In the deep drawing tests, the application of pulses began when the SHQR mode was activated or after reaching 3 mm of punch depth (NL mode). The current flowing through the samples was measured using a Rogowski coil and an oscilloscope. The FLIR 440 thermal imaging camera was used to measure the surface temperature of samples previously painted with non-conductive black spray. Each tensile and deep drawing test was repeated three times.

Observations of the microstructure of selected samples were made using a Hitachi H-800 transmission electron microscope (TEM) operating at a voltage of 150 kV. Specimens for microstructure observation were thinned by grinding and then electrochemically polished. Finally, the 3 mm thin discs were ion milled to obtain sufficient quality of specimens.

<figure><img src="image_1369.png" /><figcaption>Fig. 2. Scheme of the electrically-assisted deep drawing experimental setup.</figcaption></figure>

## Results and Discussion

The engineering strass-strain curves of the aluminium alloys 5754-H22 and 5754-H111 with and without pulsed current application are shown in Figure 3a and 3b, respectively. It is clearly seen that the application of current pulses results in an increase in the total elongation of the 5754 aluminium alloy in both the H22 (by 105%) and H111 (by 48%) states. This is less than that of 5052-H32 aluminum alloy [5], but more than that of 5083 aluminum alloy in various hardening states [16]. When a current pulse is applied, the sample temperature increases significantly. At the same time, the stress value on the stress-strain curve drops dramatically. In this study, the nominal current density (the current value, measured by the Rogowski coil, divided by the cross section area of the sample) was 200 A/mm². This drop in stress is mainly caused by thermal expansion and softening due to Joule heating. However, just before the next pulse is applied, the temperature drops almost to the room value [17]. The lack of stress increase to the value corresponding to the curve without the application of current pulse, as well as the increase in material plasticity, is explained by the annealing of the material. The maximal values of the sample surface temperature recorded by the thermal camera are 332 and 295 °C for alloys in the H22 and H111 states, respectively. Nevertheless, according to the localized Joule heat theory, the temperature near grain boundaries and dislocation clusters could have been temporarily higher [7]. Therefore, these were places particularly suitable for recovery and recrystallization processes. It should be noted that the average surface temperature of the sample during the test was less than 150 °C. The sample under the H22 condition achieved a greater increase in elongation, and was intended for further tests.
<figure><img src="image_1366.png" /><figcaption>Fig. 3. Engineering stress-strain curves of 5754 AA in the a) H22 and b) H111 state with and without pulsed current application.</figcaption></figure>

Fig. 4a-b presents the force-displacement deep drawing curves (force at punch and punch displacement) for the 5754-H22 aluminium alloy with and without pulsed current application. The force-displacement curves for samples No. 1 and 2 (for both operating modes) are presented in Fig. 4a. There are no visible changes in the course of the curve and material plasticity as a result of the application of current pulses in these processes. The detailed effect of current pulses on the punch depth for samples No. 1 and 2 is shown in Fig. 5a. Note that the stress drops in the curves for selected samples No. 2 and 3 results from their forming in the SHQR mode. A slight but visible 6% increase in punch depth was observed for sample no. 3 (Fig. 5b). The average values of the maximal temperatures recorded during deep drawing tests with the application of current pulses are shown in Fig. 6a-b.

<figure><img src="image_1367.png" /><figcaption>Fig. 4. Deep drawing force-displacement curves of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3 with and without pulsed current application.</figcaption></figure>

The sample temperatures achieved in deep drawing processes are much lower than those of tensile tests, which is the main reason for the slight or no increase in the plasticity of the material. In the case of sample No. 2, its cross-section was too large to obtain a useful current density value. The temperature for sample No. 2 was not greater than 50 °C, and for sample No. 3 it was about 100 °C, which allowed for a slight increase in the punch displacement. Although the temperature of sample No. 1 was the highest (about 150 °C), it did not change the plasticity of the material. This can be explained by the fact that the sample had a small volume and even though it temporarily reached the highest temperature values, it was then immediately cooled. Further research will be conducted, including modifications to the experimental setup, in order to increase
<figure><img src="image_1370.png" /><figcaption>Fig. 3. Engineering stress-strain curves of 5754 AA in the a) H22 and b) H111 state with and without pulsed current application.</figcaption></figure>

Fig. 4a-b presents the force-displacement deep drawing curves (force at punch and punch displacement) for the 5754-H22 aluminium alloy with and without pulsed current application. The force-displacement curves for samples No. 1 and 2 (for both operating modes) are presented in Fig. 4a. There are no visible changes in the course of the curve and material plasticity as a result of the application of current pulses in these processes. The detailed effect of current pulses on the punch depth for samples No. 1 and 2 is shown in Fig. 5a. Note that the stress drops in the curves for selected samples No. 2 and 3 results from their forming in the SHQR mode. A slight but visible 6% increase in punch depth was observed for sample no. 3 (Fig. 5b). The average values of the maximal temperatures recorded during deep drawing tests with the application of current pulses are shown in Fig. 6a-b.

<figure><img src="image_1371.png" /><figcaption>Fig. 4. Deep drawing force-displacement curves of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3 with and without pulsed current application.</figcaption></figure>

The sample temperatures achieved in deep drawing processes are much lower than those of tensile tests, which is the main reason for the slight or no increase in the plasticity of the material. In the case of sample No. 2, its cross-section was too large to obtain a useful current density value. The temperature for sample No. 2 was not greater than 50 °C, and for sample No. 3 it was about 100 °C, which allowed for a slight increase in the punch displacement. Although the temperature of sample No. 1 was the highest (about 150 °C), it did not change the plasticity of the material. This can be explained by the fact that the sample had a small volume and even though it temporarily reached the highest temperature values, it was then immediately cooled. Further research will be conducted, including modifications to the experimental setup, in order to increase
the plasticity of aluminium alloys in this process. Making dies from a high-strength copper alloy has the advantage that current pulses can be delivered only to a selected part of the formed sheet. Thanks to this, it is possible to reduce the amount of energy used in the process. Unfortunately, temperature plays a key role in electrically-assisted processes. The small volume of the heated material results in quick heat absorption and thus lower plasticity of the material.

<figure><img src="image_1368.png" /><figcaption>Fig. 5. Influence of current parameters on the height of the drawpieces of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3.</figcaption></figure>

<figure><img src="image_1369.png" /><figcaption>Fig. 6. Influence of current parameters on the maximal temperature of the drawpieces of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3.</figcaption></figure>

The application of current pulses resulted in a significant increase in the plasticity of the 5754-H22 aluminium alloy in the tensile test. Therefore, TEM studies were performed to evaluate the effect of current pulses on microstructure changes. For this purpose, two additional EA tensile tests were performed and stopped after the application of the second and fourth pulses. When the tensile test is stopped exactly after the pulse is applied, it is possible to precisely determine its effect on the microstructure. In addition, a one non-EA tensile test was performed and stopped at the same strain value as the EA tensile test stopped after the second pulse. Specimens were cut from the center of the samples thus obtained for microstructure analysis.

Fig. 7a shows the microstructure of the non-EA sample. Frequently occurring local areas with high dislocation density and the cellular dislocation structure of subgrains are characteristic images of samples after cold deformation. Subgrains formation is a typical feature of materials with such high stacking fault energy as aluminium alloys. On the other hand, subgrains were also recorded in EA samples (Fig. 7a-b, sample after the application of the fourth pulse); however, they were surrounded by low-angle grain boundaries (LAGBs) and not areas with high dislocation density
the plasticity of aluminium alloys in this process. Making dies from a high-strength copper alloy has the advantage that current pulses can be delivered only to a selected part of the formed sheet. Thanks to this, it is possible to reduce the amount of energy used in the process. Unfortunately, temperature plays a key role in electrically-assisted processes. The small volume of the heated material results in quick heat absorption and thus lower plasticity of the material.

<figure><img src="image_1372.png" /><figcaption>Fig. 5. Influence of current parameters on the height of the drawpieces of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3.</figcaption></figure>

<figure><img src="image_1373.png" /><figcaption>Fig. 6. Influence of current parameters on the maximal temperature of the drawpieces of 5754-H22 AA for a) samples No. 1 and 2 and b) sample No. 3.</figcaption></figure>

The application of current pulses resulted in a significant increase in the plasticity of the 5754-H22 aluminium alloy in the tensile test. Therefore, TEM studies were performed to evaluate the effect of current pulses on microstructure changes. For this purpose, two additional EA tensile tests were performed and stopped after the application of the second and fourth pulses. When the tensile test is stopped exactly after the pulse is applied, it is possible to precisely determine its effect on the microstructure. In addition, a one non-EA tensile test was performed and stopped at the same strain value as the EA tensile test stopped after the second pulse. Specimens were cut from the center of the samples thus obtained for microstructure analysis.

Fig. 7a shows the microstructure of the non-EA sample. Frequently occurring local areas with high dislocation density and the cellular dislocation structure of subgrains are characteristic images of samples after cold deformation. Subgrains formation is a typical feature of materials with such high stacking fault energy as aluminium alloys. On the other hand, subgrains were also recorded in EA samples (Fig. 7a-b, sample after the application of the fourth pulse); however, they were surrounded by low-angle grain boundaries (LAGBs) and not areas with high dislocation density
[18]. The presence of such subgrains with an internal structure with a low number of dislocations or without them is a typical configuration of the material after the recovery process. Single, small grains, identified as newly recrystallized, were also visible on the surface of the analyzed specimen (Fig. 7c). The temperature of the material that occurred (332 °C) and the appropriate amount of accumulated deformation energy were sufficient to start the dynamic recrystallization process (DRX) locally [19]. The application of a current pulse caused the temperature to increase to a value resulting in the initiation of the dynamic recrystallization process. However, this process took too short allow recrystallization to cover a larger volume of material. It is worth noting that the microstructure features indicated in Fig. 7b-d were present in both samples after the application of the second and fourth pulses.

<figure><img src="image_1370.png" /><figcaption>Fig. 7. Bright-field TEM images of specimens obtained from a) non-pulsed, b-d) pulsed tensile tests of 5754-H22 AA.</figcaption></figure>

## Summary

The influence of current pulses on the formability of the 5754 aluminium alloy was presented in tensile and deep drawing tests. The research used a new experimental setup (with specially designed dies) to carry out the deep drawing process with the application of current pulses. The study showed that it is possible to significantly increase the elongation of aluminium alloys in EA tensile tests. It is possible to increase the elongation by more than 100%. The main mechanism responsible for the increase in elongation was the dynamic recovery process. TEM studies showed the presence of subgrains surrounded by LAGBs, as well as single DRX grains. However, due to the too low temperature value, the formability of the 5754-H22 aluminium alloy in the deep drawing test increased slightly. These studies showed that 5754 aluminum alloy can be used in electrically-assisted forming technology, in particular in the H22 condition. Unfortunately, due to excessive heat absorption by the tools, their modifications are necessary to increase the plasticity of the material in the deep drawing process.
[18]. The presence of such subgrains with an internal structure with a low number of dislocations or without them is a typical configuration of the material after the recovery process. Single, small grains, identified as newly recrystallized, were also visible on the surface of the analyzed specimen (Fig. 7c). The temperature of the material that occurred (332 °C) and the appropriate amount of accumulated deformation energy were sufficient to start the dynamic recrystallization process (DRX) locally [19]. The application of a current pulse caused the temperature to increase to a value resulting in the initiation of the dynamic recrystallization process. However, this process took too short allow recrystallization to cover a larger volume of material. It is worth noting that the microstructure features indicated in Fig. 7b-d were present in both samples after the application of the second and fourth pulses.

<figure><img src="image_1374.png" /><figcaption>Fig. 7. Bright-field TEM images of specimens obtained from a) non-pulsed, b-d) pulsed tensile tests of 5754-H22 AA.</figcaption></figure>

## Summary

The influence of current pulses on the formability of the 5754 aluminium alloy was presented in tensile and deep drawing tests. The research used a new experimental setup (with specially designed dies) to carry out the deep drawing process with the application of current pulses. The study showed that it is possible to significantly increase the elongation of aluminium alloys in EA tensile tests. It is possible to increase the elongation by more than 100%. The main mechanism responsible for the increase in elongation was the dynamic recovery process. TEM studies showed the presence of subgrains surrounded by LAGBs, as well as single DRX grains. However, due to the too low temperature value, the formability of the 5754-H22 aluminium alloy in the deep drawing test increased slightly. These studies showed that 5754 aluminum alloy can be used in electrically-assisted forming technology, in particular in the H22 condition. Unfortunately, due to excessive heat absorption by the tools, their modifications are necessary to increase the plasticity of the material in the deep drawing process.
## Acknowledgments

This work was supported by the National Science Centre (grant No. 2022/45/N/ST8/03048).

## References

[1] T. Luo, L. Lei, K. Feng, M. Yang, Y. Jiang, Achieving high strength and large ductility of an ultrafine-grained 211ZX aluminium alloy processed by improved thermomechanical processing, Arch. Civ. Mech. Eng. 23 (2023) 1-17. https://doi.org/10.1007/s43452-023-00664-0

[2] Z. Gronostajski, K. Jaśkiewicz, P. Kaczyński, M. Sk warski, S. Polak, J. Krawczyk, W. Chorzępa, P. Trzpis, W-Temper forming of B-pillar from 7075 aluminum alloy, CIRP Ann. 71 (2022) 221-224. https://doi.org/10.1016/j.cirp.2022.03.019

[3] W. A. Salandro, J. T. Roth, Formation of 5052 aluminum channels using Electrically-Assisted Manufacturing (EAM), Proc. ASME Int. Manuf. Sci. Eng. Conf. 2 (2009) 599-608. https://doi.org/10.1115/MSEC2009-84117

[4] V. Stolyarov, A. Misochenko, A Pulsed Current Application to the Deformation Processing of Materials, Materials (Basel) 16 (2023) 1-20. https://doi.org/10.3390/ma16186270

[5] M. Kim, J. Song, H. Huh, Effect of Pre-strain on Tensile Properties of Al5052-H32 under an Electropulsing Condition, Procedia Eng. 207 (2017) 371-376. https://doi.org/10.1016/j.proeng.2017.10.790

[6] H. J. Jeong, M. J. Kim, J. W. Park, C. D. Yim, J. J. Kim, O. D. Kwon, P. P. Madakashira, H. N. Han, Effect of pulsed electric current on dissolution of Mg17Al12 phases in as-extruded AZ91 magnesium alloy, Mater. Sci. Eng. A, 684 (2017) 668-676. https://doi.org/10.1016/j.msea.2016.12.103

[7] J. Zhao, G. X. Wang, Y. Dong, C. Ye, Multiscale modeling of localized resistive heating in nanocrystalline metals subjected to electropulsing, J. Appl. Phys. 122 (2017) 1-10. https://doi.org/10.1063/1.4998938

[8] Y. H. Zhu, S. To, W. B. Lee, X. M. Liu, Y. B. Jiang, G. Y. Tang, Effects of dynamic electropulsing on microstructure and elongation of a Zn-Al alloy, Mater. Sci. Eng. A 501 (2009) 125-132. https://doi.org/10.1016/j.msea.2008.09.080

[9] S. Zhao, R. Zhang, Y. Chong, X. Li, A. Abu-Odeh, E. Rothchild, D. C. Chrzan, M. Asta, J. W. Morris Jr., A. M. Minor, Defect reconfiguration in a Ti-Al alloy via electroplasticity, Nat. Mater. 20 (2021) 468-472. https://doi.org/10.1038/s41563-020-00817-z

[10] X. Li, Q. Zhu, Y. Hong, H. Zheng, J. Wang, J. Wang, Z. Zhang, Revealing the pulse-induced electroplasticity by decoupling electron wind force, Nat. Commun. 13 (2022) 1-9. https://doi.org/10.1038/s41467-022-34333-2

[11] Z. Zimniak, G. Radkiewicz, The electroplastic effect in the cold-drawing of copper wires for the automotive industry, Arch. Civ. Mech. Eng. 8 (2008) 173-179. doi: 10.1016/S1644-9665(12)60204-0

[12] Z. Xu, G. Tang, S. Tian, F. Ding, H. Tian, Research of electroplastic rolling of AZ31 Mg alloy strip, J. Mater. Process. Technol. 182 (2007) 128-133. https://doi.org/10.1016/j.jmatprotec.2006.07.019

[13] H. Xie, X. Dong, Z. Ai, Q. Wang, F. Peng, K. Liu, F. Chen, J. Wang, Experimental investigation on electrically assisted cylindrical deep drawing of AZ31B magnesium alloy sheet, Int. J. Adv. Manuf. Technol. 86 (2016) 1063-1069. https://doi.org/10.1007/s00170-015-8246-0
Acknowledgments

This work was supported by the National Science Centre (grant No. 2022/45/N/ST8/03048).

References

[1] T. Luo, L. Lei, K. Feng, M. Yang, Y. Jiang, Achieving high strength and large ductility of an ultrafine-grained 211ZX aluminium alloy processed by improved thermomechanical processing, Arch. Civ. Mech. Eng. 23 (2023) 1-17. https://doi.org/10.1007/s43452-023-00664-0

[2] Z. Gronostajski, K. Jaśkiewicz, P. Kaczyński, M. Skwarski, S. Polak, J. Krawczyk, W. Chorzępa, P. Trzpis, W-Temper forming of B-pillar from 7075 aluminum alloy, CIRP Ann. 71 (2022) 221-224. https://doi.org/10.1016/j.cirp.2022.03.019

[3] W. A. Salandro, J. T. Roth, Formation of 5052 aluminum channels using Electrically-Assisted Manufacturing (EAM), Proc. ASME Int. Manuf. Sci. Eng. Conf. 2 (2009) 599-608. https://doi.org/10.1115/MSEC2009-84117

[4] V. Stolyarov, A. Misochenko, A Pulsed Current Application to the Deformation Processing of Materials, Materials (Basel) 16 (2023) 1-20. https://doi.org/10.3390/ma16186270

[5] M. Kim, J. Song, H. Huh, Effect of Pre-strain on Tensile Properties of Al5052-H32 under an Electropulsing Condition, Procedia Eng. 207 (2017) 371-376. https://doi.org/10.1016/j.proeng.2017.10.790

[6] H. J. Jeong, M. J. Kim, J. W. Park, C. D. Yim, J. J. Kim, O. D. Kwon, P. P. Madakashira, H. N. Han, Effect of pulsed electric current on dissolution of Mg17Al12 phases in as-extruded AZ91 magnesium alloy, Mater. Sci. Eng. A, 684 (2017) 668-676. https://doi.org/10.1016/j.msea.2016.12.103

[7] J. Zhao, G. X. Wang, Y. Dong, C. Ye, Multiscale modeling of localized resistive heating in nanocrystalline metals subjected to electropulsing, J. Appl. Phys. 122 (2017) 1-10. https://doi.org/10.1063/1.4998938

[8] Y. H. Zhu, S. To, W. B. Lee, X. M. Liu, Y. B. Jiang, G. Y. Tang, Effects of dynamic electropulsing on microstructure and elongation of a Zn-Al alloy, Mater. Sci. Eng. A 501 (2009) 125-132. https://doi.org/10.1016/j.msea.2008.09.080

[9] S. Zhao, R. Zhang, Y. Chong, X. Li, A. Abu-Odeh, E. Rothchild, D. C. Chrzan, M. Asta, J. W. Morris Jr., A. M. Minor, Defect reconfiguration in a Ti–Al alloy via electroplasticity, Nat. Mater. 20 (2021) 468-472. https://doi.org/10.1038/s41563-020-00817-z

[10] X. Li, Q. Zhu, Y. Hong, H. Zheng, J. Wang, J. Wang, Z. Zhang, Revealing the pulse-induced electroplasticity by decoupling electron wind force, Nat. Commun. 13 (2022) 1-9. https://doi.org/10.1038/s41467-022-34333-2

[11] Z. Zimniak, G. Radkiewicz, The electroplastic effect in the cold-drawing of copper wires for the automotive industry, Arch. Civ. Mech. Eng. 8 (2008) 173-179. doi: 10.1016/S1644-9665(12)60204-0

[12] Z. Xu, G. Tang, S. Tian, F. Ding, H. Tian, Research of electroplastic rolling of AZ31 Mg alloy strip, J. Mater. Process. Technol. 182 (2007) 128-133. https://doi.org/10.1016/j.jmatprotec.2006.07.019

[13] H. Xie, X. Dong, Z. Ai, Q. Wang, F. Peng, K. Liu, F. Chen, J. Wang, Experimental investigation on electrically assisted cylindrical deep drawing of AZ31B magnesium alloy sheet, Int. J. Adv. Manuf. Technol. 86 (2016) 1063-1069. https://doi.org/10.1007/s00170-015-8246-0
[14] Z. Lv, Y. Zhou, L. Zhan, Z. Zang, B. Zhou, S. Qin, Electrically assisted deep drawing on high-strength steel sheet, Int. J. Adv. Manuf. Technol. 112 (2021) 763-773. https://doi.org/10.1007/s00170-020-06335-1

[15] D. Dobras, Z. Zimniak, M. Zwierzchowski, Electrically-assisted deep drawing of 5754 aluminium alloy sheet, Mater. Res. Proc. 28 (2023) 987-1006. doi: 10.21741/9781644902479-109

[16] W.A. Salandro, J. J. Jones, T. A. McNeal, J. T. Roth, S. T. Hong, M. T. Smith, Formability of Al 5xxx sheet metals using pulsed current for various heat treatments, J. Manuf. Sci. Eng. Trans. ASME 132 (2010) 1-11. https://doi.org/10.1115/1.4002185

[17] K. Hariharan, M. G. Lee, M. J. Kim, H. N. Han, D. Kim, S. Choi, Decoupling Thermal and Electrical Effect in an Electrically Assisted Uniaxial Tensile Test Using Finite Element Analysis, Metall. Mater. Trans. A Phys. Metall. Mater. Sci., 46 (2015) 3043-3051. https://doi.org/10.1007/s11661-015-2879-3

[18] Z. C. Sun, L. S. Zheng, H. Yang, Softening mechanism and microstructure evolution of as-extruded 7075 aluminum alloy during hot deformation, Mater. Charact., 90 (2014) 71-80. https://doi.org/10.1016/j.matchar.2014.01.019

[19] H. Wang, W. Song, K. Koenigsmann, S. Zhang, L. Ren, K. Yang, The role of prismatic slip dependent dynamic recrystallization in the fabrication of a submicrocrystalline Ti-Cu alloy with high thermostability, Mater. Des., 188 (2020) 1-16. https://doi.org/10.1016/j.matdes.2020.108475
[14] Z. Lv, Y. Zhou, L. Zhan, Z. Zang, B. Zhou, S. Qin, Electrically assisted deep drawing on high-strength steel sheet, Int. J. Adv. Manuf. Technol. 112 (2021) 763-773. https://doi.org/10.1007/s00170-020-06335-1

[15] D. Dobras, Z. Zimniak, M. Zwierzchowski, Electrically-assisted deep drawing of 5754 aluminium alloy sheet, Mater. Res. Proc. 28 (2023) 987-1006. doi: 10.21741/9781644902479-109

[16] W.A. Salandro, J. J. Jones, T. A. McNeal, J. T. Roth, S. T. Hong, M. T. Smith, Formability of Al 5xxx sheet metals using pulsed current for various heat treatments, J. Manuf. Sci. Eng. Trans. ASME 132 (2010) 1-11. https://doi.org/10.1115/1.4002185

[17] K. Hariharan, M. G. Lee, M. J. Kim, H. N. Han, D. Kim, S. Choi, Decoupling Thermal and Electrical Effect in an Electrically Assisted Uniaxial Tensile Test Using Finite Element Analysis, Metall. Mater. Trans. A Phys. Metall. Mater. Sci., 46 (2015) 3043-3051. https://doi.org/10.1007/s11661-015-2879-3

[18] Z. C. Sun, L. S. Zheng, H. Yang, Softening mechanism and microstructure evolution of as-extruded 7075 aluminum alloy during hot deformation, Mater. Charact., 90 (2014) 71-80. https://doi.org/10.1016/j.matchar.2014.01.019

[19] H. Wang, W. Song, K. Koenigsmann, S. Zhang, L. Ren, K. Yang, The role of prismatic slip dependent dynamic recrystallization in the fabrication of a submicrocrystalline Ti-Cu alloy with high thermostability, Mater. Des., 188 (2020) 1-16. https://doi.org/10.1016/j.matdes.2020.108475
# Material-data-driven prediction of sheared surface tears of fine blanked parts

ORTJOHANN Lucia<fnref n="1" />,ª*, BECKER Marco<fnref n="1" />,ᵇ, NIEMIETZ Philipp<fnref n="1" />,ᶜ and BERGS Thomas<fnref n="1" />,<fnref n="2" />,ᵈ

**Keywords:** Fine Blanking, Non-Destructive Testing, NDT, Eddy Current, Quality Prediction

**Abstract.** Fine blanking is a cost-effective manufacturing technology for mass-producing sheet-metal components with high sheared surface quality. For steels with higher carbon content, the quality of fine blanking products is significantly influenced by microstructural characteristics, such as the morphology and distribution of carbides, which can be controlled through heat treatment [1]. Precisely, there is a relationship between spheroidization of carbides and the occurrence of tears at the sheared surface of fine blanked parts especially at the tip of a gear [2]. Furthermore, material characteristics can vary both along a sheet-metal coil and from coil to coil despite tight tolerances [3] leading to unpredictable tearing. To monitor the fluctuation of material characteristics at regular intervals along sheet-metal, non-destructive testing (NDT) is used before the process providing information about the microstructure. While in the state of the art, the data from NDT was used to calculate the mechanical properties and to optimize the process based on these properties [4], in this paper, NDT data is used to predict the sheared surface tears of fine blanked parts, without the reduction of the content-rich data to mechanical properties. For this purpose, an experiment was conducted on the fine blanking of the steel 42CrMo4+A to produce components resembling a gear shape. Prior to the manufacturing process, the material was measured using an eddy current sensor, and subsequently the tearing of the fine blanked parts was evaluated. For the prediction of sheared surface tears, linear regression methods were used, and a feature selection was done to find the excitation frequencies of the eddy current sensor with the highest impact on the tearing. It was shown that the eddy current measurements along the coil contain valuable information about the tearing of the fine blanked part.

**Introduction and state of the art**

Despite strict controls, stochastic fluctuations in material properties already occur during steel production [5]. During metal processing, these fluctuations are propagated all the way to the final sheet metal coil. One example of this is elongation at fracture, which can fluctuate by up to approximately 10% within a cold-rolled sheet metal coil [6], while the fluctuations between different batches can be in the range of 13% to 21% [3,6,7]. For different manufacturers, the elongation at fracture can even vary by up to 27% [7]. These fluctuations in the material properties of the input material are currently a significant problem leading to rejects and decreasing the process stability and thus, leading to expensive machine downtimes and time-consuming trial-and-error adjustment of sheet metal processes.

Fine blanking is one of those sheet metal processes used to manufacture high-accuracy sheet metal parts such as gears or sprockets [8]. Due to a blank holder, a counter punch and a vee-ring,

<figure><img src="image_1371.png" /></figure>

<footnote n="1">¹Manufacturing Technology Institute MTI of RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, Germany</footnote>

<footnote n="2">²Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen, Germany</footnote>

<footnote>ªI.ortjohann@mti.rwth-aachen.de, ᵇm.becker@mti.rwth-aachen.de,</footnote>

<footnote>ᶜp.niemietz@mti.rwth-aachen.de, ᵈt.bergs@mti.rwth-aachen.de</footnote>
# Material-data-driven prediction of sheared surface tears of fine blanked parts

ORTJOHANN Lucia<fnref n="1" />,ª*, BECKER Marco<fnref n="1" />,ᵇ, NIEMIETZ Philipp<fnref n="1" />,ᶜ and BERGS Thomas<fnref n="1" />,<fnref n="2" />,ᵈ

**Keywords:** Fine Blanking, Non-Destructive Testing, NDT, Eddy Current, Quality Prediction

**Abstract.** Fine blanking is a cost-effective manufacturing technology for mass-producing sheet-metal components with high sheared surface quality. For steels with higher carbon content, the quality of fine blanking products is significantly influenced by microstructural characteristics, such as the morphology and distribution of carbides, which can be controlled through heat treatment [1]. Precisely, there is a relationship between spheroidization of carbides and the occurrence of tears at the sheared surface of fine blanked parts especially at the tip of a gear [2]. Furthermore, material characteristics can vary both along a sheet-metal coil and from coil to coil despite tight tolerances [3] leading to unpredictable tearing. To monitor the fluctuation of material characteristics at regular intervals along sheet-metal, non-destructive testing (NDT) is used before the process providing information about the microstructure. While in the state of the art, the data from NDT was used to calculate the mechanical properties and to optimize the process based on these properties [4], in this paper, NDT data is used to predict the sheared surface tears of fine blanked parts, without the reduction of the content-rich data to mechanical properties. For this purpose, an experiment was conducted on the fine blanking of the steel 42CrMo4+A to produce components resembling a gear shape. Prior to the manufacturing process, the material was measured using an eddy current sensor, and subsequently the tearing of the fine blanked parts was evaluated. For the prediction of sheared surface tears, linear regression methods were used, and a feature selection was done to find the excitation frequencies of the eddy current sensor with the highest impact on the tearing. It was shown that the eddy current measurements along the coil contain valuable information about the tearing of the fine blanked part.

**Introduction and state of the art**

Despite strict controls, stochastic fluctuations in material properties already occur during steel production [5]. During metal processing, these fluctuations are propagated all the way to the final sheet metal coil. One example of this is elongation at fracture, which can fluctuate by up to approximately 10% within a cold-rolled sheet metal coil [6], while the fluctuations between different batches can be in the range of 13% to 21% [3,6,7]. For different manufacturers, the elongation at fracture can even vary by up to 27% [7]. These fluctuations in the material properties of the input material are currently a significant problem leading to rejects and decreasing the process stability and thus, leading to expensive machine downtimes and time-consuming trial-and-error adjustment of sheet metal processes.

Fine blanking is one of those sheet metal processes used to manufacture high-accuracy sheet metal parts such as gears or sprockets [8]. Due to a blank holder, a counter punch and a vee-ring,

<figure><img src="image_1375.png" /></figure>

<footnote n="1">¹Manufacturing Technology Institute MTI of RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, Germany</footnote>

<footnote n="2">²Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen, Germany</footnote>

<footnote>ªI.ortjohann@mti.rwth-aachen.de, ᵇm.becker@mti.rwth-aachen.de,</footnote>

<footnote>ᶜp.niemietz@mti.rwth-aachen.de, ᵈt.bergs@mti.rwth-aachen.de</footnote>
the fine blanking process is operated with three independently acting process forces [9] (cf. Fig. 1 a). The process forces combined with a small die clearance ($u \approx 0.5\%$ of the sheet thickness) and a vee-ring lead to a superimposed compressive stress (cf. Fig. 1 b) and enables the material to flow leading to a 100% smooth sheared surface, which can be used as a functional surface [2]. Die roll, tear-off and tears reduce the load-bearing proportion of functional surfaces and thus represent quality-influencing features [10].

<figure><img src="image_1372.png" /></figure>

Legend: $F_{St}$ – Punch force, $F_G$ – Counter force, $F_N$ – Blankholder force

<caption>Fig. 1. a) Fine blanking setup and b) a detailed view of the shear zone</caption>

The influence of material properties on the plastic flow and the sheared surface quality is described in various places in the literature, for example in relation to carbides and cementite structures [9] and hardening [11]. For unalloyed carbon steels with a carbon content greater than 0.15% and steels with a higher alloy content without annealing on spheroidal cementite, lamellar cementite or carbides occur and, due to their brittle properties, these can lead to tears as well as tear-offs on the sheared surface [12]. However, the distribution and shape of the carbides fluctuates statistically along the coil, so that with additional small tip radii and tip angles of the part geometries, it is difficult to achieve a stable and economic fine blanking process especially for steels with high carbon content. Moreover, these fluctuations in material properties especially microstructural differences in the distribution and shape of carbides lead to unpredictable tearing for high carbon steels. Nevertheless, material properties are typically measured only at the beginning and end of the coil using uniaxial tensile tests as well as metallographic analysis. Thus, there is no information about the exact material properties along the coil. In addition, uniaxial tensile tests cannot represent the complex stress state during fine blanking, as the material in the shear zone is subjected to three-dimensional compressive stress [13].

Monitoring the coil through non-destructive testing (NDT), such as eddy current (EC) measurements, can capture variations in material properties and create a digital shadow of the coil, referred to as Digital Coil. In sheet metal processing, electromagnetic methods are generally used for NDT, as there is a correlation between the mechanical and electromagnetic properties of sheet metal, as the microstructure influences both [14]. It has already been shown that sensors such as EC sensors, the 3MA sensor or the IMPOC sensor are successfully used for inline monitoring of coils. The data from these measurements correlate with mechanical properties and enable the prediction of tensile strength, yield strength, residual stress and hardness along the coil [14–16].

Various regressions and machine learning have been used to predict these parameters [17] and to detect cracks and material thinning [18]. Khan et al. showed a correlation between the EC measurements and austenite phase fractions [19]. Utilizing the mechanical parameters derived from EC measurements, a knowledge-based control approach was implemented to mitigate diverse factors affecting draw-in in the deep drawing process [20]. Furthermore, feedback control strategies were employed to minimize the impact of material variations [21]. Heingärtner et al. developed and tested an intelligent control system at an industrial scale. This system employed
the fine blanking process is operated with three independently acting process forces [9] (cf. Fig. 1 a). The process forces combined with a small die clearance ($u \approx 0.5\%$ of the sheet thickness) and a vee-ring lead to a superimposed compressive stress (cf. Fig. 1 b) and enables the material to flow leading to a 100% smooth sheared surface, which can be used as a functional surface [2]. Die roll, tear-off and tears reduce the load-bearing proportion of functional surfaces and thus represent quality-influencing features [10].

<figure><img src="image_1376.png" /></figure>

Legend: $F_{St}$ – Punch force, $F_G$ – Counter force, $F_N$ – Blankholder force

<caption>Fig. 1. a) Fine blanking setup and b) a detailed view of the shear zone</caption>

The influence of material properties on the plastic flow and the sheared surface quality is described in various places in the literature, for example in relation to carbides and cementite structures [9] and hardening [11]. For unalloyed carbon steels with a carbon content greater than 0.15% and steels with a higher alloy content without annealing on spheroidal cementite, lamellar cementite or carbides occur and, due to their brittle properties, these can lead to tears as well as tear-offs on the sheared surface [12]. However, the distribution and shape of the carbides fluctuates statistically along the coil, so that with additional small tip radii and tip angles of the part geometries, it is difficult to achieve a stable and economic fine blanking process especially for steels with high carbon content. Moreover, these fluctuations in material properties especially microstructural differences in the distribution and shape of carbides lead to unpredictable tearing for high carbon steels. Nevertheless, material properties are typically measured only at the beginning and end of the coil using uniaxial tensile tests as well as metallographic analysis. Thus, there is no information about the exact material properties along the coil. In addition, uniaxial tensile tests cannot represent the complex stress state during fine blanking, as the material in the shear zone is subjected to three-dimensional compressive stress [13].

Monitoring the coil through non-destructive testing (NDT), such as eddy current (EC) measurements, can capture variations in material properties and create a digital shadow of the coil, referred to as Digital Coil. In sheet metal processing, electromagnetic methods are generally used for NDT, as there is a correlation between the mechanical and electromagnetic properties of sheet metal, as the microstructure influences both [14]. It has already been shown that sensors such as EC sensors, the 3MA sensor or the IMPOC sensor are successfully used for inline monitoring of coils. The data from these measurements correlate with mechanical properties and enable the prediction of tensile strength, yield strength, residual stress and hardness along the coil [14–16].

Various regressions and machine learning have been used to predict these parameters [17] and to detect cracks and material thinning [18]. Khan et al. showed a correlation between the EC measurements and austenite phase fractions [19]. Utilizing the mechanical parameters derived from EC measurements, a knowledge-based control approach was implemented to mitigate diverse factors affecting draw-in in the deep drawing process [20]. Furthermore, feedback control strategies were employed to minimize the impact of material variations [21]. Heingärtner et al. developed and tested an intelligent control system at an industrial scale. This system employed
numeric simulations, mechanical properties obtained through EC, process settings, and draw-in measurements to optimize the deep drawing process of the production of kitchen sinks [22]. In a study for a stamping process, material fluctuations were recorded using EC measurements to analyse different motion sequences for a servo press [23]. Purr showed in a data analysis in a pressing plant that fluctuations in material properties, measured by IMPOC sensors, have a significant influence on the quality of car body parts [24]. A full overview of NDT methods for sheet-metal forming is given in [4].

The common theme of these publications regarding NDT in sheet metal processing is that first the mechanical parameters are derived from the sensor data and then the process is optimized based on these parameters. But only few studies measure material properties with NDT and relate them directly to the resulting part properties like quality or parameterization of the sheet metal processes. Since the reduction to mechanical parameters reduces the information content of the NDT data, the approach to directly combine NDT data with process information enables a big potential. Therefore, this paper answers the following research question:

(RQ) Do the eddy current measurements along the coil contain information about the expected quality of the fine blanked part, in particular about the tearing at a selected tip of the part?

To answer this question an experiment was conducted where strips from a coil were measured with an EC sensor, subsequently the strips were fine blanked and the quality of the resulting part was evaluated. The experimental setup and the resulting dataset are described in the following two sections. After the data acquisition a linear regression with a feedforward feature selection was fitted on the EC data to predict the quality of the fine blanked part, specifically the height and width of the tear on a selected tip. The feature selection also allowed to derive insights as to which excitation frequencies and evaluation harmonics are best suitable to predict the tearing. Section 4 is dedicated to the methodology of the regression. The results of the data analysis are presented in the fifth section.

## Experimental setup

To investigate the relationship between the material data measured by EC and the quality of the fine blanked part, the sheared part geometry and the material was deliberately configured to align with conditions predisposing the occurrence of tears. Since tips with small angles and radii are challenging both in terms of the resulting part quality as well as punch edge load, the chosen part geometry, shown in Figure 2 a), consists of nine tips with different tip angles and tip radii representing an analogue application for tribologically stressed functional surfaces.

As material a coil of hot rolled and annealed 42CrMo4+A (EN 10132-3 respectively AISI 4140) with a sheet thickness of 6.95 mm was separated into numbered sheet metal strips. The material properties yield strength $R_{p0.2}$, ultimate tensile strength $R_m$, elongation at fracture $A, A_{80}$ are documented in Table 1. The medium carbon steel 42CrMo4+A finds application in critical components within the automotive and aircraft industries, such as gears, spindles, rods, and rams and it is often used in forming processes. However, the high thickness of the material combined with a high carbon level causes difficulties for the resulting part quality.
numeric simulations, mechanical properties obtained through EC, process settings, and draw-in measurements to optimize the deep drawing process of the production of kitchen sinks [22]. In a study for a stamping process, material fluctuations were recorded using EC measurements to analyse different motion sequences for a servo press [23]. Purr showed in a data analysis in a pressing plant that fluctuations in material properties, measured by IMPOC sensors, have a significant influence on the quality of car body parts [24]. A full overview of NDT methods for sheet-metal forming is given in [4].

The common theme of these publications regarding NDT in sheet metal processing is that first the mechanical parameters are derived from the sensor data and then the process is optimized based on these parameters. But only few studies measure material properties with NDT and relate them directly to the resulting part properties like quality or parameterization of the sheet metal processes. Since the reduction to mechanical parameters reduces the information content of the NDT data, the approach to directly combine NDT data with process information enables a big potential. Therefore, this paper answers the following research question:

(RQ) Do the eddy current measurements along the coil contain information about the expected quality of the fine blanked part, in particular about the tearing at a selected tip of the part?

To answer this question an experiment was conducted where strips from a coil were measured with an EC sensor, subsequently the strips were fine blanked and the quality of the resulting part was evaluated. The experimental setup and the resulting dataset are described in the following two sections. After the data acquisition a linear regression with a feedforward feature selection was fitted on the EC data to predict the quality of the fine blanked part, specifically the height and width of the tear on a selected tip. The feature selection also allowed to derive insights as to which excitation frequencies and evaluation harmonics are best suitable to predict the tearing. Section 4 is dedicated to the methodology of the regression. The results of the data analysis are presented in the fifth section.

## Experimental setup

To investigate the relationship between the material data measured by EC and the quality of the fine blanked part, the sheared part geometry and the material was deliberately configured to align with conditions predisposing the occurrence of tears. Since tips with small angles and radii are challenging both in terms of the resulting part quality as well as punch edge load, the chosen part geometry, shown in Figure 2 a), consists of nine tips with different tip angles and tip radii representing an analogue application for tribologically stressed functional surfaces.

As material a coil of hot rolled and annealed 42CrMo4+A (EN 10132-3 respectively AISI 4140) with a sheet thickness of 6.95 mm was separated into numbered sheet metal strips. The material properties yield strength $R_{p0.2}$, ultimate tensile strength $R_m$, elongation at fracture $A, A_{80}$ are documented in Table 1. The medium carbon steel 42CrMo4+A finds application in critical components within the automotive and aircraft industries, such as gears, spindles, rods, and rams and it is often used in forming processes. However, the high thickness of the material combined with a high carbon level causes difficulties for the resulting part quality.
<figure><img src="image_1373.png" /><figcaption>Fig. 2. Geometry of the sheared part (a) and height and width of the tear at the tip under the microscope (b)</figcaption></figure>

After measuring the sheet metal strips with the MAGNATEST D from Foerster, the fine blanking experiments were conducted on a servomechanical fine blanking press Feintool XFT 2500 speed. Fine blanking was performed with a modular designed single part producing tool (one part per stroke). For each strip one fine blanked part was produced. The blanking punch and die were manufactured from Böhler S390 powder metallurgical high-speed steel with a hardness of 65 HRC and coated with the Platit FeinAl coating (AlCrN-based nano-coating). The chlorine-free lubricant Fuchs Wisura FMO 5020 was used for the experiments, further process and tool parameters are specified in Table 2.

<table><caption>Table 1. Mechanical properties of 42CrMo+A.</caption><thead><tr><td>Material</td><td>R<sub>p0.2</sub> [MPa]</td><td>R<sub>m</sub> [MPa]</td><td>A [%]</td><td>A<sub>80</sub> [%]</td></tr></thead><tbody><tr><td>42CrMo4+A</td><td>381</td><td>591</td><td>29.1</td><td>26.5</td></tr></tbody></table>

The tool was initially designed for 5 mm material, leading to a relative die clearance u ≈ 0.3% of the sheet thickness. In the experiment, 245 valid parts were produced, and every tip of every part was torn. To evaluate the quality, the height and the width of the tears for the tip with tip angle 80% and tip radii 1.1 mm was measured manually as shown in Figure 2 b) using a Keyence VHX-5000 digital microscope.

<table><caption>Table 2. Process and tool parameters used for the fine blanking experiment.</caption><tr><td>Blanking velocity v<sub>B</sub></td><td>45 mm/s</td><td>Die chamfer angle</td><td>35°</td></tr><tr><td>Vee-ring force F<sub>VR</sub></td><td>440 kN</td><td>Die chamfer height</td><td>0.3 mm</td></tr><tr><td>Counter force F<sub>CP</sub></td><td>170 kN</td><td>Vee-ring distance</td><td>2.5 mm</td></tr><tr><td>Die clearance u</td><td>20 µm</td><td>Vee-ring height</td><td>0.7 mm</td></tr></table>

## Dataset description

The measuring system of the MAGNATEST D sensor consists of two electromagnetic coils. Applying a high frequency alternating current to the transmitting coil creates a primary field that induces eddy currents on the material. The secondary field generated by these eddy currents is then measured by the sensor's receiving coil and the data generated is represented as the amplitude (X-value) and phase shift (Y-value) between the transmitted and received signals. The sensor is used with an high frequency coil and can measure with excitation frequencies from 2 Hz to 128 kHz and it offers the flexibility to evaluate the measurements using higher harmonics [25]. This results in 48 features that are obtained for each measuring point, i.e. for each metal strip in the experiment. In Figure 3, two measurements with different frequencies are presented. The figure indicates the
<figure><img src="image_1377.png" /><figcaption>Fig. 2. Geometry of the sheared part (a) and height and width of the tear at the tip under the microscope (b)</figcaption></figure>

After measuring the sheet metal strips with the *MAGNATEST D* from Foerster, the fine blanking experiments were conducted on a servomechanical fine blanking press Feintool XFT 2500 speed. Fine blanking was performed with a modular designed single part producing tool (one part per stroke). For each strip one fine blanked part was produced. The blanking punch and die were manufactured from Böhler S390 powder metallurgical high-speed steel with a hardness of 65 HRC and coated with the Platit FeinAl coating (AlCrN-based nano-coating). The chlorine-free lubricant Fuchs Wisura FMO 5020 was used for the experiments, further process and tool parameters are specified in Table 2.

<table><caption>Table 1. Mechanical properties of 42CrMo+A.</caption><thead><tr><td>Material</td><td>R<sub>p0.2</sub> [MPa]</td><td>R<sub>m</sub> [MPa]</td><td>A [%]</td><td>A<sub>80</sub> [%]</td></tr></thead><tbody><tr><td>42CrMo4+A</td><td>381</td><td>591</td><td>29.1</td><td>26.5</td></tr></tbody></table>

The tool was initially designed for 5 mm material, leading to a relative die clearance $u \approx 0.3\%$ of the sheet thickness. In the experiment, 245 valid parts were produced, and every tip of every part was torn. To evaluate the quality, the height and the width of the tears for the tip with tip angle 80% and tip radii 1.1 mm was measured manually as shown in Figure 2 b) using a Keyence VHX-5000 digital microscope.

<table><caption>Table 2. Process and tool parameters used for the fine blanking experiment.</caption><tr><td>Blanking velocity v<sub>B</sub></td><td>45 mm/s</td><td>Die chamfer angle</td><td>35°</td></tr><tr><td>Vee-ring force F<sub>VR</sub></td><td>440 kN</td><td>Die chamfer height</td><td>0.3 mm</td></tr><tr><td>Counter force F<sub>CP</sub></td><td>170 kN</td><td>Vee-ring distance</td><td>2.5 mm</td></tr><tr><td>Die clearance u</td><td>20 µm</td><td>Vee-ring height</td><td>0.7 mm</td></tr></table>

## Dataset description

The measuring system of the *MAGNATEST D* sensor consists of two electromagnetic coils. Applying a high frequency alternating current to the transmitting coil creates a primary field that induces eddy currents on the material. The secondary field generated by these eddy currents is then measured by the sensor's receiving coil and the data generated is represented as the amplitude (X-value) and phase shift (Y-value) between the transmitted and received signals. The sensor is used with an high frequency coil and can measure with excitation frequencies from 2 Hz to 128 kHz and it offers the flexibility to evaluate the measurements using higher harmonics [25]. This results in 48 features that are obtained for each measuring point, i.e. for each metal strip in the experiment. In Figure 3, two measurements with different frequencies are presented. The figure indicates the
presence of collinearity in the dataset by showing exemplary that individual features are highly correlated.

<figure><img src="image_1374.png" /><figcaption>Fig. 3. Two different normalised EC measurements.</figcaption></figure>

The height and width of the measured tears in the fine-blanked parts exhibit considerable variance throughout the dataset, as illustrated in Figure 4. This variability can be partly attributed to the inherent fluctuations of the manual measuring system. The standard deviation of nine measurements of one identical part is 13 µm for the height and 12 µm for the width of the tear of the part. The three parts with the highest and lowest values are highlighted in red for the evaluation in Section 4.

<figure><img src="image_1375.png" /><figcaption>Fig. 4. Width (a) and height (b) of the tears for every measured part.</figcaption></figure>

While the height displays a subtle drift across the coil length (part number), the width exhibits a discernible drift over the same coil length. In summary, the dataset consists of 245 data points for which there are 48 features (EC data) and two labels (quality data).

## Methodology for the data analysis

To model the relationship between the EC data and the quality data linear regression is chosen. This choice is motivated by the model's high interpretability, facilitated by the availability of various statistical methods for example methods designed for testing assumptions or diagnostic methods for the model fit. Moreover, linear regression allows for the inclusion or exclusion of features based on their significance and contribution to the model. To evaluate the goodness of the fit of the linear model, it must be ensured that there is no collinearity, no overfitting, linearity between the features and labels, no correlation of error terms, constant variance of error terms and no outliers [26].

Because of the collinearity in the EC data, where multiple features display significant correlation, there is a risk of overfitting, leading to an increase in the standard error. Consequently, a forward feature selection method is employed, leveraging the Akaike information criterion (AIC) as the evaluation metric. The forward feature selection with AIC starts with the null model, i.e. the model that contains only the intercept, and then iteratively adds the feature that generates the model
presence of collinearity in the dataset by showing exemplary that individual features are highly correlated.

<figure><img src="image_1378.png" /><figcaption>Fig. 3. Two different normalised EC measurements.</figcaption></figure>

The height and width of the measured tears in the fine-blanked parts exhibit considerable variance throughout the dataset, as illustrated in Figure 4. This variability can be partly attributed to the inherent fluctuations of the manual measuring system. The standard deviation of nine measurements of one identical part is 13 µm for the height and 12 µm for the width of the tear of the part. The three parts with the highest and lowest values are highlighted in red for the evaluation in Section 4.

<figure><img src="image_1379.png" /><figcaption>Fig. 4. Width (a) and height (b) of the tears for every measured part.</figcaption></figure>

While the height displays a subtle drift across the coil length (part number), the width exhibits a discernible drift over the same coil length. In summary, the dataset consists of 245 data points for which there are 48 features (EC data) and two labels (quality data).

## Methodology for the data analysis

To model the relationship between the EC data and the quality data linear regression is chosen. This choice is motivated by the model's high interpretability, facilitated by the availability of various statistical methods for example methods designed for testing assumptions or diagnostic methods for the model fit. Moreover, linear regression allows for the inclusion or exclusion of features based on their significance and contribution to the model. To evaluate the goodness of the fit of the linear model, it must be ensured that there is no collinearity, no overfitting, linearity between the features and labels, no correlation of error terms, constant variance of error terms and no outliers [26].

Because of the collinearity in the EC data, where multiple features display significant correlation, there is a risk of overfitting, leading to an increase in the standard error. Consequently, a forward feature selection method is employed, leveraging the Akaike information criterion (AIC) as the evaluation metric. The forward feature selection with AIC starts with the null model, i.e. the model that contains only the intercept, and then iteratively adds the feature that generates the model
with the smallest AIC [27]. The smallest AIC leads to the model with the best model fit compared to the true model fit, while also giving penalties for overfitting. The AIC is calculated as follows:

$$AIC = 2p - 2 \ln(\hat{L}), \qquad (1)$$

where $\hat{L}$ is the maximum of the likelihood function and p the number of features [28]. The feature selection is used to reduce overfitting and the selected features are less correlated than the total features of the dataset. Furthermore, this method directly identifies features with the most substantial impact on label.

To evaluate the performance and generalization of the linear regression model a k-fold cross-validation is used. Therefore, the dataset is randomly divided into k equal-sized subsets. Each subset is then used as test dataset and the rest of the data is used as a training dataset for the linear regression. Then the mean of the mean-squared error (MSE) and the mean of the coefficient of determination (R²) of all linear regressions is computed. If the training and test errors, along with the coefficient of determinations, exhibit similar size, it indicates that the model can be generalized effectively, and there is no apparent issue with overfitting [27].

Residual plots can assess the relationship between the features and the label and whether the error terms do not correlate and have a constant variance. Ideally, a residual plot should not reveal any discernible pattern that would suggest a violation of these conditions [26]. To analyze outliers and data points with high influence the Cook's distance and the studentized residual can be calculated as well. The Cook's distance gives an estimate of the influence of a datapoint by evaluating how much the regression model changes when the datapoint is removed [28]. The studentized residual can be computed by dividing each residual by its estimated standard error. Data points with a studentized residual greater than 3 in absolute value are potential outliers [26].

Once it has been ensured that the model has approximated the data well, the F-test can be carried out. The F-test is a hypothesis test used to test whether there is a relationship between the features and the label of a linear regression. The null hypothesis is that all regression coefficients (except the intercept) are equal to zero, indicating that the features do not significantly contribute to explaining the variance in the label. It is tested against the hypothesis that at least one regression coefficient is non-zero. The F-statistic is calculated as follows:

$$F = \frac{(TSS-RSS)/p}{RSS/(n-p-1)}, \quad TSS = \sum(y_i - \bar{y})^2, \quad RSS = \sum(y_i - \hat{y}_i)^2, \qquad (2)$$

where $y_i$ is the true value, $\hat{y}_i$ is the fitted value, $\bar{y}$ the mean of the label, n number of data point and p the number of features. From the F-statistic a p-value can be deduced and if this p-value is smaller than a selected significance level (e.g. 0.01) the null hypothesis can be rejected, and it can be concluded that the features contain relevant information about the label [26].

## Results and discussion

To answer the research questions linear regressions were fitted with the EC data as features and the height and the width of the tears of the selected tip of the fine blanked part as labels. Moreover, to analyze the impact of different frequencies and different harmonics a feature selection was performed. Initially, a 5-fold cross-validation with a linear regression model fitted on the entire dataset showed that even the linear regression is not generalizable on this dataset (see Table 3a). Considering the high collinearity of the dataset, this result was to be expected. Thus, the feature selection approach presented in Section 4 was implemented and the linear model fitted on the selected features exhibited less overfitting in the cross-validation (see Table 3b).
with the smallest AIC [27]. The smallest AIC leads to the model with the best model fit compared to the true model fit, while also giving penalties for overfitting. The AIC is calculated as follows:

$$AIC = 2p - 2 \ln(\hat{L}), \qquad (1)$$

where $\hat{L}$ is the maximum of the likelihood function and p the number of features [28]. The feature selection is used to reduce overfitting and the selected features are less correlated than the total features of the dataset. Furthermore, this method directly identifies features with the most substantial impact on label.

To evaluate the performance and generalization of the linear regression model a k-fold cross-validation is used. Therefore, the dataset is randomly divided into k equal-sized subsets. Each subset is then used as test dataset and the rest of the data is used as a training dataset for the linear regression. Then the mean of the mean-squared error (MSE) and the mean of the coefficient of determination (R²) of all linear regressions is computed. If the training and test errors, along with the coefficient of determinations, exhibit similar size, it indicates that the model can be generalized effectively, and there is no apparent issue with overfitting [27].

Residual plots can assess the relationship between the features and the label and whether the error terms do not correlate and have a constant variance. Ideally, a residual plot should not reveal any discernible pattern that would suggest a violation of these conditions [26]. To analyze outliers and data points with high influence the Cook's distance and the studentized residual can be calculated as well. The Cook's distance gives an estimate of the influence of a datapoint by evaluating how much the regression model changes when the datapoint is removed [28]. The studentized residual can be computed by dividing each residual by its estimated standard error. Data points with a studentized residual greater than 3 in absolute value are potential outliers [26].

Once it has been ensured that the model has approximated the data well, the F-test can be carried out. The F-test is a hypothesis test used to test whether there is a relationship between the features and the label of a linear regression. The null hypothesis is that all regression coefficients (except the intercept) are equal to zero, indicating that the features do not significantly contribute to explaining the variance in the label. It is tested against the hypothesis that at least one regression coefficient is non-zero. The F-statistic is calculated as follows:

$$F = \frac{(TSS-RSS)/p}{RSS/(n-p-1)}, \quad TSS = \sum(y_i - \bar{y})^2, \quad RSS = \sum(y_i - \hat{y}_i)^2, \qquad (2)$$

where $y_i$ is the true value, $\hat{y}_i$ is the fitted value, $\bar{y}$ the mean of the label, n number of data point and p the number of features. From the F-statistic a p-value can be deduced and if this p-value is smaller than a selected significance level (e.g. 0.01) the null hypothesis can be rejected, and it can be concluded that the features contain relevant information about the label [26].

## Results and discussion

To answer the research questions linear regressions were fitted with the EC data as features and the height and the width of the tears of the selected tip of the fine blanked part as labels. Moreover, to analyze the impact of different frequencies and different harmonics a feature selection was performed. Initially, a 5-fold cross-validation with a linear regression model fitted on the entire dataset showed that even the linear regression is not generalizable on this dataset (see Table 3a). Considering the high collinearity of the dataset, this result was to be expected. Thus, the feature selection approach presented in Section 4 was implemented and the linear model fitted on the selected features exhibited less overfitting in the cross-validation (see Table 3b).
The MSE is still quite high and the R² quite low, but considering the high variance in the labels, it is coherent with the dataset. Note that the R² values of the model of all features and the model with the selected features cannot be compared since R² is influenced by the number of features.

<table><caption>Table 3. Results of the cross-validation on all features (a) and on the selected features (b).</caption><thead><tr><th rowspan="2"></th><th colspan="2">a) Cross-Validation on all features</th><th colspan="2">b) Cross-Validation on selected features</th></tr><tr><th>Height</th><th>Width</th><th>Height</th><th>Width</th></tr></thead><tbody><tr><th>MSE Train</th><td>3,642</td><td>8,472</td><td>4,631</td><td>11,296</td></tr><tr><th>MSE Test</th><td>6,340</td><td>15,750</td><td>4,997</td><td>12,142</td></tr><tr><th>R<sup>2</sup> Train</th><td>0.46</td><td>0.69</td><td>0.32</td><td>0.58</td></tr><tr><th>R<sup>2</sup> Test</th><td>0</td><td>0.34</td><td>0.22</td><td>0.51</td></tr></tbody></table>

The selected features are shown in Table 4, here, “harmonic” is abbreviated by “h.”. Apart from the 8192 Hz 5th harmonic Y feature (phase shift of the 5th harmonic for the excitation frequency 8192Hz), the selected features of both labels have no overlaps. In addition, no frequency spectrum is particularly emphasized. However, it is noticeable that the 3rd and 5th harmonic were selected very frequently. Since the harmonics show the permeability of the material this suggests that the permeability has a stronger influence on the formation of tears and this again confirms the influence of the microstructure on the formation of tears, as the microstructure has a strong influence on the permeability of the material [25].

<table><caption>Table 4. Selected features of forward feature selection.</caption><thead><tr><th>Label</th><th>Selected features</th></tr></thead><tbody><tr><td>Height</td><td>8192 Hz 5<sup>th</sup> h. Y, 4096 Hz 5<sup>th</sup> h. X, 256 Hz X, 256 Hz 3<sup>rd</sup> h. X, 32 Hz Y</td></tr><tr><td>Width</td><td>8192 Hz 3<sup>rd</sup> h. X, 8192 Hz 5<sup>th</sup> h. Y, 2048 Hz Y, 2048 Hz 3<sup>rd</sup> h. X, 1024 Hz 3<sup>rd</sup> h. X, 512 Hz 3<sup>rd</sup> h. X and Y, 512 Hz Y, 256 Hz 3<sup>rd</sup> h. Y, 128 Hz Y</td></tr></tbody></table>

Fig. 5 shows the analysis of the model fit with the label height of the tear. The read line in the residual plot shows the smoothed curve for the residuals. The plot where the true values are plotted against the fitted values of the model highlights challenges in accurately predicting values with both low and high heights. This can be also seen in the residual plots and in the Cook’s distance since the highlighted data points have all very low or high height (cf. Fig. 4). The studentized residuals reveal data point (part) 110 and 165 as outliers, since these data points have an absolute studentized residual bigger than three. Thus, it might be that the EC data cannot predict tears with very high height. However, overall, the Cook’s distance is considerably smaller than 1 and the residual plots show no pattern, hence the model fit is valid.

In general, the fit of the model for the label width of tears is better than the fit for the height (cf. Fig. 6). Here again, the datapoints considered to be outliers are parts which have a low or a high tear width (cf. Fig. 4), nevertheless, it can again be concluded that the model fit is valid. Since both linear regressions have a good fit on the dataset, the F-test could be conducted (cf. Table 5).

<table><caption>Table 5. Results of the F-test.</caption><thead><tr><th></th><th>Height</th><th>Width</th></tr></thead><tbody><tr><th>F-statistic</th><td>22.04</td><td>32.46</td></tr><tr><th>p-value (F-statistic)</th><td>3.80e-18</td><td>6.05e-39</td></tr></tbody></table>

Because the p-value of the F-test is considerably small, the result is that the null hypothesis can be rejected, and it can be concluded that the EC data contains valuable information about the tearing of the fine blanked parts.
The MSE is still quite high and the R² quite low, but considering the high variance in the labels, it is coherent with the dataset. Note that the R² values of the model of all features and the model with the selected features cannot be compared since R² is influenced by the number of features.

<table><caption>Table 3. Results of the cross-validation on all features (a) and on the selected features (b).</caption><thead><tr><th rowspan="2"></th><th colspan="2">a) Cross-Validation on all features</th><th colspan="2">b) Cross-Validation on selected features</th></tr><tr><th>Height</th><th>Width</th><th>Height</th><th>Width</th></tr></thead><tbody><tr><th>MSE Train</th><td>3,642</td><td>8,472</td><td>4,631</td><td>11,296</td></tr><tr><th>MSE Test</th><td>6,340</td><td>15,750</td><td>4,997</td><td>12,142</td></tr><tr><th>R<sup>2</sup> Train</th><td>0.46</td><td>0.69</td><td>0.32</td><td>0.58</td></tr><tr><th>R<sup>2</sup> Test</th><td>0</td><td>0.34</td><td>0.22</td><td>0.51</td></tr></tbody></table>

The selected features are shown in Table 4, here, “harmonic” is abbreviated by “h.”. Apart from the 8192 Hz 5th harmonic Y feature (phase shift of the 5th harmonic for the excitation frequency 8192Hz), the selected features of both labels have no overlaps. In addition, no frequency spectrum is particularly emphasized. However, it is noticeable that the 3rd and 5th harmonic were selected very frequently. Since the harmonics show the permeability of the material this suggests that the permeability has a stronger influence on the formation of tears and this again confirms the influence of the microstructure on the formation of tears, as the microstructure has a strong influence on the permeability of the material [25].

<table><caption>Table 4. Selected features of forward feature selection.</caption><thead><tr><th>Label</th><th>Selected features</th></tr></thead><tbody><tr><td>Height</td><td>8192 Hz 5<sup>th</sup> h. Y, 4096 Hz 5<sup>th</sup> h. X, 256 Hz X, 256 Hz 3<sup>rd</sup> h. X, 32 Hz Y</td></tr><tr><td>Width</td><td>8192 Hz 3<sup>rd</sup> h. X, 8192 Hz 5<sup>th</sup> h. Y, 2048 Hz Y, 2048 Hz 3<sup>rd</sup> h. X, 1024 Hz 3<sup>rd</sup> h. X, 512 Hz 3<sup>rd</sup> h. X and Y, 512 Hz Y, 256 Hz 3<sup>rd</sup> h. Y, 128 Hz Y</td></tr></tbody></table>

Fig. 5 shows the analysis of the model fit with the label height of the tear. The read line in the residual plot shows the smoothed curve for the residuals. The plot where the true values are plotted against the fitted values of the model highlights challenges in accurately predicting values with both low and high heights. This can be also seen in the residual plots and in the Cook’s distance since the highlighted data points have all very low or high height (cf. Fig. 4). The studentized residuals reveal data point (part) 110 and 165 as outliers, since these data points have an absolute studentized residual bigger than three. Thus, it might be that the EC data cannot predict tears with very high height. However, overall, the Cook’s distance is considerably smaller than 1 and the residual plots show no pattern, hence the model fit is valid.

In general, the fit of the model for the label width of tears is better than the fit for the height (cf. Fig. 6). Here again, the datapoints considered to be outliers are parts which have a low or a high tear width (cf. Fig. 4), nevertheless, it can again be concluded that the model fit is valid. Since both linear regressions have a good fit on the dataset, the F-test could be conducted (cf. Table 5).

<table><caption>Table 5. Results of the F-test.</caption><thead><tr><th></th><th>Height</th><th>Width</th></tr></thead><tbody><tr><th>F-statistic</th><td>22.04</td><td>32.46</td></tr><tr><th>p-value (F-statistic)</th><td>3.80e-18</td><td>6.05e-39</td></tr></tbody></table>

Because the p-value of the F-test is considerably small, the result is that the null hypothesis can be rejected, and it can be concluded that the EC data contains valuable information about the tearing of the fine blanked parts.
<figure><img src="image_1376.png" /><figcaption>Fig. 5. Analysis of the model fit with the label height with different diagnostic plots.</figcaption></figure>

<figure><img src="image_1377.png" /><figcaption>Fig. 6. Analysis of the model fit with the label width with different diagnostic plots.</figcaption></figure>

## Conclusion and outlook

In this paper, a forward feature selection and linear regression was used to investigate the influence of the material represented by eddy current data on the quality of fine blanked part particularly the tearing behaviour of a selected tip. In an experiment, sheet metal strips were measured non-destructively and a geometry analogue to gears was fine blanked. Subsequently the height and the width of the tear of a selected tip of the resulting parts was evaluated. It was shown that eddy
<figure><img src="image_1380.png" /><figcaption>Fig. 5. Analysis of the model fit with the label height with different diagnostic plots.</figcaption></figure>

<figure><img src="image_1381.png" /><figcaption>Fig. 6. Analysis of the model fit with the label width with different diagnostic plots.</figcaption></figure>

## Conclusion and outlook

In this paper, a forward feature selection and linear regression was used to investigate the influence of the material represented by eddy current data on the quality of fine blanked part particularly the tearing behaviour of a selected tip. In an experiment, sheet metal strips were measured non-destructively and a geometry analogue to gears was fine blanked. Subsequently the height and the width of the tear of a selected tip of the resulting parts was evaluated. It was shown that eddy
current measurements along the coil contain information about the expected height and the width of the tear of the fine blanked part. Furthermore, a forward feature selection analysis indicated that no particular frequency spectrum contains the relevant information. However, the frequent choice of harmonics implies that the material's permeability likely has a significant impact on the tearing process.

As a next step, experiments are conducted in which the die clearance is designed for the thickness of the material but material with higher carbon is selected potentially resulting in tear-free parts and torn parts. The overall goal of this approach is to implement a control strategy in which the eddy current signals are evaluated by a model which analyses the tearing. Since tearing can be potentially prevented by an increased vee-ring force, which in turn accelerates wear, the model will adapt the vee-ring force based on the eddy current signals only if required.

## Acknowledgements

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2023 Internet of Production – 390621612. Furthermore, the authors would like to thank the Federal Ministry for Economics and Climate Action for the kind support within the Project "NUMA 4.X" (Project ID: 13IK029B).

## References

[1] Q. Zheng, X. Zhuang, Z. Zhao, State-of-the-art and future challenge in fine-blanking technology, Prod. Eng. Res. Devel. 13 (2019) 61–70. https://doi.org/10.1007/s11740-018-0839-7

[2] R.-A. Schmidt, Cold Forming and Fineblanking: A Handbook on Cold Processing Steel Material Properties Component Design, Carl Hanser, 2007.

[3] D. Harsch, P. Fischer, B. Berisha, J. Heingärtner, Y. Renkci, P. Hora, Considering fluctuations of material properties, stainless steel 1.4301, on manufacturability of kitchen sinks, IOP Conf. Ser.: Mater. Sci. Eng. 418 (2018) 12113. https://doi.org/10.1088/1757-899X/418/1/012113

[4] L. Ortjohann, M. Becker, P. Niemietz, T. Bergs, Monitoring of fluctuating material properties for optimizing sheet-metal forming processes: a systematic literature review, in: Materials Research Forum LLC, 2023. https://doi.org/10.21741/9781644902479-222

[5] J.M. Allwood, S.R. Duncan, J. Cao, P. Groche, G. Hirt, B. Kinsey, T. Kuboki, M. Liewald, A. Sterzing, A.E. Tekkaya, Closed-loop control of product properties in metal forming, CIRP Annals 65 (2016) 573–596. https://doi.org/10.1016/j.cirp.2016.06.002

[6] D. Banabic, G. Dragos, I. Bichis, Influence of Variability of Mechanical Data on Forming Limit Curves, Metal Forming 3 (2013) 858–863.

[7] V. Sturm, Einfluss von Chargenschwankungen auf die Verarbeitungsgrenzen von Stahlwerkstoffen. Zugl.: Erlangen-Nürnberg, Univ., Techn. Fak., Meisenbach, Bamberg, 2013.

[8] K. Gupta, N.K. Jain, R. Laubscher, Advanced Gear Manufacturing and Finishing: Classical and Modern Processes, Elsevier Academic Press, 2017. https://doi.org/10.1016/B978-0-12-804460-5.00004-3

[9] F. Klocke, Fertigungsverfahren 4, 6th ed., Springer Vieweg Berlin, Heidelberg, 2017. https://doi.org/10.1007/978-3-662-54714-4

[10] W. Volk, J. Stahl, Shear Cutting, in: L. Laperrière, G. Reinhart (Eds.), CIRP Encyclopedia of Production Engineering, Springer Berlin, Heidelberg, 2014. https://doi.org/10.1007/978-3-642-35950-7_16823-1

[11] F. Schweinshaupt, I.F. Weiser, T. Herrig, T. Bergs, Investigation of Combined Flat Coining and Fine Blanking of 16MnCr5 to Influence the Die Roll Formation, in: B.-A. Behrens, A. Brosius, W.-G. Drossel, W. Hintze, S. Ihlenfeldt, P. Nyhuis (Eds.), Production at the Leading Edge of Technology, Springer International Publishing, Cham, 2022, 112–121. https://doi.org/10.1007/978-3-030-78424-9_13
current measurements along the coil contain information about the expected height and the width of the tear of the fine blanked part. Furthermore, a forward feature selection analysis indicated that no particular frequency spectrum contains the relevant information. However, the frequent choice of harmonics implies that the material's permeability likely has a significant impact on the tearing process.

As a next step, experiments are conducted in which the die clearance is designed for the thickness of the material but material with higher carbon is selected potentially resulting in tear-free parts and torn parts. The overall goal of this approach is to implement a control strategy in which the eddy current signals are evaluated by a model which analyses the tearing. Since tearing can be potentially prevented by an increased vee-ring force, which in turn accelerates wear, the model will adapt the vee-ring force based on the eddy current signals only if required.

## Acknowledgements

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2023 Internet of Production – 390621612. Furthermore, the authors would like to thank the Federal Ministry for Economics and Climate Action for the kind support within the Project "NUMA 4.X" (Project ID: 13IK029B).

## References

[1] Q. Zheng, X. Zhuang, Z. Zhao, State-of-the-art and future challenge in fine-blanking technology, Prod. Eng. Res. Devel. 13 (2019) 61–70. https://doi.org/10.1007/s11740-018-0839-7

[2] R.-A. Schmidt, Cold Forming and Fineblanking: A Handbook on Cold Processing Steel Material Properties Component Design, Carl Hanser, 2007.

[3] D. Harsch, P. Fischer, B. Berisha, J. Heingärtner, Y. Renkci, P. Hora, Considering fluctuations of material properties, stainless steel 1.4301, on manufacturability of kitchen sinks, IOP Conf. Ser.: Mater. Sci. Eng. 418 (2018) 12113. https://doi.org/10.1088/1757-899X/418/1/012113

[4] L. Ortjohann, M. Becker, P. Niemietz, T. Bergs, Monitoring of fluctuating material properties for optimizing sheet-metal forming processes: a systematic literature review, in: Materials Research Forum LLC, 2023. https://doi.org/10.21741/9781644902479-222

[5] J.M. Allwood, S.R. Duncan, J. Cao, P. Groche, G. Hirt, B. Kinsey, T. Kuboki, M. Liewald, A. Sterzing, A.E. Tekkaya, Closed-loop control of product properties in metal forming, CIRP Annals 65 (2016) 573–596. https://doi.org/10.1016/j.cirp.2016.06.002

[6] D. Banabic, G. Dragos, I. Bichis, Influence of Variability of Mechanical Data on Forming Limit Curves, Metal Forming 3 (2013) 858–863.

[7] V. Sturm, Einfluss von Chargenschwankungen auf die Verarbeitungsgrenzen von Stahlwerkstoffen. Zugl.: Erlangen-Nürnberg, Univ., Techn. Fak., Meisenbach, Bamberg, 2013.

[8] K. Gupta, N.K. Jain, R. Laubscher, Advanced Gear Manufacturing and Finishing: Classical and Modern Processes, Elsevier Academic Press, 2017. https://doi.org/10.1016/B978-0-12-804460-5.00004-3

[9] F. Klocke, Fertigungsverfahren 4, 6th ed., Springer Vieweg Berlin, Heidelberg, 2017. https://doi.org/10.1007/978-3-662-54714-4

[10] W. Volk, J. Stahl, Shear Cutting, in: L. Laperrière, G. Reinhart (Eds.), CIRP Encyclopedia of Production Engineering, Springer Berlin, Heidelberg, 2014. https://doi.org/10.1007/978-3-642-35950-7_16823-1

[11] F. Schweinshaupt, I.F. Weiser, T. Herrig, T. Bergs, Investigation of Combined Flat Coining and Fine Blanking of 16MnCr5 to Influence the Die Roll Formation, in: B.-A. Behrens, A. Brosius, W.-G. Drossel, W. Hintze, S. Ihlenfeldt, P. Nyhuis (Eds.), Production at the Leading Edge of Technology, Springer International Publishing, Cham, 2022, 112–121. https://doi.org/10.1007/978-3-030-78424-9_13
[12] H. Hoffmann, R. Neugebauer, G. Spur (Eds.), Handbuch Umformen, 2nd ed., Carl Hanser, München, 2012. https://doi.org/10.1007/978-3-446-43004-4

[13] M.D. Gram, R.H. Wagoner, Fineblanking of high strength steels: Control of material properties for tool life, Journal of Materials Processing Technology 211 (2011) 717-728.
https://doi.org/10.1016/j.jmatprotec.2010.12.005

[14] J. Heingärtner, M. Born, P. Hora, Online Acquisition of Mechanical Material Properties of Sheet Metal for the Prediction of Product Quality by Eddy Current, 10th European Conference on Non-Destructive Testing, Moscow, Russia, 2010.

[15] B. Wolter, Y. Gabi, C. Conrad, Nondestructive Testing with 3MA—An Overview of Principles and Applications, Appl. Sci. 9 (2019) 1068. https://doi.org/10.3390/app9061068

[16] K. Herrmann, M. Irle, IMPOC: an online material properties measurement system, in: Flat-Rolled Steel Processes: Advanced Technologies, 2009.

[17] K. Lee, C. Hong, E.H. Lee, W. Yang, Comparison of Artificial Intelligence Methods for Prediction of Mechanical Properties, IOP Conf. Ser.: Mater. Sci. Eng. 967 (2020) 12031.
https://doi.org/10.1088/1757-899X/967/1/012031

[18] A. Zoesch, T. Wiener, M. Kuhl, Zero Defect Manufacturing: Detection of Cracks and Thinning of Material during Deep Drawing Processes, Procedia CIRP 33 (2015) 179-184.
https://doi.org/10.1016/j.procir.2015.06.033

[19] S.H. Khan, F. Ali, A. Nusair Khan, M.A. Iqbal, Eddy current detection of changes in stainless steel after cold reduction, Computational Materials Science 43 (2008) 623-628.
https://doi.org/10.1016/j.commatsci.2008.01.034

[20] P. Fischer, D. Harsch, J. Heingärtner, Y. Renkci, P. Hora, A knowledge-based control system for the robust manufacturing of deep drawn parts, Procedia Eng. 207 (2017) 42-47.
https://doi.org/10.1016/j.proeng.2017.10.735

[21] P. Fischer, J. Heingärtner, W. Aichholzer, D. Hortig, P. Hora, Feedback control in deep drawing based on experimental datasets, J. Phys.: Conf. Ser. 896 (2017) 12035.
https://doi.org/10.1088/1742-6596/896/1/012035

[22] J. Heingärtner, P. Fischer, D. Harsch, Y. Renkci, P. Hora, Q-Guard – an intelligent process control system, J. Phys.: Conf. Ser. 896 (2017) 12032. https://doi.org/10.1088/1742-6596/896/1/012032

[23] H. Kim, J.C. Gu, L. Zoller, Control of the servo-press in stamping considering the variation of the incoming material properties, IOP Conf. Ser.: Mater. Sci. Eng. 651 (2019) 12062.
https://doi.org/10.1088/1757-899X/651/1/012062

[24] S. Purr, Datenerfassung für die Anwendung lernender Algorithmen bei der Herstellung von Blechformteilen, FAU Studien aus dem Maschinenbau 338, 2020.

[25] Foerster Group, MAGNATEST D-HZP: Magnetinduktive Prüfung von Werkstoffen auf magnetische und elektrische Eigenschaften (2018).

[26] G. James, D. Witten, T. Hastie, R. Tibshirani, An introduction to statistical learning: With applications in R, Springer New York, NY, 2021. https://doi.org/10.1007/978-1-0716-1418-1

[27] T. Hastie, R. Tibshirani, J.H. Friedman, The elements of statistical learning: Data Mining, Inference, and Prediction, 2nd ed., Springer New York, NY, 2009. https://doi.org/10.1007/978-0-387-84858-7

[28] A. Agresti, Foundations of Linear and Generalized Linear Models, John Wiley & Sons, 2015.
[12] H. Hoffmann, R. Neugebauer, G. Spur (Eds.), Handbuch Umformen, 2nd ed., Carl Hanser, München, 2012. https://doi.org/10.1007/978-3-446-43004-4

[13] M.D. Gram, R.H. Wagoner, Fineblanking of high strength steels: Control of material properties for tool life, Journal of Materials Processing Technology 211 (2011) 717-728.
https://doi.org/10.1016/j.jmatprotec.2010.12.005

[14] J. Heingärtner, M. Born, P. Hora, Online Acquisition of Mechanical Material Properties of Sheet Metal for the Prediction of Product Quality by Eddy Current, 10th European Conference on Non-Destructive Testing, Moscow, Russia, 2010.

[15] B. Wolter, Y. Gabi, C. Conrad, Nondestructive Testing with 3MA—An Overview of Principles and Applications, Appl. Sci. 9 (2019) 1068. https://doi.org/10.3390/app9061068

[16] K. Herrmann, M. Irle, IMPOC: an online material properties measurement system, in: Flat-Rolled Steel Processes: Advanced Technologies, 2009.

[17] K. Lee, C. Hong, E.H. Lee, W. Yang, Comparison of Artificial Intelligence Methods for Prediction of Mechanical Properties, IOP Conf. Ser.: Mater. Sci. Eng. 967 (2020) 12031.
https://doi.org/10.1088/1757-899X/967/1/012031

[18] A. Zoesch, T. Wiener, M. Kuhl, Zero Defect Manufacturing: Detection of Cracks and Thinning of Material during Deep Drawing Processes, Procedia CIRP 33 (2015) 179-184.
https://doi.org/10.1016/j.procir.2015.06.033

[19] S.H. Khan, F. Ali, A. Nusair Khan, M.A. Iqbal, Eddy current detection of changes in stainless steel after cold reduction, Computational Materials Science 43 (2008) 623-628.
https://doi.org/10.1016/j.commatsci.2008.01.034

[20] P. Fischer, D. Harsch, J. Heingärtner, Y. Renkci, P. Hora, A knowledge-based control system for the robust manufacturing of deep drawn parts, Procedia Eng. 207 (2017) 42-47.
https://doi.org/10.1016/j.proeng.2017.10.735

[21] P. Fischer, J. Heingärtner, W. Aichholzer, D. Hortig, P. Hora, Feedback control in deep drawing based on experimental datasets, J. Phys.: Conf. Ser. 896 (2017) 12035.
https://doi.org/10.1088/1742-6596/896/1/012035

[22] J. Heingärtner, P. Fischer, D. Harsch, Y. Renkci, P. Hora, Q-Guard – an intelligent process control system, J. Phys.: Conf. Ser. 896 (2017) 12032. https://doi.org/10.1088/1742-6596/896/1/012032

[23] H. Kim, J.C. Gu, L. Zoller, Control of the servo-press in stamping considering the variation of the incoming material properties, IOP Conf. Ser.: Mater. Sci. Eng. 651 (2019) 12062.
https://doi.org/10.1088/1757-899X/651/1/012062

[24] S. Purr, Datenerfassung für die Anwendung lernender Algorithmen bei der Herstellung von Blechformteilen, FAU Studien aus dem Maschinenbau 338, 2020.

[25] Foerster Group, MAGNATEST D-HZP: Magnetinduktive Prüfung von Werkstoffen auf magnetische und elektrische Eigenschaften (2018).

[26] G. James, D. Witten, T. Hastie, R. Tibshirani, An introduction to statistical learning: With applications in R, Springer New York, NY, 2021. https://doi.org/10.1007/978-1-0716-1418-1

[27] T. Hastie, R. Tibshirani, J.H. Friedman, The elements of statistical learning: Data Mining, Inference, and Prediction, 2nd ed., Springer New York, NY, 2009. https://doi.org/10.1007/978-0-387-84858-7

[28] A. Agresti, Foundations of Linear and Generalized Linear Models, John Wiley & Sons, 2015.
# Improving the flow forming process by a novel closed-loop control

KERSTING Lukas¹, a, *, SANDER Sebastian¹, ARIAN Bahman², b,
ROZO VASQUEZ Julian³, c, TRÄCHTLER Ansgar¹, ⁴, HOMBERG Werner² and WALTHER Frank³

¹Fraunhofer Institute for Mechatronic Systems Design (IEM), Paderborn, Germany

²Paderborn University, Forming and Machining technology (LUF), Germany

³TU Dortmund University, Chair of Materials Test Engineering (WPT), Germany

⁴Heinz Nixdorf Institute (HNI), Paderborn University, Germany

a lukas.kersting@iem.fraunhofer.de; b ba@luf.uni-paderborn.de, c julian.rozo@tu-dortmund.de

**Keywords:** Flow Forming, Closed-Loop Control, Model-Based Control Design

**Abstract.** The incremental flow forming process is currently enhanced in research context by special closed-loop property control concepts to increase the productivity and to control the product properties making invisible property structures like a magnetic barcode possible. However, it is preferred to establish property control concepts on single roller machines instead of conventional machines with three roller actuation due to the better machine accessibility. For those single roller machines, rather poor surface qualities of flow formed workpieces were observed in the past especially for hydraulic actuators. Thus, a new actuator closed-loop position control concept is developed in this paper using model-based control design methods and taking the flow forming forces as a load into account. The novel closed-loop control is validated during workpiece production at the actual single roller flow forming machine. An analysis of the manufactured workpieces show that the surface quality is significantly enhanced by the new control to a roughness level almost similar to conventional three roller flow forming. Thus, a sincere added value to the flow forming process is offered by the novel actuator closed-loop position control.

**Introduction**

In the incremental flow forming process, it is currently difficult to control the resulting product properties and microstructure due to the large number of disturbance variables from the semifinished part and the environment (e.g. temperature, tool and machine behavior) [1]. A promising research approach to reproducibly set the properties and microstructure during flow forming despite disturbances is closed-loop property control (see [1]). In such closed-loop property control, material properties and the workpiece geometry are automatically controlled by online measurement and an online adaptation of the roller tool trajectory. The term ‘closed-loop property control’ also implies special requirements for the flow forming machine. First, the actuator dynamics have to be fast enough to change the process parameters depending on the control signal. Second, the machine control has to be accessible by an external control signal from the online property sensors so that the process parameters can be changed, e.g. by using a control prototyping system. Third, online property sensors must be placed near the roller tool for in-situ measurements at the forming zone. For this reason, single roller flow forming machines are preferred for use in closed-loop property control since there is more installation space for the property sensors than in conventional three roller machines. However, in previous research by the authors, a rather poor surface quality of workpieces manufactured by a hydraulic single roller flow forming machine was observed [2, 3]. The reason is that the existing machine control on a rapid control prototyping system does not consider the special load induced by single roller flow forming. For this purpose,

<figure><img src="image_1378.png" /></figure>
# Improving the flow forming process by a novel closed-loop control

KERSTING Lukas¹, a, *, SANDER Sebastian¹, ARIAN Bahman², b,
ROZO VASQUEZ Julian³, c, TRÄCHTLER Ansgar¹, ⁴, HOMBERG Werner² and WALTHER Frank³

¹Fraunhofer Institute for Mechatronic Systems Design (IEM), Paderborn, Germany

²Paderborn University, Forming and Machining technology (LUF), Germany

³TU Dortmund University, Chair of Materials Test Engineering (WPT), Germany

⁴Heinz Nixdorf Institute (HNI), Paderborn University, Germany

a lukas.kersting@iem.fraunhofer.de; b ba@luf.uni-paderborn.de, c julian.rozo@tu-dortmund.de

**Keywords:** Flow Forming, Closed-Loop Control, Model-Based Control Design

**Abstract.** The incremental flow forming process is currently enhanced in research context by special closed-loop property control concepts to increase the productivity and to control the product properties making invisible property structures like a magnetic barcode possible. However, it is preferred to establish property control concepts on single roller machines instead of conventional machines with three roller actuation due to the better machine accessibility. For those single roller machines, rather poor surface qualities of flow formed workpieces were observed in the past especially for hydraulic actuators. Thus, a new actuator closed-loop position control concept is developed in this paper using model-based control design methods and taking the flow forming forces as a load into account. The novel closed-loop control is validated during workpiece production at the actual single roller flow forming machine. An analysis of the manufactured workpieces show that the surface quality is significantly enhanced by the new control to a roughness level almost similar to conventional three roller flow forming. Thus, a sincere added value to the flow forming process is offered by the novel actuator closed-loop position control.

**Introduction**

In the incremental flow forming process, it is currently difficult to control the resulting product properties and microstructure due to the large number of disturbance variables from the semifinished part and the environment (e.g. temperature, tool and machine behavior) [1]. A promising research approach to reproducibly set the properties and microstructure during flow forming despite disturbances is closed-loop property control (see [1]). In such closed-loop property control, material properties and the workpiece geometry are automatically controlled by online measurement and an online adaptation of the roller tool trajectory. The term ‘closed-loop property control’ also implies special requirements for the flow forming machine. First, the actuator dynamics have to be fast enough to change the process parameters depending on the control signal. Second, the machine control has to be accessible by an external control signal from the online property sensors so that the process parameters can be changed, e.g. by using a control prototyping system. Third, online property sensors must be placed near the roller tool for in-situ measurements at the forming zone. For this reason, single roller flow forming machines are preferred for use in closed-loop property control since there is more installation space for the property sensors than in conventional three roller machines. However, in previous research by the authors, a rather poor surface quality of workpieces manufactured by a hydraulic single roller flow forming machine was observed [2, 3]. The reason is that the existing machine control on a rapid control prototyping system does not consider the special load induced by single roller flow forming. For this purpose,

<figure><img src="image_1382.png" /></figure>
this paper presents the development of a novel closed-loop position control for a single roller flow forming machine as an extension to the existing control. To especially take the requirements for property-controlled flow forming into account, a model-based development approach for hydraulic systems was chosen. The selected approach has already been successfully applied to design closed-loop controls for hydraulic robot systems [4] and HiL axle test rigs [5], but to our knowledge it has never been applied to a property-controlled single roller flow forming machine.

## Process and machine setup

**Property-controlled flow forming.** This paper focusses on the reverse flow forming of tubular parts made from metastable austenitic stainless steel AISI 304L. In the process, the semifinished part is fastened on a rotating mandrel. During the metal forming, a roller tool is moved by a flow forming actuator with a defined feed rate *f* in axial *x* direction and infeed *Δr* in radial *y* direction alongside the workpiece. This leads to a wall thickness reduction *Δw* (plastic deformation) and to a strain-induced *α'*-martensite formation in the workpiece. To ensure that wall thickness and *α'*-martensite match to a desired value, a closed-loop property control is appropriate (see Fig. 1).

<figure><img src="image_1379.png" /><figcaption>Fig. 1. Property-controlled flow forming process including actuator control</figcaption></figure>

Here, the wall thickness reduction can be measured online by two laser distance sensors. The *α'*-martensite fraction is determined by a combined approach with a magnetic Barkhausen noise (MBN) measurement and a so-called soft sensor. Both sensor signals are compared to desired values and processed by a property controller. The property controller corrects the reference roller trajectory given by the machine control. The corrected trajectory leads to a change of *f* and *Δr* and thus to change of *Δw* and *α'*-martensite. At this point, it is essential to ensure that the tool trajectory actually corresponds to the desired trajectory from the property control. For this reason, the flow forming actuator is equipped with an actuator control system which is the system of interest in this paper (highlighted in red in Fig. 1). For further information concerning the closed-loop property control, it is referred to the literature (e.g. [1]) since it is out of scope of this paper.

**Actuator and machine setup.** In this paper, the flow forming machine PLB 400 from Leifeld Metal Spinning GmbH is used. This machine basically features a cross support actuator with the roller tool, a spindle-driven mandrel carrying the workpiece and a dual roller counterholder placed opposite to the roller tool to avoid mandrel deflection by ensuring a force balance (see [2]). The cross support, which is in focus of this paper, consists of two parts: a lower machine support actuator (*x* axis) that is hydraulically moved in axial *x* direction with a certain feed *f* = *ẋ*<sub>p</sub> (*velocity*) and an upper machine support actuator (*y* axis) that is mounted on the lower part. The upper machine support actuator is rigidly connected to the roller tool and can be hydraulically
this paper presents the development of a novel closed-loop position control for a single roller flow forming machine as an extension to the existing control. To especially take the requirements for property-controlled flow forming into account, a model-based development approach for hydraulic systems was chosen. The selected approach has already been successfully applied to design closed-loop controls for hydraulic robot systems [4] and HiL axle test rigs [5], but to our knowledge it has never been applied to a property-controlled single roller flow forming machine.

## Process and machine setup

**Property-controlled flow forming.** This paper focusses on the reverse flow forming of tubular parts made from metastable austenitic stainless steel AISI 304L. In the process, the semifinished part is fastened on a rotating mandrel. During the metal forming, a roller tool is moved by a flow forming actuator with a defined feed rate $f$ in axial $x$ direction and infeed $\Delta r$ in radial $y$ direction alongside the workpiece. This leads to a wall thickness reduction $\Delta w$ (plastic deformation) and to a strain-induced $\alpha'$-martensite formation in the workpiece. To ensure that wall thickness and $\alpha'$-martensite match to a desired value, a closed-loop property control is appropriate (see Fig. 1).

<figure><img src="image_1383.png" /><figcaption>Fig. 1. Property-controlled flow forming process including actuator control</figcaption></figure>

Here, the wall thickness reduction can be measured online by two laser distance sensors. The $\alpha'$-martensite fraction is determined by a combined approach with a magnetic Barkhausen noise (MBN) measurement and a so-called soft sensor. Both sensor signals are compared to desired values and processed by a property controller. The property controller corrects the reference roller trajectory given by the machine control. The corrected trajectory leads to a change of $f$ and $\Delta r$ and thus to change of $\Delta w$ and $\alpha'$-martensite. At this point, it is essential to ensure that the tool trajectory actually corresponds to the desired trajectory from the property control. For this reason, the flow forming actuator is equipped with an actuator control system which is the system of interest in this paper (highlighted in red in Fig. 1). For further information concerning the closed-loop property control, it is referred to the literature (e.g. [1]) since it is out of scope of this paper.

**Actuator and machine setup.** In this paper, the flow forming machine PLB 400 from Leifeld Metal Spinning GmbH is used. This machine basically features a cross support actuator with the roller tool, a spindle-driven mandrel carrying the workpiece and a dual roller counterholder placed opposite to the roller tool to avoid mandrel deflection by ensuring a force balance (see [2]). The cross support, which is in focus of this paper, consists of two parts: a lower machine support actuator (x axis) that is hydraulically moved in axial $x$ direction with a certain feed $f = \dot{x}_p$ (velocity) and an upper machine support actuator (y axis) that is mounted on the lower part. The upper machine support actuator is rigidly connected to the roller tool and can be hydraulically
moved in radial y direction to realize a certain infeed $\Delta r$ to the workpiece. The setup and functionality of the two machine support axis is more detailly explained in Fig. 2.

<figure><img src="image_1380.png" /><figcaption>Fig. 2. System structure of the flow forming machine</figcaption></figure>

Each hydraulic machine support axis is composed of a hydraulic cylinder and a proportional valve (Bosch Rexroth 4WRPEH) that controls the volume flow from the pump to the cylinder leading to the piston motion. The valve opening and thus the volume flow is continuously adjustable depending on the input voltage $u_{v,x}$ or $u_{v,y}$ (within a range of 0 – 10 V). The input voltages $u_{v,x}$ and $u_{v,y}$ are generated by the machine control. The machine control is realised on the rapid control prototyping system NI cRIO 9035. The LabVIEW-based control software was originally developed by Hornjak and Lossen in [6, 7] for friction spinning purposes. It can be separated into a main control, with a user interface and software interface to the property control system (see [8]), and one control unit per axis. In each control unit, $u_{v,x}$ and $u_{v,y}$ are generated by the actuator control. The current actuator control is a mixed open-loop setup with position feedback. Depending on the desired piston velocity, a certain value of $u_{v,x}$ and $u_{v,y}$ is applied from a dataset as long until the desired piston position is reached. For this purpose, the piston positions are measured with a magnetostrictive transducer (MTS Temposonic E101) and fed back to the control. However, the current actuator control is limited concerning the use during flow forming since the forming forces are much higher like in friction spinning. This leads to inaccuracies concerning the voltage datasets. Thus, the both control units are redesigned in this paper to a full closed-loop control.

## Methodology

To develop the new closed-loop for the hydraulic actuator system, a model-based development approach for control design was chosen. Here, the controller is first designed using a simulation model and subsequently applied to the actual system. Thus, the closed-loop control can be developed time-efficiently with a good control performance. The model-based development procedure includes four steps and milestones. First, an analytic system model is created that represents the dynamic behaviour of the system to be controlled (1). The model is implemented in a simulation environment and parameterized using experimental data (2). Subsequently, the
moved in radial y direction to realize a certain infeed $\Delta r$ to the workpiece. The setup and functionality of the two machine support axis is more detailly explained in Fig. 2.

<figure><img src="image_1384.png" /><figcaption>Fig. 2. System structure of the flow forming machine</figcaption></figure>

Each hydraulic machine support axis is composed of a hydraulic cylinder and a proportional valve (Bosch Rexroth 4WRPEH) that controls the volume flow from the pump to the cylinder leading to the piston motion. The valve opening and thus the volume flow is continuously adjustable depending on the input voltage $u_{v,x}$ or $u_{v,y}$ (within a range of 0 – 10 V). The input voltages $u_{v,x}$ and $u_{v,y}$ are generated by the machine control. The machine control is realised on the rapid control prototyping system NI cRIO 9035. The LabVIEW-based control software was originally developed by Hornjak and Lossen in [6, 7] for friction spinning purposes. It can be separated into a main control, with a user interface and software interface to the property control system (see [8]), and one control unit per axis. In each control unit, $u_{v,x}$ and $u_{v,y}$ are generated by the actuator control. The current actuator control is a mixed open-loop setup with position feedback. Depending on the desired piston velocity, a certain value of $u_{v,x}$ and $u_{v,y}$ is applied from a dataset as long until the desired piston position is reached. For this purpose, the piston positions are measured with a magnetostrictive transducer (MTS Temposonic E101) and fed back to the control. However, the current actuator control is limited concerning the use during flow forming since the forming forces are much higher like in friction spinning. This leads to inaccuracies concerning the voltage datasets. Thus, the both control units are redesigned in this paper to a full closed-loop control.

## Methodology

To develop the new closed-loop for the hydraulic actuator system, a model-based development approach for control design was chosen. Here, the controller is first designed using a simulation model and subsequently applied to the actual system. Thus, the closed-loop control can be developed time-efficiently with a good control performance. The model-based development procedure includes four steps and milestones. First, an analytic system model is created that represents the dynamic behaviour of the system to be controlled (1). The model is implemented in a simulation environment and parameterized using experimental data (2). Subsequently, the
control is developed and tested virtually using the model and suitable controller parameter are selected (3). Finally, the developed control is implemented in the machine control and validated at the actual machine (4). This procedure is applied in the following to the hydraulic actuator system.

## Modelling

A simulation model was created in MATLAB/Simulink to describe the static and dynamical transfer behavior of the hydraulic machine support actuators. For this purpose, a hydraulic model by [5] and [8] was adapted. Since the machine supports in x and y direction have an identical structure, albeit with different dimensions and loads, the model is exemplary described for the x axis in the following. The overall model is structured according to the components of the real machine into a valve and a cylinder model (Fig. 3). The model additionally includes an external load model that is specifically designed for the machine application in flow forming. In the following, the models and their adaption to the flow forming machine are further described. However, for the full model equations of the hydraulic system it is referred to the literature [8].

<figure><img src="image_1381.png" /><figcaption>Fig. 3. Overall structure of the simulation model that describes the dynamic behaviour of the machine support in x direction</figcaption></figure>

**Valve.** Depending on the input voltage $u_v$, the spool inside the valve is moved to its relative position $x_v$ (range: 0% to ±100% opened). The temporal relationship between $u_v$ and $x_v$ (valve dynamics) is simply described by a second order transfer function according to [5]. The spool position $x_v$ mainly influences the volume flow through the valve $Q_A$ and $Q_B$ from the pump to cylinder chamber A or B. $Q_A$ and $Q_B$ are modelled according to the data sheet with a kinked flow characteristics and zero lapping via an orifice equation. Thus, the volume flow is a function of the actual pressures inside of the cylinder chambers $p_A$ and $p_B$.

**Hydraulic cylinder.** The pressures inside the cylinder $p_A$ and $p_B$ are calculated based on the continuity equation for each cylinder chamber. Taking the compressibility of the oil into account, the pressure rates $\dot{p}_A$ and $\dot{p}_B$ and thus the pressures inside of the cylinder are described by dynamic pressure differential equations taken from [8]. From $p_A$ and $p_B$, a resulting force $F = A_{p,A}p_A - A_{p,B}p_B$ acts on the piston side faces $A_{p,A}$ and $A_{p,B}$ that accelerates piston mass $m_p$ and that leads to a piston motion. Additionally, it assumed that the cylinder is loaded by an external force $F_{ext}$. Based on Newton's second law, the motion equation of the piston is thus formulated to:

$$m_p \ddot{x}_p = A_{p,A} p_A - A_{p,B} p_B - F_{ext}. \quad (1)$$

**External force.** The external force consists of friction forces $F_{fric}$ and, in case of flow forming, of the forming forces $F_{load}$. The friction force is assumed to be constant at a value of $F_{S0}$ and is directed opposite to the cylinder motion. This fact is incorporated in Eq. (2) by the term $\text{sign}(\dot{x}_p)$.

$$F_{ext} = F_{fric} + F_{load} = F_{S0} \cdot \text{sign}(\dot{x}_p) + F_{load}(\Delta r, f) \quad (2)$$

During positioning before or after the forming operation, $F_{ext}$ is exclusively comprised by the friction forces $F_{fric}$. By contrast, during workpiece production, the roller and consequently the
control is developed and tested virtually using the model and suitable controller parameter are selected (3). Finally, the developed control is implemented in the machine control and validated at the actual machine (4). This procedure is applied in the following to the hydraulic actuator system.

## Modelling

A simulation model was created in MATLAB/Simulink to describe the static and dynamical transfer behavior of the hydraulic machine support actuators. For this purpose, a hydraulic model by [5] and [8] was adapted. Since the machine supports in x and y direction have an identical structure, albeit with different dimensions and loads, the model is exemplary described for the x axis in the following. The overall model is structured according to the components of the real machine into a valve and a cylinder model (Fig. 3). The model additionally includes an external load model that is specifically designed for the machine application in flow forming. In the following, the models and their adaption to the flow forming machine are further described. However, for the full model equations of the hydraulic system it is referred to the literature [8].

<figure><img src="image_1385.png" /><figcaption>Fig. 3. Overall structure of the simulation model that describes the dynamic behaviour of the machine support in x direction</figcaption></figure>

**Valve.** Depending on the input voltage $u_v$, the spool inside the valve is moved to its relative position $x_v$ (range: 0% to ±100% opened). The temporal relationship between $u_v$ and $x_v$ (valve dynamics) is simply described by a second order transfer function according to [5]. The spool position $x_v$ mainly influences the volume flow through the valve $Q_A$ and $Q_B$ from the pump to cylinder chamber A or B. $Q_A$ and $Q_B$ are modelled according to the data sheet with a kinked flow characteristics and zero lapping via an orifice equation. Thus, the volume flow is a function of the actual pressures inside of the cylinder chambers $p_A$ and $p_B$.

**Hydraulic cylinder.** The pressures inside the cylinder $p_A$ and $p_B$ are calculated based on the continuity equation for each cylinder chamber. Taking the compressibility of the oil into account, the pressure rates $\dot{p}_A$ and $\dot{p}_B$ and thus the pressures inside of the cylinder are described by dynamic pressure differential equations taken from [8]. From $p_A$ and $p_B$, a resulting force $F = A_{p,A}p_A - A_{p,B}p_B$ acts on the piston side faces $A_{p,A}$ and $A_{p,B}$ that accelerates piston mass $m_p$ and that leads to a piston motion. Additionally, it assumed that the cylinder is loaded by an external force $F_{ext}$. Based on Newton's second law, the motion equation of the piston is thus formulated to:

$$m_p \ddot{x}_p = A_{p,A} p_A - A_{p,B} p_B - F_{ext}. \quad (1)$$

**External force.** The external force consists of friction forces $F_{fric}$ and, in case of flow forming, of the forming forces $F_{load}$. The friction force is assumed to be constant at a value of $F_{S0}$ and is directed opposite to the cylinder motion. This fact is incorporated in Eq. (2) by the term $\text{sign}(\dot{x}_p)$.

$$F_{ext} = F_{fric} + F_{load} = F_{S0} \cdot \text{sign}(\dot{x}_p) + F_{load}(\Delta r, f) \quad (2)$$

During positioning before or after the forming operation, $F_{ext}$ is exclusively comprised by the friction forces $F_{fric}$. By contrast, during workpiece production, the roller and consequently the
piston is exposed to mechanical load due to the forming forces $F_{load}$. Note that the axial and radial forming forces are different to each other, so $F_{load,x}$ differs from $F_{load,y}$. The forces are assumed to be a static, nonlinear function $F_{load}(\Delta r, f)$ depending on infeed $\Delta r \sim y_p$ and feed rate $f = \dot{x}_p$.

## Parameter identification

To simulate the previously described model, it is required to determine the model parameters in advance. For this purpose, the model equations are fitted with *Simulink Parameter Estimator Toolbox* to measured step response data from the forming machine using nonlinear least square algorithm. Additionally, the natural frequency of the cylinder was identified from the measurements and in consequence the piston mass $m_p$ (according to [9]). However, this procedure is not suitable for building the function $F_{load}(\Delta r, f)$ in Eq. (2) since it is a complex nonlinear function that not only depends on the machine but also on the flow forming process. Thus, additional flow forming experiments are required for the parameter identification.

**Identification of the forming forces $F_{load}$ (external load model).** A systematic, full factorial experimental study was carried out on the single roller machine. Workpieces were manufactured investigating 15 different parameter combinations (5 levels of feed rate from 0.1 to 0.5 mm/s and 3 infeed levels from 1 to 3 mm). During the experiments, the pressures were recorded and the hydraulic force for each cylinder was calculated by $F = p_A A_{p,A} - p_B A_{p,B}$. Since the forming forces are much higher than the friction force, it can be assumed that the calculated force $F$ directly corresponds to $F_{load}$. For the evaluation, $F_{load,x}$ in axial and $F_{load,y}$ in radial direction were averaged over time and plotted against the process parameters (see Fig. 4).

<figure><img src="image_1382.png" /><figcaption>Fig. 4. Meas. forming forces (load) during flow forming for different process parameters</figcaption></figure>

It is notable, that the radial forces (y direction) are much higher than the axial (x direction) for each process parameter combination. In x direction, the forming force is in a range of approx. 1.5 to 6 kN. By contrast, the forces in y direction are in a range of 10 to 30 kN. In x as well as in y direction, the measured forces depend on the process parameters used in the respective experiment, i.e. the feed rate $f (= \dot{x}_p)$ and the infeed $\Delta r (\sim y_p)$. In x direction, the measured $F_{load,x}$ is higher if the feed rate $f$ is low, or if the infeed $\Delta r$ is high. In y direction, $F_{load,y}$ clearly rises the higher the infeed $\Delta r$ is. Additionally, the force is reduced by lowering the feed rate. To include the described empiric dependency on process parameters in the model, the measurement results from Fig. 4 are modelled by an empiric lookup table $F_{load}$.

## Control design

A special closed-loop control concept for the hydraulic actuators was developed due to the special use in the flow forming process. Since flow forming depends on axial feed rate $f = \dot{x}_p$ and on the infeed $\Delta r \sim y_p$, the closed-loop control must be able to control both

* the piston positions $x_p$ and $y_p$
piston is exposed to mechanical load due to the forming forces $F_{load}$. Note that the axial and radial forming forces are different to each other, so $F_{load,x}$ differs from $F_{load,y}$. The forces are assumed to be a static, nonlinear function $F_{load}(\Delta r, f)$ depending on infeed $\Delta r \sim y_p$ and feed rate $f = \dot{x}_p$.

## Parameter identification

To simulate the previously described model, it is required to determine the model parameters in advance. For this purpose, the model equations are fitted with *Simulink Parameter Estimator Toolbox* to measured step response data from the forming machine using nonlinear least square algorithm. Additionally, the natural frequency of the cylinder was identified from the measurements and in consequence the piston mass $m_p$ (according to [9]). However, this procedure is not suitable for building the function $F_{load}(\Delta r, f)$ in Eq. (2) since it is a complex nonlinear function that not only depends on the machine but also on the flow forming process. Thus, additional flow forming experiments are required for the parameter identification.

**Identification of the forming forces $F_{load}$ (external load model).** A systematic, full factorial experimental study was carried out on the single roller machine. Workpieces were manufactured investigating 15 different parameter combinations (5 levels of feed rate from 0.1 to 0.5 mm/s and 3 infeed levels from 1 to 3 mm). During the experiments, the pressures were recorded and the hydraulic force for each cylinder was calculated by $F = p_A A_{p,A} - p_B A_{p,B}$. Since the forming forces are much higher than the friction force, it can be assumed that the calculated force $F$ directly corresponds to $F_{load}$. For the evaluation, $F_{load,x}$ in axial and $F_{load,y}$ in radial direction were averaged over time and plotted against the process parameters (see Fig. 4).

<figure><img src="image_1386.png" /><figcaption>Fig. 4. Meas. forming forces (load) during flow forming for different process parameters</figcaption></figure>

It is notable, that the radial forces (y direction) are much higher than the axial (x direction) for each process parameter combination. In x direction, the forming force is in a range of approx. 1.5 to 6 kN. By contrast, the forces in y direction are in a range of 10 to 30 kN. In x as well as in y direction, the measured forces depend on the process parameters used in the respective experiment, i.e. the feed rate $f (= \dot{x}_p)$ and the infeed $\Delta r (\sim y_p)$. In x direction, the measured $F_{load,x}$ is higher if the feed rate $f$ is low, or if the infeed $\Delta r$ is high. In y direction, $F_{load,y}$ clearly rises the higher the infeed $\Delta r$ is. Additionally, the force is reduced by lowering the feed rate. To include the described empiric dependency on process parameters in the model, the measurement results from Fig. 4 are modelled by an empiric lookup table $F_{load}$.

## Control design

A special closed-loop control concept for the hydraulic actuators was developed due to the special use in the flow forming process. Since flow forming depends on axial feed rate $f = \dot{x}_p$ and on the infeed $\Delta r \sim y_p$, the closed-loop control must be able to control both

* the piston positions $x_p$ and $y_p$
* the position velocities $\dot{x}_p$ and $\dot{y}_p$.

The piston positions $x_p$ and $y_p$ are coordinates of discrete points on the roller trajectory. The roller trajectory consists of multiple points and the roller should linearly move on a straight line from point to point with the position velocities $\dot{x}_p$ and $\dot{y}_p$. The piston positions and velocities at or between the discrete points serve as desired values for the control. The desired values are stored in a matrix $P$ that is similar to a G-Code program of an industrial CNC control.

$$ P = \begin{bmatrix} x_{p,des,1} & \dot{x}_{p,des,1} & y_{p,des,1} & \dot{y}_{p,des,1} \\ \vdots & \vdots & \vdots & \vdots \\ x_{p,des,m} & \dot{x}_{p,des,m} & y_{p,des,m} & \dot{y}_{p,des,m} \end{bmatrix} \qquad (3) $$

Each row corresponds to the desired positions $x_{p,des,i}$ and $y_{p,des,i}$ at a discrete point $i$ that should be reached from the previous point $x_{p,des,i-1}$ and $y_{p,des,i-1}$ by velocity $\dot{x}_{p,des,i}$ and $\dot{y}_{p,des,i}$. If the desired position is met, then the next row is applied, so $x_{p,des,i+1}$, $y_{p,des,i+1}$, $\dot{x}_{p,des,i+1}$ and $\dot{y}_{p,des,i+1}$ becomes to be the actual desired value. The desired values are optionally corrected by the closed-loop property control and then committed the control unit of the cylinder (see Fig. 5).

<figure><img src="image_1383.png" /><figcaption>Fig. 5. Closed-loop control structure for the X axis</figcaption></figure>

At first, the desired values are processed in an interpolator that calculates the desired value $x_{p,des}^*$ or $y_{p,des}^*$ for the controller. The interpolator equation for the x axis is given by Eq. (4).

$$ x_{p,des}^* = \begin{cases} x_{p,des} & \text{if } |x_{p,des} - x_p| < \varepsilon \\ \text{sign}(x_{des} - x_p) \cdot \dot{x}_{p,des} \cdot (t - t_0) + x_0 & \text{else} \end{cases} \qquad (4) $$

If the actual piston position $x_p$ is within a distance of threshold $\varepsilon$ (here: 0.1) to the $x_{p,des}$ from matrix $P$, then $x_{p,des}$ also acts as desired value $x_{p,des}^*$ for the controller. In this case, the control behaves like a conventional position control. If not, a fictional desired value is interpolated from processing the velocity $\dot{x}_{p,des}$ and starting from value $x_0$. Note, that $x_0$ is the actual piston position, when the control switches into the next row of $P$ or if there is a control action of the superior closed-loop property control, at time $t_0$. Thus, the complex problem of controlling both position and velocity is reduced to a simple position control task. Following to the interpolator, $x_{p,des}^*$ is compared to the actual piston position $x_p$ or $y_p$ by Eq. (5) and processed by the position controller.

$$ e_x = x_{p,des}^* - x_p \qquad (5) $$

The position controller is realized with a PI controller that includes a proportional gain $K_{p,x}$ and an integral gain $K_{i,x}$ for the x axis and gains $K_{p,y}$ and $K_{i,y}$ for the y axis. The controller outputs a voltage $u_{v,x}$ or $u_{v,y}$ to the valves of the real system or – in case of the model – to the valve model.

**Controller parameterization.** The parameters of the position controller were determined by linearizing the plant model using *Simulink Model Linearizer* and analyzing the system dynamics in frequency domain concerning the gain and phase margin. The selected controller gains should lead to closed-loop control dynamics which are as fast as possible, but also stable. Thus, Nyquist stability criterion [10] was applied and the gains were chosen to those values shown in Table 1.
* the position velocities $\dot{x}_p$ and $\dot{y}_p$.

The piston positions $x_p$ and $y_p$ are coordinates of discrete points on the roller trajectory. The roller trajectory consists of multiple points and the roller should linearly move on a straight line from point to point with the position velocities $\dot{x}_p$ and $\dot{y}_p$. The piston positions and velocities at or between the discrete points serve as desired values for the control. The desired values are stored in a matrix $P$ that is similar to a G-Code program of an industrial CNC control.

$$P = \begin{bmatrix} x_{p,des,1} & \dot{x}_{p,des,1} & y_{p,des,1} & \dot{y}_{p,des,1} \\ \vdots & \vdots & \vdots & \vdots \\ x_{p,des,m} & \dot{x}_{p,des,m} & y_{p,des,m} & \dot{y}_{p,des,m} \end{bmatrix} \qquad (3)$$

Each row corresponds to the desired positions $x_{p,des,i}$ and $y_{p,des,i}$ at a discrete point $i$ that should be reached from the previous point $x_{p,des,i-1}$ and $y_{p,des,i-1}$ by velocity $\dot{x}_{p,des,i}$ and $\dot{y}_{p,des,i}$. If the desired position is met, then the next row is applied, so $x_{p,des,i+1}$, $y_{p,des,i+1}$, $\dot{x}_{p,des,i+1}$ and $\dot{y}_{p,des,i+1}$ becomes to be the actual desired value. The desired values are optionally corrected by the closed-loop property control and then committed the control unit of the cylinder (see Fig. 5).

<figure><img src="image_1387.png" /><figcaption>Fig. 5. Closed-loop control structure for the X axis</figcaption></figure>

At first, the desired values are processed in an interpolator that calculates the desired value $x_{p,des}^*$ or $y_{p,des}^*$ for the controller. The interpolator equation for the x axis is given by Eq. (4).

$$x_{p,des}^* = \begin{cases} x_{p,des} & \text{if } |x_{p,des} - x_p| < \varepsilon \\ \text{sign}(x_{des} - x_p) \cdot \dot{x}_{p,des} \cdot (t - t_0) + x_0 & \text{else} \end{cases} \qquad (4)$$

If the actual piston position $x_p$ is within a distance of threshold $\varepsilon$ (here: 0.1) to the $x_{p,des}$ from matrix $P$, then $x_{p,des}$ also acts as desired value $x_{p,des}^*$ for the controller. In this case, the control behaves like a conventional position control. If not, a fictional desired value is interpolated from processing the velocity $\dot{x}_{p,des}$ and starting from value $x_0$. Note, that $x_0$ is the actual piston position, when the control switches into the next row of $P$ or if there is a control action of the superior closed-loop property control, at time $t_0$. Thus, the complex problem of controlling both position and velocity is reduced to a simple position control task. Following to the interpolator, $x_{p,des}^*$ is compared to the actual piston position $x_p$ or $y_p$ by Eq. (5) and processed by the position controller.

$$e_x = x_{p,des}^* - x_p \qquad (5)$$

The position controller is realized with a PI controller that includes a proportional gain $K_{p,x}$ and an integral gain $K_{i,x}$ for the x axis and gains $K_{p,y}$ and $K_{i,y}$ for the y axis. The controller outputs a voltage $u_{v,x}$ or $u_{v,y}$ to the valves of the real system or – in case of the model – to the valve model.

**Controller parameterization.** The parameters of the position controller were determined by linearizing the plant model using *Simulink Model Linearizer* and analyzing the system dynamics in frequency domain concerning the gain and phase margin. The selected controller gains should lead to closed-loop control dynamics which are as fast as possible, but also stable. Thus, Nyquist stability criterion [10] was applied and the gains were chosen to those values shown in Table 1.
<table><caption>Table 1: Model-based identified controller gains</caption><thead><tr><th></th><th></th><th>X direction</th><th>Y direction</th></tr></thead><tbody><tr><td>Proportional gain</td><td>K<sub>p</sub></td><td>0.8</td><td>0.7</td></tr><tr><td>Integral gain</td><td>K<sub>i</sub></td><td>0.4</td><td>0.54</td></tr></tbody></table>

The closed-loop controller gains were additionally tested by analyzing their performance in time using the simulation model. For this test, $x_{p,des}^*$ and $y_{p,des}^*$ were changed stepwise (±1 mm and ±2 mm) in the model and the response of the piston positions $x_p$ and $y_p$ was recorded (Fig. 6).

<figure><img src="image_1384.png" /><figcaption>Fig. 6. Controller test by step response (example: height 1 mm in x and 2 mm in y direction)</figcaption></figure>

As shown in Fig. 6, the desired values in x and y direction are controlled stable and stationary in the simulation. The system response includes a slight, well-damped overshoot of max. 0.5 mm that is acceptable to get a faster system response. Thus, the controller parameters from Table 1 are successfully proofed to be suitable for the final closed-loop control at the flow forming machine.

For this reason, the total control concept including the controllers was adapted to LabVIEW and integrated in the machine control of the flow forming machine. Then, the controllers of the closed-loop position control were commissioned by repeating the step response performance test that was already performed virtually in MATLAB with the model. According to Fig. 6, the dynamic behavior of the closed-loop position control is in a good agreement with the model.

## Experimental control validation

The proposed control concept (interpolator and closed-loop position control) was finally validated at the actual flow forming machine. For this purpose, experiments with and without load were performed using axial and radial velocities $\dot{x}_{p,des}$ and $\dot{y}_{p,des}$ from 0,01 mm/s (extremely slow flow forming) to 18 mm/s (rapid traverse without flow forming). The core of these experiments was the manufacturing of 5 workpieces by flow forming with feed rates $f = \dot{x}_{p,des}$ from 0.1 mm/s to 0.5 mm/s and an infeed $\Delta r$ of 2 and 3 mm ($y_{p,des} = 141$ mm and $y_{p,des} = 142$ mm). In the following, the validation results concerning the accuracy of the control will be deeper analyzed taking the example of the experiment $\Delta r = 2$ mm and $f = 0.1$ mm/s (see Fig. 7). This experiment is divided into three phases: prepositioning in x direction without load (I), prepositioning in y direction without (II) and the actual flow forming operation with load (III). During I, the x axis is moved from $x_p = 1$ mm to 325 mm within 46.28 s. Thus, the actuator movement corresponds very good to the desired value. During this time, the y axis is kept on a constant position of $y_p = 1$ mm (measured mean value 1.001 mm). Subsequently, the y axis is prepositioned to $y_p = 141$ mm, that corresponds to an infeed of $\Delta r = 2$ mm to the workpiece, within 35 s. The result is also in a good agreement with the desired value since $\dot{y}_{p,des}$ was set to 4 mm/s. In the last phase, the workpiece is manufactured by an axial movement with $f = \dot{x}_{p,des} = 0.1$ mm/s while the actuator position in y direction is kept constant. This phase is the most critical due to the external load from plastic deformation during flow forming which might force the actuators out of their desired position.
<table><caption>Table 1: Model-based identified controller gains</caption><thead><tr><th></th><th></th><th>X direction</th><th>Y direction</th></tr></thead><tbody><tr><td>Proportional gain</td><td>K<sub>p</sub></td><td>0.8</td><td>0.7</td></tr><tr><td>Integral gain</td><td>K<sub>i</sub></td><td>0.4</td><td>0.54</td></tr></tbody></table>

The closed-loop controller gains were additionally tested by analyzing their performance in time using the simulation model. For this test, $x_{p,des}^*$ and $y_{p,des}^*$ were changed stepwise (±1 mm and ±2 mm) in the model and the response of the piston positions $x_p$ and $y_p$ was recorded (Fig. 6).

<figure><img src="image_1388.png" /><figcaption>Fig. 6. Controller test by step response (example: height 1 mm in x and 2 mm in y direction)</figcaption></figure>

As shown in Fig. 6, the desired values in x and y direction are controlled stable and stationary in the simulation. The system response includes a slight, well-damped overshoot of max. 0.5 mm that is acceptable to get a faster system response. Thus, the controller parameters from Table 1 are successfully proofed to be suitable for the final closed-loop control at the flow forming machine.

For this reason, the total control concept including the controllers was adapted to LabVIEW and integrated in the machine control of the flow forming machine. Then, the controllers of the closed-loop position control were commissioned by repeating the step response performance test that was already performed virtually in MATLAB with the model. According to Fig. 6, the dynamic behavior of the closed-loop position control is in a good agreement with the model.

## Experimental control validation

The proposed control concept (interpolator and closed-loop position control) was finally validated at the actual flow forming machine. For this purpose, experiments with and without load were performed using axial and radial velocities $\dot{x}_{p,des}$ and $\dot{y}_{p,des}$ from 0,01 mm/s (extremely slow flow forming) to 18 mm/s (rapid traverse without flow forming). The core of these experiments was the manufacturing of 5 workpieces by flow forming with feed rates $f = \dot{x}_{p,des}$ from 0.1 mm/s to 0.5 mm/s and an infeed $\Delta r$ of 2 and 3 mm ($y_{p,des} = 141$ mm and $y_{p,des} = 142$ mm). In the following, the validation results concerning the accuracy of the control will be deeper analyzed taking the example of the experiment $\Delta r = 2$ mm and $f = 0.1$ mm/s (see Fig. 7). This experiment is divided into three phases: prepositioning in x direction without load (I), prepositioning in y direction without (II) and the actual flow forming operation with load (III). During I, the x axis is moved from $x_p = 1$ mm to 325 mm within 46.28 s. Thus, the actuator movement corresponds very good to the desired value. During this time, the y axis is kept on a constant position of $y_p = 1$ mm (measured mean value 1.001 mm). Subsequently, the y axis is prepositioned to $y_p = 141$ mm, that corresponds to an infeed of $\Delta r = 2$ mm to the workpiece, within 35 s. The result is also in a good agreement with the desired value since $\dot{y}_{p,des}$ was set to 4 mm/s. In the last phase, the workpiece is manufactured by an axial movement with $f = \dot{x}_{p,des} = 0.1$ mm/s while the actuator position in y direction is kept constant. This phase is the most critical due to the external load from plastic deformation during flow forming which might force the actuators out of their desired position.
Nevertheless, the measured, actual actuator behavior is conform with the desired despite of the load. The average value of $\dot{x}_p$ is actually 0.1 mm/s and $y_p$ is 140.999 mm. By taking a deeper look on the measurement of $y_p$, it can be seen that the impact of the load on the actuator position results only in a slight oscillation of ±0.005 mm which is significantly less than known from experiments with the flow forming machine before.

<figure><img src="image_1385.png" /><figcaption>Fig. 7. Desired and actual actuator position during flow forming ($\Delta r = 2$ mm, $f = 0.1$ mm/s).</figcaption></figure>

These measurements are also confirmed by the other experiments. To analyze the impact of the control results, the manufactured specimens were measured with MarSurf M300 and the average roughness $R_a$ was compared to specimens produced at the single roller machine in the past (from [3]), see Fig. 8. In the figure, additionally the measured $R_a$ of specimens manufactured on a three roller flow forming machine (Bohner & Koehle BD 40) is shown. Those specimens were a part of a DOE in [11]. For a better comparison, workpieces were chosen which were manufactured with an identical feed rate and a strain similar to the new specimens from single roller flow forming.

<figure><img src="image_1386.png" /><figcaption>Fig. 8. Average roughness $R_a$ of workpieces manufactured on the single roller machine with the old and new actuator control in comparison to an industrial three roller flow forming machine, for: (a) constant $\Delta r = 2$ mm, (b) constant $f = 0.1$ mm/s</figcaption></figure>

Fig. 8 shows that with the new control, $R_a$ is significantly reduced by a factor of >3 compared to the old single roller results from [3]. Due to the control enhancement, $R_a$ is minimum 0.47 µm
Nevertheless, the measured, actual actuator behavior is conform with the desired despite of the load. The average value of $\dot{x}_p$ is actually 0.1 mm/s and $y_p$ is 140.999 mm. By taking a deeper look on the measurement of $y_p$, it can be seen that the impact of the load on the actuator position results only in a slight oscillation of ±0.005 mm which is significantly less than known from experiments with the flow forming machine before.

<figure><img src="image_1389.png" /><figcaption>Fig. 7. Desired and actual actuator position during flow forming ($\Delta r = 2$ mm, $f = 0.1$ mm/s).</figcaption></figure>

These measurements are also confirmed by the other experiments. To analyze the impact of the control results, the manufactured specimens were measured with MarSurf M300 and the average roughness $R_a$ was compared to specimens produced at the single roller machine in the past (from [3]), see Fig. 8. In the figure, additionally the measured $R_a$ of specimens manufactured on a three roller flow forming machine (Bohner & Koehle BD 40) is shown. Those specimens were a part of a DOE in [11]. For a better comparison, workpieces were chosen which were manufactured with an identical feed rate and a strain similar to the new specimens from single roller flow forming.

<figure><img src="image_1390.png" /><figcaption>Fig. 8. Average roughness $R_a$ of workpieces manufactured on the single roller machine with the old and new actuator control in comparison to an industrial three roller flow forming machine, for: (a) constant $\Delta r = 2$ mm, (b) constant $f = 0.1$ mm/s</figcaption></figure>

Fig. 8 shows that with the new control, $R_a$ is significantly reduced by a factor of >3 compared to the old single roller results from [3]. Due to the control enhancement, $R_a$ is minimum 0.47 µm
at $f = 0.1$ mm/s and rises with increasing feed rate up to 3.768 µm (for $\Delta r = 2$ mm). Thus, the roughness $R_a$ in single roller flow forming is now almost on the same level as in three roller flow forming. There, $R_a$ is 0.47 µm in the case of $f = 0.1$ mm/s and $\Delta r = 2$ mm, for example. The similarity of the roughness in single roller flow forming and three roller flow forming is remarkable since the workpiece is more often overrolled with three rolls. Thus, a sincere added value concerning the workpiece quality in single roller flow forming is offered by the enhanced process parameter tracking with the new control.

## Conclusion

A novel closed-loop control for a hydraulic single roller flow forming machine was model-based developed and validated in this paper. Due to model-based procedure to design the control, it became possible to create a control that is able to accurately keep the desired position and velocity despite of the high forming forces due to flow forming. Thus, the developed control features the desired functionality to accurately control both the actuator position and velocity in the flow forming process. As shown during the validation, it is consequently possible to manufacture workpieces on the single roller flow forming machine with a better surface quality. The surface roughness of the manufactured parts is now even in a similar range to that of conventional machines with three rollers. Hence, the flow forming machine including the novel actuator control is now predestined to be prospectively used in the closed-loop property control. The closed-loop property control of the $\alpha$'-martensite fraction and wall thickness reduction has already been proposed by the authors in [1]. It includes a so-called soft sensor for the online determination of the $\alpha$'-martensite. However, the soft sensor accuracy is hardly depending on the surface roughness (see [3]). For this reason, it is expected that the $\alpha$'-martensite can also be set with an increased accuracy due to the proposed actuator control presented in this paper.

## Acknowledgement

The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for their support of the depicted research within the priority program SPP 2183 "Property-controlled metal forming processes", through project no. 424335026 "Property control during spinning of metastable austenites".

## References

[1] L. Kersting, B. Arian, J. Rozo Vasquez, A. Trächtler, W. Homberg, F. Walther, Echtzeitfähige Modellierung eines innovativen Drückwalzprozesses für die eigenschaftsgeregelte Bauteilfertigung, at – Automatisierungstechnik 71:1 (2023) 68–81. https://doi.org/10.1515/auto-2022-0106

[2] B. Arian, W. Homberg, L. Kersting, A. Trächtler, J. Rozo Vasquez, F. Walther, Produktkennzeichnung durch lokal definierte Einstellung von ferromagnetischen Eigenschaften beim Drückwalzen von metastabilen Stahlwerkstoffen, in: G. Hirt (ed.), 36. Aachener Stahlkolloquium – Umformtechnik "Ideen Form geben", Aachen, 2022, pp. 333–347

[3] J. Rozo Vasquez; L. Kersting; B. Arian; W. Homberg; A. Trächtler; F. Walther: Soft sensor model of phase transformation during flow forming of metastable austenitic steel AISI 304L. Numerical Methods in Industrial Forming Processes: Numiform 2023, Springer LNME. in press.

[4] S. Rost, Entwurf, Analyse und Regelung einer kinematisch redundanten Roboterstruktur mit hydraulischen Antrieben variabler Nachgiebigkeit, Doctoral Dissertation, TU Braunschweig, 2016. https://doi.org/10.24355/dbbs.084-201606290936-0

[5] S. Knoop, Flachheitsbasierte Positionsregelungen für Parallelkinematiken am Beispiel eines hochdynamischen hydraulischen Hexapoden, Doctoral Dissertation, Paderborn University, Heinz Nixdorf Institut, Paderborn, 2016. https://doi.org/10.17619/UNIPB/1-99
at $f = 0.1$ mm/s and rises with increasing feed rate up to 3.768 µm (for $\Delta r = 2$ mm). Thus, the roughness $R_a$ in single roller flow forming is now almost on the same level as in three roller flow forming. There, $R_a$ is 0.47 µm in the case of $f = 0.1$ mm/s and $\Delta r = 2$ mm, for example. The similarity of the roughness in single roller flow forming and three roller flow forming is remarkable since the workpiece is more often overrolled with three rolls. Thus, a sincere added value concerning the workpiece quality in single roller flow forming is offered by the enhanced process parameter tracking with the new control.

## Conclusion

A novel closed-loop control for a hydraulic single roller flow forming machine was model-based developed and validated in this paper. Due to model-based procedure to design the control, it became possible to create a control that is able to accurately keep the desired position and velocity despite of the high forming forces due to flow forming. Thus, the developed control features the desired functionality to accurately control both the actuator position and velocity in the flow forming process. As shown during the validation, it is consequently possible to manufacture workpieces on the single roller flow forming machine with a better surface quality. The surface roughness of the manufactured parts is now even in a similar range to that of conventional machines with three rollers. Hence, the flow forming machine including the novel actuator control is now predestined to be prospectively used in the closed-loop property control. The closed-loop property control of the $\alpha$'-martensite fraction and wall thickness reduction has already been proposed by the authors in [1]. It includes a so-called soft sensor for the online determination of the $\alpha$'-martensite. However, the soft sensor accuracy is hardly depending on the surface roughness (see [3]). For this reason, it is expected that the $\alpha$'-martensite can also be set with an increased accuracy due to the proposed actuator control presented in this paper.

## Acknowledgement

The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for their support of the depicted research within the priority program SPP 2183 "Property-controlled metal forming processes", through project no. 424335026 "Property control during spinning of metastable austenites".

## References

[1] L. Kersting, B. Arian, J. Rozo Vasquez, A. Trächtler, W. Homberg, F. Walther, Echtzeitfähige Modellierung eines innovativen Drückwalzprozesses für die eigenschaftsgeregelte Bauteilfertigung, at – Automatisierungstechnik 71:1 (2023) 68–81. https://doi.org/10.1515/auto-2022-0106

[2] B. Arian, W. Homberg, L. Kersting, A. Trächtler, J. Rozo Vasquez, F. Walther, Produktkennzeichnung durch lokal definierte Einstellung von ferromagnetischen Eigenschaften beim Drückwalzen von metastabilen Stahlwerkstoffen, in: G. Hirt (ed.), 36. Aachener Stahlkolloquium – Umformtechnik "Ideen Form geben", Aachen, 2022, pp. 333–347

[3] J. Rozo Vasquez; L. Kersting; B. Arian; W. Homberg; A. Trächtler; F. Walther: Soft sensor model of phase transformation during flow forming of metastable austenitic steel AISI 304L. Numerical Methods in Industrial Forming Processes: Numiform 2023, Springer LNME. in press.

[4] S. Rost, Entwurf, Analyse und Regelung einer kinematisch redundanten Roboterstruktur mit hydraulischen Antrieben variabler Nachgiebigkeit, Doctoral Dissertation, TU Braunschweig, 2016. https://doi.org/10.24355/dbbs.084-201606290936-0

[5] S. Knoop, Flachheitsbasierte Positionsregelungen für Parallelkinematiken am Beispiel eines hochdynamischen hydraulischen Hexapoden, Doctoral Dissertation, Paderborn University, Heinz Nixdorf Institut, Paderborn, 2016. https://doi.org/10.17619/UNIPB/1-99
[6] D. Hornjak, Grundlegende Untersuchungen der Prozess- und Werkzeugparameter und ihre Wechselwirkungen für das thermo-mechanisch unterstützte inkrementelle Umformverfahren des Reib-Drückens, Doctoral Dissertation, Paderborn University, Shaker, Aachen, 2013.

[7] B. Lossen, Ein Beitrag zur Herstellung von hybriden Bauteilen mittels Reibdrücken, Doctoral Dissertation, Paderborn University, Shaker, Düren, 2019.

[8] L. Kersting, B. Arian, J. Rozo Vasquez, A. Trächtler, W. Homberg, F. Walther, Innovative online measurement and modelling approach for property-controlled flow forming processes. Key Engineering Materials 926 (2022) 862–874. https://doi.org/10.4028/p-yp2hj3

[8] J. Jelali, A. Kroll, Hydraulic Servo-systems – Modelling, identification and control, Springer, London, 2003, DOI 10.1007/978-1-4471-0099-7

[9] S. Helduser (Ed.), O+P-Fachlexikon "Fluidtechnik von A bis Z" (O+P technical glossary "Fluid technology from A to Z"), HAWE Hydraulik, Aschheim, read on https://www.hawe.com/fluid-lexicon/, the 08th February 2024.

[10] H. Nyquist, Regeneration theory, Bell System Technical Journal 11:1 (1932) 126-147. https://doi.org/10.1002/j.1538-7305.1932.tb02344.x

[11] B. Arian, W. Homberg, J. Rozo Vasquez, F. Walther, M. Riepold, A. Trächtler, Forming metastable austenitic stainless steel tubes with axially graded martensite content by flow-forming, ESAFORM 2021 24th International Conference on Material Forming Liège (2021). https://doi.org/10.25518/esaform21.2759
[6] D. Hornjak, Grundlegende Untersuchungen der Prozess- und Werkzeugparameter und ihre Wechselwirkungen für das thermo-mechanisch unterstützte inkrementelle Umformverfahren des Reib-Drückens, Doctoral Dissertation, Paderborn University, Shaker, Aachen, 2013.

[7] B. Lossen, Ein Beitrag zur Herstellung von hybriden Bauteilen mittels Reibdrücken, Doctoral Dissertation, Paderborn University, Shaker, Düren, 2019.

[8] L. Kersting, B. Arian, J. Rozo Vasquez, A. Trächtler, W. Homberg, F. Walther, Innovative online measurement and modelling approach for property-controlled flow forming processes. Key Engineering Materials 926 (2022) 862–874. https://doi.org/10.4028/p-yp2hj3

[8] J. Jelali, A. Kroll, Hydraulic Servo-systems – Modelling, identification and control, Springer, London, 2003, DOI 10.1007/978-1-4471-0099-7

[9] S. Helduser (Ed.), O+P-Fachlexikon "Fluidtechnik von A bis Z" (O+P technical glossary "Fluid technology from A to Z"), HAWE Hydraulik, Aschheim, read on https://www.hawe.com/fluid-lexicon/, the 08th February 2024.

[10] H. Nyquist, Regeneration theory, Bell System Technical Journal 11:1 (1932) 126-147. https://doi.org/10.1002/j.1538-7305.1932.tb02344.x

[11] B. Arian, W. Homberg, J. Rozo Vasquez, F. Walther, M. Riepold, A. Trächtler, Forming metastable austenitic stainless steel tubes with axially graded martensite content by flow-forming, ESAFORM 2021 24th International Conference on Material Forming Liège (2021). https://doi.org/10.25518/esaform21.2759
# Predicting fine blanking process signals from sheet metal thickness

MOON Jiyoung¹,*, GELBICH Daria¹,ᵇ, BECKER Marco¹,ᶜ, NIEMIETZ Philipp¹,ᵈ
and BERGS Thomas¹,²,ᵉ

¹Manufacturing Technology Institute MTI of RWTH Aachen University, Campus-Boulevard 30,
52074 Aachen, Germany

²Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen, Germany

ᵃj.moon@mti.rwth-aachen.de, ᵇd.gelbich@mti.rwth-aachen.de, ᶜm.becker@mti.rwth-aachen.de, ᵈp.niemietz@mti.rwth-aachen.de, ᵉt.bergs@mti.rwth-aachen.de

**Keywords:** Sheet Metal Forming, Process Monitoring, Process Signal Modeling, CGAN

**Abstract.** In sheet metal forming and blanking processes, the direct assessment of process conditions and product quality poses a challenge due to high production rates and the inaccessibility of the tool. In this context, the process signals generated by the manufacturing process, such as force and acoustic emissions, have the potential to serve as a valuable source of information, containing important insights into the quality of the final product as well as the complexity of the process itself. To date, it is not yet fully understood how these process signals depend on different influencing factors, such as process parameters. However, knowing how process signals, which reflect the process state, change with influencing factors is relevant to put observed signals into context and make informed decisions with respect to parameter adjustments. Conditional generative AI models, such as conditional generative adversarial networks (CGANs) offer a promising approach to the aforementioned issue by generating probable process signals based on specified conditions. In this study, thin metal sheets with three different thicknesses were provided into a fine blanking process, and corresponding punching force signals were measured. With these signals, a conditional-deep convolutional GAN (C-DCGAN), a model that combines the principles of both CGAN and deep convolutional GAN (DCGAN), is trained with sheet metal thickness specified as a condition. The trained generator is employed to predict process signals for different sheet thickness values. The presented model is evaluated with respect to thickness values that were known during training time as well as with thickness values that were not presented to the model during training.

**Introduction**

Sheet metal forming and blanking processes are widely used in the automotive and aerospace industries due to their high production rates and stable quality, making them suitable for high production rates. Fine blanking, specifically, stands out with its capability to create a high proportion of smooth cutting surface [1], enabling its use in production of safety-related products, such as automotive seat belt tongues. Given the applications of the products resulting from this process, it becomes significant to monitor the tool's condition and strive to extend the tool's lifespan. While direct assessment of this condition is difficult due to their high production rates and the inaccessibility of tools [2], it has been recognized that indirect assessments based on process signals show potential in tackling these challenges. In wear monitoring, Unterberg et al. [3] analyzed acoustic emission (AE) signals in an industrial-grade fine blanking process and revealed potential correlations with the surface roughness of scrap webs, as a proxy for tool wear. They suggested an approach for developing models that predict tool wear based on extracted features from AE signals. In another publication, Kubik et al. [4] presented a machine learning (ML)-based inline wear state quantification model using torque and force signals in the roll

<figure><img src="image_1387.png" /></figure>
# Predicting fine blanking process signals from sheet metal thickness

MOON Jiyoung¹,*, GELBICH Daria¹,ᵇ, BECKER Marco¹,ᶜ, NIEMIETZ Philipp¹,ᵈ
and BERGS Thomas¹,²,ᵉ

¹Manufacturing Technology Institute MTI of RWTH Aachen University, Campus-Boulevard 30,
52074 Aachen, Germany

²Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen, Germany

ᵃj.moon@mti.rwth-aachen.de, ᵇd.gelbich@mti.rwth-aachen.de, ᶜm.becker@mti.rwth-aachen.de, ᵈp.niemietz@mti.rwth-aachen.de, ᵉt.bergs@mti.rwth-aachen.de

**Keywords:** Sheet Metal Forming, Process Monitoring, Process Signal Modeling, CGAN

**Abstract.** In sheet metal forming and blanking processes, the direct assessment of process conditions and product quality poses a challenge due to high production rates and the inaccessibility of the tool. In this context, the process signals generated by the manufacturing process, such as force and acoustic emissions, have the potential to serve as a valuable source of information, containing important insights into the quality of the final product as well as the complexity of the process itself. To date, it is not yet fully understood how these process signals depend on different influencing factors, such as process parameters. However, knowing how process signals, which reflect the process state, change with influencing factors is relevant to put observed signals into context and make informed decisions with respect to parameter adjustments. Conditional generative AI models, such as conditional generative adversarial networks (CGANs) offer a promising approach to the aforementioned issue by generating probable process signals based on specified conditions. In this study, thin metal sheets with three different thicknesses were provided into a fine blanking process, and corresponding punching force signals were measured. With these signals, a conditional-deep convolutional GAN (C-DCGAN), a model that combines the principles of both CGAN and deep convolutional GAN (DCGAN), is trained with sheet metal thickness specified as a condition. The trained generator is employed to predict process signals for different sheet thickness values. The presented model is evaluated with respect to thickness values that were known during training time as well as with thickness values that were not presented to the model during training.

**Introduction**

Sheet metal forming and blanking processes are widely used in the automotive and aerospace industries due to their high production rates and stable quality, making them suitable for high production rates. Fine blanking, specifically, stands out with its capability to create a high proportion of smooth cutting surface [1], enabling its use in production of safety-related products, such as automotive seat belt tongues. Given the applications of the products resulting from this process, it becomes significant to monitor the tool's condition and strive to extend the tool's lifespan. While direct assessment of this condition is difficult due to their high production rates and the inaccessibility of tools [2], it has been recognized that indirect assessments based on process signals show potential in tackling these challenges. In wear monitoring, Unterberg et al. [3] analyzed acoustic emission (AE) signals in an industrial-grade fine blanking process and revealed potential correlations with the surface roughness of scrap webs, as a proxy for tool wear. They suggested an approach for developing models that predict tool wear based on extracted features from AE signals. In another publication, Kubik et al. [4] presented a machine learning (ML)-based inline wear state quantification model using torque and force signals in the roll

<figure><img src="image_1391.png" /></figure>
forming – fine blanking process chain. They classified the abrasive wear states of the punch into five stages, and based on this classification, they trained a ML model that is able to predict the wear states.

Despite recent research of indirect assessment of the process state through process signals, adjusting process parameters based on these signals still remains a challenge. Difficulties arise due to the lack of knowledge regarding how the changing values of process parameters impact the state of the process. Simulations are developed to tackle these problems, but simulation models often face a trade-off between high accuracy and computational complexity [5]. However, the fact that process signals reflect process states suggests an approach to overcome this problem associated with utilizing reference process signals. For example, by considering the shape of a process signal that mirrors the desired process state as a target, process parameters can be adjusted to align the current process signal with the target process signal while monitoring corresponding changes in the current process signal. However, in the absence of a thorough comprehension of the behavior of the process signal, it becomes challenging to make such informed adjustments to process parameters. To comprehend the complex dynamics of process signals, a thorough analysis must be attempted with signals generated with a wide variety of parameters [6]. Unfortunately, the current scenario in production lines is characterized by signals generated within restricted parameter ranges, primarily due to safety constraints or economic considerations, such as tool breakage. These limited and frequently imbalanced datasets hinder a thorough understanding of the process signal behavior, therefore results in the selection of right target parameters and the adjustment of their values becoming complex tasks. In order to overcome these limitations, exploiting synthetic process signals in yet unexplored or scarce parameter spaces becomes an essential step.

In recent study in manufacturing, generating synthetic data using deep learning models are actively investigated. Their ability to generate synthetic, but realistic data has already been demonstrated, for instance, in the context of predicting SEM images of a material's microstructure using a CGAN under previously unknown processing conditions [7]. Analogously, the work by Link et al. [8] conducted a comprehensive investigation into the metamodeling of deep drawing processes. Their study demonstrated the feasibility of employing CGANs in sheet metal forming for predicting sheet thickness of forming result from finite element simulations, achieving high precision with limited data and robustness against varying input parameters. The study by Molitor et al. [9] addressed the challenges of data efficiency in the context of utilizing deep learning models for tool wear classification in stamping process. Using various types of GANs, their work demonstrated the effectiveness of data augmentation techniques to improve classification accuracies of deep learning models even with low data availability. However, most of the existing research does not utilize conditional generative models for the synthesis of time series process signals, but rather focuses on image data. Those for time series have primarily emphasized the balancing of dataset through categorical conditions of the machine state [10] or the models are used to predict missing data by leveraging relationship within and between input data, rather than relying solely on modifying condition to obtain them [11].

In this paper, the C-DCGAN model is trained using sheet metal thickness as the conditioning parameter, employing stamping force signals obtained from a fine blanking machine. We demonstrate the effectiveness of the trained generator in learning the distinctions between force signals for specific sheet thicknesses and show its ability to generate synthetic force signals accurately under these conditions. These synthetic signals are then compared to real signals to assess the feasibility of employing an approach that utilizes synthetic process signals for signal-based parameter adjustments in the manufacturing process under specific parameter conditions. In this context, the following research questions are outlined:
forming – fine blanking process chain. They classified the abrasive wear states of the punch into five stages, and based on this classification, they trained a ML model that is able to predict the wear states.

Despite recent research of indirect assessment of the process state through process signals, adjusting process parameters based on these signals still remains a challenge. Difficulties arise due to the lack of knowledge regarding how the changing values of process parameters impact the state of the process. Simulations are developed to tackle these problems, but simulation models often face a trade-off between high accuracy and computational complexity [5]. However, the fact that process signals reflect process states suggests an approach to overcome this problem associated with utilizing reference process signals. For example, by considering the shape of a process signal that mirrors the desired process state as a target, process parameters can be adjusted to align the current process signal with the target process signal while monitoring corresponding changes in the current process signal. However, in the absence of a thorough comprehension of the behavior of the process signal, it becomes challenging to make such informed adjustments to process parameters. To comprehend the complex dynamics of process signals, a thorough analysis must be attempted with signals generated with a wide variety of parameters [6]. Unfortunately, the current scenario in production lines is characterized by signals generated within restricted parameter ranges, primarily due to safety constraints or economic considerations, such as tool breakage. These limited and frequently imbalanced datasets hinder a thorough understanding of the process signal behavior, therefore results in the selection of right target parameters and the adjustment of their values becoming complex tasks. In order to overcome these limitations, exploiting synthetic process signals in yet unexplored or scarce parameter spaces becomes an essential step.

In recent study in manufacturing, generating synthetic data using deep learning models are actively investigated. Their ability to generate synthetic, but realistic data has already been demonstrated, for instance, in the context of predicting SEM images of a material's microstructure using a CGAN under previously unknown processing conditions [7]. Analogously, the work by Link et al. [8] conducted a comprehensive investigation into the metamodeling of deep drawing processes. Their study demonstrated the feasibility of employing CGANs in sheet metal forming for predicting sheet thickness of forming result from finite element simulations, achieving high precision with limited data and robustness against varying input parameters. The study by Molitor et al. [9] addressed the challenges of data efficiency in the context of utilizing deep learning models for tool wear classification in stamping process. Using various types of GANs, their work demonstrated the effectiveness of data augmentation techniques to improve classification accuracies of deep learning models even with low data availability. However, most of the existing research does not utilize conditional generative models for the synthesis of time series process signals, but rather focuses on image data. Those for time series have primarily emphasized the balancing of dataset through categorical conditions of the machine state [10] or the models are used to predict missing data by leveraging relationship within and between input data, rather than relying solely on modifying condition to obtain them [11].

In this paper, the C-DCGAN model is trained using sheet metal thickness as the conditioning parameter, employing stamping force signals obtained from a fine blanking machine. We demonstrate the effectiveness of the trained generator in learning the distinctions between force signals for specific sheet thicknesses and show its ability to generate synthetic force signals accurately under these conditions. These synthetic signals are then compared to real signals to assess the feasibility of employing an approach that utilizes synthetic process signals for signal-based parameter adjustments in the manufacturing process under specific parameter conditions. In this context, the following research questions are outlined:
RQ1. How effectively can the generated process signals align with real process signals across different thickness classes?

RQ2. How effectively can the generated process signals align with conditions that were not presented to the model during training?

## Methods

In the experiment of this study, a 16MnCr5 (AISI 5115) thin metal sheet with three different thicknesses was provided to the Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University. The sheet underwent processing through the fine blanking process line at a stroke speed of 30 strokes per minute, as illustrated in Fig. 1.

<figure><img src="image_1388.png" /><figcaption>Fig. 1. Fine blanking process line</figcaption></figure>

The stamping force is measured via four in-tool piezoelectric force sensors integrated into the fine blanking machine. Each sensor captures signals at a sampling rate of 10 kHz, and the acquired signals are segmented based on the stroke. This yields a multivariate time series for each sensor, where each time series of 10,500 data points varies with the number of strokes. The start and end parts of each stroke are adjusted to attain zero force values, and these corrected force signals from the four sensors are averaged to create a unified multivariate time series. This led to in total of 287, 270 and 181 time series for each thickness class: 3.95 mm, 4.00 mm and 4.05 mm, respectively.

For a detailed analysis of force signal variations concerning sheet thickness, the shearing and stripping stages are isolated from the overall time series. This isolation yields 2,000 data points of the shearing stage and 1,201 data points of the stripping stage. The time series for these isolated stages are then aligned along the time-axis with specified reference points, which are identified as the maximum peaks for shearing and minimum peaks for stripping within each stage's time series.

To reduce the amount of data points per time series for model training, each stage is further divided into two segments for shearing and three segments for stripping, respectively. On one hand, these segments are scaled, resulting in each data point across the time series being scaled to have a mean of 0 and a unit variance. Each scalar model is saved before training phase (Fig. 2 (a)) and utilized for the rescaling of the generated data in the after training phase (Fig. 2 (c)). In the training phase (Fig. 2 (b)), the total of 738 scaled segments are employed as the training data for the model. For balanced training across each class, the training data is complemented by randomly sampling additional training data from each class, which leads to 288 time series for each class. On the other hand, average time series from the non-scaled segments are computed for each thickness class. These average time series serve as the ground truth for selecting trained models based on time series plots, as depicted by $x_{ground\_truth}$ in Fig. 2 (c).
RQ1. How effectively can the generated process signals align with real process signals across different thickness classes?

RQ2. How effectively can the generated process signals align with conditions that were not presented to the model during training?

## Methods

In the experiment of this study, a 16MnCr5 (AISI 5115) thin metal sheet with three different thicknesses was provided to the Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University. The sheet underwent processing through the fine blanking process line at a stroke speed of 30 strokes per minute, as illustrated in Fig. 1.

<figure><img src="image_1392.png" /><figcaption>Fig. 1. Fine blanking process line</figcaption></figure>

The stamping force is measured via four in-tool piezoelectric force sensors integrated into the fine blanking machine. Each sensor captures signals at a sampling rate of 10 kHz, and the acquired signals are segmented based on the stroke. This yields a multivariate time series for each sensor, where each time series of 10,500 data points varies with the number of strokes. The start and end parts of each stroke are adjusted to attain zero force values, and these corrected force signals from the four sensors are averaged to create a unified multivariate time series. This led to in total of 287, 270 and 181 time series for each thickness class: 3.95 mm, 4.00 mm and 4.05 mm, respectively.

For a detailed analysis of force signal variations concerning sheet thickness, the shearing and stripping stages are isolated from the overall time series. This isolation yields 2,000 data points of the shearing stage and 1,201 data points of the stripping stage. The time series for these isolated stages are then aligned along the time-axis with specified reference points, which are identified as the maximum peaks for shearing and minimum peaks for stripping within each stage's time series.

To reduce the amount of data points per time series for model training, each stage is further divided into two segments for shearing and three segments for stripping, respectively. On one hand, these segments are scaled, resulting in each data point across the time series being scaled to have a mean of 0 and a unit variance. Each scalar model is saved before training phase (Fig. 2 (a)) and utilized for the rescaling of the generated data in the after training phase (Fig. 2 (c)). In the training phase (Fig. 2 (b)), the total of 738 scaled segments are employed as the training data for the model. For balanced training across each class, the training data is complemented by randomly sampling additional training data from each class, which leads to 288 time series for each class. On the other hand, average time series from the non-scaled segments are computed for each thickness class. These average time series serve as the ground truth for selecting trained models based on time series plots, as depicted by $x_{ground\_truth}$ in Fig. 2 (c).
<figure><img src="image_1389.png" /><figcaption>Fig. 2. Training and evaluation of the model</figcaption></figure>

The model used in this paper follows the C-DCGAN architecture, which is the combination of CGAN [12] and DCGAN [13]. The generator network operates by taking input from noise z, which is composed of random numbers from the standard normal distribution. Additionally, the generator receives the label y of the real data x as the 2nd input. Both the generator and the discriminator receive this label as the auxiliary information. Under this condition y, the generator network G strives to produce realistic data G(z|y), whereas the discriminator tries to distinguish between the real data x and the synthetic data G(z|y). The model's objective function can be described as a two-player minmax game:

$$ \min_G \max_D V(D, G) = \mathbb{E}_{x \sim p_{\text{data}}(x)}[\log D(x|y)] + \mathbb{E}_{z \sim p_z(z)}[\log(1 - D(G(z|y)))] \quad (1) $$

where the terms $\mathbb{E}_{x \sim p_{\text{data}}(x)}[\log D(x|y)]$ denotes the expected value of the log-likelihood of the discriminator D on the conditioned real data x|y and $\mathbb{E}_{z \sim p_z(z)}[\log(1 - D(G(z|y)))]$ represents the expected value of the negative log-likelihood of the discriminator D on the generated data G(z|y) [12]. In this experiment, the label y corresponds to the sheet metal thickness as a conditioning factor. These labels are encoded as 0, 1, and 2 for each thickness class.

For the training of the model, an NVIDIA Tesla V100 GPU is used. After training, the best models were selected with different learning rates and number of epochs for each segment because of the different length of the data points and the data distributions across the time series segments. Furthermore, recognition of the model's convergence through generator losses became less straightforward due to the adversarial relationship between the generator and the discriminator network, i.e., low generator losses do not necessarily mean that the generator can produce realistic data [14]. Because of these issues, training results are acquired by visually inspecting data plots, that were generated at intervals of 250 epochs, comparing generated data with the ground truth of the corresponding thickness class. Based on the adequacy of the visual inspection result from these checkpoints, the models are selected that correspond to the respective number of epochs. This resulted in five distinct generator models per research question, each trained on a different time series segment accordingly.

## Results and Discussion

To address the research questions, individual training strategies are developed. For the first question (RQ1), the model is trained across all three thickness classes to investigate the fitness of
<figure><img src="image_1393.png" /><figcaption>Fig. 2. Training and evaluation of the model</figcaption></figure>

The model used in this paper follows the C-DCGAN architecture, which is the combination of CGAN [12] and DCGAN [13]. The generator network operates by taking input from noise z, which is composed of random numbers from the standard normal distribution. Additionally, the generator receives the label y of the real data x as the 2nd input. Both the generator and the discriminator receive this label as the auxiliary information. Under this condition y, the generator network G strives to produce realistic data G(z|y), whereas the discriminator tries to distinguish between the real data x and the synthetic data G(z|y). The model's objective function can be described as a two-player minmax game:

$$ \min_G \max_D V(D, G) = \mathbb{E}_{x \sim p_{\text{data}}(x)}[\log D(x|y)] + \mathbb{E}_{z \sim p_z(z)}[\log(1 - D(G(z|y)))] \quad (1) $$

where the terms $\mathbb{E}_{x \sim p_{\text{data}}(x)}[\log D(x|y)]$ denotes the expected value of the log-likelihood of the discriminator D on the conditioned real data x|y and $\mathbb{E}_{z \sim p_z(z)}[\log(1 - D(G(z|y)))]$ represents the expected value of the negative log-likelihood of the discriminator D on the generated data G(z|y) [12]. In this experiment, the label y corresponds to the sheet metal thickness as a conditioning factor. These labels are encoded as 0, 1, and 2 for each thickness class.

For the training of the model, an NVIDIA Tesla V100 GPU is used. After training, the best models were selected with different learning rates and number of epochs for each segment because of the different length of the data points and the data distributions across the time series segments. Furthermore, recognition of the model's convergence through generator losses became less straightforward due to the adversarial relationship between the generator and the discriminator network, i.e., low generator losses do not necessarily mean that the generator can produce realistic data [14]. Because of these issues, training results are acquired by visually inspecting data plots, that were generated at intervals of 250 epochs, comparing generated data with the ground truth of the corresponding thickness class. Based on the adequacy of the visual inspection result from these checkpoints, the models are selected that correspond to the respective number of epochs. This resulted in five distinct generator models per research question, each trained on a different time series segment accordingly.

## Results and Discussion

To address the research questions, individual training strategies are developed. For the first question (RQ1), the model is trained across all three thickness classes to investigate the fitness of
the presented model by generating synthetic process signals, solely manipulating the thickness as the given condition. In the evaluation phase, the generated data from the trained generator is compared to real data within each thickness class. For each thickness class, an equivalent amount of time series is generated by the trained generator to match the number of real time series.

Fig. 3 and Fig. 4 depict time series plots for the real and generated force signals for each stage across different thickness classes. In general, the trained generators could imitate the original time series well, with the exception of the last 100 data points in the shearing stage and the data points between 950th and 1000th positions in the stripping stage, constituting part of the 2nd stripping segment. The training for the 2nd stripping segment was particularly challenging due to its small yet frequent fluctuations of the data points, in comparison to other segments' data distributions.

<figure><img src="image_1390.png" /><figcaption>Fig. 3. Real and generated force signals (shearing stage) – RQ1</figcaption></figure>
the presented model by generating synthetic process signals, solely manipulating the thickness as the given condition. In the evaluation phase, the generated data from the trained generator is compared to real data within each thickness class. For each thickness class, an equivalent amount of time series is generated by the trained generator to match the number of real time series.

Fig. 3 and Fig. 4 depict time series plots for the real and generated force signals for each stage across different thickness classes. In general, the trained generators could imitate the original time series well, with the exception of the last 100 data points in the shearing stage and the data points between 950th and 1000th positions in the stripping stage, constituting part of the 2nd stripping segment. The training for the 2nd stripping segment was particularly challenging due to its small yet frequent fluctuations of the data points, in comparison to other segments' data distributions.

<figure><img src="image_1394.png" /><figcaption>Fig. 3. Real and generated force signals (shearing stage) – RQ1</figcaption></figure>
<figure><img src="image_1391.png" /><figcaption>Fig. 4. Real and generated force signals (stripping stage) – RQ1</figcaption></figure>

This could be observed in Fig. 5 (e) as well, which is the violin plot of the 2nd stripping segment. In the following Fig. 5, each region corresponds to a Gaussian kernel density estimate (KDE), depicting the density of respective values. The horizontal dashed line within each violin indicates the median, while the dotted lines indicate the first and third quartiles. The shapes of KDE for generated signals look similar to those of real signals. Although there are some deviations in the medians for 4.00 mm and 4.05 mm, the scale of the 2nd stripping segment is still smaller than that of shearing segments. This is because the real time series of the shearing stage cover a much broader range of force values compared to that of the stripping stage.

For numerical comparison, the first Wasserstein distances are calculated between real and generated time series across different thickness classes to measure the similarity of two time series. Given i.i.d. samples X₁, ..., Xₙ~P and Y₁, ..., Yₘ~Q, the first Wasserstein distance between two probability distributions P and Q is defined as the minimum cost of transforming one distribution into the other, i.e.:

$$W_1(P, Q) = \inf_{\pi \in \Gamma(P,Q)} \int_{\mathbb{R} \times \mathbb{R}} |X - Y| d\pi \quad (2)$$
<figure><img src="image_1395.png" /><figcaption>Fig. 4. Real and generated force signals (stripping stage) – RQ1</figcaption></figure>

This could be observed in Fig. 5 (e) as well, which is the violin plot of the 2nd stripping segment. In the following Fig. 5, each region corresponds to a Gaussian kernel density estimate (KDE), depicting the density of respective values. The horizontal dashed line within each violin indicates the median, while the dotted lines indicate the first and third quartiles. The shapes of KDE for generated signals look similar to those of real signals. Although there are some deviations in the medians for 4.00 mm and 4.05 mm, the scale of the 2nd stripping segment is still smaller than that of shearing segments. This is because the real time series of the shearing stage cover a much broader range of force values compared to that of the stripping stage.

For numerical comparison, the first Wasserstein distances are calculated between real and generated time series across different thickness classes to measure the similarity of two time series. Given i.i.d. samples X₁, ..., Xₙ ~ P and Y₁, ..., Yₘ ~ Q, the first Wasserstein distance between two probability distributions P and Q is defined as the minimum cost of transforming one distribution into the other, i.e.:

$$W_1(P, Q) = \inf_{\pi \in \Gamma(P,Q)} \int_{\mathbb{R} \times \mathbb{R}} |X - Y| d\pi \quad (2)$$
where $\Gamma(P, Q)$ is the set of all joint probability measures on $\mathbb{R} \times \mathbb{R}$ [15].

<figure><img src="image_1392.png" /><figcaption>Fig. 5. Violin plot for Gaussian KDE of real and generated force signals – RQ1</figcaption></figure>

<figure><img src="image_1393.png" /><figcaption>Fig. 6. Heatmap of Wasserstein distance between real and generated force signals – RQ1</figcaption></figure>

The heatmaps with Wasserstein distance in Fig. 6 visualize the calculated results, rounded up to two decimal places. Lower value indicates high similarity between real and generated time series. When examining the heatmap in Fig. 6 derived from the generated data side, it becomes apparent that the darkest color within the values corresponding to each thickness class aligns with the thickness classes of the actual real data, except for the 2nd stripping segment. However, considering that there is a significant scale difference between the shearing stage (Fig. 6 (a), (b)
where $\Gamma(P, Q)$ is the set of all joint probability measures on $\mathbb{R} \times \mathbb{R}$ [15].

<figure><img src="image_1396.png" /><figcaption>Fig. 5. Violin plot for Gaussian KDE of real and generated force signals – RQ1</figcaption></figure>

<figure><img src="image_1397.png" /><figcaption>Fig. 6. Heatmap of Wasserstein distance between real and generated force signals – RQ1</figcaption></figure>

The heatmaps with Wasserstein distance in Fig. 6 visualize the calculated results, rounded up to two decimal places. Lower value indicates high similarity between real and generated time series. When examining the heatmap in Fig. 6 derived from the generated data side, it becomes apparent that the darkest color within the values corresponding to each thickness class aligns with the thickness classes of the actual real data, except for the 2nd stripping segment. However, considering that there is a significant scale difference between the shearing stage (Fig. 6 (a), (b)
and (c)) and the stripping stage (Fig. 6 (d) and (e)), the dissimilarity in thickness between 4 mm and 4.05 mm for the 2^nd^ stripping segment is not deemed critical. Nevertheless, despite of that the last 100 data points generated by targeting a thickness of 4.05 mm in the third shearing segment appeared closer to thickness 4.00 mm (refer to Fig. 4), the Fig. 6 (c) reveals that the Wasserstein distance still indicates a greater proximity of the data generated with a target of 4.05 mm rather than 4.00 mm. This implies that, despite the last 100 data points aligning more closely with thickness 4.00 mm, when considering the entire dataset comprising approximately 2000 points, this favorable alignment consists only a small fraction.

For RQ2, training is exclusively conducted on two thickness classes, namely 3.95 mm and 4.00 mm, to explore the capability of the trained generator in producing synthetic process signals for thickness classes that were not included in the training set. The generator, trained under this specific setting, is employed to generate data conditioned on all thickness classes, including 4.05 mm. Subsequently, the generated data is compared to real data in this previously unseen condition. Owing to the difficulties in visually comparing using time series and violin plots that illustrate differences between the results of two research questions, only the numerical comparison using the Wasserstein distances is presented for RQ2 as Fig. 7.

<figure><img src="image_1394.png" /><figcaption>Fig. 7. Heatmap of Wasserstein distance between real and generated force signals – RQ2</figcaption></figure>

As illustrated in Fig. 7 (b), (c) and (d), the generators trained under limited conditions can predict the time series for 4.05 mm with some degree of error, yet the predictions are still closer to the target time series compared to those for 3.95 mm and 4.00 mm. This also further validates the extrapolation ability of conditional GANs, as demonstrated by Fu et al. [16]. Although the model failed to predict accurate time series for the 1^st^ shearing segment and the 2^nd^ stripping segment (Fig. 7 (a) and (e)), an interesting point is that these generators exhibit even better prediction results than when trained with all thickness classes (compared to Fig. 6 (b), (c) and (d)). This might be due to the typical problems of deep learning model such as overfitting or catastrophic forgetting, implying that the model performance can be improved through fine-tuning of the hyperparameters.
and (c)) and the stripping stage (Fig. 6 (d) and (e)), the dissimilarity in thickness between 4 mm and 4.05 mm for the 2^nd^ stripping segment is not deemed critical. Nevertheless, despite of that the last 100 data points generated by targeting a thickness of 4.05 mm in the third shearing segment appeared closer to thickness 4.00 mm (refer to Fig. 4), the Fig. 6 (c) reveals that the Wasserstein distance still indicates a greater proximity of the data generated with a target of 4.05 mm rather than 4.00 mm. This implies that, despite the last 100 data points aligning more closely with thickness 4.00 mm, when considering the entire dataset comprising approximately 2000 points, this favorable alignment consists only a small fraction.

For RQ2, training is exclusively conducted on two thickness classes, namely 3.95 mm and 4.00 mm, to explore the capability of the trained generator in producing synthetic process signals for thickness classes that were not included in the training set. The generator, trained under this specific setting, is employed to generate data conditioned on all thickness classes, including 4.05 mm. Subsequently, the generated data is compared to real data in this previously unseen condition. Owing to the difficulties in visually comparing using time series and violin plots that illustrate differences between the results of two research questions, only the numerical comparison using the Wasserstein distances is presented for RQ2 as Fig. 7.

<figure><img src="image_1398.png" /><figcaption>Fig. 7. Heatmap of Wasserstein distance between real and generated force signals – RQ2</figcaption></figure>

As illustrated in Fig. 7 (b), (c) and (d), the generators trained under limited conditions can predict the time series for 4.05 mm with some degree of error, yet the predictions are still closer to the target time series compared to those for 3.95 mm and 4.00 mm. This also further validates the extrapolation ability of conditional GANs, as demonstrated by Fu et al. [16]. Although the model failed to predict accurate time series for the 1^st^ shearing segment and the 2^nd^ stripping segment (Fig. 7 (a) and (e)), an interesting point is that these generators exhibit even better prediction results than when trained with all thickness classes (compared to Fig. 6 (b), (c) and (d)). This might be due to the typical problems of deep learning model such as overfitting or catastrophic forgetting, implying that the model performance can be improved through fine-tuning of the hyperparameters.
**Summary**

This study explores the application of C-DCGAN in generating synthetic process signals for sheet metal forming processes, particularly in fine blanking. In the context of process parameter adjustments, synthetic process signals have the potential to serve as the baselines for understanding complex dynamics of the process signals with given parameter conditions. This research addresses two main questions: examining the effectiveness of generated process signals across different sheet thickness classes (RQ1) and assessing the model's ability to predict signals for conditions not presented during training (RQ2). For RQ1, the trained generators demonstrated the capability to approximate the original time series for three different thickness classes: 3.05 mm, 4.00 mm and 4.05 mm. This suggests that the selected conditional generative model can predict process signal by employing the given influencing parameter as the condition. For RQ2, training under limited conditions on two thickness classes allowed the generator to predict time series for previously unseen condition. This extrapolation capability of conditional generative models can be further utilized to generate synthetic process signals by exploring as-yet-unknown process parameter spaces.

This paper serves as a feasibility study to determine the potential for generating synthetic yet realistic process signals under specified conditions. The generated synthetic process signals can be utilized as the baselines for further analogy experiments related to understanding process signal behavior. While environmental factors or system parameters (e.g., sheet thickness) are beyond the scope of in-line control, leveraging the synthetic process signals can be extended to signal-based adjustments of in-line controllable process parameters. Hence, evaluating the model conditioned on in-line controllable process parameters has to be considered as main focus of future work. A more efficient model selection metric could also be considered to reduce the manual labor in selecting the best models. In addition, to further assess the validity of the synthetic process signals, additional statistical tests measuring (dis)similarity of two probability distributions could be considered, such as the Kolmogorov-Smirnov test [17].

**Acknowledgements**

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

**References**

[1] F. Klocke, Fertigungsverfahren, Springer, Berlin, 2017.

[2] C. Kubik, D.A. Molitor, M. Rojahn, P. Groche, Towards a real-time tool state detection in sheet metal forming processes validated by wear classification during blanking, IOP Conf. Ser.: Mater. Sci. Eng. 1238 (2022) 12067. https://doi.org/10.1088/1757-899X/1238/1/012067

[3] M. Unterberg, M. Becker, P. Niemietz, T. Bergs, Data-driven indirect punch wear monitoring in sheet-metal stamping processes, Journal of Intelligent Manufacturing (2023). https://doi.org/10.1007/s10845-023-02129-w

[4] C. Kubik, M. Becker, D.-A. Molitor, P. Groche, Towards a systematical approach for wear detection in sheet metal forming using machine learning, Prod. Eng. Res. Devel. 17 (2023) 21–36. https://doi.org/10.1007/s11740-022-01150-x

[5] R. Alizadeh, J.K. Allen, F. Mistree, Managing computational complexity using surrogate models: a critical review, Res Eng Design 31 (2020) 275–298. https://doi.org/10.1007/s00163-020-00336-7

[6] T. Wuest, C. Irgens, K.-D. Thoben, An approach to monitoring quality in manufacturing using supervised machine learning on product state data, Journal of Intelligent Manufacturing 25 (2014) 1167–1180. https://doi.org/10.1007/s10845-013-0761-y
## Summary

This study explores the application of C-DCGAN in generating synthetic process signals for sheet metal forming processes, particularly in fine blanking. In the context of process parameter adjustments, synthetic process signals have the potential to serve as the baselines for understanding complex dynamics of the process signals with given parameter conditions. This research addresses two main questions: examining the effectiveness of generated process signals across different sheet thickness classes (RQ1) and assessing the model's ability to predict signals for conditions not presented during training (RQ2). For RQ1, the trained generators demonstrated the capability to approximate the original time series for three different thickness classes: 3.05 mm, 4.00 mm and 4.05 mm. This suggests that the selected conditional generative model can predict process signal by employing the given influencing parameter as the condition. For RQ2, training under limited conditions on two thickness classes allowed the generator to predict time series for previously unseen condition. This extrapolation capability of conditional generative models can be further utilized to generate synthetic process signals by exploring as-yet-unknown process parameter spaces.

This paper serves as a feasibility study to determine the potential for generating synthetic yet realistic process signals under specified conditions. The generated synthetic process signals can be utilized as the baselines for further analogy experiments related to understanding process signal behavior. While environmental factors or system parameters (e.g., sheet thickness) are beyond the scope of in-line control, leveraging the synthetic process signals can be extended to signal-based adjustments of in-line controllable process parameters. Hence, evaluating the model conditioned on in-line controllable process parameters has to be considered as main focus of future work. A more efficient model selection metric could also be considered to reduce the manual labor in selecting the best models. In addition, to further assess the validity of the synthetic process signals, additional statistical tests measuring (dis)similarity of two probability distributions could be considered, such as the Kolmogorov-Smirnov test [17].

## Acknowledgements

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

## References

[1] F. Klocke, Fertigungsverfahren, Springer, Berlin, 2017.

[2] C. Kubik, D.A. Molitor, M. Rojahn, P. Groche, Towards a real-time tool state detection in sheet metal forming processes validated by wear classification during blanking, IOP Conf. Ser.: Mater. Sci. Eng. 1238 (2022) 12067. https://doi.org/10.1088/1757-899X/1238/1/012067

[3] M. Unterberg, M. Becker, P. Niemietz, T. Bergs, Data-driven indirect punch wear monitoring in sheet-metal stamping processes, Journal of Intelligent Manufacturing (2023). https://doi.org/10.1007/s10845-023-02129-w

[4] C. Kubik, M. Becker, D.-A. Molitor, P. Groche, Towards a systematical approach for wear detection in sheet metal forming using machine learning, Prod. Eng. Res. Devel. 17 (2023) 21–36. https://doi.org/10.1007/s11740-022-01150-x

[5] R. Alizadeh, J.K. Allen, F. Mistree, Managing computational complexity using surrogate models: a critical review, Res Eng Design 31 (2020) 275–298. https://doi.org/10.1007/s00163-020-00336-7

[6] T. Wuest, C. Irgens, K.-D. Thoben, An approach to monitoring quality in manufacturing using supervised machine learning on product state data, Journal of Intelligent Manufacturing 25 (2014) 1167–1180. https://doi.org/10.1007/s10845-013-0761-y