process routes the global maxima of thinning $\Delta t_{max,global}$ are equal to the corresponding local maxima of thinning $\Delta t_{max,local}$ in the characteristic area LR of SH 1.1. Therefore, the characteristic area LR of SH 1.1 is regarded as the critical area regarding thinning $\Delta t$ in the following. In addition to the thinning $\Delta t$ that occurs, differences in the maximum x-values $x_{max}$ achieved in AM are noticeable. While S123 shows the lowest maximum x-value $x_{max}$ of $x_{max} = 4.66$ mm, REF shows a slightly higher maximum x-value $x_{max}$ of $x_{max} = 4.70$ mm. S321 achieves the comparatively highest maximum x-value $x_{max}$ of $x_{max} = 4.85$ mm. As the initial length of the sheet is set to be the same in all process routes, different maximum x-values $x_{max}$ achieved in AM result in different material volumes $V$ that are drawn into the tool depending on the process route. This leads to the highest material volume drawn into the tool $V$ by S123, while S321 shows the least material volume $V$ drawn into the tool (Table 2).

<table><caption>Table 2: Material volume $V$ in tool geometry</caption><thead><tr><td>Process route</td><td>REF</td><td>S123</td><td>S321</td></tr></thead><tbody><tr><td>Material volume V drawn into tool/mm³</td><td>0.463</td><td>0.467</td><td>0.448</td></tr></tbody></table>

After SH 1.1 is identified as the critical segment halve regarding thinning $\Delta t$, the thinning $\Delta t$ in SH 1.1 is visualised in Fig. 4a). It is noticeable that almost no thinning $\Delta t$ occurs in the characteristic areas UB, W and LB. In the characteristic areas UR, thinning $\Delta t$ occurs at the upper sheet edge and negative thinning $\Delta t$, meaning thickening of the sheet, occurs at the lower sheet edge, while in the characteristic area LR, thickening occurs at the upper sheet edge and thinning $\Delta t$ at the lower sheet edge. In the middle of the sheet in the characteristic areas UR and LR nearly no thinning $\Delta t$ occurs. In both characteristic areas UR and LR, the highest thickening and the lowest thinning $\Delta t$ occur at the respective sheet edges in S123.

<figure><img src="image_2230.png" /><figcaption>Figure 4: a) Thinning $\Delta t$ in SH 1.1 for different process routes b) Points of evaluation in characteristic area LR of SH 1.1 regarding stress states</figcaption></figure>

In contrast, the highest thinning $\Delta t$ and simultaneously nearly no thickening occurs in S321. The thinning $\Delta t$ occurring in the characteristic area LR exceeds the thinning $\Delta t$ in the characteristic area UR, therefore the characteristic area LR of SH 1.1 is considered the critical area of thinning $\Delta t$. In the characteristic area LR of SH 1.1, the stress states that lead to thinning $\Delta t$ are subsequently analysed. For this purpose, three points of intersection between the upper and lower sheet edges, the middle of the sheet and the straight line perpendicular to the sheet thickness where the greatest thinning $\Delta t$ occurred are considered (Fig. 4b)).
process routes the global maxima of thinning $\Delta t_{max,global}$ are equal to the corresponding local maxima of thinning $\Delta t_{max,local}$ in the characteristic area LR of SH 1.1. Therefore, the characteristic area LR of SH 1.1 is regarded as the critical area regarding thinning $\Delta t$ in the following. In addition to the thinning $\Delta t$ that occurs, differences in the maximum x-values $x_{max}$ achieved in AM are noticeable. While S123 shows the lowest maximum x-value $x_{max}$ of $x_{max} = 4.66$ mm, REF shows a slightly higher maximum x-value $x_{max}$ of $x_{max} = 4.70$ mm. S321 achieves the comparatively highest maximum x-value $x_{max}$ of $x_{max} = 4.85$ mm. As the initial length of the sheet is set to be the same in all process routes, different maximum x-values $x_{max}$ achieved in AM result in different material volumes $V$ that are drawn into the tool depending on the process route. This leads to the highest material volume drawn into the tool $V$ by S123, while S321 shows the least material volume $V$ drawn into the tool (Table 2).

<table><caption>Table 2: Material volume $V$ in tool geometry</caption><thead><tr><td>Process route</td><td>REF</td><td>S123</td><td>S321</td></tr></thead><tbody><tr><td>Material volume V drawn into tool/mm³</td><td>0.463</td><td>0.467</td><td>0.448</td></tr></tbody></table>

After SH 1.1 is identified as the critical segment halve regarding thinning $\Delta t$, the thinning $\Delta t$ in SH 1.1 is visualised in Fig. 4a). It is noticeable that almost no thinning $\Delta t$ occurs in the characteristic areas UB, W and LB. In the characteristic areas UR, thinning $\Delta t$ occurs at the upper sheet edge and negative thinning $\Delta t$, meaning thickening of the sheet, occurs at the lower sheet edge, while in the characteristic area LR, thickening occurs at the upper sheet edge and thinning $\Delta t$ at the lower sheet edge. In the middle of the sheet in the characteristic areas UR and LR nearly no thinning $\Delta t$ occurs. In both characteristic areas UR and LR, the highest thickening and the lowest thinning $\Delta t$ occur at the respective sheet edges in S123.

<figure><img src="image_2221.png" /><figcaption>Figure 4: a) Thinning $\Delta t$ in SH 1.1 for different process routes b) Points of evaluation in characteristic area LR of SH 1.1 regarding stress states</figcaption></figure>

In contrast, the highest thinning $\Delta t$ and simultaneously nearly no thickening occurs in S321. The thinning $\Delta t$ occurring in the characteristic area LR exceeds the thinning $\Delta t$ in the characteristic area UR, therefore the characteristic area LR of SH 1.1 is considered the critical area of thinning $\Delta t$. In the characteristic area LR of SH 1.1, the stress states that lead to thinning $\Delta t$ are subsequently analysed. For this purpose, three points of intersection between the upper and lower sheet edges, the middle of the sheet and the straight line perpendicular to the sheet thickness where the greatest thinning $\Delta t$ occurred are considered (Fig. 4b)).
Influence of process route on stress states. Fig. 5a) shows the triaxiality $\eta$ and the lode angle parameter $\bar{\theta}$ in dependence of the punch path $s$ in the lower sheet edge, while the VON MISES stress $\sigma_{vM}$ in dependence of the punch path $s$ in the lower sheet edge is visualized in Fig. 5b).

<figure><img src="image_2231.png" /><figcaption>Figure 5: a) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and b) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ for different process routes in lower sheet edge, c) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and d) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ in middle of sheet, e) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and f) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ for different process routes in upper sheet edge</figcaption></figure>

In the lower sheet edge the course of triaxiality $\eta$ is almost constant for all process routes with a triaxiality $\eta$ of $\eta = 0.33$. After a steep drop at the beginning of the punch path, the course of lode angle parameter reaches a constant lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 1$. The combination of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ results in an identical uniaxial tensile stress state for all process routes. Unlike the course of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$, the course of VON MISES stress $\sigma_{vM}$ differs within the process routes. The VON MISES stress $\sigma_{vM}$ increases monotonically with the punch path $s$ for all process routes. For S321 the VON MISES stress $\sigma_{vM}$ starts with a value greater than zero due to the stresses induced in segment 1 by the forming of segment 2 and segment 3, which has already taken place in S321 before the forming of segment 1. The VON MISES stress $\sigma_{vM}$ of S321 is greater than the VON MISES stress $\sigma_{vM}$ of REF and the VON MISES stress $\sigma_{vM}$ of REF in turn is greater than the VON MISES stress $\sigma_{vM}$ of S123. In the middle of the sheet, S123 shows a nearly constant triaxiality $\eta$ of $\eta = 0$ and a lode angle
Influence of process route on stress states. Fig. 5a) shows the triaxiality $\eta$ and the lode angle parameter $\bar{\theta}$ in dependence of the punch path $s$ in the lower sheet edge, while the VON MISES stress $\sigma_{vM}$ in dependence of the punch path $s$ in the lower sheet edge is visualized in Fig. 5b).

<figure><img src="image_2222.png" /><figcaption>Figure 5: a) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and b) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ for different process routes in lower sheet edge, c) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and d) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ in middle of sheet, e) Triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ and f) VON MISES stress $\sigma_{vM}$ in dependence of punch path $s$ for different process routes in upper sheet edge</figcaption></figure>

In the lower sheet edge the course of triaxiality $\eta$ is almost constant for all process routes with a triaxiality $\eta$ of $\eta = 0.33$. After a steep drop at the beginning of the punch path, the course of lode angle parameter reaches a constant lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 1$. The combination of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ results in an identical uniaxial tensile stress state for all process routes. Unlike the course of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$, the course of VON MISES stress $\sigma_{vM}$ differs within the process routes. The VON MISES stress $\sigma_{vM}$ increases monotonically with the punch path $s$ for all process routes. For S321 the VON MISES stress $\sigma_{vM}$ starts with a value greater than zero due to the stresses induced in segment 1 by the forming of segment 2 and segment 3, which has already taken place in S321 before the forming of segment 1. The VON MISES stress $\sigma_{vM}$ of S321 is greater than the VON MISES stress $\sigma_{vM}$ of REF and the VON MISES stress $\sigma_{vM}$ of REF in turn is greater than the VON MISES stress $\sigma_{vM}$ of S123. In the middle of the sheet, S123 shows a nearly constant triaxiality $\eta$ of $\eta = 0$ and a lode angle
parameter $\bar{\theta}$ of $\bar{\theta} = 0$, while S321 shows a nearly constant triaxiality $\eta$ of $\eta = 0.33$ and constant lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 1$ (Fig. 5c)). REF shows a slight increase in triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ with a maximum triaxiality $\eta$ below $\eta < 0.33$ and a maximum lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 0.66$. This results in a uniaxial tensile stress state for REF and S321 and a sheer stress state for S123. The VON MISES stress $\sigma_{VM}$ shows the same characteristics in the middle of the sheet as in the lower sheet edge. Therefore, S321 shows the highest and S123 the lowest course of the VON MISES stress $\sigma_{VM}$ (Fig. 5d)). In the upper sheet edge the triaxiality $\eta$ of REF and S123 stays constant at a triaxiality $\eta$ of $\eta = -0.33$ and slightly drops in the end of the forming of segment 1 to a triaxiality $\eta$ of $\eta = -0.66$ (Fig. 5e)). The lode angle parameter $\bar{\theta}$ stays constant with a lode angle parameter $\bar{\theta}$ of $\bar{\theta} = -1$ until a steep increase of the lode angle parameter $\bar{\theta}$ to $\bar{\theta} = 0.45$ at the end of the forming process. The triaxiality $\eta$ of S321 oscillates between $-0.66 < \eta < 0.33$, while the lode angle parameter $\bar{\theta}$ changes between $-1 < \bar{\theta} < 1$. For REF and S123 the occurring combinations of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ lead to a uniaxial to biaxial compressive stress state, while the stress states of S321 vary between uniaxial tensile, uniaxial compressive and biaxial tensile. In the upper sheet edge the VON MISES stress $\sigma_{VM}$ of REF and S123 shows the same characteristics as in the lower sheet edge and middle of the sheet (Fig. 5f)). Additionally, the VON MISES stress $\sigma_{VM}$ of REF and S123 show nearly no distinction. In contrast, the VON MISES stress $\sigma_{VM}$ of S321 differs greatly. In the upper sheet edge the VON MISES stress $\sigma_{VM}$ of S321 drops steeply at first and then oscillates mostly below the VON MISES stress $\sigma_{VM}$ of REF and S123.

## Conclusion and Outlook

The comparison of the thinning using the three process routes showed that S321 generally led to the highest thinning, while S123 resulted in the lowest thinning. For all process routes the highest thinning occurred in the lower radius of segment 1, which resulted in the lower radius to be considered as the most sensitive area regarding thinning. In addition to the thinning, the material volume drawn into the tool was compared between the three process routes. The most material volume was drawn into the tool using S123, while the least material volume inside the tool was found within S321. Therefore, the material volume drawn into the tool corresponds to the described tendencies between the three different process routes regarding thinning. It is assumed that the difference in thinning between the process routes are due to an improved material flow in S123 and a deteriorated material flow in S321 compared to REF. In S123 the most inner segment is formed first, resulting in a nearly unobstructed material flow from the outside of the tool to the inner segment. In contrast, in S321 the most outer segment 3 is formed first, effectively cutting off the material flow from the outside of the tool for the rest of forming.

The comparison of stress states at the lower and upper sheet edge and the middle of the sheet showed distinctions between the stress states and total stress regarding the point of evaluation and the process route used. In the lower sheet edge a very similar tensile stress state was found for all process routes. S321 showed the highest and S123 showed the lowest total stress, corresponding to the results of thinning for the different process routes at the lower sheet edge. It is concluded that tensile stresses lead to plastic strain in direction of the tensile stress which considering volume constancy leads to a thinning perpendicular to the direction of tensile stress. While the stress state dictates the direction of the plastic strain of the material, the total stress corresponds to the total amount of thinning. However, the stress states and total stress in the middle of the sheet and the upper sheet edge did not show the same tendencies for the different process routes. In the upper sheet edge REF and S123 showed both a similar compressive stress state and similar total stress, while showing a different thinning in the formed part. Moreover, REF and S123 showed similar stress states and only slightly lower total stresses in the middle of the sheet compared to the lower sheet edge, while resulting in no visible thinning within the middle of the sheet. Therefore, it was not possible to clearly identify cause effect relations between the thinning and the stress states in
parameter $\bar{\theta}$ of $\bar{\theta} = 0$, while S321 shows a nearly constant triaxiality $\eta$ of $\eta = 0.33$ and constant lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 1$ (Fig. 5c)). REF shows a slight increase in triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ with a maximum triaxiality $\eta$ below $\eta < 0.33$ and a maximum lode angle parameter $\bar{\theta}$ of $\bar{\theta} = 0.66$. This results in a uniaxial tensile stress state for REF and S321 and a sheer stress state for S123. The VON MISES stress $\sigma_{VM}$ shows the same characteristics in the middle of the sheet as in the lower sheet edge. Therefore, S321 shows the highest and S123 the lowest course of the VON MISES stress $\sigma_{VM}$ (Fig. 5d)). In the upper sheet edge the triaxiality $\eta$ of REF and S123 stays constant at a triaxiality $\eta$ of $\eta = -0.33$ and slightly drops in the end of the forming of segment 1 to a triaxiality $\eta$ of $\eta = -0.66$ (Fig. 5e)). The lode angle parameter $\bar{\theta}$ stays constant with a lode angle parameter $\bar{\theta}$ of $\bar{\theta} = -1$ until a steep increase of the lode angle parameter $\bar{\theta}$ to $\bar{\theta} = 0.45$ at the end of the forming process. The triaxiality $\eta$ of S321 oscillates between $-0.66 < \eta < 0.33$, while the lode angle parameter $\bar{\theta}$ changes between $-1 < \bar{\theta} < 1$. For REF and S123 the occurring combinations of triaxiality $\eta$ and lode angle parameter $\bar{\theta}$ lead to a uniaxial to biaxial compressive stress state, while the stress states of S321 vary between uniaxial tensile, uniaxial compressive and biaxial tensile. In the upper sheet edge the VON MISES stress $\sigma_{VM}$ of REF and S123 shows the same characteristics as in the lower sheet edge and middle of the sheet (Fig. 5f)). Additionally, the VON MISES stress $\sigma_{VM}$ of REF and S123 show nearly no distinction. In contrast, the VON MISES stress $\sigma_{VM}$ of S321 differs greatly. In the upper sheet edge the VON MISES stress $\sigma_{VM}$ of S321 drops steeply at first and then oscillates mostly below the VON MISES stress $\sigma_{VM}$ of REF and S123.

## Conclusion and Outlook

The comparison of the thinning using the three process routes showed that S321 generally led to the highest thinning, while S123 resulted in the lowest thinning. For all process routes the highest thinning occurred in the lower radius of segment 1, which resulted in the lower radius to be considered as the most sensitive area regarding thinning. In addition to the thinning, the material volume drawn into the tool was compared between the three process routes. The most material volume was drawn into the tool using S123, while the least material volume inside the tool was found within S321. Therefore, the material volume drawn into the tool corresponds to the described tendencies between the three different process routes regarding thinning. It is assumed that the difference in thinning between the process routes are due to an improved material flow in S123 and a deteriorated material flow in S321 compared to REF. In S123 the most inner segment is formed first, resulting in a nearly unobstructed material flow from the outside of the tool to the inner segment. In contrast, in S321 the most outer segment 3 is formed first, effectively cutting off the material flow from the outside of the tool for the rest of forming.

The comparison of stress states at the lower and upper sheet edge and the middle of the sheet showed distinctions between the stress states and total stress regarding the point of evaluation and the process route used. In the lower sheet edge a very similar tensile stress state was found for all process routes. S321 showed the highest and S123 showed the lowest total stress, corresponding to the results of thinning for the different process routes at the lower sheet edge. It is concluded that tensile stresses lead to plastic strain in direction of the tensile stress which considering volume constancy leads to a thinning perpendicular to the direction of tensile stress. While the stress state dictates the direction of the plastic strain of the material, the total stress corresponds to the total amount of thinning. However, the stress states and total stress in the middle of the sheet and the upper sheet edge did not show the same tendencies for the different process routes. In the upper sheet edge REF and S123 showed both a similar compressive stress state and similar total stress, while showing a different thinning in the formed part. Moreover, REF and S123 showed similar stress states and only slightly lower total stresses in the middle of the sheet compared to the lower sheet edge, while resulting in no visible thinning within the middle of the sheet. Therefore, it was not possible to clearly identify cause effect relations between the thinning and the stress states in
the middle of the sheet and the upper sheet edge in this work. It is believed that while a tensile stress state leads to thinning, a compressive stress state reduces thinning or even leads to negative thinning, meaning thickening of the sheet. Thereby, it is expected that the total stress amplifies the effect of thinning or thickening.

Overall, it has been shown that a segmental forming approach can be used to reduce thinning by allowing more material to be drawn into the tool. In segmental forming, the sequence of segments formed is critical to the forming results. While a sequence of segments formed from the centre of the part outwards (S123) is recommended, a reverse sequence of segments formed (S321) should not be used.

In the future improvements will be made to the simulation to increase the reliability of the numerical analysis. On the one hand, the material model will be further developed to model the material behaviour of foil metal more accurately. The HENSEL-SPITTEL material model currently used does not take microforming effects into account and therefore allows only a rough estimate of the material behaviour. On the other hand, the COULOMB friction model needs to be improved. In the future experimental investigations will be carried out to validate the numerical analysis. The process routes S123 and REF will be selected for this purpose based on the present results. Nevertheless, the present results have already shown the potential of a segmental forming approach and form the basis for further investigations numerical and experimental investigations.

## Acknowledgements

This research was funded by Bundesministerium für Wirtschaft und Klimaschutz (BMWK, Federal Ministry for Economic Affairs and Climate Action; Projectnumber 20N2204D – KeyTech2GreenPower).

## References

[1] Information on https://www.destatis.de/Europa/DE/Thema/GreenDeal/GreenDeal.html

[2] A. Cornet, H. Deubener, R. Dhawan, T. Möller, A. Padhi, P. Schaufuss, T. Tschiesner, Race 2050 – A Vision for the European Automotive Industry, McKinsey & Company, 2019. Information on https://www.mckinsey.de/publikationen/2019-01-08-race-2050-publikation

[3] Information on https://climate.ec.europa.eu/eu-action/transport/reducing-emissions-aviation

[4] R. Whalen, T. Eisenhart, A. Gordon, M. Deimler, P. Losada, C. Follette, Plotting Aviation's Uncharted Course to Net Zero, Boston Consulting Group, 2021. Information on https://www.bcg.com/publications/2021/net-zero-aviation-is-the-future-of-aviation

[5] A. Cornet, R. Heuss, A. Tschiesner, R. Hensley, P. Hertzke, T. Möller, P. Schaufuss, J. Conzade, S. Schenk, K. von Laufenberg, Why the automotive future is electric, McKinsey & Company, 2021. Information on https://www.mckinsey.com/industries/automotive-and-assembly/our-insights/why-the-automotive-future-is-electric

[6] C. Baum, H. Janssen C. Brecher, G. Schuh, M. Aretz, C. Hamm, R. Horstkotte, M. Kersting, S. Lee, A. Masonett, C. Müller, M. Nadicksbernd, U. Panchenko, L. Schenk, P. Scholz, T. Voebel, The Relevance of Fuel Cells for Mobility Applications, Fraunhofer IPT, Aachen, 2021. https://doi.org/10.24406/IPT-N-633591

[7] P. Breeze, An introduction to Fuel Cells, Academic Press, 2018. https://doi.org/10.1016/B978-0-08-101039-6.00001-7

[8] W. Hwang, Y.-E. Sung, Recent Developments of Polymer Electrolyte Membrane Fuel Cell Design, J. Electrochemical Sci. Technol. 14(2) (2023) 120-130. https://doi.org/10.33961/jecst.2022.00808
the middle of the sheet and the upper sheet edge in this work. It is believed that while a tensile stress state leads to thinning, a compressive stress state reduces thinning or even leads to negative thinning, meaning thickening of the sheet. Thereby, it is expected that the total stress amplifies the effect of thinning or thickening.

Overall, it has been shown that a segmental forming approach can be used to reduce thinning by allowing more material to be drawn into the tool. In segmental forming, the sequence of segments formed is critical to the forming results. While a sequence of segments formed from the centre of the part outwards (S123) is recommended, a reverse sequence of segments formed (S321) should not be used.

In the future improvements will be made to the simulation to increase the reliability of the numerical analysis. On the one hand, the material model will be further developed to model the material behaviour of foil metal more accurately. The HENSEL-SPITTEL material model currently used does not take microforming effects into account and therefore allows only a rough estimate of the material behaviour. On the other hand, the COULOMB friction model needs to be improved. In the future experimental investigations will be carried out to validate the numerical analysis. The process routes S123 and REF will be selected for this purpose based on the present results. Nevertheless, the present results have already shown the potential of a segmental forming approach and form the basis for further investigations numerical and experimental investigations.

## Acknowledgements

This research was funded by Bundesministerium für Wirtschaft und Klimaschutz (BMWK, Federal Ministry for Economic Affairs and Climate Action; Projectnumber 20N2204D – KeyTech2GreenPower).

## References

[1] Information on https://www destatis.de/Europa/DE/Thema/GreenDeal/GreenDeal.html

[2] A. Cornet, H. Deubener, R. Dhawan, T. Möller, A. Padhi, P. Schaufuss, T. Tschiesner, Race 2050 – A Vision for the European Automotive Industry, McKinsey & Company, 2019. Information on https://www.mckinsey.de/publikationen/2019-01-08-race-2050-publikation

[3] Information on https://climate.ec.europa.eu/eu-action/transport/reducing-emissions-aviation

[4] R. Whalen, T. Eisenhart, A. Gordon, M. Deimler, P. Losada, C. Follette, Plotting Aviation's Uncharted Course to Net Zero, Boston Consulting Group, 2021. Information on https://www.bcg.com/publications/2021/net-zero-aviation-is-the-future-of-aviation

[5] A. Cornet, R. Heuss, A. Tschiesner, R. Hensley, P. Hertzke, T. Möller, P. Schaufuss, J. Conzade, S. Schenk, K. von Laufenberg, Why the automotive future is electric, McKinsey & Company, 2021. Information on https://www.mckinsey.com/industries/automotive-and-assembly/our-insights/why-the-automotive-future-is-electric

[6] C. Baum, H. Janssen C. Brecher, G. Schuh, M. Aretz, C. Hamm, R. Horstkotte, M. Kersting, S. Lee, A. Masonett, C. Müller, M. Nadicksbernd, U. Panchenko, L. Schenk, P. Scholz, T. Voebel, The Relevance of Fuel Cells for Mobility Applications, Fraunhofer IPT, Aachen, 2021. https://doi.org/10.24406/IPT-N-633591

[7] P. Breeze, An introduction to Fuel Cells, Academic Press, 2018. https://doi.org/10.1016/B978-0-08-101039-6.00001-7

[8] W. Hwang, Y.-E. Sung, Recent Developments of Polymer Electrolyte Membrane Fuel Cell Design, J. Electrochemical Sci. Technol. 14(2) (2023) 120-130. https://doi.org/10.33961/jecst.2022.00808
[9] D.-H. Chang, S.-Y. Wu, The effects of channel depth on the performance of miniature proton exchange membrane fuel cells with serpentine-type flow fields, International Journal of Hydrogen Energy 40 (2015) 11659-11667. https://doi.org/10.1016/j.ijhydene.2015.04.153

[10] Information on https://www.now-gmbh.de/wp-content/uploads/2022/10/Deep-Dive_Bipolarplatte.pdf

[11] M. Fiedler, K. Kittner, B. Awiszus, Production of Metallic Bipolar Plates Made of Stainless Steel by Incremental Hollow Embossing Using Rollers, Eng. Proc. 26(1) (2022) 1-9. https://doi.org/10.3390/engproc2022026015

[12] J. Sommer, M. Müller, T. Herrig, T. Bergs, Simulative and Empirical Investigation of Test Specimen Geometries for the Determination of Forming Limit States in the Tensile-Compression Range for Austenitic Stainless Steel Foil Material, Proc. of the 14th International Conference on the Techn. of Plasticity (2023). https://doi.org/10.1007/978-3-031-42093-1_25
[9] D.-H. Chang, S.-Y. Wu, The effects of channel depth on the performance of miniature proton exchange membrane fuel cells with serpentine-type flow fields, International Journal of Hydrogen Energy 40 (2015) 11659-11667. https://doi.org/10.1016/j.ijhydene.2015.04.153

[10] Information on https://www.now-gmbh.de/wp-content/uploads/2022/10/Deep-Dive_Bipolarplatte.pdf

[11] M. Fiedler, K. Kittner, B. Awiszus, Production of Metallic Bipolar Plates Made of Stainless Steel by Incremental Hollow Embossing Using Rollers, Eng. Proc. 26(1) (2022) 1-9. https://doi.org/10.3390/engproc2022026015

[12] J. Sommer, M. Müller, T. Herrig, T. Bergs, Simulative and Empirical Investigation of Test Specimen Geometries for the Determination of Forming Limit States in the Tensile-Compression Range for Austenitic Stainless Steel Foil Material, Proc. of the 14th International Conference on the Techn. of Plasticity (2023). https://doi.org/10.1007/978-3-031-42093-1_25
# Experimental evidence on the twisting of incrementally formed polymer sheets by varying the toolpath strategy

FORMISANO Antonio¹,ª*, BOCCARUSSO Luca¹,ᵇ, DE FAZIO Dario¹,ᶜ, PRISCO Umberto¹,ᵈ, DURANTE Massimo¹,ᵉ and LANGELLA Antonio¹,ᵉ

¹Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le V. Tecchio 80, 80125 Napoli, Italy

ªaformisa@unina.it, ᵇluca.boccarusso@unina.it, ᶜdario.defazio@unina.it, ᵈumberto.prisco@unina.it, ᵉmdurante@unina.it, ᵇantgella@unina.it

**Keywords:** Incremental Forming, Polycarbonate, Toolpath Strategy, Forming Forces

**Abstract.** In recent years, polymer sheets have been formed by a relatively innovative technology, born for metals and in line with the layered manufacturing principle of rapid prototyping, the incremental sheet forming. This process guarantees high customization and cost-effectiveness but, at the same time, activates some peculiar defects like the twisting phenomenon. To reduce the risk of twisting and the occurrence of failures, it is preferable to reduce the forming forces and one of the solutions is the choice of opportune toolpath strategies. Concerning this, the present experimental research is along the same lines as recent numerical works of the authors; thermoplastic sheets were worked by incremental forming by varying the toolpath strategy. Following the realization of cone frusta, the forming forces and the deformation of the sheets were monitored, to investigate a toolpath strategy capable of reducing the risk of failures and defects for incrementally formed polymer sheets.

**Introduction**

Incremental sheet forming represents a viable way for customized production in a brief time and at a low cost, starting from sheets of pure metals, alloys, polymers, and composites [1]. Among them, the interest in the processing of thermoplastic polymers with this technique has been increasing over the past few years, starting from the studies of Franzen et al. on polyvinylchloride sheets [2] and going on with other commercial polymers [3], since it can represent a valid alternative to conventional technologies, based on heating-shaping-cooling manufacturing routes [4].

One of the main attractive features of this forming process is the achieving of high materials' formability with low-forming forces; on the other hand, incremental formed parts suffer from peculiar defects like twisting and wrinkling, and this is particularly true when using thermoplastic sheets [5].

A way to reduce the risk of the above-mentioned defects, as well as the occurrence of failures and the worsening of formed surfaces' quality, is to act on the toolpath strategy; consider, for example, that the twisting was significantly reduced by using an alternating toolpath in anticlockwise and clockwise directions [6,7]. Moreover, another solution is the reduction of the forming forces, particularly the ones acting in the sheet plane. Concerning the twisting phenomenon, its occurrence is more probable in the case of higher and more regular plane forces, which determine a combination of continued strain accumulation and asymmetric strain levels [8,9].

According to the considerations reported above and in line with previous authors' work aiming to optimize the forming process through a numerical approach [10], cone frusta with fixed wall angle were manufactured starting from thin polycarbonate sheets by the most common variant of the process under exam, named single-point incremental forming (involving the use of a simple

<figure><img src="image_2232.png" /></figure>
# Experimental evidence on the twisting of incrementally formed polymer sheets by varying the toolpath strategy

FORMISANO Antonio¹,ª*, BOCCARUSSO Luca¹,ᵇ, DE FAZIO Dario¹,ᶜ, PRISCO Umberto¹,ᵈ, DURANTE Massimo¹,ᵉ and LANGELLA Antonio¹,ᵉ

¹Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le V. Tecchio 80, 80125 Napoli, Italy

ªaformisa@unina.it, ᵇluca.boccarusso@unina.it, ᶜdario.defazio@unina.it, ᵈumberto.prisco@unina.it, ᵉmdurante@unina.it, ᵇantgella@unina.it

**Keywords:** Incremental Forming, Polycarbonate, Toolpath Strategy, Forming Forces

**Abstract.** In recent years, polymer sheets have been formed by a relatively innovative technology, born for metals and in line with the layered manufacturing principle of rapid prototyping, the incremental sheet forming. This process guarantees high customization and cost-effectiveness but, at the same time, activates some peculiar defects like the twisting phenomenon. To reduce the risk of twisting and the occurrence of failures, it is preferable to reduce the forming forces and one of the solutions is the choice of opportune toolpath strategies. Concerning this, the present experimental research is along the same lines as recent numerical works of the authors; thermoplastic sheets were worked by incremental forming by varying the toolpath strategy. Following the realization of cone frusta, the forming forces and the deformation of the sheets were monitored, to investigate a toolpath strategy capable of reducing the risk of failures and defects for incrementally formed polymer sheets.

**Introduction**

Incremental sheet forming represents a viable way for customized production in a brief time and at a low cost, starting from sheets of pure metals, alloys, polymers, and composites [1]. Among them, the interest in the processing of thermoplastic polymers with this technique has been increasing over the past few years, starting from the studies of Franzen et al. on polyvinylchloride sheets [2] and going on with other commercial polymers [3], since it can represent a valid alternative to conventional technologies, based on heating-shaping-cooling manufacturing routes [4].

One of the main attractive features of this forming process is the achieving of high materials' formability with low-forming forces; on the other hand, incremental formed parts suffer from peculiar defects like twisting and wrinkling, and this is particularly true when using thermoplastic sheets [5].

A way to reduce the risk of the above-mentioned defects, as well as the occurrence of failures and the worsening of formed surfaces' quality, is to act on the toolpath strategy; consider, for example, that the twisting was significantly reduced by using an alternating toolpath in anticlockwise and clockwise directions [6,7]. Moreover, another solution is the reduction of the forming forces, particularly the ones acting in the sheet plane. Concerning the twisting phenomenon, its occurrence is more probable in the case of higher and more regular plane forces, which determine a combination of continued strain accumulation and asymmetric strain levels [8,9].

According to the considerations reported above and in line with previous authors' work aiming to optimize the forming process through a numerical approach [10], cone frusta with fixed wall angle were manufactured starting from thin polycarbonate sheets by the most common variant of the process under exam, named single-point incremental forming (involving the use of a simple

<figure><img src="image_2223.png" /></figure>
tool and a clamping frame, and the absence of dies, for the superimposition of local deformations in the sheets), by setting typical process parameters [7] and by varying the toolpath strategy.

Some features from the experimental work were analysed, like the forming forces and the geometrical features connected to the occurrence of twisting, to individuate a toolpath strategy capable of reducing both and, also, the risk of failures and other defects on incrementally formed components.

## Materials and methods

Cone frusta with fixed wall angle $α$, height $h$, and radius of the major base $R$ (geometrical features and corresponding values reported in Fig. 1) were manufactured starting from 1.5 mm thick polycarbonate sheets. Polycarbonate is also known as a “transparency metal” because of its relevant mechanical and physiochemical properties [11] that make it strongly used in several applications in the fields of communication, transport, medical apparatus, aerospace environment, and so on [12].

<figure><img src="image_2233.png" /><figcaption>Fig. 1. Geometrical features of the cone frusta</figcaption></figure>

The sheets were formed by using a C.B. Ferrari high-speed four-axis vertical machining centre, a clamping frame with an internal square area having a side of 100 mm and a 10 mm diameter hemispherical head stainless steel forming non-rotating tool. Fig. 2 reports the experimental setup during an incremental forming test, while the main properties of the sheet are the following: density of 1.2 g/cm³, Young's modulus of 2.3 GPa, Poisson's ratio of 0.3, yield stress of 60 MPa and ultimate elongation of 110%. The surfaces of the sheets in contact with the tool were lubricated with a thin layer of mineral oil for cold forming to reduce the risks of damage because of the tool/sheet interaction.

Three different paths of the forming tool, described with a feed rate of 1000 mm/min, were considered to deform the sheets; concerning this, see the not-to-scale schematization in Fig. 3. In all the cases, the tool covered points of a spiral path, equally spaced around an angle $β$ from each other; the vertical distance between two consecutive spirals was vs (see Fig. 3a, in which five exemplary consecutive points, from A to E, are reported, as well as the values of the geometrical features).

The three different toolpaths differed in the way they covered the distance between two consecutive points: in the first case, by describing a segment (reference toolpath, ref_TP, see Fig. 3b); in the other two cases, by alternating an upward and a vertical segment (hr0.5_TP and hr1.5_TP, where hr is the ramp height, see Fig. 3c).
tool and a clamping frame, and the absence of dies, for the superimposition of local deformations in the sheets), by setting typical process parameters [7] and by varying the toolpath strategy.

Some features from the experimental work were analysed, like the forming forces and the geometrical features connected to the occurrence of twisting, to individuate a toolpath strategy capable of reducing both and, also, the risk of failures and other defects on incrementally formed components.

## Materials and methods

Cone frusta with fixed wall angle $α$, height $h$, and radius of the major base $R$ (geometrical features and corresponding values reported in Fig. 1) were manufactured starting from 1.5 mm thick polycarbonate sheets. Polycarbonate is also known as a “transparency metal” because of its relevant mechanical and physiochemical properties [11] that make it strongly used in several applications in the fields of communication, transport, medical apparatus, aerospace environment, and so on [12].

<figure><img src="image_2224.png" /><figcaption>Fig. 1. Geometrical features of the cone frusta</figcaption></figure>

The sheets were formed by using a C.B. Ferrari high-speed four-axis vertical machining centre, a clamping frame with an internal square area having a side of 100 mm and a 10 mm diameter hemispherical head stainless steel forming non-rotating tool. Fig. 2 reports the experimental setup during an incremental forming test, while the main properties of the sheet are the following: density of 1.2 g/cm³, Young's modulus of 2.3 GPa, Poisson's ratio of 0.3, yield stress of 60 MPa and ultimate elongation of 110%. The surfaces of the sheets in contact with the tool were lubricated with a thin layer of mineral oil for cold forming to reduce the risks of damage because of the tool/sheet interaction.

Three different paths of the forming tool, described with a feed rate of 1000 mm/min, were considered to deform the sheets; concerning this, see the not-to-scale schematization in Fig. 3. In all the cases, the tool covered points of a spiral path, equally spaced around an angle $β$ from each other; the vertical distance between two consecutive spirals was vs (see Fig. 3a, in which five exemplary consecutive points, from A to E, are reported, as well as the values of the geometrical features).

The three different toolpaths differed in the way they covered the distance between two consecutive points: in the first case, by describing a segment (reference toolpath, ref_TP, see Fig. 3b); in the other two cases, by alternating an upward and a vertical segment (hr0.5_TP and hr1.5_TP, where hr is the ramp height, see Fig. 3c).
<figure><img src="image_2234.png" /><figcaption>Fig. 2. Experimental setup during an incremental forming test</figcaption></figure>

<figure><img src="image_2235.png" /><figcaption>Fig. 3. Details of the toolpath (a) and toolpath strategies (b-c)</figcaption></figure>

Two components of the forming force, $F_Z$ and $F_X$ (see the reference axes in Fig. 1), were acquired through a Kistler 9257A piezoelectric transducer; the data were collected at 2000 Hz and subsequently filtered using a NI 9239 input module and the VBA 1.0 B software.
<figure><img src="image_2225.png" /><figcaption>Fig. 2. Experimental setup during an incremental forming test</figcaption></figure>

<figure><img src="image_2226.png" /><figcaption>Fig. 3. Details of the toolpath (a) and toolpath strategies (b-c)</figcaption></figure>

Two components of the forming force, $F_Z$ and $F_X$ (see the reference axes in Fig. 1), were acquired through a Kistler 9257A piezoelectric transducer; the data were collected at 2000 Hz and subsequently filtered using a NI 9239 input module and the VBA 1.0 B software.
Moreover, from the tests also the twisting magnitude was evaluated [13]; the twist angle $\theta$ was measured by CAD in terms of the rotation of a cross, marked on the bottom flat surface of the cone frusta, to their original position (see Fig. 4).

<figure><img src="image_2236.png" /><figcaption>Fig. 4. Evaluation of the twist angle</figcaption></figure>

## Results and discussion

Before showing the results in terms of forces and twisting, it is worth highlighting that all the tests were conducted without incurring failures; then, all the toolpath strategies guaranteed the correct execution of the incremental forming process.

Fig. 5a and Fig. 5b report a particular of the vertical and the horizontal components of the forming force for the different toolpaths. Note that the time on the abscissa axis is expressed in percentage terms, for the processing time of each case, to simply compare the forces, because of the different lengths of the toolpaths by varying the strategy; moreover, the two-time windows are different to better understand the force trends (longer for the horizontal forces, to cover two entire spirals of the toolpath).

Fig. 5a highlights that the ref TP strategy determines a continuous and constant tool/sheet contact condition (vertical force of about 450 N), because of a continuous vertical down movement of the tool. For the non-reference strategies, the trend is less regular and $F_z$ fluctuates (reaching a minimum value of about 200 N for the hr1.5 TP strategy) due to a partial elastic recovery [14]. For a comparison of the vertical forces, the mean values in the time window of Fig. 5a were evaluated. It is possible to affirm that the mean value of $F_z$ decreases from 443 (ref TP) to 335 N (hr1.5 TP), passing from 375 N for the hr0.5 TP strategy.
Moreover, from the tests also the twisting magnitude was evaluated [13]; the twist angle $\theta$ was measured by CAD in terms of the rotation of a cross, marked on the bottom flat surface of the cone frusta, to their original position (see Fig. 4).

<figure><img src="image_2227.png" /><figcaption>Fig. 4. Evaluation of the twist angle</figcaption></figure>

## Results and discussion

Before showing the results in terms of forces and twisting, it is worth highlighting that all the tests were conducted without incurring failures; then, all the toolpath strategies guaranteed the correct execution of the incremental forming process.

Fig. 5a and Fig. 5b report a particular of the vertical and the horizontal components of the forming force for the different toolpaths. Note that the time on the abscissa axis is expressed in percentage terms, for the processing time of each case, to simply compare the forces, because of the different lengths of the toolpaths by varying the strategy; moreover, the two-time windows are different to better understand the force trends (longer for the horizontal forces, to cover two entire spirals of the toolpath).

Fig. 5a highlights that the ref TP strategy determines a continuous and constant tool/sheet contact condition (vertical force of about 450 N), because of a continuous vertical down movement of the tool. For the non-reference strategies, the trend is less regular and $F_z$ fluctuates (reaching a minimum value of about 200 N for the hr1.5 TP strategy) due to a partial elastic recovery [14]. For a comparison of the vertical forces, the mean values in the time window of Fig. 5a were evaluated. It is possible to affirm that the mean value of $F_z$ decreases from 443 (ref TP) to 335 N (hr1.5 TP), passing from 375 N for the hr0.5 TP strategy.
The effects of the upward segments are also visible in terms of horizontal force (Fig. 5b), which shows the typical sinusoidal trend but partially irregular when using $hr0.5\_tp$ and $hr1.5\_tp$ strategies.

Fig. 6 reports the twist angle for the different toolpath strategies. From the histogram, it is possible to note that $ref\_tp$ determines the most severe contact conditions and the twisting phenomenon can be mitigated through the choice of the non-reference toolpath strategies, as supposed in [15].

Despite this, it can be affirmed that the toolpath can be further optimized; in fact, one can think of different solutions to reduce the sliding forces and point the twist angle towards zero.

<figure><img src="image_2237.png" /><figcaption>Fig. 5. Particular of the vertical (a) and the horizontal component of the forming force (b)</figcaption></figure>
The effects of the upward segments are also visible in terms of horizontal force (Fig. 5b), which shows the typical sinusoidal trend but partially irregular when using $hr0.5\_tp$ and $hr1.5\_tp$ strategies.

Fig. 6 reports the twist angle for the different toolpath strategies. From the histogram, it is possible to note that $ref\_tp$ determines the most severe contact conditions and the twisting phenomenon can be mitigated through the choice of the non-reference toolpath strategies, as supposed in [15].

Despite this, it can be affirmed that the toolpath can be further optimized; in fact, one can think of different solutions to reduce the sliding forces and point the twist angle towards zero.

<figure><img src="image_2228.png" /><figcaption>Fig. 5. Particular of the vertical (a) and the horizontal component of the forming force (b)</figcaption></figure>
<figure><img src="image_2238.png" /><figcaption>Fig. 6. Twist angle by varying the toolpath strategy</figcaption></figure>

**Conclusions**

The present work presents the results of an experimental work involving the manufacture of fixed wall angle cone frusta by varying the toolpath strategy, intending to reduce the forming forces and the magnitude of the twisting phenomenon.

The tests highlight that, in comparison with a reference toolpath, it is possible to reduce the forming forces by adopting toolpaths with an alternation of diagonal up and vertical down steps, because of a partial elastic recovery during the process; most likely, this could imply a positive impact on the environment, in terms of energy consumption. At the same time, a slight reduction of the twist angle occurs.

Future works could aim to extend the research, both numerically and experimentally. For example, new variants of toolpath could be considered. In so doing, a further decrease of the twisting could be expected; moreover, the influence of the toolpath on the surface roughness could be investigated.

**Acknowledgements**

This work was supported by the “Programma per il Finanziamento della Ricerca di Ateneo (FRA) 2022” of the University of Naples Federico II.

**References**

[1] L. Bertini, A. Kubit, R. Al-Sabur, A. Gradzik, K. Ochał, J. Slota, M. Korzeniowski, Investigating Residual Stresses in Metal-Plastic Composites Stiffening Ribs Formed Using the Single Point Incremental Forming Method, Materials 15 (2022) 8252. https://doi.org/10.3390/MA15228252

[2] V. Franzen, L. Kwiatkowski, P.A.F. Martins, A.E. Tekkaya, Single Point Incremental Forming of PVC, J. Mater. Process. Technol. 209 (2009), 462-469. https://doi.org/10.1016/j.jmatprotec.2008.02.013

[3] P.A.F. Martins, L. Kwiatkowski, V. Franzen, A.E. Tekkaya, M. Kleiner, Single Point Incremental Forming of Polymers, CIRP Ann. 58 (2009), 229-232. https://doi.org/10.1016/J.CIRP.2009.03.095
<figure><img src="image_2229.png" /><figcaption>Fig. 6. Twist angle by varying the toolpath strategy</figcaption></figure>

**Conclusions**

The present work presents the results of an experimental work involving the manufacture of fixed wall angle cone frusta by varying the toolpath strategy, intending to reduce the forming forces and the magnitude of the twisting phenomenon.

The tests highlight that, in comparison with a reference toolpath, it is possible to reduce the forming forces by adopting toolpaths with an alternation of diagonal up and vertical down steps, because of a partial elastic recovery during the process; most likely, this could imply a positive impact on the environment, in terms of energy consumption. At the same time, a slight reduction of the twist angle occurs.

Future works could aim to extend the research, both numerically and experimentally. For example, new variants of toolpath could be considered. In so doing, a further decrease of the twisting could be expected; moreover, the influence of the toolpath on the surface roughness could be investigated.

**Acknowledgements**

This work was supported by the “Programma per il Finanziamento della Ricerca di Ateneo (FRA) 2022” of the University of Naples Federico II.

**References**

[1] L. Bertini, A. Kubit, R. Al-Sabur, A. Gradzik, K. Ochał, J. Slota, M. Korzeniowski, Investigating Residual Stresses in Metal-Plastic Composites Stiffening Ribs Formed Using the Single Point Incremental Forming Method, Materials 15 (2022) 8252. https://doi.org/10.3390/MA15228252

[2] V. Franzen, L. Kwiatkowski, P.A.F. Martins, A.E. Tekkaya, Single Point Incremental Forming of PVC, J. Mater. Process. Technol. 209 (2009), 462-469. https://doi.org/10.1016/j.jmatprotec.2008.02.013

[3] P.A.F. Martins, L. Kwiatkowski, V. Franzen, A.E. Tekkaya, M. Kleiner, Single Point Incremental Forming of Polymers, CIRP Ann. 58 (2009), 229-232. https://doi.org/10.1016/J.CIRP.2009.03.095
[4] A. Rosa-Sainz, G. Centeno, M.B. Silva, J. Andrés López-Fernández, A. Jesus Martínez-Donaire, C. Vallellano, On the determination of forming limits in polycarbonate sheets, Materials 13 (2020) 928. https://doi.org/10.3390/ma13040928

[5] H. Zhu, H. Ou, A. Popov, Incremental Sheet Forming of Thermoplastics: A Review, Int. J. Adv. Manuf. Technol. 111 (2020) 565-587. https://doi.org/10.1007/s00170-020-06056-5

[6] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric Single Point Incremental Forming of Sheet Metal, CIRP Ann. 54 (2005), 88-114. https://doi.org/10.1016/S0007-8506(07)60021-3

[7] M. Durante, A. Formisano, F. Lambiase, Incremental forming of polycarbonate sheets, J. Mater. Process. Technol. 253 (2018) 57-63. https://doi.org/10.1016/j.jmatprotec.2017.11.005

[8] Z. Chang, J. Chen, Mechanism of the Twisting in Incremental Sheet Forming Process, J. Mater. Process. Technol. 276 (2020) 116396. https://doi.org/10.1016/J.JMATPROTEC.2019.116396

[9] J.R. Duflou, H. Vanhove, J. Verbert, J. Gu, I. Vasilakos, P. Eyckens, Twist revisited: Twist phenomena in single point incremental forming, CIRP Ann. 59 (2010) 307-310. https://doi.org/10.1016/J.CIRP.2010.03.018

[10] A. Formisano, M. Durante, L. Boccarusso, F. Memola Capece, A numerical approach to optimize the toolpath strategy for polymers forming, Mater. Res. Proc. 28 (2023) 1697-1702. https://doi.org/10.21741/9781644902479-183

[11] Z.X. Hou, J. Wu, Z.R. Wang, A Study of the Bulge-Forming of Polycarbonate (PC) Sheet, J. Mater. Process. Technol. 151 (2004) 312-315. https://doi.org/10.1016/j.jmatprotec.2004.04.080

[12] I. Beşliu, I. Tamaşag, L. Slătineanu, An Experimental Study on Incremental Forming Process of Polycarbonate Sheets, Macromol. Symp. 395 (2021) 2000282. https://doi.org/10.1002/masy.202000282

[13] M. Durante, A. Formisano, F. Lambiase, Formability of Polycarbonate Sheets in Single-Point Incremental Forming, Int. J. Adv. Manuf. Technol. 102 (2019) 2049-2062. https://doi.org/10.1007/s00170-019-03298-w

[14] H. Wei, L. Zhou, B. Heidarshenas, I.K. Ashraf, C. Han, Investigation on the Influence of Springback on Precision of Symmetric-Cone-Like Parts in Sheet Metal Incremental Forming Process, Int. J. Light. Mater. Manuf. 2 (2019) 140-145. https://doi.org/10.1016/j.ijlmm.2019.05.002

[15] A. Formisano, L. Boccarusso, M. Durante, Optimization of single-point incremental forming of polymer sheets through FEM, Materials 16 (2023) 451. https://doi.org/10.3390/ma16010451
[4] A. Rosa-Sainz, G. Centeno, M.B. Silva, J. Andrés López-Fernández, A. Jesus Martínez-Donaire, C. Vallellano, On the determination of forming limits in polycarbonate sheets, Materials 13 (2020) 928. https://doi.org/10.3390/ma13040928

[5] H. Zhu, H. Ou, A. Popov, Incremental Sheet Forming of Thermoplastics: A Review, Int. J. Adv. Manuf. Technol. 111 (2020) 565-587. https://doi.org/10.1007/s00170-020-06056-5

[6] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric Single Point Incremental Forming of Sheet Metal, CIRP Ann. 54 (2005), 88-114. https://doi.org/10.1016/S0007-8506(07)60021-3

[7] M. Durante, A. Formisano, F. Lambiase, Incremental forming of polycarbonate sheets, J. Mater. Process. Technol. 253 (2018) 57-63. https://doi.org/10.1016/j.jmatprotec.2017.11.005

[8] Z. Chang, J. Chen, Mechanism of the Twisting in Incremental Sheet Forming Process, J. Mater. Process. Technol. 276 (2020) 116396. https://doi.org/10.1016/J.JMATPROTEC.2019.116396

[9] J.R. Duflou, H. Vanhove, J. Verbert, J. Gu, I. Vasilakos, P. Eyckens, Twist revisited: Twist phenomena in single point incremental forming, CIRP Ann. 59 (2010) 307-310. https://doi.org/10.1016/J.CIRP.2010.03.018

[10] A. Formisano, M. Durante, L. Boccarusso, F. Memola Capece, A numerical approach to optimize the toolpath strategy for polymers forming, Mater. Res. Proc. 28 (2023) 1697-1702. https://doi.org/10.21741/9781644902479-183

[11] Z.X. Hou, J. Wu, Z.R. Wang, A Study of the Bulge-Forming of Polycarbonate (PC) Sheet, J. Mater. Process. Technol. 151 (2004) 312-315. https://doi.org/10.1016/j.jmatprotec.2004.04.080

[12] I. Beşliu, I. Tamaşag, L. Slătineanu, An Experimental Study on Incremental Forming Process of Polycarbonate Sheets, Macromol. Symp. 395 (2021) 2000282. https://doi.org/10.1002/masy.202000282

[13] M. Durante, A. Formisano, F. Lambiase, Formability of Polycarbonate Sheets in Single-Point Incremental Forming, Int. J. Adv. Manuf. Technol. 102 (2019) 2049-2062. https://doi.org/10.1007/s00170-019-03298-w

[14] H. Wei, L. Zhou, B. Heidarshenas, I.K. Ashraf, C. Han, Investigation on the Influence of Springback on Precision of Symmetric-Cone-Like Parts in Sheet Metal Incremental Forming Process, Int. J. Light. Mater. Manuf. 2 (2019) 140-145. https://doi.org/10.1016/j.ijlmm.2019.05.002

[15] A. Formisano, L. Boccarusso, M. Durante, Optimization of single-point incremental forming of polymer sheets through FEM, Materials 16 (2023) 451. https://doi.org/10.3390/ma16010451
# Investigation of the Influences on the Indentation of tubes under lateral loads by segmented forming tools using DoE

REUTER Jonas¹,ª*, ASLANIDIS Apostolos¹,ᵇ and ENGEL Bernd¹,ᶜ

¹Chair of Forming Technology, Institute of Production Technologies, University of Siegen, Breite
Straße 11, 57076 Siegen, Germany

ªjonas.reuter@uni-siegen.de, ᵇapostolos.aslanidis@uni-siegen.de, ᶜbernd.engel@uni-siegen.de

**Keywords:** Flexible Profile Bending, Profile Forming, Adjustable Forming Tools, Segmented Bending Tools, Lateral Indentation

**Abstract.** Making the widely used bending processes with geometry-specific tools, such as compression bending, more flexible in terms of the part geometries that can be produced with a single tool set, is a current challenge as mass customization and small batch sizes demands on manufacturing technologies. One approach is to segment the tools and thus add degrees of freedom that allow the die to adapt to different part geometries. However, the discrete surface can cause part defects such as localized indentations and until now, there has been no design method for segmented surfaces. As a step to close this gap, this study presents a statistical, finite element (FE) simulation-based design of experiments (DoE) to investigate the main influences on the indentation depth in the lateral indentation of circular steel tubes by segmented tool surfaces, considering both tool surface parameters and tube properties. The resulting regression equation is then used to compare the prognosticated indentation depths with those obtained from FE simulations and to develop a first pre-design approach for segmented tool surfaces. The results of the simulation-based DoE show that the segment spacing, the wall thickness factor, the interaction between them, the segment radius and the interaction between the segment radius and the segment spacing are the main influencing parameters and, interestingly, the mechanical tube properties have no significant influence. Finally, it is outlined that the regression equation can be used as a pre-design tool and that refinements are necessary for its usage as a valid design tool.

**Introduction**

Megatrends are very long-term, dominant economic and social developments [1]. From the point of view of production technologies, the megatrends of neo-ecology, connectivity and individualization in particular open up challenging fields of action for industry and research [2]. Sustainability is the paradigm of our time, against which every product and the production systems required to manufacture it must be measured. According to *Stock et al.* [3], the connected *Industry 4.0* with its smart factories offers opportunities to make production sustainable and at the same time to meet the individualized customer demands. This mass customization requires highly flexible, smart manufacturing systems, not least in metal forming [4].

Considering profile bending processes, we can distinguish between kinematic processes or those with generic tools respectively on the one hand and processes with geometry-specific tools on the other hand [5]. Kinematic processes (e.g., three-roll push bending) are much more flexible in terms of the variety of part geometries that can be produced with a single tool set due to their shape-defining, free tool movement. In contrast, processes using geometry-specific tools (e.g., rotary-draw bending, compression bending) are limited in this way. However, these processes are widely used in industry because of their advantages in process controllability, dimensional part accuracy and the ability to form strong curvatures. Consequently, adjustable forming tools are needed to make geometry-specific processes more flexible while maintaining their advantages.

<figure><img src="image_2239.png" /></figure>
# Investigation of the Influences on the Indentation of tubes under lateral loads by segmented forming tools using DoE

REUTER Jonas¹,ª*, ASLANIDIS Apostolos¹,ᵇ and ENGEL Bernd¹,ᶜ

¹Chair of Forming Technology, Institute of Production Technologies, University of Siegen, Breite
Straße 11, 57076 Siegen, Germany

ªjonas.reuter@uni-siegen.de, ᵇapostolos.aslanidis@uni-siegen.de, ᶜbernd.engel@uni-siegen.de

**Keywords:** Flexible Profile Bending, Profile Forming, Adjustable Forming Tools, Segmented Bending Tools, Lateral Indentation

**Abstract.** Making the widely used bending processes with geometry-specific tools, such as compression bending, more flexible in terms of the part geometries that can be produced with a single tool set, is a current challenge as mass customization and small batch sizes demands on manufacturing technologies. One approach is to segment the tools and thus add degrees of freedom that allow the die to adapt to different part geometries. However, the discrete surface can cause part defects such as localized indentations and until now, there has been no design method for segmented surfaces. As a step to close this gap, this study presents a statistical, finite element (FE) simulation-based design of experiments (DoE) to investigate the main influences on the indentation depth in the lateral indentation of circular steel tubes by segmented tool surfaces, considering both tool surface parameters and tube properties. The resulting regression equation is then used to compare the prognosticated indentation depths with those obtained from FE simulations and to develop a first pre-design approach for segmented tool surfaces. The results of the simulation-based DoE show that the segment spacing, the wall thickness factor, the interaction between them, the segment radius and the interaction between the segment radius and the segment spacing are the main influencing parameters and, interestingly, the mechanical tube properties have no significant influence. Finally, it is outlined that the regression equation can be used as a pre-design tool and that refinements are necessary for its usage as a valid design tool.

**Introduction**

Megatrends are very long-term, dominant economic and social developments [1]. From the point of view of production technologies, the megatrends of neo-ecology, connectivity and individualization in particular open up challenging fields of action for industry and research [2]. Sustainability is the paradigm of our time, against which every product and the production systems required to manufacture it must be measured. According to *Stock et al.* [3], the connected *Industry 4.0* with its smart factories offers opportunities to make production sustainable and at the same time to meet the individualized customer demands. This mass customization requires highly flexible, smart manufacturing systems, not least in metal forming [4].

Considering profile bending processes, we can distinguish between kinematic processes or those with generic tools respectively on the one hand and processes with geometry-specific tools on the other hand [5]. Kinematic processes (e.g., three-roll push bending) are much more flexible in terms of the variety of part geometries that can be produced with a single tool set due to their shape-defining, free tool movement. In contrast, processes using geometry-specific tools (e.g., rotary-draw bending, compression bending) are limited in this way. However, these processes are widely used in industry because of their advantages in process controllability, dimensional part accuracy and the ability to form strong curvatures. Consequently, adjustable forming tools are needed to make geometry-specific processes more flexible while maintaining their advantages.

<figure><img src="image_2230.png" /></figure>
In a previous work, the authors have defined three levels of tool flexibility based on the scale of surface adjustment and on its impact on the process [6]. While the required surface adjustments in the range of tenths of millimeters at the first level of flexibility, which is used for example to control the material flow in deep drawing by means of adjustable blankholder systems [7], could be realized by elastic tool deformations, at the second level of flexibility, adjustments in the millimeter range to compensate for springback or to adapt the tools to different workpiece dimensions, require other tool structure concepts and design methods as presented for example by Heftrich et al. [8]. The third flexibility level, the reshaping of the entire tool contour, requires large tool adjustments. For this, some kind of break-up or segmentation of the conventionally closed tool surfaces is necessary, as seen for example in multi-point forming (MPF) techniques [9, 10] or as shown in Reuter et al. for compression bending [11]. However, the discrete tool contact can cause defects such as local indentations, wrinkles and shape deviations [11,12].

Since MPF has been used in industrial and research applications, it has been investigated mostly for large-sized parts, not for profile bending with small bending radii. Although some work has focused on the influence of the geometry of the discrete surface on part defects such as dimples, until now there is no design method for tool surface segmentation. As a step towards closing this gap, this contribution presents a design approach based on a statistical regression model. First, a validation of a FE-model based on experiments on the lateral indentation of segments and segmented surfaces in circular tubes made of E235 +N/+C steel is shown. Afterwards, a statistical design of experiments (DoE) of geometric surface parameters and tube properties is performed with respect to the quality criterion "indentation depth" as output based on FE simulations in order to obtain both, an insight into the main influencing parameters and a linear regression model. The statistical regression model is finally used to develop a pre-design rule for geometric surface parameters as a function of tube properties, which is again compared with the results from FE simulations.

## Validation of the FE-models

Lateral indentation tests on circular tubes have been performed using the Zwick Roell Z250 universal testing machine to characterize the load-deformation behavior and to validate FE models, see also [13]. Steel tubes of grade E235 +N/+C with a circular cross section, a constant outer diameter of $D = 30$ mm, but various tube lengths and wall thicknesses of $t = 1.5$ mm, 2.0 mm and 3.0 mm are used as test material. Fig. 1 shows the test setup, used in [13] also. Straight segments

<figure><img src="image_2240.png" /><figcaption>Fig. 1: Test setup for the lateral indentation tests according to [13].</figcaption></figure>

with different radii represent the segmented tool surface and can be placed with different spacings in a fixture. A Gom Aramis 12M DIC system with a calibrated field of view of 200x147 mm² (resolution of 20.5 pixels/mm) is used to measure the strain distribution on the specimen surface
In a previous work, the authors have defined three levels of tool flexibility based on the scale of surface adjustment and on its impact on the process [6]. While the required surface adjustments in the range of tenths of millimeters at the first level of flexibility, which is used for example to control the material flow in deep drawing by means of adjustable blankholder systems [7], could be realized by elastic tool deformations, at the second level of flexibility, adjustments in the millimeter range to compensate for springback or to adapt the tools to different workpiece dimensions, require other tool structure concepts and design methods as presented for example by Heftrich et al. [8]. The third flexibility level, the reshaping of the entire tool contour, requires large tool adjustments. For this, some kind of break-up or segmentation of the conventionally closed tool surfaces is necessary, as seen for example in multi-point forming (MPF) techniques [9, 10] or as shown in Reuter et al. for compression bending [11]. However, the discrete tool contact can cause defects such as local indentations, wrinkles and shape deviations [11,12].

Since MPF has been used in industrial and research applications, it has been investigated mostly for large-sized parts, not for profile bending with small bending radii. Although some work has focused on the influence of the geometry of the discrete surface on part defects such as dimples, until now there is no design method for tool surface segmentation. As a step towards closing this gap, this contribution presents a design approach based on a statistical regression model. First, a validation of a FE-model based on experiments on the lateral indentation of segments and segmented surfaces in circular tubes made of E235 +N/+C steel is shown. Afterwards, a statistical design of experiments (DoE) of geometric surface parameters and tube properties is performed with respect to the quality criterion "indentation depth" as output based on FE simulations in order to obtain both, an insight into the main influencing parameters and a linear regression model. The statistical regression model is finally used to develop a pre-design rule for geometric surface parameters as a function of tube properties, which is again compared with the results from FE simulations.

## Validation of the FE-models

Lateral indentation tests on circular tubes have been performed using the Zwick Roell Z250 universal testing machine to characterize the load-deformation behavior and to validate FE models, see also [13]. Steel tubes of grade E235 +N/+C with a circular cross section, a constant outer diameter of $D = 30$ mm, but various tube lengths and wall thicknesses of $t = 1.5$ mm, 2.0 mm and 3.0 mm are used as test material. Fig. 1 shows the test setup, used in [13] also. Straight segments

<figure><img src="image_2231.png" /><figcaption>Fig. 1: Test setup for the lateral indentation tests according to [13].</figcaption></figure>

with different radii represent the segmented tool surface and can be placed with different spacings in a fixture. A Gom Aramis 12M DIC system with a calibrated field of view of 200x147 mm² (resolution of 20.5 pixels/mm) is used to measure the strain distribution on the specimen surface
and to measure the local tool displacements based on the applied reference points, together with the coupled 0-10 V DC force signal from the testing machine, allowing for the determination of a local force-displacement curves with eliminated system stiffness.

The FE solver LS-Dyna R 12.0.0 is used for the simulations. The choice of the model parameters, which are described in [13] in detail, is based on a comprehensive sensitivity analysis. The tube is discretized with fully integrated hexahedral solid elements with a nominal element size of 0.5 mm in the square and 5 elements over the thickness. The isotropic v. Mises plasticity model is used, while the segments are discretized with constant stress tetrahedral solid elements and a linear elastic material law is applied. The base plate is modeled as a rigid surface with shell elements. The required flow curves were determined in uniaxial tensile tests on circular tubes and were approximated by using the El-Magd approach with approximation parameters determined by curve fitting using least-squares optimization. To simulate the contact between the tool and tube, the one-way surface-to-surface forming contact with a static Coulomb friction coefficient of 0.1 is used. Fig. 2 shows the comparison between selected experimental data and the numerical results.

<figure><img src="image_2241.png" /><figcaption>Fig. 2: Comparison of results from experiment and FE simulation of lateral indentation of tubes by segments and segmented surfaces in terms of force-displacement curves (top), v. Mises strain paths along the longitudinal axis in the center of the tube on its surface (middle) and in terms of surface deviation of the resulting part geometries (bottom). The tubes are steel tubes of grade E235+N/+C with a nominal outer diameter of D = 30 mm, different nominal wall thicknesses t and different tube lengths L. Also, different segment radii R and segment spacings a are used, cf. Fig. 1.</figcaption></figure>

The FE simulations are compared with the experimental results based on the force-displacement curves (top), the DIC measurements (middle) and on the surface deviations (bottom) between the
and to measure the local tool displacements based on the applied reference points, together with the coupled 0-10 V DC force signal from the testing machine, allowing for the determination of a local force-displacement curves with eliminated system stiffness.

The FE solver LS-Dyna R 12.0.0 is used for the simulations. The choice of the model parameters, which are described in [13] in detail, is based on a comprehensive sensitivity analysis. The tube is discretized with fully integrated hexahedral solid elements with a nominal element size of 0.5 mm in the square and 5 elements over the thickness. The isotropic v. Mises plasticity model is used, while the segments are discretized with constant stress tetrahedral solid elements and a linear elastic material law is applied. The base plate is modeled as a rigid surface with shell elements. The required flow curves were determined in uniaxial tensile tests on circular tubes and were approximated by using the El-Magd approach with approximation parameters determined by curve fitting using least-squares optimization. To simulate the contact between the tool and tube, the one-way surface-to-surface forming contact with a static Coulomb friction coefficient of 0.1 is used. Fig. 2 shows the comparison between selected experimental data and the numerical results.

<figure><img src="image_2232.png" /><figcaption>Fig. 2: Comparison of results from experiment and FE simulation of lateral indentation of tubes by segments and segmented surfaces in terms of force-displacement curves (top), v. Mises strain paths along the longitudinal axis in the center of the tube on its surface (middle) and in terms of surface deviation of the resulting part geometries (bottom). The tubes are steel tubes of grade E235+N/+C with a nominal outer diameter of D = 30 mm, different nominal wall thicknesses t and different tube lengths L. Also, different segment radii R and segment spacings a are used, cf. Fig. 1.</figcaption></figure>

The FE simulations are compared with the experimental results based on the force-displacement curves (top), the DIC measurements (middle) and on the surface deviations (bottom) between the
simulated and experimental geometries. The comparison of the v. Mises strains from experiment and simulation is done based on paths along the tube axis in the center of the specimen. To obtain the surface strains from the simulation with solid elements, thin shell elements with a thickness of 0.001 mm were created and evaluated along this path on the surface. To obtain the strain path from the DIC measurement exactly in the center of the specimen, an analysis coordinate system is defined in the initial configuration in the *Gom Correlate* software, based on a fitting cylinder to the undeformed tube specimen. To compare the part geometries, the deformed specimens were digitized with a *Gom Atos Core 3D-scanner*, and the surface comparison is done with the *Gom Inspect* software.

The force-displacement curves show a very good correlation between experiment and simulation, only in Fig. 2a small deviations can be observed. In addition, the v. Mises strain in the center of the tube along the longitudinal axis measured by DIC generally agrees well with the calculated values. However, the simulation underestimates the measured strain, except for the tube with a wall thickness of 3.0 mm, where no significant differences are observed. The surface deviations of the part geometries after springback between the tests and simulations show good correlations with maximum deviations of about 0.36 mm. Overall, there is a good correlation between the test data and the numerical results. Concluding, the FE model is capable of reliably predicting the load-deformation behavior of circular steel tubes in lateral indentation and thus can be used for further virtual investigations in this study.

## Methodology

To develop a design method for segmented tool surfaces, it's crucial to know which surface parameters mainly influence the quality of the part, taking into account the tube properties. Therefore, we perform a sensitivity analysis using a statistical DoE approach on the lateral indentation of tubes by segmented tools. In fact, the seven potential influencing factors defined for this study would lead to 129 runs including the central point within a full factorial DoE. In our procedure, which will be explained in detail later, this would cause 258 simulations. To reduce the number of simulations, we use a 1/4 fractional DoE with two factor levels and one central point and we focus on circular steel tubes. Fig. 3 shows the factors and the output of our DoE.

<figure><img src="image_2242.png" /><figcaption>Fig. 3: Factors and output of the simulation-based Design of Experiment (DoE) on lateral indentation of tubes by segmented tool surfaces.</figcaption></figure>

Since several authors have pointed out that in bending processes not the whole die surface is in contact with the workpiece, but only some parts [8,14], and in addition with regard to the required adjustability of the forming tools not only with respect to the bending line, but also with respect to
simulated and experimental geometries. The comparison of the v. Mises strains from experiment and simulation is done based on paths along the tube axis in the center of the specimen. To obtain the surface strains from the simulation with solid elements, thin shell elements with a thickness of 0.001 mm were created and evaluated along this path on the surface. To obtain the strain path from the DIC measurement exactly in the center of the specimen, an analysis coordinate system is defined in the initial configuration in the *Gom Correlate* software, based on a fitting cylinder to the undeformed tube specimen. To compare the part geometries, the deformed specimens were digitized with a *Gom Atos Core 3D-scanner*, and the surface comparison is done with the *Gom Inspect* software.

The force-displacement curves show a very good correlation between experiment and simulation, only in Fig. 2a small deviations can be observed. In addition, the v. Mises strain in the center of the tube along the longitudinal axis measured by DIC generally agrees well with the calculated values. However, the simulation underestimates the measured strain, except for the tube with a wall thickness of 3.0 mm, where no significant differences are observed. The surface deviations of the part geometries after springback between the tests and simulations show good correlations with maximum deviations of about 0.36 mm. Overall, there is a good correlation between the test data and the numerical results. Concluding, the FE model is capable of reliably predicting the load-deformation behavior of circular steel tubes in lateral indentation and thus can be used for further virtual investigations in this study.

## Methodology

To develop a design method for segmented tool surfaces, it's crucial to know which surface parameters mainly influence the quality of the part, taking into account the tube properties. Therefore, we perform a sensitivity analysis using a statistical DoE approach on the lateral indentation of tubes by segmented tools. In fact, the seven potential influencing factors defined for this study would lead to 129 runs including the central point within a full factorial DoE. In our procedure, which will be explained in detail later, this would cause 258 simulations. To reduce the number of simulations, we use a 1/4 fractional DoE with two factor levels and one central point and we focus on circular steel tubes. Fig. 3 shows the factors and the output of our DoE.

<figure><img src="image_2233.png" /><figcaption>Fig. 3: Factors and output of the simulation-based Design of Experiment (DoE) on lateral indentation of tubes by segmented tool surfaces.</figcaption></figure>

Since several authors have pointed out that in bending processes not the whole die surface is in contact with the workpiece, but only some parts [8,14], and in addition with regard to the required adjustability of the forming tools not only with respect to the bending line, but also with respect to
the diameter, we choose non-enclosing surfaces. On the part of the segmented tool surfaces, the parameters are the segment width *b*, the ratio *q* of the tube diameter *D* to the segment radius *R* and the distance *a* between the segments. The tube length *L* = 200 mm and the outer diameter *D* = 30 mm are kept constant, so that the variation of *q* and *a* is achieved by the variation of *R* and the number of segments *z* within the given tube length *L*. On the part of the tube parameters, we distinguish between geometric and mechanical parameters. The geometric parameter is the wall thickness factor *W* = *D*/*t*, which is defined as the ratio of the tube diameter *D* to the wall thickness *t* [15]. The mechanical behavior of the tube material is parameterized by a bilinear flow curve approximation, which allows us to vary the material stiffness, strength and strain hardening behavior with only three scalar parameters in the simulation environment. While there are many quality criteria, that could be considered as output, in this paper we focus on the local indentation depth.

Table 1 shows the range of values for the factors used for the DoE. As we are focusing on steel tubes, the Young's modulus *E* covers the typical range of different steel grades, while the yield stress *R*<sub>p</sub> and the linear hardening coefficient *m* cover a wide range of steel grades with very different strength and hardening behavior as investigated in [16]. The value *q* = 0 means that the segment radius *R* → ∞, so that it is flat surface.

<table><caption>Table 1: Value range of factors used for the DoE. The tube length *L* = 200 mm and tube diameter *D* = 30 mm are indirect parameters and are kept constant.</caption><thead><tr><th></th><th>Factor</th><th>Min</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td rowspan="4">Tube</td><td>Wall thickness factor <i>W</i> = <i>D</i>/<i>t</i> [-]</td><td>10</td><td>20</td><td>30</td></tr><tr><td>Yield stress <i>R</i><sub>p</sub> [MPa]</td><td>200</td><td>467.5</td><td>735</td></tr><tr><td>Linear hardening coefficient <i>m</i> [MPa]</td><td>850</td><td>1900</td><td>2950</td></tr><tr><td>Young's modulus <i>E</i> [GPa]</td><td>195</td><td>205</td><td>215</td></tr><tr><td rowspan="3">Tool</td><td>Ratio <i>q</i> = <i>D</i>/<i>R</i> [-]</td><td>0</td><td>3</td><td>6</td></tr><tr><td>Segment width <i>b</i> [mm]</td><td>5</td><td>7.5</td><td>10</td></tr><tr><td>Distance between the segments <i>a</i> = <i>L</i>/(<i>z</i>+1) [mm]</td><td>12.5</td><td>25</td><td>40</td></tr></tbody></table>

The procedure to obtain the output values according to the parameter variations from the DoE is shown in Fig. 4. Initially, for each combination of tube parameters, a reference simulation is performed with an imposed velocity and two opposing plates as the closed tool surface. In the second step, a collapse force *F*<sub>collapse</sub> is extracted from the resulting force-displacement curves, which represents the transition between elastic and plastic cross-sectional deformation. In order to determine the collapse force consistently for each parameter set, a criterion has been defined. Straight lines are fitted to the linear elastic and linear plastic regions. The force at the intersection of another straight line, which is orthogonal to the linear curve fit to the plastic region and passes through the intersection of both linear curve fits, and the force-displacement curve is defined as the collapse force. Third, the segmented tool surface with the DoE parametrization is loaded by this collapse force. We choose this load case for a very specific reason. Considering the long-term goal of this research, the development of a design method for segmented bending tool surfaces, the global load of the bending die for a dedicated bending process is predefined by the bending task (bending radius, wall thickness factor, mechanical material properties). Therefore, the load case must be an imposed force and the local indentations must be induced mandatorily. Thus, the collapse force is the global load, that the specific tube can just withstand without cross-sectional plastic deformation, so to speak a forming process with a resulting in-specification part. By reducing the contact area through segmentation, the local contact pressure arises, local indentation occurs and the impact of the influencing parameters on their value can be investigated.
the diameter, we choose non-enclosing surfaces. On the part of the segmented tool surfaces, the parameters are the segment width *b*, the ratio *q* of the tube diameter *D* to the segment radius *R* and the distance *a* between the segments. The tube length *L* = 200 mm and the outer diameter *D* = 30 mm are kept constant, so that the variation of *q* and *a* is achieved by the variation of *R* and the number of segments *z* within the given tube length *L*. On the part of the tube parameters, we distinguish between geometric and mechanical parameters. The geometric parameter is the wall thickness factor *W* = *D*/*t*, which is defined as the ratio of the tube diameter *D* to the wall thickness *t* [15]. The mechanical behavior of the tube material is parameterized by a bilinear flow curve approximation, which allows us to vary the material stiffness, strength and strain hardening behavior with only three scalar parameters in the simulation environment. While there are many quality criteria, that could be considered as output, in this paper we focus on the local indentation depth.

Table 1 shows the range of values for the factors used for the DoE. As we are focusing on steel tubes, the Young's modulus *E* covers the typical range of different steel grades, while the yield stress *R*<sub>p</sub> and the linear hardening coefficient *m* cover a wide range of steel grades with very different strength and hardening behavior as investigated in [16]. The value *q* = 0 means that the segment radius *R* → ∞, so that it is flat surface.

<table><caption>Table 1: Value range of factors used for the DoE. The tube length *L* = 200 mm and tube diameter *D* = 30 mm are indirect parameters and are kept constant.</caption><thead><tr><th></th><th>Factor</th><th>Min</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td rowspan="4">Tube</td><td>Wall thickness factor <i>W</i> = <i>D</i>/<i>t</i> [-]</td><td>10</td><td>20</td><td>30</td></tr><tr><td>Yield stress <i>R</i><sub>p</sub> [MPa]</td><td>200</td><td>467.5</td><td>735</td></tr><tr><td>Linear hardening coefficient <i>m</i> [MPa]</td><td>850</td><td>1900</td><td>2950</td></tr><tr><td>Young's modulus <i>E</i> [GPa]</td><td>195</td><td>205</td><td>215</td></tr><tr><td rowspan="3">Tool</td><td>Ratio <i>q</i> = <i>D</i>/<i>R</i> [-]</td><td>0</td><td>3</td><td>6</td></tr><tr><td>Segment width <i>b</i> [mm]</td><td>5</td><td>7.5</td><td>10</td></tr><tr><td>Distance between the segments <i>a</i> = <i>L</i>/(<i>z</i>+1) [mm]</td><td>12.5</td><td>25</td><td>40</td></tr></tbody></table>

The procedure to obtain the output values according to the parameter variations from the DoE is shown in Fig. 4. Initially, for each combination of tube parameters, a reference simulation is performed with an imposed velocity and two opposing plates as the closed tool surface. In the second step, a collapse force *F*<sub>collapse</sub> is extracted from the resulting force-displacement curves, which represents the transition between elastic and plastic cross-sectional deformation. In order to determine the collapse force consistently for each parameter set, a criterion has been defined. Straight lines are fitted to the linear elastic and linear plastic regions. The force at the intersection of another straight line, which is orthogonal to the linear curve fit to the plastic region and passes through the intersection of both linear curve fits, and the force-displacement curve is defined as the collapse force. Third, the segmented tool surface with the DoE parametrization is loaded by this collapse force. We choose this load case for a very specific reason. Considering the long-term goal of this research, the development of a design method for segmented bending tool surfaces, the global load of the bending die for a dedicated bending process is predefined by the bending task (bending radius, wall thickness factor, mechanical material properties). Therefore, the load case must be an imposed force and the local indentations must be induced mandatorily. Thus, the collapse force is the global load, that the specific tube can just withstand without cross-sectional plastic deformation, so to speak a forming process with a resulting in-specification part. By reducing the contact area through segmentation, the local contact pressure arises, local indentation occurs and the impact of the influencing parameters on their value can be investigated.
<figure><img src="image_2243.png" /><figcaption>Fig. 4: Procedure for performing the simulation-based DoE.</figcaption></figure>

The last step in our procedure is the examination of the local indentations with respect to the reference simulation by means of surface comparison analysis using Gom Correlate 2021 software.

## Results

Minitab Statistical Software is used to perform the statistical analysis of the experimental design. The selection of the factors and the interactions that are part of the linear regression model is done in a hierarchical procedure based on the p-values with a confidence level of $\alpha = 0.05$. This means that factors and interactions are systematically eliminated from the model until the model consists only of statistically significant parameters. The main effects of the factors that are part of the generated regression model are shown in Fig. 5a. It is observed that the indentation depth $e$ increases as the segment spacing $a$, the ratio $q$ and the yield stress $R_p$ increase. Furthermore, the indentation depth increases as the wall thickness factor $W$ decreases, that means that the indentation depth increases with increasing wall thickness. The slopes of the straight lines in the main effect diagrams indicate the strength of the effect. Additionally, Fig. 5b shows two statistically significant interactions. One is the interaction between the segment spacing and the wall thickness factor. Increasing segment spacing results in considerably greater indentation depths for a wall thickness factor of $W = 10$ compared to $W = 30$. Secondly, there is an interaction between the ratio $q$ and the segment spacing $a$. While the segment radius has hardly any influence on the indentation depth for a small segment spacing, it has an even greater influence for large segment spacings. Finally, the Pareto diagram of the standardized effects of the individual factors and the interactions shows a ranking of the influencing parameters. Note, that the influence of the yield strength is not statistically significant, but still has a sufficiently large influence. It was also included in the regression model because it slightly improves the prediction quality of the model. The regression equation of the statistical model for the indentation depth follows

$$e = c_0 + c_1 \cdot a + c_2 \cdot W - c_3 \cdot a \cdot W - c_4 \cdot q + c_5 \cdot q \cdot a + c_6 \cdot R_p, \quad (1)$$

with the constants $c_0 = -0.418$, $c_1 = 0.02868$, $c_2 = 0.00999$, $c_3 = -0.000784$, $c_4 = -0.0159$, $c_5 = 0.001523$ and $c_6 = 0.000127$. The prognosticated mean square deviation $R^2$ between the model
<figure><img src="image_2234.png" /><figcaption>Fig. 4: Procedure for performing the simulation-based DoE.</figcaption></figure>

The last step in our procedure is the examination of the local indentations with respect to the reference simulation by means of surface comparison analysis using Gom Correlate 2021 software.

## Results

Minitab Statistical Software is used to perform the statistical analysis of the experimental design. The selection of the factors and the interactions that are part of the linear regression model is done in a hierarchical procedure based on the p-values with a confidence level of $\alpha = 0.05$. This means that factors and interactions are systematically eliminated from the model until the model consists only of statistically significant parameters. The main effects of the factors that are part of the generated regression model are shown in Fig. 5a. It is observed that the indentation depth $e$ increases as the segment spacing $a$, the ratio $q$ and the yield stress $R_p$ increase. Furthermore, the indentation depth increases as the wall thickness factor $W$ decreases, that means that the indentation depth increases with increasing wall thickness. The slopes of the straight lines in the main effect diagrams indicate the strength of the effect. Additionally, Fig. 5b shows two statistically significant interactions. One is the interaction between the segment spacing and the wall thickness factor. Increasing segment spacing results in considerably greater indentation depths for a wall thickness factor of $W = 10$ compared to $W = 30$. Secondly, there is an interaction between the ratio $q$ and the segment spacing $a$. While the segment radius has hardly any influence on the indentation depth for a small segment spacing, it has an even greater influence for large segment spacings. Finally, the Pareto diagram of the standardized effects of the individual factors and the interactions shows a ranking of the influencing parameters. Note, that the influence of the yield strength is not statistically significant, but still has a sufficiently large influence. It was also included in the regression model because it slightly improves the prediction quality of the model. The regression equation of the statistical model for the indentation depth follows

$$e = c_0 + c_1 \cdot a + c_2 \cdot W - c_3 \cdot a \cdot W - c_4 \cdot q + c_5 \cdot q \cdot a + c_6 \cdot R_p, \quad (1)$$

with the constants $c_0 = -0.418$, $c_1 = 0.02868$, $c_2 = 0.00999$, $c_3 = -0.000784$, $c_4 = -0.0159$, $c_5 = 0.001523$ and $c_6 = 0.000127$. The prognosticated mean square deviation $R^2$ between the model
and the experimental values is $R^2 = 0.85$, whereby the central point is not part of the model because its consideration worsens the model quality.

<figure><img src="image_2244.png" /><figcaption>Fig. 5: Results of the statistical analysis of the simulation-based DoE on lateral indentation of circular steel tubes by segmented surfaces.</figcaption></figure>

Even if the predicted $R^2$ value initially promises a sufficiently good predictive capability of the model regarding the target variable "indentation depth $e$", there are some critical points to consider when using the model. Non-linearities occur in the underlying problem of lateral indentation of tubes by means of segmented tool surfaces. Although the elastic and plastic deformation behavior in the simulations of this study is linear due to the chosen material parameterization (bilinear flow curve approximation, see Fig. 3) the geometric deformation of the entire tube cross-section over the tube length as well as the local deformation in the contact zone is non-linear. The contact between the tool and the tube causes additional non-linearity. However, with the ¼ fractional design of experiments, only a linear regression model can be generated, which means that the actual non-linearity of the problem is not taken into account. In addition, some parameter combinations are missing due to the reduced factorial experimental design, which means that not any possible influencing variables and interactions, especially higher order interactions, are captured.

Knowing these systematically introduced uncertainties, the regression model is subsequently used on the one hand to compare the predicted indentation depths with those obtained from the FE simulations. On the other hand, it is investigated to what extent it is possible to predict segmented tool surface parameter based on the regression model. For this purpose, the workpiece parameters and the segment width are specified as the only tool parameters and the two remaining tool parameters, namely the segment radius ratio $q$ and the segment distance $a$, are determined with respect to a specified maximum indentation depth of $e_{allowed} = 0.2$ mm using least squares optimization. Fig. 6 shows the chosen and optimized tool and workpiece parameters on the right and the comparison between the indentation depths from the regression model and the FE simulation on the left. The indentation depths from the FE simulation are determined according to steps (3.2) and (4) from Fig. 4.
and the experimental values is $R^2 = 0.85$, whereby the central point is not part of the model because its consideration worsens the model quality.

<figure><img src="image_2235.png" /><figcaption>Fig. 5: Results of the statistical analysis of the simulation-based DoE on lateral indentation of circular steel tubes by segmented surfaces.</figcaption></figure>

Even if the predicted $R^2$ value initially promises a sufficiently good predictive capability of the model regarding the target variable "indentation depth $e$", there are some critical points to consider when using the model. Non-linearities occur in the underlying problem of lateral indentation of tubes by means of segmented tool surfaces. Although the elastic and plastic deformation behavior in the simulations of this study is linear due to the chosen material parameterization (bilinear flow curve approximation, see Fig. 3) the geometric deformation of the entire tube cross-section over the tube length as well as the local deformation in the contact zone is non-linear. The contact between the tool and the tube causes additional non-linearity. However, with the ¼ fractional design of experiments, only a linear regression model can be generated, which means that the actual non-linearity of the problem is not taken into account. In addition, some parameter combinations are missing due to the reduced factorial experimental design, which means that not any possible influencing variables and interactions, especially higher order interactions, are captured.

Knowing these systematically introduced uncertainties, the regression model is subsequently used on the one hand to compare the predicted indentation depths with those obtained from the FE simulations. On the other hand, it is investigated to what extent it is possible to predict segmented tool surface parameter based on the regression model. For this purpose, the workpiece parameters and the segment width are specified as the only tool parameters and the two remaining tool parameters, namely the segment radius ratio $q$ and the segment distance $a$, are determined with respect to a specified maximum indentation depth of $e_{allowed} = 0.2$ mm using least squares optimization. Fig. 6 shows the chosen and optimized tool and workpiece parameters on the right and the comparison between the indentation depths from the regression model and the FE simulation on the left. The indentation depths from the FE simulation are determined according to steps (3.2) and (4) from Fig. 4.
<table><caption>Fig. 6: Comparison between the indentation depths prognosticated by the regression model and determined in the FE-simulations (left) and corresponding parameter variations (right).</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="8">Parameter variation</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th></tr></thead><tbody><tr><td rowspan="8">choosen parameters<br>least square<br>optimized<br>parameters using<br>regression model for<br>e<sub>allowed</sub> = 0.2 mm</td><td>W [-]</td><td>30</td><td>10</td><td>30</td><td>30</td><td>10</td><td>10</td><td>10</td><td>30</td></tr><tr><td>R<sub>p</sub> [MPa]</td><td>735</td><td>200</td><td>200</td><td>735</td><td>735</td><td>200</td><td>735</td><td>735</td></tr><tr><td>m [MPa]</td><td>885</td><td>850</td><td>850</td><td>2950</td><td>850</td><td>850</td><td>850</td><td>2950</td></tr><tr><td>E [GPa]</td><td>215</td><td>215</td><td>195</td><td>195</td><td>195</td><td>215</td><td>195</td><td>195</td></tr><tr><td>b [mm]</td><td>5</td><td>10</td><td>5</td><td>5</td><td>10</td><td>10</td><td>10</td><td>5</td></tr><tr><td>q [-]</td><td>6</td><td>0</td><td>6</td><td>15</td><td>0</td><td>3.05</td><td>3.3</td><td>3.1</td></tr><tr><td>a [mm]</td><td>20</td><td>20</td><td>25</td><td>10</td><td>20</td><td>20</td><td>16.7</td><td>25</td></tr><tr><td>imposed collapse<br>force</td><td>F<sub>collapse</sub> [kN]</td><td>9.3</td><td>31.9</td><td>3.1</td><td>9.8</td><td>106.2</td><td>31.9</td><td>106.2</td><td>9.8</td></tr></tbody></table>

When comparing the indentation depths from simulation and regression in Fig. 6, it is noticeable that the regression model always predicts larger values than those obtained from the FE simulations. The ratio between the prognosticated value and the actual value ranges from 1.08 (parameter variation 8) to 12.41 (parameter variation 2) and is 4.20 on average for all variations performed. This indicates that the regression equation in this form cannot yet be used to make valid quantitative statements about the expected indentation depth. However, since the predicted values for the parameter sets considered here are always significantly greater than the calculated indentation depths from the FE simulations, the regression model can be used as a pre-design tool for the segmentation of tool surfaces.

## Conclusions

Since mass customization is an increasing demand for production technology, flexible manufacturing processes are needed in metal forming. While kinematic bending processes have inherent flexibility due to their shape-defining tool motion, the widely used tool-related processes are limited in this way. One approach to making them more flexible is to segment the closed tool surfaces, which adds degrees of freedom to the tool and allows it to adapt to different part geometries. However, these discrete surfaces can affect the quality of the part, in particular causing localized indentations. Although multi-point forming techniques have been investigated for a long time, until now there is no design approach for segmented tool surfaces that takes into account the properties of the workpiece and the boundary conditions.

In this study, the authors have presented a statistical, FE simulation-based design of experiments (DoE) to investigate the main influences on the indentation depth in the lateral indentation of circular steel tubes by segmented tool surfaces. Since valid data are required for the statistical evaluation, we first validated the FE model through experiments on lateral indentation of tubes by segmented tool surfaces in terms of the features force-displacement curves, strain distributions, and the resulting part geometries. The regression equation of the statistical model is then used to compare the prognosticated indentation depths with those obtained from FE simulations and to develop a first approach for the pre-design of segmented tool surfaces for an allowable indentation depth e<sub>allowed</sub>. Finally, the predicted indentation depths from the regression model are compared with those obtained from the FE simulations. A graphical summary of the procedure followed in this paper is given in Fig. 7.
<table><caption>Fig. 6: Comparison between the indentation depths prognosticated by the regression model and determined in the FE-simulations (left) and corresponding parameter variations (right).</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="8">Parameter variation</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th></tr></thead><tbody><tr><td rowspan="8">choosen parameters<br>least square<br>optimized<br>parameters using<br>regression model for<br>e<sub>allowed</sub> = 0.2 mm</td><td>W [-]</td><td>30</td><td>10</td><td>30</td><td>30</td><td>10</td><td>10</td><td>10</td><td>30</td></tr><tr><td>R<sub>p</sub> [MPa]</td><td>735</td><td>200</td><td>200</td><td>735</td><td>735</td><td>200</td><td>735</td><td>735</td></tr><tr><td>m [MPa]</td><td>885</td><td>850</td><td>850</td><td>2950</td><td>850</td><td>850</td><td>850</td><td>2950</td></tr><tr><td>E [GPa]</td><td>215</td><td>215</td><td>195</td><td>195</td><td>195</td><td>215</td><td>195</td><td>195</td></tr><tr><td>b [mm]</td><td>5</td><td>10</td><td>5</td><td>5</td><td>10</td><td>10</td><td>10</td><td>5</td></tr><tr><td>q [-]</td><td>6</td><td>0</td><td>6</td><td>15</td><td>0</td><td>3.05</td><td>3.3</td><td>3.1</td></tr><tr><td>a [mm]</td><td>20</td><td>20</td><td>25</td><td>10</td><td>20</td><td>20</td><td>16.7</td><td>25</td></tr><tr><td>imposed collapse<br>force</td><td>F<sub>collapse</sub> [kN]</td><td>9.3</td><td>31.9</td><td>3.1</td><td>9.8</td><td>106.2</td><td>31.9</td><td>106.2</td><td>9.8</td></tr></tbody></table>

When comparing the indentation depths from simulation and regression in Fig. 6, it is noticeable that the regression model always predicts larger values than those obtained from the FE simulations. The ratio between the prognosticated value and the actual value ranges from 1.08 (parameter variation 8) to 12.41 (parameter variation 2) and is 4.20 on average for all variations performed. This indicates that the regression equation in this form cannot yet be used to make valid quantitative statements about the expected indentation depth. However, since the predicted values for the parameter sets considered here are always significantly greater than the calculated indentation depths from the FE simulations, the regression model can be used as a pre-design tool for the segmentation of tool surfaces.

## Conclusions

Since mass customization is an increasing demand for production technology, flexible manufacturing processes are needed in metal forming. While kinematic bending processes have inherent flexibility due to their shape-defining tool motion, the widely used tool-related processes are limited in this way. One approach to making them more flexible is to segment the closed tool surfaces, which adds degrees of freedom to the tool and allows it to adapt to different part geometries. However, these discrete surfaces can affect the quality of the part, in particular causing localized indentations. Although multi-point forming techniques have been investigated for a long time, until now there is no design approach for segmented tool surfaces that takes into account the properties of the workpiece and the boundary conditions.

In this study, the authors have presented a statistical, FE simulation-based design of experiments (DoE) to investigate the main influences on the indentation depth in the lateral indentation of circular steel tubes by segmented tool surfaces. Since valid data are required for the statistical evaluation, we first validated the FE model through experiments on lateral indentation of tubes by segmented tool surfaces in terms of the features force-displacement curves, strain distributions, and the resulting part geometries. The regression equation of the statistical model is then used to compare the prognosticated indentation depths with those obtained from FE simulations and to develop a first approach for the pre-design of segmented tool surfaces for an allowable indentation depth e<sub>allowed</sub>. Finally, the predicted indentation depths from the regression model are compared with those obtained from the FE simulations. A graphical summary of the procedure followed in this paper is given in Fig. 7.
<figure><img src="image_2245.png" /><figcaption>Fig. 7: Summary of the procedure followed in this paper.</figcaption></figure>

The FE simulations of the lateral indentation show a very good correlation to the experiments and can therefore be used as valid digital twins for the following simulation-based DoE. Of the seven potential influencing parameters defined, the segment distance *a*, the wall thickness factor *W* and the interaction between *a* and *W* have the largest influence on the indentation depth *e*. The ratio *q* of tube diameter to segment radius and the interaction between *q* and *a* also have a statistically significant influence. Although the resulting regression equation has a R²-value of 0.85, the prognosticated indentation depths differ considerably from those obtained from the FE simulations. This could be due to the chosen ¼ fractional experimental design, which lacks ¾ of the possible factor combinations and allows only linear regression models to be conducted, while the actual problem is nonlinear in character. However, the prognosticated indentation depths are always greater than the simulated ones. Therefore, the regression model can be used as a pre-design tool for segmented tool surfaces. Future work has to focus on improving the statistical model. This could be done by using only the statistically significant parameters for further full factorial DoE. Another option is to use sequential design of experiments (SDOE) approaches, which improve the model quality by gradually refining the sets of space-filling input parameters.

Indeed, this study considers the lateral indentation of segmented surfaces on tubes lying on a flat plate. Nevertheless, very important information can be derived from this study also for the segmentation of bending tools, which is the goal of our research project. It is shown that the mechanical properties of the tube have no or negligible influence on the local indentation. Instead, the wall thickness factor as geometric parameter has a large influence. This significance and that of the surface parameters as well as the interactions that have been identified will also be transferable to bending processes to a certain extent, although it should be noted that the process boundary conditions in the form of compressive stresses at the inner arch will influence the indentation depth.

## Funding Acknowledgement

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 509709804.

## References

[1] Megatrends. Accessed: Nov. 28, 2023. https://www.zukunftsinstitut.de/dossier/megatrends/

[2] B. Engel, Biegen - Quo vadis, in: B. Engel, Transformation in der Biegetechnik - Tagungsband zum 6 Biegeforum Siegen, Universi-Verlag, Siegen, 2023, pp. 1-4. http://dx.doi.org/10.25819/ubsi/10365

[3] T. Stock and G. Seliger, Opportunities of Sustainable Manufacturing in Industry 4.0, Procedia CIRP. 40 (2016) 536-541. https://doi.org/10.1016/j.procir.2016.01.129

[4] D.Y. Yang et al., Flexibility in metal forming, CIRP Ann. 67/2 (2018) 743-765. https://doi.org/10.1016/j.cirp.2018.05.004
<figure><img src="image_2236.png" /><figcaption>Fig. 7: Summary of the procedure followed in this paper.</figcaption></figure>

The FE simulations of the lateral indentation show a very good correlation to the experiments and can therefore be used as valid digital twins for the following simulation-based DoE. Of the seven potential influencing parameters defined, the segment distance *a*, the wall thickness factor *W* and the interaction between *a* and *W* have the largest influence on the indentation depth *e*. The ratio *q* of tube diameter to segment radius and the interaction between *q* and *a* also have a statistically significant influence. Although the resulting regression equation has a R²-value of 0.85, the prognosticated indentation depths differ considerably from those obtained from the FE simulations. This could be due to the chosen ¼ fractional experimental design, which lacks ¾ of the possible factor combinations and allows only linear regression models to be conducted, while the actual problem is nonlinear in character. However, the prognosticated indentation depths are always greater than the simulated ones. Therefore, the regression model can be used as a pre-design tool for segmented tool surfaces. Future work has to focus on improving the statistical model. This could be done by using only the statistically significant parameters for further full factorial DoE. Another option is to use sequential design of experiments (SDOE) approaches, which improve the model quality by gradually refining the sets of space-filling input parameters.

Indeed, this study considers the lateral indentation of segmented surfaces on tubes lying on a flat plate. Nevertheless, very important information can be derived from this study also for the segmentation of bending tools, which is the goal of our research project. It is shown that the mechanical properties of the tube have no or negligible influence on the local indentation. Instead, the wall thickness factor as geometric parameter has a large influence. This significance and that of the surface parameters as well as the interactions that have been identified will also be transferable to bending processes to a certain extent, although it should be noted that the process boundary conditions in the form of compressive stresses at the inner arch will influence the indentation depth.

## Funding Acknowledgement

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 509709804.

## References

[1] Megatrends. Accessed: Nov. 28, 2023. https://www.zukunftsinstitut.de/dossier/megatrends/

[2] B. Engel, Biegen - Quo vadis, in: B. Engel, Transformation in der Biegetechnik - Tagungsband zum 6 Biegeforum Siegen, Universi-Verlag, Siegen, 2023, pp. 1-4. http://dx.doi.org/10.25819/ubsi/10365

[3] T. Stock and G. Seliger, Opportunities of Sustainable Manufacturing in Industry 4.0, Procedia CIRP. 40 (2016) 536-541. https://doi.org/10.1016/j.procir.2016.01.129

[4] D.Y. Yang et al., Flexibility in metal forming, CIRP Ann. 67/2 (2018) 743-765. https://doi.org/10.1016/j.cirp.2018.05.004
[5] F. Vollertsen, A. Sprenger, J. Kraus, and H. Arnet, Extrusion, channel, and profile bending: a review, J. Mater. Process. Technol. 87 (1999) 1-27. https://doi.org/10.1016/S0924-0136(98)00339-2

[6] C. Kuhnhen, J. Knoche, J. Reuter, S.S. Hassan Al-Maeeni, and B. Engel, Hybrid tool design for a bending machine, Procedia CIRP. 99 (2021) 370-374. https://doi.org/10.1016/j.procir.2021.03.052

[7] L.-E. Elend, Einsatz elastischer Niederhaltersysteme zur Erweiterung der Prozeßgrenzen beim Tiefziehen, Doctoral Thesis, Leibniz University Hannover, Hannover, 2001. https://doi.org/10.15488/5808

[8] C. Heftrich, R. Steinheimer, and B. Engel, Rotary-draw-bending using tools with reduced geometries, Procedia Manuf. 15 (2018) 804-811. https://doi.org/10.1016/j.promfg.2018.07.410

[9] M.-Z. Li, Z.-Y. Cai, and C.-G. Liu, Flexible manufacturing of sheet metal parts based on digitized-die, Robot. Comput.-Integr. Manuf. 23 (2007) 107-115. https://doi.org/10.1016/j.rcim.2005.09.005

[10] M.Z. Li, Z.Y. Cai, Z. Sui, and Q.G. Yan, Multi-point forming technology for sheet metal, J. Mater. Process. Technol. 129 (2002) 333-338. https://doi.org/10.1016/S0924-0136(02)00685-4

[11] J. Reuter, A. Aslanidis, and B. Engel, Segmentierung von Biegeformen als Grundlage für die Entwicklung von Transformer-Werkzeugen, in: B. Engel, Transformation in der Biegetechnik - Tagungsband zum 6 Biegeforum Siegen, Universi-Verlag, Siegen, 2023, pp. 91-101. http://dx.doi.org/10.25819/ubsi/10398

[12] Z.-Y. Cai, S.-H. Wang, and M.-Z. Li, Numerical investigation of multi-point forming process for sheet metal: wrinkling, dimpling and springback, Int. J. Adv. Manuf. Technol. 37 (2008) 927-936. https://doi.org/10.1007/s00170-007-1045-5

[13] J. Reuter, P. Frohn-Sörensen and B. Engel, Segmentation Method for Bending Tools – Fundamental Investigation of Profile Forming by Segmented Tools, in: K. Mocellin, Po. Bouchard, R. Bigot, T. Balan (Eds.), Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity, pp. 547-559. ICTP2023. Lecture Notes in Mechanical Engineering. Springer, Cham, 2023. https://doi.org/10.1007/978-3-031-41023-9_55

[14] S.A. Tronvoll, J. Ma, and T. Welo, Deformation behavior in tube bending: a comparative study of compression bending and rotary draw bending, Int. J. Adv. Manuf. Technol. 124 (2023) 801-816. https://doi.org/10.1007/s00170-022-10433-7

[15] VDI 3430, Rotary draw bending of profiles, technical standard, VDI, 2014. Access on: https://www.vdi.de/richtlinien/details/vdi-3430-rotationszugbiegen-von-profilen

[16] P. Frohn-Sörensen, Process Development of Incremental Swivel Bending – ISB, Doctoral Thesis, University of Siegen, Siegen, 2023. http://dx.doi.org/10.25819/ubsi/10305
[5] F. Vollertsen, A. Sprenger, J. Kraus, and H. Arnet, Extrusion, channel, and profile bending: a review, J. Mater. Process. Technol. 87 (1999) 1-27. https://doi.org/10.1016/S0924-0136(98)00339-2

[6] C. Kuhnhen, J. Knoche, J. Reuter, S.S. Hassan Al-Maeeni, and B. Engel, Hybrid tool design for a bending machine, Procedia CIRP. 99 (2021) 370-374. https://doi.org/10.1016/j.procir.2021.03.052

[7] L.-E. Elend, Einsatz elastischer Niederhaltersysteme zur Erweiterung der Prozeßgrenzen beim Tiefziehen, Doctoral Thesis, Leibniz University Hannover, Hannover, 2001. https://doi.org/10.15488/5808

[8] C. Heftrich, R. Steinheimer, and B. Engel, Rotary-draw-bending using tools with reduced geometries, Procedia Manuf. 15 (2018) 804-811. https://doi.org/10.1016/j.promfg.2018.07.410

[9] M.-Z. Li, Z.-Y. Cai, and C.-G. Liu, Flexible manufacturing of sheet metal parts based on digitized-die, Robot. Comput.-Integr. Manuf. 23 (2007) 107-115. https://doi.org/10.1016/j.rcim.2005.09.005

[10] M.Z. Li, Z.Y. Cai, Z. Sui, and Q.G. Yan, Multi-point forming technology for sheet metal, J. Mater. Process. Technol. 129 (2002) 333-338. https://doi.org/10.1016/S0924-0136(02)00685-4

[11] J. Reuter, A. Aslanidis, and B. Engel, Segmentierung von Biegeformen als Grundlage für die Entwicklung von Transformer-Werkzeugen, in: B. Engel, Transformation in der Biegetechnik - Tagungsband zum 6 Biegeforum Siegen, Universi-Verlag, Siegen, 2023, pp. 91-101. http://dx.doi.org/10.25819/ubsi/10398

[12] Z.-Y. Cai, S.-H. Wang, and M.-Z. Li, Numerical investigation of multi-point forming process for sheet metal: wrinkling, dimpling and springback, Int. J. Adv. Manuf. Technol. 37 (2008) 927-936. https://doi.org/10.1007/s00170-007-1045-5

[13] J. Reuter, P. Frohn-Sörensen and B. Engel, Segmentation Method for Bending Tools – Fundamental Investigation of Profile Forming by Segmented Tools, in: K. Mocellin, Po. Bouchard, R. Bigot, T. Balan (Eds.), Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity, pp. 547-559. ICTP2023. Lecture Notes in Mechanical Engineering. Springer, Cham, 2023. https://doi.org/10.1007/978-3-031-41023-9_55

[14] S.A. Tronvoll, J. Ma, and T. Welo, Deformation behavior in tube bending: a comparative study of compression bending and rotary draw bending, Int. J. Adv. Manuf. Technol. 124 (2023) 801-816. https://doi.org/10.1007/s00170-022-10433-7

[15] VDI 3430, Rotary draw bending of profiles, technical standard, VDI, 2014. Access on: https://www.vdi.de/richtlinien/details/vdi-3430-rotationszugbiegen-von-profilen

[16] P. Frohn-Sörensen, Process Development of Incremental Swivel Bending – ISB, Doctoral Thesis, University of Siegen, Siegen, 2023. http://dx.doi.org/10.25819/ubsi/10305
# Simulation-based analysis of electrical current induction in a device for electrochemical precision machining of Nd-Fe-B permanent magnets

THIELECKE Alexander<sup>1,a*</sup>, HACKERT-OSCHÄTZCHEN Matthias<sup>1,b</sup>, MEICHSNER Gunnar<sup>1,c</sup>, BERGER Thomas<sup>2,d</sup>, LOEBEL Sascha<sup>2,e</sup>, MARTIN André<sup>2,f</sup>, SCHULZE Robin<sup>3,g</sup>, SCHUBERT Andreas<sup>2,h</sup>

**Keywords:** Electrochemical Machining, Permanent Magnets, Multiphysics Simulation

**Abstract.** Sintered permanent magnets, consisting of the neodymium-iron-boron (Nd-Fe-B) alloy, are installed as rotor magnets in small and precision electric drives due to their high magnetic forces in small volumes. When permanent magnets are brought into their final shape by electrical discharge machining (EDM), the thermal influence of this manufacturing process has negative effects on the magnetic properties of the workpieces. In consequence, re-magnetization of the workpieces is necessary after the finishing process. As an alternative manufacturing technology, electrochemical precision machining with an oscillating electrode and pulsed direct current (PECM) has the potential to eliminate this subsequent processing step. Based on Faraday's law of induction, an electrical induction current is expected to be generated by the cathode oscillation during the manufacturing process. In this study, the effect of the magnetic field of the workpiece on the process current and on the ablation-effective local electrical current density of the PECM process is analyzed based on multiphysics simulation.

**Introduction**

Permanent magnets are used as rotor magnets for small or precision drives with two degrees of freedom. These permanent magnets are installed in pairs due to the required degrees of freedom and are, for instance, double spherical in shape. High-performance Nd-Fe-B alloys are applied as the material for the rotor magnets. One of the factors that determines the extent to which undesirable cogging torques of the electric drive result is the shape of the rotor magnets, which makes precise machining of these permanent magnets essential.

After the sintered permanent magnets have been machined into their final shape using EDM, a subsequent magnetization process of the components is required [1]. The additional process step is necessary because the Nd-Fe-B materials are characterized by low application temperatures, so that temperatures above 80 °C are expected to affect the magnetization [2]. PECM offers an alternative finishing process without re-magnetizing the components after shaping. Compared to EDM, PECM machining takes place in an aqueous electrolyte solution, which is usually pre-tempered to less than 30 °C and only heats up slightly during the machining process. As a result,

<figure><img src="image_2246.png" /></figure>

<footnote n="1"><sup>1</sup>Chair of Manufacturing Technology with Focus Machining, Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany</footnote>

<footnote n="2"><sup>2</sup>Professorship Micromanufacturing Technology, Chemnitz University of Technology, 09107 Chemnitz, Germany</footnote>

<footnote n="3"><sup>3</sup>SITEC Industrietechnologie GmbH, 09114 Chemnitz, Germany</footnote>

<footnote><sup>a</sup>alexander.thielecke@ovgu.de, <sup>b</sup>matthias.hackert-oschaetzchen@ovgu.de,</footnote>

<footnote><sup>c</sup>gunnar.meichsner@ovgu.de, <sup>d</sup>thomas.berger@mb.tu-chemnitz.de,</footnote>

<footnote><sup>e</sup>sascha.loebel@mb.tu-chemnitz.de, <sup>f</sup>andre.martin@mb.tu-chemnitz.de,</footnote>

<footnote><sup>g</sup>robin.schulze@sitec-technology.de, <sup>h</sup>andreas.schubert@mb.tu-chemnitz.de</footnote>
# Simulation-based analysis of electrical current induction in a device for electrochemical precision machining of Nd-Fe-B permanent magnets

THIELECKE Alexander<sup>1, a *</sup>, HACKERT-OSCHÄTZCHEN Matthias<sup>1, b</sup>, MEICHSNER Gunnar<sup>1, c</sup>, BERGER Thomas<sup>2, d</sup>, LOEBEL Sascha<sup>2, e</sup>, MARTIN André<sup>2, f</sup>, SCHULZE Robin<sup>3, g</sup>, SCHUBERT Andreas<sup>2, h</sup>

**Keywords:** Electrochemical Machining, Permanent Magnets, Multiphysics Simulation

**Abstract.** Sintered permanent magnets, consisting of the neodymium-iron-boron (Nd-Fe-B) alloy, are installed as rotor magnets in small and precision electric drives due to their high magnetic forces in small volumes. When permanent magnets are brought into their final shape by electrical discharge machining (EDM), the thermal influence of this manufacturing process has negative effects on the magnetic properties of the workpieces. In consequence, re-magnetization of the workpieces is necessary after the finishing process. As an alternative manufacturing technology, electrochemical precision machining with an oscillating electrode and pulsed direct current (PECM) has the potential to eliminate this subsequent processing step. Based on Faraday's law of induction, an electrical induction current is expected to be generated by the cathode oscillation during the manufacturing process. In this study, the effect of the magnetic field of the workpiece on the process current and on the ablation-effective local electrical current density of the PECM process is analyzed based on multiphysics simulation.

**Introduction**

Permanent magnets are used as rotor magnets for small or precision drives with two degrees of freedom. These permanent magnets are installed in pairs due to the required degrees of freedom and are, for instance, double spherical in shape. High-performance Nd-Fe-B alloys are applied as the material for the rotor magnets. One of the factors that determines the extent to which undesirable cogging torques of the electric drive result is the shape of the rotor magnets, which makes precise machining of these permanent magnets essential.

After the sintered permanent magnets have been machined into their final shape using EDM, a subsequent magnetization process of the components is required [1]. The additional process step is necessary because the Nd-Fe-B materials are characterized by low application temperatures, so that temperatures above 80 °C are expected to affect the magnetization [2]. PECM offers an alternative finishing process without re-magnetizing the components after shaping. Compared to EDM, PECM machining takes place in an aqueous electrolyte solution, which is usually pre-tempered to less than 30 °C and only heats up slightly during the machining process. As a result,

<figure><img src="image_2237.png" /></figure>

<footnote n="1"><sup>1</sup>Chair of Manufacturing Technology with Focus Machining, Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany</footnote>

<footnote n="2"><sup>2</sup>Professorship Micromanufacturing Technology, Chemnitz University of Technology, 09107 Chemnitz, Germany</footnote>

<footnote n="3"><sup>3</sup>SITEC Industrietechnologie GmbH, 09114 Chemnitz, Germany</footnote>

<footnote><sup>a</sup>alexander.thielecke@ovgu.de, <sup>b</sup>matthias.hackert-oschaetzchen@ovgu.de,</footnote>

<footnote><sup>c</sup>gunnar.meichsner@ovgu.de, <sup>d</sup>thomas.berger@mb.tu-chemnitz.de,</footnote>

<footnote><sup>e</sup>sascha.loebel@mb.tu-chemnitz.de, <sup>f</sup>andre.martin@mb.tu-chemnitz.de,</footnote>

<footnote><sup>g</sup>robin.schulze@sitec-technology.de, <sup>h</sup>andreas.schubert@mb.tu-chemnitz.de</footnote>
only minor thermal effects occur, which are expected to not affect the magnetic properties of the components. The PECM principle is illustrated in Fig. 1.

<figure><img src="image_2247.png" /><figcaption>Figure 1 – Principle of ECM with pulsed direct current and an oscillating cathode according to [3]</figcaption></figure>

During electrochemical machining, the gas concentration and the degree of contamination of the electrolyte increase in the working gap. This results in a reduction in the reaction components of the electrolyte and consequently a decrease in electrical conductivity. To prevent this negative effect, pulsation of the current is used in the PECM process. This allows fresh electrolyte to flow into the process area during the pulse interruption. With PECM, the current pulse is often combined with an oscillation of the cathode in order to achieve an even stronger localization of the current density and thus an even higher accuracy of the workpiece shape.

In a previous study was shown that the oscillating movement of the cathode causes an electrical current induction in form of eddy currents during the PECM process in a rotationally symmetrical workpiece and in a rotationally symmetrical cathode [4]. Circular eddy currents are induction currents that are induced in an electrically conductive material in a magnetic field that changes over time or in a moving electrically conductive material in a magnetic field that remains constant over time. The interaction between the electric and magnetic fields that lead to current induction can be explained by the differential form of Faraday's law of electromagnetic induction in Eq. 1 [5].

$$ \nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} \qquad (1) $$

Eq. 1 states that a time-varying magnetic field is accompanied by a spatially varying electric field and vice versa. Where E represents the electric field, B the magnetic field and $\nabla \times$ the curl operator. In this study the effect of electrical current induction on the initial state and during the machining of the spherical shape of a rotor magnet is to be analyzed using 2 transient simulation models with the commercial FEM software COMSOL Multiphysics.

## Model description

### Geometry and material parameters

The PECM device shown in previous experiments is designed for 2-sided machining of the rotor magnets [6]. In the first step, the concave surface is machined. In the second step, the component is re-clamped to machine the convex shape. The dimensions of the workpiece are shown in Fig. 2.
only minor thermal effects occur, which are expected to not affect the magnetic properties of the components. The PECM principle is illustrated in Fig. 1.

<figure><img src="image_2238.png" /><figcaption>Figure 1 – Principle of ECM with pulsed direct current and an oscillating cathode according to [3]</figcaption></figure>

During electrochemical machining, the gas concentration and the degree of contamination of the electrolyte increase in the working gap. This results in a reduction in the reaction components of the electrolyte and consequently a decrease in electrical conductivity. To prevent this negative effect, pulsation of the current is used in the PECM process. This allows fresh electrolyte to flow into the process area during the pulse interruption. With PECM, the current pulse is often combined with an oscillation of the cathode in order to achieve an even stronger localization of the current density and thus an even higher accuracy of the workpiece shape.

In a previous study was shown that the oscillating movement of the cathode causes an electrical current induction in form of eddy currents during the PECM process in a rotationally symmetrical workpiece and in a rotationally symmetrical cathode [4]. Circular eddy currents are induction currents that are induced in an electrically conductive material in a magnetic field that changes over time or in a moving electrically conductive material in a magnetic field that remains constant over time. The interaction between the electric and magnetic fields that lead to current induction can be explained by the differential form of Faraday's law of electromagnetic induction in Eq. 1 [5].

$$ \nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} \qquad (1) $$

Eq. 1 states that a time-varying magnetic field is accompanied by a spatially varying electric field and vice versa. Where E represents the electric field, B the magnetic field and $\nabla \times$ the curl operator. In this study the effect of electrical current induction on the initial state and during the machining of the spherical shape of a rotor magnet is to be analyzed using 2 transient simulation models with the commercial FEM software COMSOL Multiphysics.

## Model description

### Geometry and material parameters

The PECM device shown in previous experiments is designed for 2-sided machining of the rotor magnets [6]. In the first step, the concave surface is machined. In the second step, the component is re-clamped to machine the convex shape. The dimensions of the workpiece are shown in Fig. 2.
<figure><img src="image_2248.png" /><figcaption>Figure 2 – Cross-sectional view of a rotary drive with three terminal pairs (a), top view of a single rotor magnet (b) and detailed cross-sectional view (c); dimensions in mm [6]</figcaption></figure>

To investigate if the different shapes of the workpiece during the PECM process have a different effect on the strength and distribution of the induced eddy currents, 2 transient 2D simulation models were set up to analyze the induced current. Fig. 3 shows the 2 different machining stages of the first step of the machining process.

<figure><img src="image_2249.png" /><figcaption>Figure 3 – Initial- and processing states of the workpiece in the PECM process</figcaption></figure>

The design of the model geometries, material data and PECM input parameters were derived from previously performed experiments [6]. In the following, the geometry representing the workpiece in its initial state is referred to as “Model initial state” and the machined workpiece as “Model final state”. As an example, the 2D model geometry of Model initial state derived from the cross-section of the PECM device, is shown in Fig. 4.

<figure><img src="image_2250.png" /><figcaption>Figure 4 – Cross-section of the PECM device (left) and derived 2D model geometry (right)</figcaption></figure>
<figure><img src="image_2239.png" /><figcaption>Figure 2 – Cross-sectional view of a rotary drive with three terminal pairs (a), top view of a single rotor magnet (b) and detailed cross-sectional view (c); dimensions in mm [6]</figcaption></figure>

To investigate if the different shapes of the workpiece during the PECM process have a different effect on the strength and distribution of the induced eddy currents, 2 transient 2D simulation models were set up to analyze the induced current. Fig. 3 shows the 2 different machining stages of the first step of the machining process.

<figure><img src="image_2240.png" /><figcaption>Figure 3 – Initial- and processing states of the workpiece in the PECM process</figcaption></figure>

The design of the model geometries, material data and PECM input parameters were derived from previously performed experiments [6]. In the following, the geometry representing the workpiece in its initial state is referred to as “Model initial state” and the machined workpiece as “Model final state”. As an example, the 2D model geometry of Model initial state derived from the cross-section of the PECM device, is shown in Fig. 4.

<figure><img src="image_2241.png" /><figcaption>Figure 4 – Cross-section of the PECM device (left) and derived 2D model geometry (right)</figcaption></figure>
The model geometry includes the domains workpiece (I), cathode (II), electrolyte (III), clamping jaws (IV) and insulation (V). For the calculation and the analysis of the induction current, it is essential to model additional air domains (VI-XI) for the realistic dispersion of the magnetic field of the workpiece. The workpiece, cathode, insulation and clamping jaw components were first imported from the 3D CAD file as a 3D model into the simulation environment and then modelled as a 2D model using a cross-section. Since all components used have symmetry, the z-symmetry plane was utilized to halve the elements and nodes of the model geometry in order to reduce computing time. The electrolyte area was added as a negative of the working gap between the cathode and the workpiece. The electrical conductivity, relative permeability and relative permittivity of the materials are defined for calculating and analyzing the electrical induction current. Table 1 allocates the materials and material parameters to the domains shown in Fig. 4.

<table><caption>Table 1 - Material parameters of the simulation model</caption><thead><tr><td>Domain</td><td>Material</td><td>σ [S/m]</td><td>μ<sub>r</sub></td><td>ε<sub>r</sub></td></tr></thead><tbody><tr><td>I</td><td>Nd-Fe-B/N45</td><td>6.67 · 10<sup>5</sup></td><td>1.05</td><td>1.05</td></tr><tr><td>II</td><td>1.4301/AISI 304</td><td>1.4 · 10<sup>6</sup></td><td>1.075</td><td>1</td></tr><tr><td>III</td><td>Electrolyte (NaNO<sub>3</sub>)</td><td>7.2</td><td>0.28</td><td>1</td></tr><tr><td>IV</td><td>1.4305/AISI 303</td><td>1.37 · 10<sup>6</sup></td><td>1.26</td><td>1</td></tr><tr><td>V</td><td>PEEK</td><td>10<sup>-10</sup></td><td>1</td><td>3.2</td></tr><tr><td>VI</td><td>Air</td><td>3 · 10<sup>-15</sup></td><td>1</td><td>1.006</td></tr></tbody></table>

## Physics and boundary conditions

In order to calculate magnetic fields and electromagnetic induction, the Magnetic Fields interface was assigned to all domains of the model geometry. The physical interface solves Maxwell's equations, which are formulated using the magnetic vector potential and the scalar electric potential as the dependent variables. The measurement of the remanent magnetic flux density of experimental samples was carried out using a PCE-MFM 3000 magnetic field tester from PCE Deutschland GmbH. The target value for calibrating the workpiece is a magnetic flux density of $B_r = 0.46 \text{ T} \pm 5 \%$ on the face of the workpiece.

The air domains VII-XI are defined as regions of infinite elements. The Infinite element domain represents a region that is stretched along the x- and z coordinate axes with the effect of approximating an infinitely large domain to ensure the realistic dispersion of the magnetic field. Further magnetic boundary conditions are summarized in Table 2.
The model geometry includes the domains workpiece (I), cathode (II), electrolyte (III), clamping jaws (IV) and insulation (V). For the calculation and the analysis of the induction current, it is essential to model additional air domains (VI-XI) for the realistic dispersion of the magnetic field of the workpiece. The workpiece, cathode, insulation and clamping jaw components were first imported from the 3D CAD file as a 3D model into the simulation environment and then modelled as a 2D model using a cross-section. Since all components used have symmetry, the z-symmetry plane was utilized to halve the elements and nodes of the model geometry in order to reduce computing time. The electrolyte area was added as a negative of the working gap between the cathode and the workpiece. The electrical conductivity, relative permeability and relative permittivity of the materials are defined for calculating and analyzing the electrical induction current. Table 1 allocates the materials and material parameters to the domains shown in Fig. 4.

<table><caption>Table 1 - Material parameters of the simulation model</caption><thead><tr><td>Domain</td><td>Material</td><td>σ [S/m]</td><td>μ<sub>r</sub></td><td>ε<sub>r</sub></td></tr></thead><tbody><tr><td>I</td><td>Nd-Fe-B/N45</td><td>6.67 · 10<sup>5</sup></td><td>1.05</td><td>1.05</td></tr><tr><td>II</td><td>1.4301/AISI 304</td><td>1.4 · 10<sup>6</sup></td><td>1.075</td><td>1</td></tr><tr><td>III</td><td>Electrolyte (NaNO<sub>3</sub>)</td><td>7.2</td><td>0.28</td><td>1</td></tr><tr><td>IV</td><td>1.4305/AISI 303</td><td>1.37 · 10<sup>6</sup></td><td>1.26</td><td>1</td></tr><tr><td>V</td><td>PEEK</td><td>10<sup>-10</sup></td><td>1</td><td>3.2</td></tr><tr><td>VI</td><td>Air</td><td>3 · 10<sup>-15</sup></td><td>1</td><td>1.006</td></tr></tbody></table>

## Physics and boundary conditions

In order to calculate magnetic fields and electromagnetic induction, the Magnetic Fields interface was assigned to all domains of the model geometry. The physical interface solves Maxwell's equations, which are formulated using the magnetic vector potential and the scalar electric potential as the dependent variables. The measurement of the remanent magnetic flux density of experimental samples was carried out using a PCE-MFM 3000 magnetic field tester from PCE Deutschland GmbH. The target value for calibrating the workpiece is a magnetic flux density of $B_r = 0.46 \text{ T} \pm 5 \%$ on the face of the workpiece.

The air domains VII-XI are defined as regions of infinite elements. The Infinite element domain represents a region that is stretched along the x- and z coordinate axes with the effect of approximating an infinitely large domain to ensure the realistic dispersion of the magnetic field. Further magnetic boundary conditions are summarized in Table 2.
<table><caption>Table 2 - Domain and boundary conditions of the Magnetic Fields interface</caption><thead><tr><th>Domain condition</th><th>Domain</th><th>Property</th></tr></thead><tbody><tr><td>Ampère's Law I</td><td>II-XI</td><td>μ<sub>r</sub> from material (Tab. 1)</td></tr><tr><td>Ampère's Law II</td><td>I</td><td>Magnetization model:<br>Remanent flux density<br>B<sub>r</sub> = 1.35 T [6]<br>Remanent flux direction<br>e<sub>X</sub> = 0; e<sub>Y</sub> = 0; e<sub>Z</sub> = 1</td></tr><tr><td>Infinite Element Domain</td><td>VII-XI</td><td>f(ξ) = <sup>ξ</sup>/<sub>γ - ξ</sub> · Δ<sub>p</sub></td></tr><tr><td>Boundary condition</td><td>Boundary</td><td>Property</td></tr><tr><td>Axis symmetry</td><td>3-9</td><td>-</td></tr></tbody></table>

The oscillation parameters of the simulation models are summarized in Table 3.

<table><caption>Table 3 - Motion parameters of the cathode derived from [6]</caption><thead><tr><th>Description</th><th>Symbol</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Amplitude</td><td>ẑ</td><td>0.185</td><td>[mm]</td></tr><tr><td>Oscillation frequency</td><td>f<sub>z</sub></td><td>50</td><td>[Hz]</td></tr><tr><td>Period</td><td>T</td><td>0.02</td><td>[s]</td></tr><tr><td>Initial working distance (Model initial state)</td><td>S<sub>F-A</sub></td><td>0.1</td><td>[mm]</td></tr><tr><td>End front working distance (Model final state)</td><td>S<sub>F-E</sub></td><td>0.085</td><td>[mm]</td></tr></tbody></table>

Oscillating components of the simulation models are the cathode (II) and the insulation unit (V). The *Moving Mesh* interface was applied to implement the oscillation of the corresponding domains. The oscillation can be described with a time-dependent cosine function as provided in Eq. 2.

$$Z(t) = \hat{z} \cdot \cos (2 \cdot \pi \cdot f_z \cdot t + \frac{\pi}{2}) \qquad (2)$$

The upper and lower dead center of the cathode position during oscillation is defined by the amplitude $\hat{z}$. The oscillation frequency is $f_z$, from which the period time $T$ results. To evaluate the results of the induced current, 2 periods are analyzed in this simulation study. Domain and boundary conditions of the *Moving Mesh* Interface are listed and described in Table 4.
<table><caption>Table 2 - Domain and boundary conditions of the Magnetic Fields interface</caption><thead><tr><th>Domain condition</th><th>Domain</th><th>Property</th></tr></thead><tbody><tr><td>Ampère's Law I</td><td>II-XI</td><td>μ<sub>r</sub> from material (Tab. 1)</td></tr><tr><td>Ampère's Law II</td><td>I</td><td>Magnetization model:<br>Remanent flux density<br>B<sub>r</sub> = 1.35 T [6]<br>Remanent flux direction<br>e<sub>X</sub> = 0; e<sub>Y</sub> = 0; e<sub>Z</sub> = 1</td></tr><tr><td>Infinite Element Domain</td><td>VII-XI</td><td>f(ξ) = <sup>ξ</sup>/<sub>γ - ξ</sub> · Δ<sub>p</sub></td></tr><tr><td>Boundary condition</td><td>Boundary</td><td>Property</td></tr><tr><td>Axis symmetry</td><td>3-9</td><td>-</td></tr></tbody></table>

The oscillation parameters of the simulation models are summarized in Table 3.

<table><caption>Table 3 - Motion parameters of the cathode derived from [6]</caption><thead><tr><th>Description</th><th>Symbol</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Amplitude</td><td>ẑ</td><td>0.185</td><td>[mm]</td></tr><tr><td>Oscillation frequency</td><td>f<sub>z</sub></td><td>50</td><td>[Hz]</td></tr><tr><td>Period</td><td>T</td><td>0.02</td><td>[s]</td></tr><tr><td>Initial working distance (Model initial state)</td><td>S<sub>F-A</sub></td><td>0.1</td><td>[mm]</td></tr><tr><td>End front working distance (Model final state)</td><td>S<sub>F-E</sub></td><td>0.085</td><td>[mm]</td></tr></tbody></table>

Oscillating components of the simulation models are the cathode (II) and the insulation unit (V). The *Moving Mesh* interface was applied to implement the oscillation of the corresponding domains. The oscillation can be described with a time-dependent cosine function as provided in Eq. 2.

$$Z(t) = ẑ \cdot \cos (2 \cdot \pi \cdot f_z \cdot t + \frac{\pi}{2}) \qquad (2)$$

The upper and lower dead center of the cathode position during oscillation is defined by the amplitude $ẑ$. The oscillation frequency is $f_z$, from which the period time $T$ results. To evaluate the results of the induced current, 2 periods are analyzed in this simulation study. Domain and boundary conditions of the *Moving Mesh* Interface are listed and described in Table 4.
<table><caption>Table 4 - Domain and boundary condition of the Moving Mesh interface</caption><thead><tr><th>Domain condition</th><th>Domain</th><th>Property</th></tr></thead><tbody><tr><td>Prescribed Deformation I</td><td>II, V</td><td>d<sub>x</sub> = d<sub>y</sub> = 0 m;<br>d<sub>z</sub> = Z(t) = &zeta; &middot; cos (2 &middot; &pi; &middot; f<sub>z</sub> &middot; t + &pi;/2)</td></tr><tr><td>Prescribed Deformation II</td><td>I, IV, VII-XI</td><td>d<sub>x</sub> = d<sub>y</sub> = d<sub>z</sub> = 0 m</td></tr><tr><td>Deforming Domain</td><td>III, VI</td><td>Initial deformation<br>d<sub>x</sub> = d<sub>y</sub> = d<sub>z</sub> = 0 m</td></tr><tr><td>Boundary condition</td><td>Boundary</td><td>Property</td></tr><tr><td>Prescribed Mesh Displacement in Normal Direction</td><td>4, 6, 8, 11</td><td>d<sub>n</sub> = 0 m</td></tr></tbody></table>

The process input parameters of the pulsed electric potential are summarized in Table 5.

<table><caption>Table 5 - Pulsed electric potential parameters derived from [6]</caption><thead><tr><th>Description</th><th>Symbol</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Pulse width</td><td>t<sub>pulse</sub></td><td>0.004</td><td>[s]</td></tr><tr><td>Pulse start</td><td>t<sub>start</sub></td><td>0.003 / 0.023</td><td>[s]</td></tr><tr><td>Pulse end</td><td>t<sub>end</sub></td><td>0.007 / 0.027</td><td>[s]</td></tr><tr><td>Process voltage</td><td>U<sub>min</sub></td><td>14</td><td>[V]</td></tr></tbody></table>

The *Electric Current* interface was applied to supply the PECM process with external electric potential. Eq. 3 was defined to integrate the pulsed voltage $U_{pulsed}(t)$ into the simulation model.

$$U_{pulsed}(t) = U_{control} \cdot U_{min} \cdot \frac{(p_0 - p_1)}{s_{F-A/E}} \quad (3)$$

$U_{control}$ is defined as a discrete variable in the *Event* interface and switches the electrical voltage on and off in the specified period time. $U_{min}$ is calculated from the sum of all overvoltages of the boundary layers of workpiece and cathode and the voltage drop in the electrolyte solution. The value $U_{min}$ is taken from the experiments shown [6]. The aim of PECM is to maintain a constant electrical process current. Accordingly, the electrical voltage is controlled dynamically depending on the changing working gap during the PECM process. For the PEMCenter 8000 from *PEMTec SNC* used in the experiments, 4 generators are used to provide the required electrical voltage. The control technology of the PEMCenter 8000 is realized in the simulation of the 3rd term of Eq. 3. During the transient calculation, the geometric point $p_0$ is tracked using a software internal probe function. The Point $p_1$ is a fixed point on the surface of the respective workpieces. Both points are shown in Fig. 3. The different working distances depending on the different models are $S_{F-A/E}$. The boundary conditions and variables for implementing the electrical voltage are summarized in Table 6.
<table><caption>Table 4 - Domain and boundary condition of the Moving Mesh interface</caption><thead><tr><th>Domain condition</th><th>Domain</th><th>Property</th></tr></thead><tbody><tr><td>Prescribed Deformation I</td><td>II, V</td><td>d<sub>x</sub> = d<sub>y</sub> = 0 m;<br>d<sub>z</sub> = Z(t) = ẑ · cos (2 · π · f<sub>z</sub> · t + π/2)</td></tr><tr><td>Prescribed Deformation II</td><td>I, IV, VII-XI</td><td>d<sub>x</sub> = d<sub>y</sub> = d<sub>z</sub> = 0 m</td></tr><tr><td>Deforming Domain</td><td>III, VI</td><td>Initial deformation<br>d<sub>x</sub> = d<sub>y</sub> = d<sub>z</sub> = 0 m</td></tr><tr><td>Boundary condition</td><td>Boundary</td><td>Property</td></tr><tr><td>Prescribed Mesh Displacement<br>in Normal Direction</td><td>4, 6, 8, 11</td><td>d<sub>n</sub> = 0 m</td></tr></tbody></table>

The process input parameters of the pulsed electric potential are summarized in Table 5.

<table><caption>Table 5 - Pulsed electric potential parameters derived from [6]</caption><thead><tr><th>Description</th><th>Symbol</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Pulse width</td><td>t<sub>pulse</sub></td><td>0.004</td><td>[s]</td></tr><tr><td>Pulse start</td><td>t<sub>start</sub></td><td>0.003 / 0.023</td><td>[s]</td></tr><tr><td>Pulse end</td><td>t<sub>end</sub></td><td>0.007 / 0.027</td><td>[s]</td></tr><tr><td>Process voltage</td><td>U<sub>min</sub></td><td>14</td><td>[V]</td></tr></tbody></table>

The *Electric Current* interface was applied to supply the PECM process with external electric potential. Eq. 3 was defined to integrate the pulsed voltage $U_{pulsed}(t)$ into the simulation model.

$$U_{pulsed}(t) = U_{control} \cdot U_{min} \cdot \frac{(p_0 - p_1)}{s_{F-A/E}} \quad (3)$$

$U_{control}$ is defined as a discrete variable in the *Event* interface and switches the electrical voltage on and off in the specified period time. $U_{min}$ is calculated from the sum of all overvoltages of the boundary layers of workpiece and cathode and the voltage drop in the electrolyte solution. The value $U_{min}$ is taken from the experiments shown [6]. The aim of PECM is to maintain a constant electrical process current. Accordingly, the electrical voltage is controlled dynamically depending on the changing working gap during the PECM process. For the PEMCenter 8000 from *PEMTec SNC* used in the experiments, 4 generators are used to provide the required electrical voltage. The control technology of the PEMCenter 8000 is realized in the simulation of the 3rd term of Eq. 3. During the transient calculation, the geometric point $p_0$ is tracked using a software internal probe function. The Point $p_1$ is a fixed point on the surface of the respective workpieces. Both points are shown in Fig. 3. The different working distances depending on the different models are $S_{F-A/E}$. The boundary conditions and variables for implementing the electrical voltage are summarized in Table 6.
<table><caption>Table 6 - Domain and boundary conditions of the Electric Current and the Event interfaces</caption><thead><tr><th>Boundary condition</th><th>Boundary</th><th>Property</th></tr></thead><tbody><tr><td>Electric potential</td><td>2</td><td>U<sub>pulsed</sub>(t)</td></tr><tr><td>Ground</td><td>1</td><td>φ<sub>el</sub> = 0 V</td></tr><tr><td>Axis symmetry</td><td>3-9</td><td>-</td></tr></tbody></table><table><thead><tr><th>Event interface condition</th><th>Variable/States</th><th>Property</th></tr></thead><tbody><tr><td>Discrete variable</td><td>U<sub>control</sub></td><td>0 or 1</td></tr><tr><td>Indicator states I</td><td>U<sub>start</sub></td><td>t - t<sub>start</sub></td></tr><tr><td>Indicator states II</td><td>U<sub>end</sub></td><td>t - t<sub>end</sub></td></tr><tr><td>Implicit event I</td><td>U<sub>start</sub> > 0</td><td>U<sub>control</sub> = 1</td></tr><tr><td>Implicit event II</td><td>U<sub>end</sub> > 0</td><td>U<sub>control</sub> = 0</td></tr></tbody></table>

The boundary conditions of the electrical voltage and the oscillation movement of the cathode are shown as graphs in Fig. 5.

<figure><img src="image_2251.png" /><figcaption>Figure 5 – Integrated boundary conditions of oscillation movement, electrical voltage and resulting current density plotted in one period</figcaption></figure>

## Results of the simulation

The average remanent magnetic flux density on the face of the workpiece surface in the Model initial state is $B_r = 0.45$ T and thus within the tolerance of the remanent magnetic flux density of the measured samples. On the face of the workpiece surface in Model final state, the magnetic flux density increases to $B_r = 0.51$ T due to the change in geometry. Fig. 6 shows the magnetic flux density in the models.
<table><caption>Table 6 - Domain and boundary conditions of the Electric Current and the Event interfaces</caption><thead><tr><th>Boundary condition</th><th>Boundary</th><th>Property</th></tr></thead><tbody><tr><td>Electric potential</td><td>2</td><td>U<sub>pulsed</sub>(t)</td></tr><tr><td>Ground</td><td>1</td><td>φ<sub>el</sub> = 0 V</td></tr><tr><td>Axis symmetry</td><td>3-9</td><td>-</td></tr></tbody></table><table><thead><tr><th>Event interface condition</th><th>Variable/States</th><th>Property</th></tr></thead><tbody><tr><td>Discrete variable</td><td>U<sub>control</sub></td><td>0 or 1</td></tr><tr><td>Indicator states I</td><td>U<sub>start</sub></td><td>t - t<sub>start</sub></td></tr><tr><td>Indicator states II</td><td>U<sub>end</sub></td><td>t - t<sub>end</sub></td></tr><tr><td>Implicit event I</td><td>U<sub>start</sub> > 0</td><td>U<sub>control</sub> = 1</td></tr><tr><td>Implicit event II</td><td>U<sub>end</sub> > 0</td><td>U<sub>control</sub> = 0</td></tr></tbody></table>

The boundary conditions of the electrical voltage and the oscillation movement of the cathode are shown as graphs in Fig. 5.

<figure><img src="image_2242.png" /><figcaption>Figure 5 – Integrated boundary conditions of oscillation movement, electrical voltage and resulting current density plotted in one period</figcaption></figure>

## Results of the simulation

The average remanent magnetic flux density on the face of the workpiece surface in the Model initial state is $B_r = 0.45$ T and thus within the tolerance of the remanent magnetic flux density of the measured samples. On the face of the workpiece surface in Model final state, the magnetic flux density increases to $B_r = 0.51$ T due to the change in geometry. Fig. 6 shows the magnetic flux density in the models.
<figure><img src="image_2252.png" /><figcaption>Figure 6 – False color representation of the magnetic flux density and the magnetic field lines (white cones) in Model initial state (left) and Model final state (right)</figcaption></figure>

The density of the magnetic field lines increases at the workpiece corners of the north and south pole. Accordingly, the maximum magnetic flux density is localized at the corners of the workpiece and measures up to $B_r = 1.6$ T.

As described in Eq. 1, the oscillating movement of the cathode relative to the stationary magnetic field of the workpiece leads to an electrical current induction in the cathode and workpiece domains. Fig. 7 shows the electrical current induction in a false color representation.

<figure><img src="image_2253.png" /><figcaption>Figure 7 – Induced current density at $t = 0.001$ s at Model initial state (left) and Model final state (right)</figcaption></figure>

A maximum induced current density of 6 A/cm² for Model initial state and 8 A/cm² for Model final state was determined in the cathode. A lower induced current of a maximum of 0.7 A/cm² in Model initial state and up to 1 A/cm² in Model final state is detected on the workpiece surface on boundary 10. The induced current is significantly lower than the current flowing due to the externally applied potential.

For comparison, Fig. 8 shows the distribution of the electrical current density with external potential in the models.
<figure><img src="image_2243.png" /><figcaption>Figure 6 – False color representation of the magnetic flux density and the magnetic field lines (white cones) in Model initial state (left) and Model final state (right)</figcaption></figure>

The density of the magnetic field lines increases at the workpiece corners of the north and south pole. Accordingly, the maximum magnetic flux density is localized at the corners of the workpiece and measures up to $B_r = 1.6$ T.

As described in Eq. 1, the oscillating movement of the cathode relative to the stationary magnetic field of the workpiece leads to an electrical current induction in the cathode and workpiece domains. Fig. 7 shows the electrical current induction in a false color representation.

<figure><img src="image_2244.png" /><figcaption>Figure 7 – Induced current density at $t = 0.001$ s at Model initial state (left) and Model final state (right)</figcaption></figure>

A maximum induced current density of 6 A/cm² for Model initial state and 8 A/cm² for Model final state was determined in the cathode. A lower induced current of a maximum of 0.7 A/cm² in Model initial state and up to 1 A/cm² in Model final state is detected on the workpiece surface on boundary 10. The induced current is significantly lower than the current flowing due to the externally applied potential.

For comparison, Fig. 8 shows the distribution of the electrical current density with external potential in the models.
<figure><img src="image_2254.png" /><figcaption>Figure 8 - False color representation of electric current density with external potential and the direction of current (black Arrows on boundary 10) at t = 0.005 s at Model initial state (left) and Model final state (right)</figcaption></figure>

The high current densities of up to 250 A/cm² are caused by electrical peak effects, which are not decisive for ECM removal due to their localization in the contact area between the workpiece and the clamping jaws. The maximum current densities on the workpiece surface on boundary 10 are 100 A/cm² in Model initial state and 120 A/cm² in Model final state. In addition to the magnitudes of the electrical current density, the direction of the current is decisive for the charge transport, without which there is no removal from the workpiece in an ECM process. In the case of the applied coordinate system of the 2D models, it is necessary for the electric current to flow in the z-direction, as with the current with external potential (Fig. 8). Applying the *Out-of-Plane* node, it is possible to extrude the 2D geometry in the y-direction in order to make the 2D equation identical to the equation used for 3D components. Fig. 9 shows the induced current in the x-direction, in the z-direction and in the extruded y-direction of the 2D models.

<figure><img src="image_2255.png" /><figcaption>Figure 9 – Induced current direction in the workpiece (half of domain I) of Model initial state (left) and Model final state (right)</figcaption></figure>

Fig. 9 shows that the induced electric current distributes in the rectangular workpiece as a circular eddy current before and during processing. Furthermore, it can be seen that the polarity of the induced current changes during the machining process as soon as the cathode has reached bottom or top dead center. Despite the induced eddy currents in the workpiece, no removal-effective charges flow in the z-direction during induction in the PECM process. The differences
<figure><img src="image_2245.png" /><figcaption>Figure 8 - False color representation of electric current density with external potential and the direction of current (black Arrows on boundary 10) at t = 0.005 s at Model initial state (left) and Model final state (right)</figcaption></figure>

The high current densities of up to 250 A/cm² are caused by electrical peak effects, which are not decisive for ECM removal due to their localization in the contact area between the workpiece and the clamping jaws. The maximum current densities on the workpiece surface on boundary 10 are 100 A/cm² in Model initial state and 120 A/cm² in Model final state. In addition to the magnitudes of the electrical current density, the direction of the current is decisive for the charge transport, without which there is no removal from the workpiece in an ECM process. In the case of the applied coordinate system of the 2D models, it is necessary for the electric current to flow in the z-direction, as with the current with external potential (Fig. 8). Applying the *Out-of-Plane* node, it is possible to extrude the 2D geometry in the y-direction in order to make the 2D equation identical to the equation used for 3D components. Fig. 9 shows the induced current in the x-direction, in the z-direction and in the extruded y-direction of the 2D models.

<figure><img src="image_2246.png" /><figcaption>Figure 9 - Induced current direction in the workpiece (half of domain I) of Model initial state (left) and Model final state (right)</figcaption></figure>

Fig. 9 shows that the induced electric current distributes in the rectangular workpiece as a circular eddy current before and during processing. Furthermore, it can be seen that the polarity of the induced current changes during the machining process as soon as the cathode has reached bottom or top dead center. Despite the induced eddy currents in the workpiece, no removal-effective charges flow in the z-direction during induction in the PECM process. The differences
between the current induced by the magnetic field of the workpiece and the oscillating cathode and the pulsed current with external potential are summarized in Table 7.

<table><caption>Table 7 - Summarized simulation results</caption><thead><tr><td>Characteristic</td><td>Induction current</td><td>Pulsed current</td></tr></thead><tbody><tr><td>Current type</td><td>Alternating current (AC)</td><td>Direct current (DC)</td></tr><tr><td>Direction of current</td><td>Circular</td><td>Straight</td></tr><tr><td>Current density (on workpiece surface)</td><td>Max. 1 A/cm²</td><td>Max. 120 A/cm²</td></tr></tbody></table>

## Summary

In this study, 2 transient 2D models were shown for the simulation of precise electrochemical machining of a permanent magnet applying COMSOL Multiphysics. The simulation results show that the oscillating movement of the cathode relative to the workpiece causes an electrical induction current in the areas of the cathode and the workpiece in accordance with Faraday's law of induction. Due to the circular propagation of the induction current and the relatively low current density of a maximum of 1 A/cm² induced on the workpiece surface, it is not assumed that the induction current has an influence on the removal-effective process current. Based on this study, it is not necessary to change the process input parameters in PECM experiments if the machining strategy and magnetization of the workpieces are the same. In further studies a 3D model for further evaluation of the induced current in the PECM process will be investigated.

## Acknowledgements

This project is funded by the Federal Ministry for Economic Affairs and Climate Action, following a decision of the German Bundestag.

## References

[1] B. J. Smith, M. E. Riddle, M. R. Earlam, C. Iloeje, D. Diamond, "EERE Technical Report Template: Rare Earth Permanent Magnets," p. 15, 2022. [Online]. Available: https://www.energy.gov/sites/default/files/2022-02/Neodymium%20Magnets%20Supply%20Chain%20Report%20-%20Final.pdf

[2] H. Takezawa, N. Hirakawa, and N. Mohri, "Surface Magnetic Flux Density Patterning in EDM of Permanent Magnets," Procedia CIRP, vol. 42, pp. 668-672, 2016. https://doi.org/10.1016/j.procir.2016.02.299.

[3] A. Schubert, G. Meichsner, M. Hackert-Oschätzchen, M. Zinecker, and J. Edelmann, "Pulsed Electrochemical Machining of Powder Metallurgy Steels, 7th International Symposium on Electrochemical Machining Technology. (2011), https://doi.org/10.24406/publica-fhg-372620

[4] A. Thielecke, M. Hackert-Oschätzchen, N. Komilov, G. Meichsner, T. Petzold, S. Loebel, A. Martin, R. Schulze, and A. Schubert, "Simulation-based analysis of electrical current induction in electrochemical precision machining of Nd-Fe-B permanent magnets," Procedia CIRP, 2023. https://doi.org/10.1016/j.procir.2023.03.039.

[5] N. Ida, Engineering Electromagnetics. Cham: Springer International Publishing, 2015.

[6] A. Martin, T. Berger, S. Loebel, R. Schulze, A. Thielecke, M. Hackert-Oschätzchen, and A. Schubert, "Accuracy of pulsed electrochemical machining of NdFeB rotor magnets," in International Symposium on Electrochemical Machining Technology 2023 (INSECT 2023), Saarbrücken: Center for Mechatronics and Automation Technology, 2023, 2023.
between the current induced by the magnetic field of the workpiece and the oscillating cathode and the pulsed current with external potential are summarized in Table 7.

<table><caption>Table 7 - Summarized simulation results</caption><thead><tr><td>Characteristic</td><td>Induction current</td><td>Pulsed current</td></tr></thead><tbody><tr><td>Current type</td><td>Alternating current (AC)</td><td>Direct current (DC)</td></tr><tr><td>Direction of current</td><td>Circular</td><td>Straight</td></tr><tr><td>Current density (on workpiece surface)</td><td>Max. 1 A/cm²</td><td>Max. 120 A/cm²</td></tr></tbody></table>

## Summary

In this study, 2 transient 2D models were shown for the simulation of precise electrochemical machining of a permanent magnet applying COMSOL Multiphysics. The simulation results show that the oscillating movement of the cathode relative to the workpiece causes an electrical induction current in the areas of the cathode and the workpiece in accordance with Faraday's law of induction. Due to the circular propagation of the induction current and the relatively low current density of a maximum of 1 A/cm² induced on the workpiece surface, it is not assumed that the induction current has an influence on the removal-effective process current. Based on this study, it is not necessary to change the process input parameters in PECM experiments if the machining strategy and magnetization of the workpieces are the same. In further studies a 3D model for further evaluation of the induced current in the PECM process will be investigated.

## Acknowledgements

This project is funded by the Federal Ministry for Economic Affairs and Climate Action, following a decision of the German Bundestag.

## References

[1] B. J. Smith, M. E. Riddle, M. R. Earlam, C. Iloeje, D. Diamond, "EERE Technical Report Template: Rare Earth Permanent Magnets," p. 15, 2022. [Online]. Available: https://www.energy.gov/sites/default/files/2022-02/Neodymium%20Magnets%20Supply%20Chain%20Report%20-%20Final.pdf

[2] H. Takezawa, N. Hirakawa, and N. Mohri, "Surface Magnetic Flux Density Patterning in EDM of Permanent Magnets," Procedia CIRP, vol. 42, pp. 668-672, 2016. https://doi.org/10.1016/j.procir.2016.02.299.

[3] A. Schubert, G. Meichsner, M. Hackert-Oschätzchen, M. Zinecker, and J. Edelmann, "Pulsed Electrochemical Machining of Powder Metallurgy Steels, 7th International Symposium on Electrochemical Machining Technology. (2011), https://doi.org/10.24406/publica-fhg-372620

[4] A. Thielecke, M. Hackert-Oschätzchen, N. Komilov, G. Meichsner, T. Petzold, S. Loebel, A. Martin, R. Schulze, and A. Schubert, "Simulation-based analysis of electrical current induction in electrochemical precision machining of Nd-Fe-B permanent magnets," Procedia CIRP, 2023. https://doi.org/10.1016/j.procir.2023.03.039.

[5] N. Ida, Engineering Electromagnetics. Cham: Springer International Publishing, 2015.

[6] A. Martin, T. Berger, S. Loebel, R. Schulze, A. Thielecke, M. Hackert-Oschätzchen, and A. Schubert, "Accuracy of pulsed electrochemical machining of NdFeB rotor magnets," in International Symposium on Electrochemical Machining Technology 2023 (INSECT 2023), Saarbrücken: Center for Mechatronics and Automation Technology, 2023, 2023.
# Recycling of thermoset fiberglass by direct molding of ground powders

BELLISARIO Denise<fnref n="1" />,ª*, IORIO Leandro<fnref n="2" />,ᵇ, PROIETTI Alice<fnref n="2" />,ᶜ, QUADRINI Fabrizio<fnref n="2" />,ᵈ and SANTO Loredana<fnref n="2" />,ᵉ

**Keywords:** Fiberglass, Recycling, Direct Molding, Compression Molding, Thermosets

**Abstract.** Fiberglass production in western Europe exceeds one million tons per year, and data of the European Commission inform that at their end-of-life, 25% of waste fiberglass is sent to landfill. Being a thermosetting material, it polymerizes during its production, when a molecular network is generated into the matrix. This network is responsible for its optimal properties, but it prevents the material flow under heating and thus reprocessing. A new recycling process for fiberglass waste has been proposed by the authors without any use of virgin materials or additives. This technology consists of a *direct molding* (i.e., compression molding) of pulverized fiberglass. The material agglomeration depends on the combination of several mechanisms, from residual reactivity, to powder re-activation and incipient degradation during molding. Residual fiberglass powder has been recovered from a factory that specializes in technical laminates, where a grinding process is used to provide the expected tolerance to the products. The recovered powder has been direct molded to manufacture small samples for mechanical testing. Such powder shows thermal activation in the DSC (differential scanning calorimetry) at low temperature (about 80°C). This study shows the feasibility of recycling waste fiberglass without using any virgin material; these new findings are related to the use of industrial powders, their testing under 4-point bending and the obtaining a good, molded surface.

**Introduction**

In recent decades, fiberglass has become widely used in many applications, from technical to commercial, domestic, but also sports and construction. Specifically, fiberglass is, as widely known, a composite material formed by the combination of a polymer matrix and glass fibers in different shapes. Generally, the use of glass fibers is due to several properties such as lightness, durability, anti-corrosiveness, and relative cost-effectiveness. All this has led to its use in both traditional and high-tech industries. Fiberglass can consist of a thermoplastic matrix (e.g., polypropylene) or a thermosetting matrix (e.g., epoxy or polyester). Typically, thermoset matrix such as polyester is used in many applications due to the ease of process in obtaining large and complex parts such as boats, wind blades or tanks. On the other hand, the use of thermoplastic matrix is rarer; except for injection-molded parts with discrete glass fibers. Nowadays, the global fiberglass industry has undergone steady growth due to versatility and low cost of this material. In addition, such growth is expected to continue given the increasing demand for alternative and green energy sources, like wind energy.

The above-mentioned properties of fiberglass have contributed to the development of more advanced and efficient systems and products in various sectors. This is likely to lead to a further expansion of market demand for fiberglass products in coming years. Factually, in 2022 the global

<figure><img src="image_2256.png" /></figure>

<footnote n="1">¹Mercatorum University, p.zza Mattei 10, Rome, Italy</footnote>

<footnote n="2">²University of Rome Tor Vergata, via del Politecnico 1, Rome, Italy</footnote>

<footnote>ªdenise.bellisario@unimercatorum.it, ᵇleandro.iorio@uniroma2.it, ᶜalice.proietti@uniroma2.it,</footnote>

<footnote>ᵈfabrizio.quadrini@uniroma2.it, ᶜloredana.santo@uniroma2.it</footnote>
# Recycling of thermoset fiberglass by direct molding of ground powders

BELLISARIO Denise<fnref n="1" />,ª*, IORIO Leandro<fnref n="2" />,ᵇ, PROIETTI Alice<fnref n="2" />,ᶜ, QUADRINI Fabrizio<fnref n="2" />,ᵈ and SANTO Loredana<fnref n="2" />,ᵉ

**Keywords:** Fiberglass, Recycling, Direct Molding, Compression Molding, Thermosets

**Abstract.** Fiberglass production in western Europe exceeds one million tons per year, and data of the European Commission inform that at their end-of-life, 25% of waste fiberglass is sent to landfill. Being a thermosetting material, it polymerizes during its production, when a molecular network is generated into the matrix. This network is responsible for its optimal properties, but it prevents the material flow under heating and thus reprocessing. A new recycling process for fiberglass waste has been proposed by the authors without any use of virgin materials or additives. This technology consists of a *direct molding* (i.e., compression molding) of pulverized fiberglass. The material agglomeration depends on the combination of several mechanisms, from residual reactivity, to powder re-activation and incipient degradation during molding. Residual fiberglass powder has been recovered from a factory that specializes in technical laminates, where a grinding process is used to provide the expected tolerance to the products. The recovered powder has been direct molded to manufacture small samples for mechanical testing. Such powder shows thermal activation in the DSC (differential scanning calorimetry) at low temperature (about 80°C). This study shows the feasibility of recycling waste fiberglass without using any virgin material; these new findings are related to the use of industrial powders, their testing under 4-point bending and the obtaining a good, molded surface.

**Introduction**

In recent decades, fiberglass has become widely used in many applications, from technical to commercial, domestic, but also sports and construction. Specifically, fiberglass is, as widely known, a composite material formed by the combination of a polymer matrix and glass fibers in different shapes. Generally, the use of glass fibers is due to several properties such as lightness, durability, anti-corrosiveness, and relative cost-effectiveness. All this has led to its use in both traditional and high-tech industries. Fiberglass can consist of a thermoplastic matrix (e.g., polypropylene) or a thermosetting matrix (e.g., epoxy or polyester). Typically, thermoset matrix such as polyester is used in many applications due to the ease of process in obtaining large and complex parts such as boats, wind blades or tanks. On the other hand, the use of thermoplastic matrix is rarer; except for injection-molded parts with discrete glass fibers. Nowadays, the global fiberglass industry has undergone steady growth due to versatility and low cost of this material. In addition, such growth is expected to continue given the increasing demand for alternative and green energy sources, like wind energy.

The above-mentioned properties of fiberglass have contributed to the development of more advanced and efficient systems and products in various sectors. This is likely to lead to a further expansion of market demand for fiberglass products in coming years. Factually, in 2022 the global

<figure><img src="image_2247.png" /></figure>

<footnote n="1">¹Mercatorum University, p.zza Mattei 10, Rome, Italy</footnote>

<footnote n="2">²University of Rome Tor Vergata, via del Politecnico 1, Rome, Italy</footnote>

<footnote>ªdenise.bellisario@unimercatorum.it, ᵇleandro.iorio@uniroma2.it, ᶜalice.proietti@uniroma2.it,</footnote>

<footnote>ᵈfabrizio.quadrini@uniroma2.it, ᶜloredana.santo@uniroma2.it</footnote>
composites market size was estimated at USD 93.69 billion and is expected to grow at a compound annual growth rate (CAGR) of 7.2% from 2023 to 2030 [1].

From this point of view, these quantities of produced and utilized fiberglass represent a big issue for the environment. Given the countless and disparate applications of this material, fiberglass recycling is an important issue to address. Throughout the years many technological solutions have been proposed for fiberglass waste management. Generally, in mechanical composite recycling processes there are always disassembly and/or pulverization steps. As pulverization can also be a way to reduce the volumes to be sent to landfills research on this process step date back to 1994 with Ferguson [2], however, a real recycling process, should also involve the re-processing of the final powders. Unfortunately, there are only a few industrial solutions for the recycling of pulverized powders, and they have two main applications: the use of powders for the filling of composites or for energy recovery [3,4].

The scientific literature for fiberglass recycling has been more active in the past. In 1997, Yoon et al. and Rastelly et al. proposed chemical methods to recycle unsaturated polyester (UP), used as a fiberglass matrix. The first uses propylene glycol to recycle UP, to extract reagents that can be cured by adding maleic anhydride; the downsides of this method are the use of large amounts of virgin UP (up to 90%) and chemical reagents [5]. The second proposed similar chemical recycling process to obtain glycolic raw materials to synthesize again UP resin by reaction with dibasic acid or a diisocyanate compound [6]. However, the idea of chemically reprocessing UP waste was shelved, and the research then focused mainly on combustion and pyrolysis of this waste. The recovery of fibers from waste thermoset composites via fluidized bed process has been proposed by Kennerley et al. [7]. However, the fibers thus recovered had a strength reduced to about half that of virgin fiber.

Thermal processes for fiberglass recycling were also investigated in literature. These processes involve the use of heat to break the scrap composites down; the differentiation between them revolves around the amounts of energy and recovered material. Pyrolysis has been studied with fine results by Cunliffe et al. [8] and Kaminsky et al. [9], however, the cost of the equipment used, as well as the overall energy loss during the process, make pyrolysis products unattractive for industrial applications. This is also due to additional processes required to increase the efficiency of pyrolysis products, such as cleaning the glass fibers or burning the pyrolytic oil. Lopez et al. studied the thermolysis of fiberglass to recover valuable products and energy, particularly 68 wt% solid residue, 24 wt% of the liquid (oil) and 8.0 wt% of gas fractions. The remaining solid phase can be converted in a wollastonite and plagioclase-based glass-ceramic materials. The method, although interesting, involves complex and energy-intensive costs and processes.

Currently, the state of the art is basically unvaried, and fiberglass is typically sent to landfill at a cost that depends on the country. The fact that fiberglass recycling research has fallen out of grace for years is confirmed by Pickering in his review of recycling technologies for thermoset composites [10]. More recent studies have not changed the situation, for despite the variety of methods and studies on the subject, no one has yet found commercial success or industrial diffusion. For example, Kamimura et al. (2011) investigated de-polymerization of UP and waste fiberglass by using ionic liquids and microwave to accelerate the reaction rate [11]. Unfortunately, the process is set-up to recover only glass fibers and no mention is given to the re-use of the organic part. At the same time, all the most recent studies are based on the pulverization and reuse of powders as fillers for composites [12-14]. As a result, it seems that this method remains the easiest way to recycle. However, fiberglass consumption rates are much higher than those of powder reuse as a filler.

A new recycling process for fiberglass waste has been proposed by the current authors without any use of virgin materials or additives [15]. This technology consists of a *direct molding* (i.e. compression molding) of pulverized fiberglass. The material agglomeration depends on the
composites market size was estimated at USD 93.69 billion and is expected to grow at a compound annual growth rate (CAGR) of 7.2% from 2023 to 2030 [1].

From this point of view, these quantities of produced and utilized fiberglass represent a big issue for the environment. Given the countless and disparate applications of this material, fiberglass recycling is an important issue to address. Throughout the years many technological solutions have been proposed for fiberglass waste management. Generally, in mechanical composite recycling processes there are always disassembly and/or pulverization steps. As pulverization can also be a way to reduce the volumes to be sent to landfills research on this process step date back to 1994 with Ferguson [2], however, a real recycling process, should also involve the re-processing of the final powders. Unfortunately, there are only a few industrial solutions for the recycling of pulverized powders, and they have two main applications: the use of powders for the filling of composites or for energy recovery [3,4].

The scientific literature for fiberglass recycling has been more active in the past. In 1997, Yoon et al. and Rastelly et al. proposed chemical methods to recycle unsaturated polyester (UP), used as a fiberglass matrix. The first uses propylene glycol to recycle UP, to extract reagents that can be cured by adding maleic anhydride; the downsides of this method are the use of large amounts of virgin UP (up to 90%) and chemical reagents [5]. The second proposed similar chemical recycling process to obtain glycolic raw materials to synthesize again UP resin by reaction with dibasic acid or a diisocyanate compound [6]. However, the idea of chemically reprocessing UP waste was shelved, and the research then focused mainly on combustion and pyrolysis of this waste. The recovery of fibers from waste thermoset composites via fluidized bed process has been proposed by Kennerley et al. [7]. However, the fibers thus recovered had a strength reduced to about half that of virgin fiber.

Thermal processes for fiberglass recycling were also investigated in literature. These processes involve the use of heat to break the scrap composites down; the differentiation between them revolves around the amounts of energy and recovered material. Pyrolysis has been studied with fine results by Cunliffe et al. [8] and Kaminsky et al. [9], however, the cost of the equipment used, as well as the overall energy loss during the process, make pyrolysis products unattractive for industrial applications. This is also due to additional processes required to increase the efficiency of pyrolysis products, such as cleaning the glass fibers or burning the pyrolytic oil. Lopez et al. studied the thermolysis of fiberglass to recover valuable products and energy, particularly 68 wt% solid residue, 24 wt% of the liquid (oil) and 8.0 wt% of gas fractions. The remaining solid phase can be converted in a wollastonite and plagioclase-based glass-ceramic materials. The method, although interesting, involves complex and energy-intensive costs and processes.

Currently, the state of the art is basically unvaried, and fiberglass is typically sent to landfill at a cost that depends on the country. The fact that fiberglass recycling research has fallen out of grace for years is confirmed by Pickering in his review of recycling technologies for thermoset composites [10]. More recent studies have not changed the situation, for despite the variety of methods and studies on the subject, no one has yet found commercial success or industrial diffusion. For example, Kamimura et al. (2011) investigated de-polymerization of UP and waste fiberglass by using ionic liquids and microwave to accelerate the reaction rate [11]. Unfortunately, the process is set-up to recover only glass fibers and no mention is given to the re-use of the organic part. At the same time, all the most recent studies are based on the pulverization and reuse of powders as fillers for composites [12-14]. As a result, it seems that this method remains the easiest way to recycle. However, fiberglass consumption rates are much higher than those of powder reuse as a filler.

A new recycling process for fiberglass waste has been proposed by the current authors without any use of virgin materials or additives [15]. This technology consists of a *direct molding* (i.e. compression molding) of pulverized fiberglass. The material agglomeration depends on the
combination of several mechanisms, from residual reactivity, to powder re-activation and incipient degradation during molding [16]. In fact, pulverizing can be a way to give new reactivity to the final powder. Specifically, on the outer surface of the powder particles broken bonds can act as polymerizing sites. In addition, if there is a residual reactivity of the material, this can increase the reactivity of the powder itself. This study represents a step forward compared to the previous ones, as an industrial fiberglass powder is molded by direct molding without the addition of binders or virgin material. The results were very promising in terms of process easiness and proven feasibility, starting from industrially grounded powders.

## Experimental

### Fiberglass powder evaluation

A powder of waste fiberglass has been recovered from a factory of technical laminates, where a grinding process is used to reseize the products. Specifically, the powder was collected during the grinding of insulation panels of refrigerated trucks. These fiberglass laminates have a polyester matrix. At first, powder size distribution was measured by means of a stereo microscope (Leica S9i). A burning test was carried out in an oven at 600 °C for 2 h to measure the real glass content of grinded powders. Moreover, to evaluate glass transition temperature of polyester resin, differential scanning calorimetry (by Perkin Elmer DSC6) was performed on a sample of fiberglass powder. A double scan was carried out from room temperature to 150 °C, at 10 °C/min and the second scan was used to extract the glass transition temperature.

### Fiberglass recycling

Recycled fiberglass samples were produced by compression molding of the industrial grinded powders without any addition of virgin material or linking agent (direct molding), according to the process scheme shown in Fig.1.

Rectangular samples (90x15 mm²) were molded by using an aluminum alloy mold which consisted of several parts (Fig. 2a): a shaped upper punch ①, with a blind hole for the placement of a compression spring ②, an intermediate plate with four removable walls ③ fixed by screws, matching with the shaped punch and a bottom flat mold ④. After the spring is placed on the top of the mold with a positioning pin, the mold was positioned between two steel plates ⑤ with long screws ⑥ inserted into the walls for mold clamping. The removable bottom plate was chosen for simplifying sample extraction after molding. Moreover, the spring (269.2 N/mm, 32 mm of diameter) was inserted to guarantee the compression pressure of the mold during heating, because of the high contraction of the particulate under pressure during molding.

At first 6 g of fiberglass powder was inserted into the mold, then the mold was compressed by means of an electromechanical press (MTS Insight 5) up to 3.45 kN (for a related pressure of 2.55 MPa) at a loading rate of 1 mm/min and with a load holding time of 800 s (Fig. 2b).

Sample consolidation was carried out in a muffle furnace (Nabertherm, Controller B 170) at different temperatures 150 °C, 200 °C and 250 °C and for a molding time of 60 min. After molding, the mold was left in the muffle to cool down to room temperature before sample extraction.
combination of several mechanisms, from residual reactivity, to powder re-activation and incipient degradation during molding [16]. In fact, pulverizing can be a way to give new reactivity to the final powder. Specifically, on the outer surface of the powder particles broken bonds can act as polymerizing sites. In addition, if there is a residual reactivity of the material, this can increase the reactivity of the powder itself. This study represents a step forward compared to the previous ones, as an industrial fiberglass powder is molded by direct molding without the addition of binders or virgin material. The results were very promising in terms of process easiness and proven feasibility, starting from industrially grounded powders.

## Experimental

### Fiberglass powder evaluation

A powder of waste fiberglass has been recovered from a factory of technical laminates, where a grinding process is used to reseize the products. Specifically, the powder was collected during the grinding of insulation panels of refrigerated trucks. These fiberglass laminates have a polyester matrix. At first, powder size distribution was measured by means of a stereo microscope (Leica S9i). A burning test was carried out in an oven at 600 °C for 2 h to measure the real glass content of grinded powders. Moreover, to evaluate glass transition temperature of polyester resin, differential scanning calorimetry (by Perkin Elmer DSC6) was performed on a sample of fiberglass powder. A double scan was carried out from room temperature to 150 °C, at 10 °C/min and the second scan was used to extract the glass transition temperature.

### Fiberglass recycling

Recycled fiberglass samples were produced by compression molding of the industrial grinded powders without any addition of virgin material or linking agent (direct molding), according to the process scheme shown in Fig.1.

Rectangular samples (90x15 mm²) were molded by using an aluminum alloy mold which consisted of several parts (Fig. 2a): a shaped upper punch ①, with a blind hole for the placement of a compression spring ②, an intermediate plate with four removable walls ③ fixed by screws, matching with the shaped punch and a bottom flat mold ④. After the spring is placed on the top of the mold with a positioning pin, the mold was positioned between two steel plates ⑤ with long screws ⑥ inserted into the walls for mold clamping. The removable bottom plate was chosen for simplifying sample extraction after molding. Moreover, the spring (269.2 N/mm, 32 mm of diameter) was inserted to guarantee the compression pressure of the mold during heating, because of the high contraction of the particulate under pressure during molding.

At first 6 g of fiberglass powder was inserted into the mold, then the mold was compressed by means of an electromechanical press (MTS Insight 5) up to 3.45 kN (for a related pressure of 2.55 MPa) at a loading rate of 1 mm/min and with a load holding time of 800 s (Fig. 2b).

Sample consolidation was carried out in a muffle furnace (Nabertherm, Controller B 170) at different temperatures 150 °C, 200 °C and 250 °C and for a molding time of 60 min. After molding, the mold was left in the muffle to cool down to room temperature before sample extraction.
<figure><img src="image_2257.png" /><figcaption>Figure 1: Process set-up scheme</figcaption></figure>

<figure><img src="image_2258.png" /><figcaption>Figure 2: a) Aluminum mold details and b) loading vs time program of the compression step of the mold.</figcaption></figure>

In direct molding, high temperatures are necessary to promote particle mobility and agglomeration, and high pressures to ensure better contact between particles. Different consolidation temperatures were evaluated to assess the most suitable molding conditions avoiding material degradation. Moreover, using a spring to compress, the maximum pressure is limited by its maximum packing force.

## Physical and Mechanical testing

Density of the recycled fiberglass samples was extracted by measuring sizes and weights. Four-point bending tests were used for testing mechanical properties of the molded samples. The tests were performed following the ASTM D6272-02 (2008) by means of the MTS Insight 5 electro-mechanical testing machine. The applied load was displacement controlled (at 1 mm/min) and the span length among supports was 60 mm and the central span (pure bending) length was 20 mm.
<figure><img src="image_2248.png" /><figcaption>Figure 1: Process set-up scheme</figcaption></figure>

<figure><img src="image_2249.png" /><figcaption>Figure 2: a) Aluminum mold details and b) loading vs time program of the compression step of the mold.</figcaption></figure>

In direct molding, high temperatures are necessary to promote particle mobility and agglomeration, and high pressures to ensure better contact between particles. Different consolidation temperatures were evaluated to assess the most suitable molding conditions avoiding material degradation. Moreover, using a spring to compress, the maximum pressure is limited by its maximum packing force.

## Physical and Mechanical testing

Density of the recycled fiberglass samples was extracted by measuring sizes and weights. Four-point bending tests were used for testing mechanical properties of the molded samples. The tests were performed following the ASTM D6272-02 (2008) by means of the MTS Insight 5 electro-mechanical testing machine. The applied load was displacement controlled (at 1 mm/min) and the span length among supports was 60 mm and the central span (pure bending) length was 20 mm.
The test set-up is shown in Fig.3. The deflection and the applied load were recorded and the flexural strength, the maximum deformation and the flexural modulus have been calculated according to ASTM D 6272-02.

<figure><img src="image_2259.png" /><figcaption>Figure 3: 4-point bending step configuration.</figcaption></figure>

## Result and analysis

Images of samples from grinded fiberglass powder are reported in Fig.4 and they show how the powders are made of a mixture of resin particles and chopped fibers (of about 200-300 µm of length). Moreover, the real glass content of recycled powders was evaluated by burning tests. The initial mass of fiberglass powder was 0.5 g while the residual after the test was 0.09 g. Accordingly, the glass content was about 18.7%.

<figure><img src="image_2260.png" /><figcaption>Figure 4: Fiberglass powder stereoscope images.</figcaption></figure>

A DSC scan was performed on a sample of initial fiberglass powder. A peak is visible in the first scan, around 80 °C (Fig. 5), showing a residual activity of the polyester resin matrix for that
The test set-up is shown in Fig.3. The deflection and the applied load were recorded and the flexural strength, the maximum deformation and the flexural modulus have been calculated according to ASTM D 6272-02.

<figure><img src="image_2250.png" /><figcaption>Figure 3: 4-point bending step configuration.</figcaption></figure>

## Result and analysis

Images of samples from grinded fiberglass powder are reported in Fig.4 and they show how the powders are made of a mixture of resin particles and chopped fibers (of about 200-300 µm of length). Moreover, the real glass content of recycled powders was evaluated by burning tests. The initial mass of fiberglass powder was 0.5 g while the residual after the test was 0.09 g. Accordingly, the glass content was about 18.7%.

<figure><img src="image_2251.png" /><figcaption>Figure 4: Fiberglass powder stereoscope images.</figcaption></figure>

A DSC scan was performed on a sample of initial fiberglass powder. A peak is visible in the first scan, around 80 °C (Fig. 5), showing a residual activity of the polyester resin matrix for that
temperature. This datum was considered to define the minimum value for the molding temperature of recycled fiberglass.

<figure><img src="image_2261.png" /><figcaption>Figure 5: Fiberglass powder DSC curves.</figcaption></figure>

After molding, recycled samples showed a dark yellow surface which was related to surface oxidation (Fig. 6a). However, the surface appearance of all samples is good. There are no particles being released from the surface, which is continuous, smooth and consistent. To evaluate the efficiency of the recycling stage, density and flexural properties were evaluated on the rectangular recycled fiberglass samples. Average sample dimensions and density values after direct molding process are about: 3.5± 0.29 mm in thickness, 16.1±0.26 mm in width and 1.14±0.055 g/cm³ in density. Analyzing the measured data, it was noted that for the same mass of powder inserted into the mold, the average thickness decrease as the process temperature increases (at 250 °C is about 3.2 ±0.08 mm). This trend can be attributed to the increasing viscosity of the polymer as the temperature increases. This allows a better compaction of the powders, therefore a slight increase in the density of the samples (up to 1.19 g/cm³ at 250 °C). This implies that during the heating step in the muffle, a higher setting temperature allowed to obtain a greater agglomeration of particles. The flexural tests depicted in Figure 6b then showed that the higher process temperature has given a greater consolidation to the recycled fiberglass powder, therefore showing major flexural resistance (Fig. 6b).