critical parameter to accurately compute the radiative heat source term, and the results showed good agreement on a 2D scenario when compared to a ray-tracing approach reported in the literature. Furthermore, the RTE-conductive coupling was successfully solved on an artificial generated composite micro-structure resulting in 5-6°C maximal process temperature difference with respect to experimental and numerical results. These results propose a solid base for the accurate modeling of the laser-matter interaction on complex micro-structure geometries, and future works concern proper
<figure><img src="image_2181.png" /><figcaption>Figure 6: 3D radiative heat transfer on composite micro-structure: (a) reduced computational domain, (b) unstructured mesh of tetrahedral elements, and (c) the resulting radiative density field.</figcaption></figure>

In contrast, during the cooling phase, such delta temperature diminishes to less than 1°C. It can further be noticed from Fig. 7 that, as expected, the heat flux is much higher within the fibers than within the matrix. This is mainly due to the higher fiber thermal conductivity, which is of roughly one order of magnitude superior compared to the one of the matrix.

<figure><img src="image_2182.png" /><figcaption>Figure 7: Result of the 3D RTE-conductive coupling 3D on the composite micro-structure showcasing the temperature field at the irradiated surface, and the heat flux within the composite.</figcaption></figure>

## Conclusions and future work

A numerical methodology based on a one-way coupling of the finite element radiative-conductive heat transfer equations specifically conceived for accurate modeling of the temperature evolution within a composite micro-structure facing typical AFP process conditions with varying laser beam incidence and intensity was presented in this work. The scheme allows addressing materials with high contrast thermal properties encountered within the composite material for the matrix and fibers such as the absorption coefficient and the thermal conductivity. A parametric study allowed the proper identification of the absorption coefficient of the carbon fibers, a critical parameter to accurately compute the radiative heat source term, and the results showed good agreement on a 2D scenario when compared to a ray-tracing approach reported in the literature. Furthermore, the RTE-conductive coupling was successfully solved on an artificial generated composite micro-structure resulting in 5-6°C maximal process temperature difference with respect to experimental and numerical results. These results propose a solid base for the accurate modeling of the laser-matter interaction on complex micro-structure geometries, and future works concern proper
heating law identifications in the AFP context featuring varying fiber orientations and volume fractions. Furthermore, internal reflections effects will be also considered.

References

[1] A. Levy, J. Tierney, D. Heider, J. Gillespie, P. Lefebure, D. Lang, Modeling of inter-layer thermal contact resistance during thermoplastic tape placement, in: International SAMPE Technical Conference, Baltimore, MA, USA, 2012.

[2] M. J. Donough, N. A. St John, A. W. Philips, B. G. Prusty, et al., Process modelling of in-situ consolidated thermoplastic composite by automated fibre placement-a review, Composites Part A: Applied Science and Manufacturing (2022) 107179. https://doi.org/10.1016/j.compositesa.2022.107179

[3] P. Hörmann, D. Stelzl, R. Lichtinger, S. Van Nieuwenhove, G. M. Carro, K. Drechsler, On the numerical prediction of radiative heat transfer for thermoset automated fiber placement, Composites Part A: Applied Science and Manufacturing 67 (2014) 282-288. https://doi.org/10.1016/j.compositesa.2014.08.019

[4] V. Le Louët, Etude du comportement thermique de bandes composites pré-imprégnées au cours du procédé de fabrication AFP avec chauffage laser, Ph.D. thesis, Université de Nantes (2018).

[5] O. Baho, G. Ausias, Y. Grohens, J. Férec, Simulation of laser heating distribution for a thermoplastic composite: Effects of AFP head parameters, The International Journal of Advanced Manufacturing Technology 110 (2020) 2105-2117. https://doi.org/10.1007/s00170-020-05876-9

[6] A. Le Reun, V. Le Louët, V. Sobotka, S. Le Corre, Numerical simulation at the micro-scale for the heat transfer modeling in the thermoplastic composites laser-assisted AFP process, Composites Part A: Applied Science and Manufacturing 28 (2023) 1897-1906. https://doi.org/10.1016/j.compositesa.2024.108010

[7] V. Le Louët, A. Le Reun, V. Sobotka, S. Le Corre, Experimental measurement of CF/PEKK tapes heating behavior in the laser assisted automated fiber placement process, in: 26th International ESAFORM Conference, 28 (2023) 1897-1906. https://doi.org/10.21741/9781644902479-205

[8] C. Stokes-Griffin, P. Compston, A combined optical-thermal model for near-infrared laser heating of thermoplastic composites in an automated tape placement process, Composites Part A: Applied Science and Manufacturing 75 (2015) 104-115. https://doi.org/10.1016/j.compositesa.2014.08.006

[9] F. Hecht, New development in FreeFEM++, Journal of numerical mathematics 20 (3-4) (2012) 251-266. https://doi.org/10.1515/jnum-2012-0013

[10] M. A. Badri, Efficient finite element strategies for solving the radiative transfer equation, Ph.D. thesis, Université de Nantes (2018). https://doi.org/10.1016/j.jqsrt.2018.03.024

[11] M. Badri, P. Jolivet, B. Rousseau, S. Le Corre, H. Digonnet, Y. Favennec, Vectorial finite elements for solving the radiative transfer equation, Journal of Quantitative Spectroscopy and Radiative Transfer 212 (2018) 59-74. https://doi.org/10.1016/j.jqsrt.2018.03.024

[12] M. Avila, R. Codina, J. Principe, Spatial approximation of the radiation transport equation using a subgrid-scale finite element method, Computer Methods in Applied Mechanics and Engineering 200 (5-8) (2011) 425-438. https://doi.org/10.1016/j.cma.2010.11.003