prevent adhesive-related problems such as galling [5]. In the case of hot working tool steels, in contact with oxygen, metal surfaces can form oxide layers. When working in air at temperatures higher than 400 °C, the wear of the steels is typical oxidation wear [6]. In certain cases, these oxides can also serve as a protective barrier, preventing the steels from undergoing further oxidation. In addition, oxide layers can reduce metal-to-metal contact during the sliding motion of metal components, thus protecting them from wear [7].

The tribological behavior of the oxide layer resulting from the oxidation of hot work steels depends on many variables. A fundamental aspect is the type of oxide that makes up the tribo-layer. In the case of low carbon steels treated in air at high temperature, Zambrano et. al. [8] distinguished up to three types of iron oxide, namely Hematite, Magnetite and Wüstite. At room temperature, Hematite exhibits a hardness of approximately 1000 HV, leading to abrasive wear, while Magnetite, with a hardness of 500 HV in similar conditions, demonstrates a comparatively lower resistance. In contrast, Wüstite is renowned for its diminished hardness of 300 HV and stands out for possessing the highest lubricity among these oxides. As the temperature is increased to 900°C, some authors have reported hardness values for FeO, Fe₃O₄, and Fe₂O₃ of 105, 366, and 516 HV, respectively [9]. In the case of Magnetite and Wüsite, these are the iron oxides that exhibit the highest ductility and resistance to wear at high temperature [10]. Typical morphology ratio reported at temperatures up to 1200°C is 95:4:1 (FeO:Fe₃O₄:Fe₂O₃) [11]. In addition, the thickness of the layer has been identified as a factor that severely affects the coefficient of friction, along with the temperature of the sample. A thick oxide scale produces a lower coefficient of friction, providing a certain degree of lubricity [12].

The presence of alloying elements in the steel also affects the oxide formation. Elements such as chromium, silicon or aluminum can enrich those oxide layers generated at the scale/substrate interface, leading to different mechanical properties and contact behavior. In addition, elements such as Ni or Cu, could increase the adherence of the oxides to the substrate, which increases the friction coefficient as oxides are not separating from the metallic interface, resulting in oxide-oxide contact [13].

In the case of hot rolling processes, several studies have focused on evaluating the effect of the oxide tribo-layer on the process. Pellizzari et al. [14] analysed the behaviour of high-speed steels and high chromium iron with regard to friction and wear at high temperature during hot rolling. Abrasion was identified as being caused by the oxide scale that develops on the hot carbon steel counterpart. Tieu et al. [15] determined that the rolling force and friction of pre-oxidised rolls are superior to those of virgin surface rolls for all thickness reductions and temperatures considered in their study. Utsunomiya et al. [16] identified that the relative sliding of the scale is the mechanism responsible for its apparent lubricating effect, and that the amount of the relative sliding increased with an increase in scale thickness. Nevertheless, one of the main challenges in examining the tribological behavior of a specific process is the lack of experimental procedure that effectively reproduces the forming process.

In this study, the tribological behavior of the oxide layer present on the mandrel used in rotary piercing tube manufacturing operations has been analyzed. A hot upsetting sliding test campaign has been carried out, which is able to reproduce industrial process contact conditions, including deformation during sliding contact. The contact of hot working tool steel with and without oxidation treatment has been evaluated and the type of contact and friction between tool-material assessed.

## Materials and methods

The materials considered in this study are a high-strength low-alloy (HSLA) steel grade for the tube and a hot working tool steel for the plug. Both the tube and tool materials were provided by an industrial partner, and its chemical composition was evaluated in the laboratory. The chemical composition is listed in Table 1.
<table><caption>Table 1. Chemical composition (wt%) of tube and plug materials.</caption><thead><tr><th></th><th>C</th><th>Si</th><th>Mn</th><th>Cr</th><th>Ni</th><th>Mo</th><th>Cu</th><th>Al</th><th>Sn</th><th>Ti</th><th>V</th><th>N</th><th>Fe</th></tr></thead><tbody><tr><td>Tube</td><td>0.236</td><td>0.24</td><td>1.03</td><td>0.16</td><td>0.09</td><td>0.06</td><td>0.26</td><td>0.003</td><td>0.01</td><td>0.043</td><td>0.043</td><td>0.01</td><td>rest</td></tr><tr><td>Plug</td><td>0.27</td><td>0.35</td><td>0.32</td><td>0.83</td><td>2.31</td><td>0.56</td><td>0.1</td><td>0.014</td><td>0.006</td><td>0.001</td><td>0.25</td><td>-</td><td>rest</td></tr></tbody></table>

The contactor (plug) and the specimen (tube) samples were machined directly from the interior of a plug and an as-cast billet, respectively. In order to prepare the contactor material in a comparable method to that used at industrial level, a one-hour oxidation treatment was carried out in a furnace at 700°C with ambient air, which contained 21% oxygen, 78% nitrogen, with small amounts of carbon dioxide and other gases. In addition, some contactors without oxidation treatment were preserved. Regarding the specimen, it had no oxidation treatment. The microstructure and oxide layer after the heat treatment were assessed using optical microscopy. In Fig. 1a, it can be observed how the average oxide layer thickness resulted in approximately 11 µm. In Fig. 1b, the detail of the microstructure is shown. Some presence of martensite and bainite was observed, being mainly composed of acicular ferrite, with a hardness of 25 HRC.

<figure><img src="image_1204.png" /><figcaption>Fig. 1. (a) Oxide layer in the contactor after the heat treatment and (b) material structure in the contactor.</figcaption></figure>

The surface of the contactor was also assessed before performing the tribological tests. The roughness of the surface was Sa = 3.1 µm and, to characterize the composition of the tribo-layer, XRD tests were performed. Results revealed three different types of Iron-oxide, namely, Hematite, Magnetite and Wüstite. In addition, the presence of pure Iron and Chromium-Iron was identified. Regarding the specimen, heating tests were developed following the heating ramp used in the tests to assess the thickness of the oxide layer developed during the heating of this element into air. The mean thickness of the oxide layer was 500 µm.

The tribological testing campaign was carried out with the WHUST tribometer, by means of upsetting-sliding tests. During the test, the contactor (plug) penetrates the specimen (tube) and moves along the specimen surface while keeping the values of penetration and sliding velocity constant [17]. The geometries of the contact surfaces for the specimen and contactor were cylindrical with a radius of 15 mm and 10 mm, respectively. The physical tribometer and the schematic illustration of the test are shown in Fig. 2.
<table><caption>Table 1. Chemical composition (wt%) of tube and plug materials.</caption><thead><tr><th></th><th>C</th><th>Si</th><th>Mn</th><th>Cr</th><th>Ni</th><th>Mo</th><th>Cu</th><th>Al</th><th>Sn</th><th>Ti</th><th>V</th><th>N</th><th>Fe</th></tr></thead><tbody><tr><td>Tube</td><td>0.236</td><td>0.24</td><td>1.03</td><td>0.16</td><td>0.09</td><td>0.06</td><td>0.26</td><td>0.003</td><td>0.01</td><td>0.043</td><td>0.043</td><td>0.01</td><td>rest</td></tr><tr><td>Plug</td><td>0.27</td><td>0.35</td><td>0.32</td><td>0.83</td><td>2.31</td><td>0.56</td><td>0.1</td><td>0.014</td><td>0.006</td><td>0.001</td><td>0.25</td><td>-</td><td>rest</td></tr></tbody></table>

The contactor (plug) and the specimen (tube) samples were machined directly from the interior of a plug and an as-cast billet, respectively. In order to prepare the contactor material in a comparable method to that used at industrial level, a one-hour oxidation treatment was carried out in a furnace at 700°C with ambient air, which contained 21% oxygen, 78% nitrogen, with small amounts of carbon dioxide and other gases. In addition, some contactors without oxidation treatment were preserved. Regarding the specimen, it had no oxidation treatment. The microstructure and oxide layer after the heat treatment were assessed using optical microscopy. In Fig. 1a, it can be observed how the average oxide layer thickness resulted in approximately 11 µm. In Fig. 1b, the detail of the microstructure is shown. Some presence of martensite and bainite was observed, being mainly composed of acicular ferrite, with a hardness of 25 HRC.

<figure><img src="image_1206.png" /><figcaption>Fig. 1. (a) Oxide layer in the contactor after the heat treatment and (b) material structure in the contactor.</figcaption></figure>

The surface of the contactor was also assessed before performing the tribological tests. The roughness of the surface was Sa = 3.1 µm and, to characterize the composition of the tribo-layer, XRD tests were performed. Results revealed three different types of Iron-oxide, namely, Hematite, Magnetite and Wüstite. In addition, the presence of pure Iron and Chromium-Iron was identified. Regarding the specimen, heating tests were developed following the heating ramp used in the tests to assess the thickness of the oxide layer developed during the heating of this element into air. The mean thickness of the oxide layer was 500 µm.

The tribological testing campaign was carried out with the WHUST tribometer, by means of upsetting-sliding tests. During the test, the contactor (plug) penetrates the specimen (tube) and moves along the specimen surface while keeping the values of penetration and sliding velocity constant [17]. The geometries of the contact surfaces for the specimen and contactor were cylindrical with a radius of 15 mm and 10 mm, respectively. The physical tribometer and the schematic illustration of the test are shown in Fig. 2.
<figure><img src="image_1205.png" /><figcaption>Fig. 2 WHUST (a) tribometer set-up and (b) schematic illustration of the test.</figcaption></figure>

In order to set the test conditions, temperature measures were carried out in an industrial piercing mill on the surface of the plug both, before and after piercing operation, yielding a maximum temperature of 450-500°C. However, it is difficult to estimate this value experimentally since, depending on the size of the tube to be perforated, the heating can be higher or lower and, furthermore, when the plug is positioned between the rolls in the piercing mill is exposed to cooling fluid that reduces its initial temperature. Therefore, in order to estimate the surface heating of the mandrel during piercing, and to define the normal stress distribution at the contact, first, a FE simulation of the tube piercing process was carried out using Forge NtT software. From the results of the simulation, it was stated that in the contact temperature ranged from 275 to 475 °C, the normal stress values were between 100 and 180 MPa. There was a high fluctuation in the sliding velocity, which showed minimum values of 150 mm/s at the tip of the plug and maximum values of 700 mm/s in the region with highest diameter (highest area reduction). In order to reproduce these conditions in the tribology tests, first the setup was simulated and different penetrations were tested. Finally, two penetrations (0.2 mm and 0.4mm) and two sliding velocities (200 mm/s and 450 mm/s) were defined, and three tests were performed for each condition.

The initial temperatures of the contactor and specimen were set to 250°C and 1250°C and, to reach them, a heating cartridge and an inductor system were used, respectively. The temperature in the surface contact is increased during the test reaching values up to 390°C, depending on the configuration. In addition, three extra tests were performed at the maximum values of penetration and sliding velocity with the contactor what were not heat treated to generate the tribo-layer on their surface. The summary of all the tests performed is given in Table 2.

<table><caption>Table 2 Summary of the test conditions analysed in the WHUST tribometer.</caption><thead><tr><td>Condition number</td><td>Depth of penetration (mm)</td><td>Relative sliding velocity (mm/s)</td><td>Oxide layer in the contactor</td></tr></thead><tbody><tr><td>1</td><td>0.2</td><td>200</td><td>Yes</td></tr><tr><td>2</td><td>0.2</td><td>450</td><td>Yes</td></tr><tr><td>3</td><td>0.4</td><td>200</td><td>Yes</td></tr><tr><td>4</td><td>0.4</td><td>450</td><td>Yes</td></tr><tr><td>5</td><td>0.4</td><td>450</td><td>No</td></tr></tbody></table>
<figure><img src="image_1207.png" /><figcaption>Fig. 2 WHUST (a) tribometer set-up and (b) schematic illustration of the test.</figcaption></figure>

In order to set the test conditions, temperature measures were carried out in an industrial piercing mill on the surface of the plug both, before and after piercing operation, yielding a maximum temperature of 450-500°C. However, it is difficult to estimate this value experimentally since, depending on the size of the tube to be perforated, the heating can be higher or lower and, furthermore, when the plug is positioned between the rolls in the piercing mill is exposed to cooling fluid that reduces its initial temperature. Therefore, in order to estimate the surface heating of the mandrel during piercing, and to define the normal stress distribution at the contact, first, a FE simulation of the tube piercing process was carried out using Forge NtT software. From the results of the simulation, it was stated that in the contact temperature ranged from 275 to 475 °C, the normal stress values were between 100 and 180 MPa. There was a high fluctuation in the sliding velocity, which showed minimum values of 150 mm/s at the tip of the plug and maximum values of 700 mm/s in the region with highest diameter (highest area reduction). In order to reproduce these conditions in the tribology tests, first the setup was simulated and different penetrations were tested. Finally, two penetrations (0.2 mm and 0.4mm) and two sliding velocities (200 mm/s and 450 mm/s) were defined, and three tests were performed for each condition.

The initial temperatures of the contactor and specimen were set to 250°C and 1250°C and, to reach them, a heating cartridge and an inductor system were used, respectively. The temperature in the surface contact is increased during the test reaching values up to 390°C, depending on the configuration. In addition, three extra tests were performed at the maximum values of penetration and sliding velocity with the contactor what were not heat treated to generate the tribo-layer on their surface. The summary of all the tests performed is given in Table 2.

<table><caption>Table 2 Summary of the test conditions analysed in the WHUST tribometer.</caption><thead><tr><td>Condition number</td><td>Depth of penetration (mm)</td><td>Relative sliding velocity (mm/s)</td><td>Oxide layer in the contactor</td></tr></thead><tbody><tr><td>1</td><td>0.2</td><td>200</td><td>Yes</td></tr><tr><td>2</td><td>0.2</td><td>450</td><td>Yes</td></tr><tr><td>3</td><td>0.4</td><td>200</td><td>Yes</td></tr><tr><td>4</td><td>0.4</td><td>450</td><td>Yes</td></tr><tr><td>5</td><td>0.4</td><td>450</td><td>No</td></tr></tbody></table>
## Results and discussion

Surface contact analysis. The contact analysis was performed by optical microscopy on the surface traces of the specimens and contactors after the test, as shown in Fig. 3. The specimen trace can be divided into three regions (see Fig. 3a), the third region has been excluded from the test since unwanted deformation of the specimen has occurred in this area due to the high contact pressure. This limits the usefulness of the tests after 30 mm displacement.

<figure><img src="image_1206.png" /><figcaption>Fig. 3. (a) Trace of the specimen and optical microscopy of (b) specimen in test condition 4, (c) specimen in test condition 5, (d) contactor in test condition 4 and (e) contactor in test condition 5.</figcaption></figure>

In Fig. 3b, no cracks are visible on the surface, although spallation of the oxides can be observed, the abrasion marks follow the sliding direction. Wear debris that have been welded to the surface of the trace are noted. In Fig. 3c, the abrasion marks are more pronounced. This condition corresponds to a metal/oxide contact. Furthermore, on the outer edges of the trace, scale debris that have been deformed and agglomerated on the surface of the specimen are noticed.

The result of the surface of the contactors after the test is shown in Figs. 3d and 3e. It can be noticed how there is transfer of oxides from the specimen to the surface of the contactors by means of adhesion mechanisms. The contactor in Fig. 3d was cross-sectioned, and no damage to the initial oxide layer was observed. A comparison of the two cases (contactor with and without oxide layer) reveals a higher amount of oxides transferred to the contactor without oxide layer. The reason behind the higher transfer may be caused by a higher degree of adhesion with the surface of the hot working steel, as well as the low adherence of the oxide layer generated on the specimen to
## Results and discussion

Surface contact analysis. The contact analysis was performed by optical microscopy on the surface traces of the specimens and contactors after the test, as shown in Fig. 3. The specimen trace can be divided into three regions (see Fig. 3a), the third region has been excluded from the test since unwanted deformation of the specimen has occurred in this area due to the high contact pressure. This limits the usefulness of the tests after 30 mm displacement.

<figure><img src="image_1208.png" /><figcaption>Fig. 3. (a) Trace of the specimen and optical microscopy of (b) specimen in test condition 4, (c) specimen in test condition 5, (d) contactor in test condition 4 and (e) contactor in test condition 5.</figcaption></figure>

In Fig. 3b, no cracks are visible on the surface, although spallation of the oxides can be observed, the abrasion marks follow the sliding direction. Wear debris that have been welded to the surface of the trace are noted. In Fig. 3c, the abrasion marks are more pronounced. This condition corresponds to a metal/oxide contact. Furthermore, on the outer edges of the trace, scale debris that have been deformed and agglomerated on the surface of the specimen are noticed.

The result of the surface of the contactors after the test is shown in Figs. 3d and 3e. It can be noticed how there is transfer of oxides from the specimen to the surface of the contactors by means of adhesion mechanisms. The contactor in Fig. 3d was cross-sectioned, and no damage to the initial oxide layer was observed. A comparison of the two cases (contactor with and without oxide layer) reveals a higher amount of oxides transferred to the contactor without oxide layer. The reason behind the higher transfer may be caused by a higher degree of adhesion with the surface of the hot working steel, as well as the low adherence of the oxide layer generated on the specimen to
the substrate. No spallation of the oxide layer of the contactor, generated by the oxidation treatment, is visible. The presence of Nickel may explain the higher adhesion of the layer generated in the oxidizing treatment.

The wear tracks of the specimens shown in Fig. 3b and Fig. 3c (depth of penetration of 0.4mm and 450 mm/s of relative sliding velocity) were analyzed by means of focus variation techniques (Alicona). In Fig. 4, the profilometry of the trace of the aforementioned specimens, acquired across the sliding direction, is shown.

<figure><img src="image_1207.png" /><figcaption>Fig. 4. Surface topography of (a) conditions 4 and (b) conditions 5, and transverse roughness profile of (c) conditions 4 and (d) conditions 5.</figcaption></figure>

The surfaces were processed with Mountains®9 software, the areas of the trace corresponding to Region II have been extracted, and the level has been corrected by Least Square Plane Leveling (LSPL). In Fig. 4a, it can be seen how on the edges of the trace there are areas where the oxide has been spalled, while in the central zone some adhered wear debris alternate with marked valleys that indicate abrasion marks in the sliding direction of the sample. Regions where valleys show greater depth alternate with areas with less pronounced marks. In Fig. 5b, the abrasive wear marks are much more pronounced and remain throughout the entire area studied. In addition, some deformed and embedded oxides can be found on the surface. The surface roughness profiles of both conditions are shown in Figs. 5c and 5d. From their analysis, it can be stated that abrasive sliding wear is the dominating mechanism. During sliding, oxides tend to break and generate wear debris, and crushed oxides can be accumulated in the contactor yielding to oxide/oxide contact condition. From the analyzed profilometries and optical Fig.s, it's difficult to confirm if the test under condition 5 presents metal/oxide contact or oxide/oxide contact. In the case of condition 4, it can be identified as oxide/oxide.

Friction. Friction has been analyzed for all the conditions listed in Table 2. For each condition, three tests have been analyzed, obtaining a mean value for the friction factor *m* according to constant friction model, hereinafter referred as COF. The procedure to calculate COF depends on measured forces, contact penetration and length, not accounting for the material pile up [18]. In
the substrate. No spallation of the oxide layer of the contactor, generated by the oxidation treatment, is visible. The presence of Nickel may explain the higher adhesion of the layer generated in the oxidizing treatment.

The wear tracks of the specimens shown in Fig. 3b and Fig. 3c (depth of penetration of 0.4mm and 450 mm/s of relative sliding velocity) were analyzed by means of focus variation techniques (Alicona). In Fig. 4, the profilometry of the trace of the aforementioned specimens, acquired across the sliding direction, is shown.

<figure><img src="image_1209.png" /><figcaption>Fig. 4. Surface topography of (a) conditions 4 and (b) conditions 5, and transverse roughness profile of (c) conditions 4 and (d) conditions 5.</figcaption></figure>

The surfaces were processed with Mountains®9 software, the areas of the trace corresponding to Region II have been extracted, and the level has been corrected by Least Square Plane Leveling (LSPL). In Fig. 4a, it can be seen how on the edges of the trace there are areas where the oxide has been spalled, while in the central zone some adhered wear debris alternate with marked valleys that indicate abrasion marks in the sliding direction of the sample. Regions where valleys show greater depth alternate with areas with less pronounced marks. In Fig. 5b, the abrasive wear marks are much more pronounced and remain throughout the entire area studied. In addition, some deformed and embedded oxides can be found on the surface. The surface roughness profiles of both conditions are shown in Figs. 5c and 5d. From their analysis, it can be stated that abrasive sliding wear is the dominating mechanism. During sliding, oxides tend to break and generate wear debris, and crushed oxides can be accumulated in the contactor yielding to oxide/oxide contact condition. From the analyzed profilometries and optical Fig.s, it's difficult to confirm if the test under condition 5 presents metal/oxide contact or oxide/oxide contact. In the case of condition 4, it can be identified as oxide/oxide.

Friction. Friction has been analyzed for all the conditions listed in Table 2. For each condition, three tests have been analyzed, obtaining a mean value for the friction factor *m* according to constant friction model, hereinafter referred as COF. The procedure to calculate COF depends on measured forces, contact penetration and length, not accounting for the material pile up [18]. In
addition, the evolution of COF throughout the displacement of the contactor along the specimen trace has been analyzed. Along the displacement, the first 5 mm of the trace are not useful since the specimen presents a chamfer, and after 30 mm, the results cannot be considered valid since some specimens showed unwanted deformation from that point onwards. Fig. 5 shows the evolution of COF with displacement for certain conditions, as well as the dependence of the COF with respect to relative velocity and contact pressure.

<figure><img src="image_1208.png" /><figcaption>Fig. 5 COF evolution with displacement in (a) test conditions 1, (b) test conditions 4, (c) test conditions 5 and (d) COF evolution with sliding velocity and depth of penetration with the oxide layer in the contactor.</figcaption></figure>

Fig.s 5a and 5b show the evolution of COF with displacement for condition 1 (low relative velocity and pressure) and condition 4 (high relative velocity and pressure), respectively. Both contactors have the oxidation treatment described in Sec. 2. The average COF at high contact pressure and relative speed is 0.18, while at conditions of low relative speed and contact pressure, it increases to a mean value of 0.42. Fig. 5c shows the evolution of the COF with displacement when the contactor does not have the oxidation treatment, under conditions of high relative velocity and pressure. The mean COF results in 0.28. If compared with its homologous case, it confirms that the presence of the oxide layer provides lubricity since COF has been increased from
addition, the evolution of COF throughout the displacement of the contactor along the specimen trace has been analyzed. Along the displacement, the first 5 mm of the trace are not useful since the specimen presents a chamfer, and after 30 mm, the results cannot be considered valid since some specimens showed unwanted deformation from that point onwards. Fig. 5 shows the evolution of COF with displacement for certain conditions, as well as the dependence of the COF with respect to relative velocity and contact pressure.

<figure><img src="image_1210.png" /><figcaption>Fig. 5 COF evolution with displacement in (a) test conditions 1, (b) test conditions 4, (c) test conditions 5 and (d) COF evolution with sliding velocity and depth of penetration with the oxide layer in the contactor.</figcaption></figure>

Fig.s 5a and 5b show the evolution of COF with displacement for condition 1 (low relative velocity and pressure) and condition 4 (high relative velocity and pressure), respectively. Both contactors have the oxidation treatment described in Sec. 2. The average COF at high contact pressure and relative speed is 0.18, while at conditions of low relative speed and contact pressure, it increases to a mean value of 0.42. Fig. 5c shows the evolution of the COF with displacement when the contactor does not have the oxidation treatment, under conditions of high relative velocity and pressure. The mean COF results in 0.28. If compared with its homologous case, it confirms that the presence of the oxide layer provides lubricity since COF has been increased from
0.18 to 0.28. Finally, in Fig. 5d, the mean COF results of cases 1 to 4 (all contactors are oxidation-treated) are represented in a surface, which makes COF dependent on the penetration depth (normal contact stress) and the relative sliding velocity. From the results, two clear trends can be observed. On the one hand, the increase in the relative sliding velocity yields a reduction in the COF. On the other hand, as higher contact pressures are applied, the COF is reduced. Among these two parameters, the COF shows greater sensitivity to changes in relative velocity at contact.

## Conclusions

This study analyzes the tribological behavior of the oxide layer present on the mandrel used in rotary tube piercing operations. A hot upsetting sliding test campaign has been carried out. From the test results and their analysis, the following conclusions have been drawn:

- The oxide layer generated in the treatment is composed of Hematite, Magnetite and Wüstite. Its thickness is 11 microns and, in the tests, it has presented a good adhesion to the substrate without any apparent spalling.

- Adhesion of specimen oxides on the contactor surface occurred in all tested conditions. In the cases tested with oxidation treatment on the contactor this resulted in a type of oxide/oxide contact that was shown to be abrasive in nature.

- In the cases without oxidation treatment on the contactor, the sliding abrasion has been much more severe, showing grooves and abrasion marks of higher depth.

- Friction is lower when the contactor has the oxidation treatment, which confirms the lubricity of this layer.

- The COF value decreases with increasing relative velocity and contact pressure.

## References

[1] Murillo-Marrodán A, García E, Barco J, Cortés F. Application of an Incremental Constitutive Model for the FE Analysis of Material Dynamic Restoration in the Rotary Tube Piercing Process. Materials 2020;13:4289. https://doi.org/10.3390/ma13194289.

[2] Zhang Y, Zhang C, Li F, Wang Z, Wang X, Wang C, et al. High-Temperature Oxidation Behavior of Cr-Ni-Mo Hot-Work Die Steels. Materials 2022;15:5145. https://doi.org/10.3390/ma15155145

[3] Cao J, Brinksmeier E, Fu M, Gao RX, Liang B, Merklein M, et al. Manufacturing of advanced smart tooling for metal forming. CIRP Annals 2019;68:605-28. https://doi.org/10.1016/j.cirp.2019.05.001

[4] Zhou R, Cao J, Wang QJ, Meng F, Zimowski K, Xia ZC. Effect of EDT surface texturing on tribological behavior of aluminum sheet. Journal of Materials Processing Technology 2011;211:1643-9. https://doi.org/10.1016/j.jmatprotec.2011.05.004

[5] Pelcastre L, Hardell J, Prakash B. Galling mechanisms during interaction of tool steel and Al-Si coated ultra-high strength steel at elevated temperature. Tribology International 2013;67:263-71. https://doi.org/10.1016/j.triboint.2013.08.007

[6] Wang SQ, Wei MX, Wang F, Cui XH, Chen KM. Effect of morphology of oxide scale on oxidation wear in hot working die steels. Materials Science and Engineering: A 2009;505:20-6. https://doi.org/10.1016/j.msea.2008.10.032

[7] Fontalvo GA, Mitterer C. The effect of oxide-forming alloying elements on the high temperature wear of a hot work steel. Wear 2005;258:1491-9. https://doi.org/10.1016/j.wear.2004.04.014
0.18 to 0.28. Finally, in Fig. 5d, the mean COF results of cases 1 to 4 (all contactors are oxidation-treated) are represented in a surface, which makes COF dependent on the penetration depth (normal contact stress) and the relative sliding velocity. From the results, two clear trends can be observed. On the one hand, the increase in the relative sliding velocity yields a reduction in the COF. On the other hand, as higher contact pressures are applied, the COF is reduced. Among these two parameters, the COF shows greater sensitivity to changes in relative velocity at contact.

## Conclusions

This study analyzes the tribological behavior of the oxide layer present on the mandrel used in rotary tube piercing operations. A hot upsetting sliding test campaign has been carried out. From the test results and their analysis, the following conclusions have been drawn:

- The oxide layer generated in the treatment is composed of Hematite, Magnetite and Wüstite. Its thickness is 11 microns and, in the tests, it has presented a good adhesion to the substrate without any apparent spalling.

- Adhesion of specimen oxides on the contactor surface occurred in all tested conditions. In the cases tested with oxidation treatment on the contactor this resulted in a type of oxide/oxide contact that was shown to be abrasive in nature.

- In the cases without oxidation treatment on the contactor, the sliding abrasion has been much more severe, showing grooves and abrasion marks of higher depth.

- Friction is lower when the contactor has the oxidation treatment, which confirms the lubricity of this layer.

- The COF value decreases with increasing relative velocity and contact pressure.

## References

[1] Murillo-Marrodán A, García E, Barco J, Cortés F. Application of an Incremental Constitutive Model for the FE Analysis of Material Dynamic Restoration in the Rotary Tube Piercing Process. Materials 2020;13:4289. https://doi.org/10.3390/ma13194289.

[2] Zhang Y, Zhang C, Li F, Wang Z, Wang X, Wang C, et al. High-Temperature Oxidation Behavior of Cr-Ni-Mo Hot-Work Die Steels. Materials 2022;15:5145. https://doi.org/10.3390/ma15155145

[3] Cao J, Brinksmeier E, Fu M, Gao RX, Liang B, Merklein M, et al. Manufacturing of advanced smart tooling for metal forming. CIRP Annals 2019;68:605-28. https://doi.org/10.1016/j.cirp.2019.05.001

[4] Zhou R, Cao J, Wang QJ, Meng F, Zimowski K, Xia ZC. Effect of EDT surface texturing on tribological behavior of aluminum sheet. Journal of Materials Processing Technology 2011;211:1643-9. https://doi.org/10.1016/j.jmatprotec.2011.05.004

[5] Pelcastre L, Hardell J, Prakash B. Galling mechanisms during interaction of tool steel and Al-Si coated ultra-high strength steel at elevated temperature. Tribology International 2013;67:263-71. https://doi.org/10.1016/j.triboint.2013.08.007

[6] Wang SQ, Wei MX, Wang F, Cui XH, Chen KM. Effect of morphology of oxide scale on oxidation wear in hot working die steels. Materials Science and Engineering: A 2009;505:20-6. https://doi.org/10.1016/j.msea.2008.10.032

[7] Fontalvo GA, Mitterer C. The effect of oxide-forming alloying elements on the high temperature wear of a hot work steel. Wear 2005;258:1491-9. https://doi.org/10.1016/j.wear.2004.04.014
[8] Zambrano OA, Coronado JJ, Rodríguez SA. Mechanical properties and phases determination of low carbon steel oxide scales formed at 1200°C in air. Surface and Coatings Technology 2015;282:155-62. https://doi.org/10.1016/j.surfcoat.2015.10.028

[9] Lundberg S-E, Gustafsson T. The influence of rolling temperature on roll wear, investigated in a new high temperature test rig. Journal of Materials Processing Technology 1994;42:239-91. https://doi.org/10.1016/0924-0136(94)90181-3

[10] Dohda K, Boher C, Rezai-Aria F, Mahayotsanun N. Tribology in metal forming at elevated temperatures. Friction 2015;3:1-27. https://doi.org/10.1007/s40544-015-0077-3

[11] Sheasby JS, Boggs WE, Turkdogan ET. Scale growth on steels at 1200°C: rationale of rate and morphology. Metal Science 1984;18:127-36. https://doi.org/10.1179/msc.1984.18.3.127

[12] Munther PA, Lenard JG. The effect of scaling on interfacial friction in hot rolling of steels. Journal of Materials Processing Technology 1999;88:105-13. https://doi.org/10.1016/S0924-0136(98)00392-6

[13] Beynon JH. Tribology of hot metal forming. Tribology International 1998;31:73-7. https://doi.org/10.1016/S0301-679X(98)00009-7

[14] Pellizzari M, Cescato D, De Flora MG. Hot friction and wear behaviour of high speed steel and high chromium iron for rolls. Wear 2009;267:467-75. https://doi.org/10.1016/j.wear.2009.01.049

[15] Tieu AK, Zhu Q, Zhu H, Lu C. An investigation into the tribological behaviour of a work roll material at high temperature. Wear 2011;273:43-8. https://doi.org/10.1016/j.wear.2011.06.003

[16] Utsunomiya H, Nakagawa T, Matsumoto R. Mechanism of oxide scale to decrease friction in hot steel rolling. Procedia Manufacturing 2018;15:46-51. https://doi.org/10.1016/j.promfg.2018.07.168

[17] Dubois A, Dubar M, Dubar L. Warm and Hot Upsetting Sliding Test: Tribology of Metal Processes at High Temperature. Procedia Engineering, vol. 81, 2014, p. 1964-9. https://doi.org/10.1016/j.proeng.2014.10.265

[18] Dubois A, Dubar M, Debras C, Hermange K, Nivot C, Courtois C. New environmentally friendly coatings for hot forging tools. Surface and Coatings Technology 2018;344:342-52. https://doi.org/10.1016/j.surfcoat.2018.03.055
[8] Zambrano OA, Coronado JJ, Rodríguez SA. Mechanical properties and phases determination of low carbon steel oxide scales formed at 1200°C in air. Surface and Coatings Technology 2015;282:155-62. https://doi.org/10.1016/j.surfcoat.2015.10.028

[9] Lundberg S-E, Gustafsson T. The influence of rolling temperature on roll wear, investigated in a new high temperature test rig. Journal of Materials Processing Technology 1994;42:239-91. https://doi.org/10.1016/0924-0136(94)90181-3

[10] Dohda K, Boher C, Rezai-Aria F, Mahayotsanun N. Tribology in metal forming at elevated temperatures. Friction 2015;3:1-27. https://doi.org/10.1007/s40544-015-0077-3

[11] Sheasby JS, Boggs WE, Turkdogan ET. Scale growth on steels at 1200°C: rationale of rate and morphology. Metal Science 1984;18:127-36. https://doi.org/10.1179/msc.1984.18.3.127

[12] Munther PA, Lenard JG. The effect of scaling on interfacial friction in hot rolling of steels. Journal of Materials Processing Technology 1999;88:105-13. https://doi.org/10.1016/S0924-0136(98)00392-6

[13] Beynon JH. Tribology of hot metal forming. Tribology International 1998;31:73-7. https://doi.org/10.1016/S0301-679X(98)00009-7

[14] Pellizzari M, Cescato D, De Flora MG. Hot friction and wear behaviour of high speed steel and high chromium iron for rolls. Wear 2009;267:467-75. https://doi.org/10.1016/j.wear.2009.01.049

[15] Tieu AK, Zhu Q, Zhu H, Lu C. An investigation into the tribological behaviour of a work roll material at high temperature. Wear 2011;273:43-8. https://doi.org/10.1016/j.wear.2011.06.003

[16] Utsunomiya H, Nakagawa T, Matsumoto R. Mechanism of oxide scale to decrease friction in hot steel rolling. Procedia Manufacturing 2018;15:46-51. https://doi.org/10.1016/j.promfg.2018.07.168

[17] Dubois A, Dubar M, Dubar L. Warm and Hot Upsetting Sliding Test: Tribology of Metal Processes at High Temperature. Procedia Engineering, vol. 81, 2014, p. 1964-9. https://doi.org/10.1016/j.proeng.2014.10.265

[18] Dubois A, Dubar M, Debras C, Hermange K, Nivot C, Courtois C. New environmentally friendly coatings for hot forging tools. Surface and Coatings Technology 2018;344:342-52. https://doi.org/10.1016/j.surfcoat.2018.03.055
# Effect of process parameters on friction in aluminum sheet forming

JALALI MOGHADAS Farshid¹,ᵃ*, DE ROOIJ Matthijn¹,ᵇ,
VAN DEN BOOGAARD Ton²,ᶜ, HAZRATI Javad²,ᵈ

¹Surface Technology and Tribology, Faculty of ET, University of Twente, The Netherlands

²Nonlinear Solid Mechanics, Faculty of ET, University of Twente, The Netherlands

ᵃf.jalalimoghadas@utwente.nl; ᵇm.b.derooij@utwente.nl; ᶜa.h.vandenboogaard@utwente.nl;

ᵈj.hazratimarangalou@utwente.nl

**Keywords:** Aluminum, Friction, Sheet Metal Forming, Bending Under Tension Test

**Abstract.** The bending under tension (BUT) test is used to mimic aluminum sheet forming process and study the effect of friction on drawing force. Multidraw Drylube E1 was used to lubricate the samples. Experiments were designed and executed to study the effects of rolling direction, lubricant amount, roll temperature and contact pressure on the drawing force. Strain in the sample was measured using digital image correlation (DIC) technique. Real area of contact is calculated using height distribution histograms of the surface in contact. Apart from the back force, variations in drawing force results from changes in bending and unbending force and friction force. The results imply that the friction force will not necessarily increase with increasing the back force and it depends on the contact pressure.

**Introduction**

Sheet metal forming is one of the most prominent manufacturing processes in many different industries. Friction has been shown as a key parameter in sheet metal forming that directly affects the formability of the final product. Different parameters determine friction, such as surface topographies and mechanical properties of sheet metal and forming tool, lubricant properties, contact pressure, strain and temperature in sheet metal and tool contact [1]. Therefore, it is necessary to understand the effect of these parameters on friction for the proper design of the process.

Many researchers have studied the effect of different parameters on friction in aluminum forming, using different test methods such as strip draw test, draw-bead simulator, pin-on-plate test, flat-on-flat tests and bending under tension (BUT) test. Tung et al. [2] developed an in-situ tribotest method to study the correlation between friction coefficient and process parameters. These included the tooling material and the lubricant in warm and hot aluminum forming process. Zhou et al. [3] examined the influence of Electro-Discharge-Texturing (EDT) of aluminum automotive sheet at different contact pressures and sliding speeds using a flat-on-flat friction test. They found that EDT texturing reduces the friction coefficient at relatively high contact pressure, but increases it at relatively low contact pressures (below 62 MPa). Dou et al. [4, 5] carried out research on aluminum alloy stamping and warm stamping process. Their approach used a pin-on-disk sliding wear test and studied the effects of temperature, sliding speed and normal load on friction coefficient. They concluded that friction coefficient increases for samples in higher temperatures. Wu et al. [6] conducted high temperature strip drawing for aluminum sheets. The results showed that the friction coefficient increased with an increase in preheating temperature of the die, applying a larger normal load or reducing the sliding velocity. Shafiee Sabet et al. [7] conducted pin-on-plate experiments on aluminum sheets and showed the friction coefficient tends to decrease with increasing nominal contact pressure and sliding velocity, but increase with an increase in the surface temperature. Meiler et al. [8, 9] compared the application of different dry

<figure><img src="image_1209.png" /></figure>
# Effect of process parameters on friction in aluminum sheet forming

JALALI MOGHADAS Farshid¹,ᵃ*, DE ROOIJ Matthijn¹,ᵇ,
VAN DEN BOOGAARD Ton²,ᶜ, HAZRATI Javad²,ᵈ

¹Surface Technology and Tribology, Faculty of ET, University of Twente, The Netherlands

²Nonlinear Solid Mechanics, Faculty of ET, University of Twente, The Netherlands

ᵃf.jalalimoghadas@utwente.nl; ᵇm.b.derooij@utwente.nl; ᶜa.h.vandenboogaard@utwente.nl;

ᵈj.hazratimarangalou@utwente.nl

**Keywords:** Aluminum, Friction, Sheet Metal Forming, Bending Under Tension Test

**Abstract.** The bending under tension (BUT) test is used to mimic aluminum sheet forming process and study the effect of friction on drawing force. Multidraw Drylube E1 was used to lubricate the samples. Experiments were designed and executed to study the effects of rolling direction, lubricant amount, roll temperature and contact pressure on the drawing force. Strain in the sample was measured using digital image correlation (DIC) technique. Real area of contact is calculated using height distribution histograms of the surface in contact. Apart from the back force, variations in drawing force results from changes in bending and unbending force and friction force. The results imply that the friction force will not necessarily increase with increasing the back force and it depends on the contact pressure.

**Introduction**

Sheet metal forming is one of the most prominent manufacturing processes in many different industries. Friction has been shown as a key parameter in sheet metal forming that directly affects the formability of the final product. Different parameters determine friction, such as surface topographies and mechanical properties of sheet metal and forming tool, lubricant properties, contact pressure, strain and temperature in sheet metal and tool contact [1]. Therefore, it is necessary to understand the effect of these parameters on friction for the proper design of the process.

Many researchers have studied the effect of different parameters on friction in aluminum forming, using different test methods such as strip draw test, draw-bead simulator, pin-on-plate test, flat-on-flat tests and bending under tension (BUT) test. Tung et al. [2] developed an in-situ tribotest method to study the correlation between friction coefficient and process parameters. These included the tooling material and the lubricant in warm and hot aluminum forming process. Zhou et al. [3] examined the influence of Electro-Discharge-Texturing (EDT) of aluminum automotive sheet at different contact pressures and sliding speeds using a flat-on-flat friction test. They found that EDT texturing reduces the friction coefficient at relatively high contact pressure, but increases it at relatively low contact pressures (below 62 MPa). Dou et al. [4, 5] carried out research on aluminum alloy stamping and warm stamping process. Their approach used a pin-on-disk sliding wear test and studied the effects of temperature, sliding speed and normal load on friction coefficient. They concluded that friction coefficient increases for samples in higher temperatures. Wu et al. [6] conducted high temperature strip drawing for aluminum sheets. The results showed that the friction coefficient increased with an increase in preheating temperature of the die, applying a larger normal load or reducing the sliding velocity. Shafiee Sabet et al. [7] conducted pin-on-plate experiments on aluminum sheets and showed the friction coefficient tends to decrease with increasing nominal contact pressure and sliding velocity, but increase with an increase in the surface temperature. Meiler et al. [8, 9] compared the application of different dry

<figure><img src="image_1211.png" /></figure>
film lubricants with oil lubricants for aluminum sheet forming within the automotive industry. They showed that by using hot-melt lubricants, apart from advantages in reducing the manufacturing and assembly time due to eliminating washing and relubricating processes, increased formability, homogeneous sheet thickness distribution and reduced scattering of the results can be achieved.

Some studies compared different friction test methods. Trzepiecinski [10] showed that for the tested steel sheets, in the BUT test, in contrast to the strip drawing test, with increasing the contact pressure, the friction coefficient tends to increase. Out of all the studies, only a few used the BUT test for investigation on friction in aluminum forming [11, 12]. In the BUT test, a strip, which is under tension, experiences bending and unbending over a fixed roll (and free rotating roll for measurement without friction). The BUT test can simulate the actual forming conditions at die and punch radius without adding any complexity and provides the opportunity to examine the effect of each parameter separately. Since the contact pressure is not the same all over the contact roll, different parts of the sample width experience different friction conditions. Multiple studies have investigated friction using BUT test, but few have addressed aluminum.

Initially, Vallance et al. [13] used the BUT test to study the friction behavior of coated steels in forming and showed that it is a suitable test for both fundamental and production operation studies. Their results indicate that the friction coefficient in coated steels varies with contact pressure. Later, Nanayakkara et al. [14] studied the effect of different roll diameters and different lubricants on BUT test results of galvannealed steel and concluded that the contact pressure together with the lubrication regime can determine the friction coefficient. Lemu and Trzepiecinski [12, 15] investigated the effect of lubrication condition (dry or lubricated) and tool surface roughness, using the BUT test for steel, brass and aluminum sheets. They evaluated the bending force numerically, in order to eliminate the variation of experimentally calculated bending force, specially when steady-state condition is not achieved during the test.

In overall, bending under tension experiments mimic basic kinematics of a real sheet metal forming. Therefore, it provides a quick assessment of different parameters on friction in real production setting. In this study, the influence of different parameters on frictional behavior of aluminum sheets with hot-melt lubricant are investigated using bending under tension experiments. The effects of back force, sheet rolling direction, roll temperature and hot-melt lubricant amount on friction in sheet forming of aluminum grade, AA5182 with EDT surface will be presented.

## Materials and Methods

Material and Surface Properties. Aluminum sheets of AA5182 with EDT surface and 1.5 mm thickness were tested. The mechanical properties of the sheets were determined along three directions using uniaxial tensile tests according to ASTM E8M while the strains were measured using the DIC technique (GOM Aramis 3D). Fig. 1 depicts the true stress-true strain results of the tensile tests. AA5182 sheets in rolling direction had a slightly higher yield stress and hardening curve. The yield stress was 137 MPa in rolling direction (RD), 136 MPa in diagonal direction (DD) and 134 MPa in Transverse direction (TD).
film lubricants with oil lubricants for aluminum sheet forming within the automotive industry. They showed that by using hot-melt lubricants, apart from advantages in reducing the manufacturing and assembly time due to eliminating washing and relubricating processes, increased formability, homogeneous sheet thickness distribution and reduced scattering of the results can be achieved.

Some studies compared different friction test methods. Trzepiecinski [10] showed that for the tested steel sheets, in the BUT test, in contrast to the strip drawing test, with increasing the contact pressure, the friction coefficient tends to increase. Out of all the studies, only a few used the BUT test for investigation on friction in aluminum forming [11, 12]. In the BUT test, a strip, which is under tension, experiences bending and unbending over a fixed roll (and free rotating roll for measurement without friction). The BUT test can simulate the actual forming conditions at die and punch radius without adding any complexity and provides the opportunity to examine the effect of each parameter separately. Since the contact pressure is not the same all over the contact roll, different parts of the sample width experience different friction conditions. Multiple studies have investigated friction using BUT test, but few have addressed aluminum.

Initially, Vallance et al. [13] used the BUT test to study the friction behavior of coated steels in forming and showed that it is a suitable test for both fundamental and production operation studies. Their results indicate that the friction coefficient in coated steels varies with contact pressure. Later, Nanayakkara et al. [14] studied the effect of different roll diameters and different lubricants on BUT test results of galvannealed steel and concluded that the contact pressure together with the lubrication regime can determine the friction coefficient. Lemu and Trzepiecinski [12, 15] investigated the effect of lubrication condition (dry or lubricated) and tool surface roughness, using the BUT test for steel, brass and aluminum sheets. They evaluated the bending force numerically, in order to eliminate the variation of experimentally calculated bending force, specially when steady-state condition is not achieved during the test.

In overall, bending under tension experiments mimic basic kinematics of a real sheet metal forming. Therefore, it provides a quick assessment of different parameters on friction in real production setting. In this study, the influence of different parameters on frictional behavior of aluminum sheets with hot-melt lubricant are investigated using bending under tension experiments. The effects of back force, sheet rolling direction, roll temperature and hot-melt lubricant amount on friction in sheet forming of aluminum grade, AA5182 with EDT surface will be presented.

## Materials and Methods

Material and Surface Properties. Aluminum sheets of AA5182 with EDT surface and 1.5 mm thickness were tested. The mechanical properties of the sheets were determined along three directions using uniaxial tensile tests according to ASTM E8M while the strains were measured using the DIC technique (GOM Aramis 3D). Fig. 1 depicts the true stress-true strain results of the tensile tests. AA5182 sheets in rolling direction had a slightly higher yield stress and hardening curve. The yield stress was 137 MPa in rolling direction (RD), 136 MPa in diagonal direction (DD) and 134 MPa in Transverse direction (TD).
<figure><img src="image_1210.png" /><figcaption>Fig. 1. True stress-true curves of aluminum sheets.</figcaption></figure>

Strips of 50 mm×600 mm were cut from the sheets in three different directions, RD, DD and TD.

To choose proper values for test parameters like roll diameter, back force, and lubricant amount a preliminary study were done. Using the finite element (FE) simulation, contact pressures for different roll diameters, 10 mm and 20 mm, and back forces of 1 kN to 4 kN were assessed for AA5182 material (1.5 mm thickness). The average contact pressure in the contact area for 10 mm roll was between 36 MPa to 62 MPa, while for 20 mm roll, it was lower, between 15 MPa to 20 MPa. Therefore, roll with 10 mm diameter was chosen. The roll for BUT test was made from GGG-70 cast iron and roll surface was polished to 0.15 µm roughness. 1 kN, 2 kN and 4 kN back forces were selected for the experiments.

Different amounts of Multidraw Drylube E1 were used to lubricate the samples. The solidification point of the E1 lubricant is approximately 40°C. Assuming that the lubricant will distribute to fill the valleys and stay in one height level, the lubricant amount was calculated using confocal images of strips to achieve different lubrication conditions. The results show that 1.4 g/m² drylube is needed to fill all the valleys. Therefore, three levels for lubricant amount were selected to be 0.5 g/m², 1g/m² and 2 g/m², to test different lubrication conditions.

In order to make a repeatable and controllable procedure to apply the hot-melt lubricant on BUT samples, a laboratory-scale setup was manufactured. In this setup the specimen is placed on a moving saddle which is pulled by a rope, connected to a servo motor. The distance between the hot spray gun and the specimen is adjustable. Air pressure and temperature can also be adjusted. The amount of lubricant on the specimen has been calibrated based on the speed of spraying. Additionally before the test, the weight of the applied lubricant was measured for 20% of the samples, to make sure it will not deviate from the expected amount.

## Bending Under Tension Experiments.
The bending under tension (BUT) test setup and DIC setup are shown in Fig. 2.a. First, sample was bent over the roll and clamped in the grippers, then the back force was applied and finally it was pulled down for 140 mm. The GOM Aramis setup was used to look at the sample from the top on the bending area and measure the strain in the strip while it was passing the roll. In Fig. 2.b. line 1 applies the back force and line 2 applies the draw force. Using an analog voltage output from the BUT machine, the displacement in Line 2 (the drawing gripper) was recorded for each image taken by the DIC. The strip is pulled down with a constant speed (1 mm/s) while the machine tries to keep the back force constant. In Fig. 2.c, the force in line 1 and 2 is shown against the displacement of line 2 (the drawing gripper). For the rest of this paper, to make the results more comparable, the difference between these two forces against displacement of line 2 will be depicted.
<figure><img src="image_1212.png" /><figcaption>Fig. 1. True stress-true curves of aluminum sheets.</figcaption></figure>

Strips of 50 mm×600 mm were cut from the sheets in three different directions, RD, DD and TD.

To choose proper values for test parameters like roll diameter, back force, and lubricant amount a preliminary study were done. Using the finite element (FE) simulation, contact pressures for different roll diameters, 10 mm and 20 mm, and back forces of 1 kN to 4 kN were assessed for AA5182 material (1.5 mm thickness). The average contact pressure in the contact area for 10 mm roll was between 36 MPa to 62 MPa, while for 20 mm roll, it was lower, between 15 MPa to 20 MPa. Therefore, roll with 10 mm diameter was chosen. The roll for BUT test was made from GGG-70 cast iron and roll surface was polished to 0.15 µm roughness. 1 kN, 2 kN and 4 kN back forces were selected for the experiments.

Different amounts of Multidraw Drylube E1 were used to lubricate the samples. The solidification point of the E1 lubricant is approximately 40°C. Assuming that the lubricant will distribute to fill the valleys and stay in one height level, the lubricant amount was calculated using confocal images of strips to achieve different lubrication conditions. The results show that 1.4 g/m² drylube is needed to fill all the valleys. Therefore, three levels for lubricant amount were selected to be 0.5 g/m², 1g/m² and 2 g/m², to test different lubrication conditions.

In order to make a repeatable and controllable procedure to apply the hot-melt lubricant on BUT samples, a laboratory-scale setup was manufactured. In this setup the specimen is placed on a moving saddle which is pulled by a rope, connected to a servo motor. The distance between the hot spray gun and the specimen is adjustable. Air pressure and temperature can also be adjusted. The amount of lubricant on the specimen has been calibrated based on the speed of spraying. Additionally before the test, the weight of the applied lubricant was measured for 20% of the samples, to make sure it will not deviate from the expected amount.

## Bending Under Tension Experiments.
The bending under tension (BUT) test setup and DIC setup are shown in Fig. 2.a. First, sample was bent over the roll and clamped in the grippers, then the back force was applied and finally it was pulled down for 140 mm. The GOM Aramis setup was used to look at the sample from the top on the bending area and measure the strain in the strip while it was passing the roll. In Fig. 2.b. line 1 applies the back force and line 2 applies the draw force. Using an analog voltage output from the BUT machine, the displacement in Line 2 (the drawing gripper) was recorded for each image taken by the DIC. The strip is pulled down with a constant speed (1 mm/s) while the machine tries to keep the back force constant. In Fig. 2.c, the force in line 1 and 2 is shown against the displacement of line 2 (the drawing gripper). For the rest of this paper, to make the results more comparable, the difference between these two forces against displacement of line 2 will be depicted.
<figure><img src="image_1211.png" /><figcaption>Fig. 2. a) BUT and DIC setup. b) Aluminum strip bent over the fixed roll. c) A sample of force-displacement curves output.</figcaption></figure>

Finite Element (FE) Simulations. FE simulations of the BUT test without friction has been done to distinguish between bending and unbending forces and estimate the friction force. It has been assumed that the friction force does not affect the bending and unbending force, therefore, this force can be calculated by considering the coefficient of friction equal to zero in the simulation.

The FE simulations were done using MSC Marc software. First the strip was bent over the roll, then the back force was applied and finally the strip was drawn for 50 mm. Five elements in the thickness and fine elements in the deformation zone with 0.5 mm in the length direction and 1mm in the width direction were selected after performing a mesh sensitivity analysis for strain results. BUT test simulations were conducted for a coarser mesh size (1 mm by 1 mm) and also a finer mesh size (0.5 mm by 0.5 mm). It has been seen that the strain results of different simulations converged by reducing the mesh size. But the contact pressure results are mesh size dependent. A mesh size with 0.5 mm in the length direction and 1 mm in the width direction was chosen for the FE simulations.

Design of Experiments. Experiments were designed to see the effects of different parameters. Three levels were considered for each variable. A central design with defined parameters was selected (strip in rolling direction; roll in room temperature; 2 kN back force; 1 g/m² lubricant). In each test, the level of only one variable is changed. All tests were repeated at least once to ensure the repeatability of the results. Fig. 3 depicts all the conducted experiments with the number of experiments conducted at each point (number in parentheses). The test order was selected completely random.

<figure><img src="image_1212.png" /><figcaption>Fig. 3. Design of experiments and all tests and repetitions done.</figcaption></figure>
<figure><img src="image_1213.png" /><figcaption>Fig. 2. a) BUT and DIC setup. b) Aluminum strip bent over the fixed roll. c) A sample of force-displacement curves output.</figcaption></figure>

Finite Element (FE) Simulations. FE simulations of the BUT test without friction has been done to distinguish between bending and unbending forces and estimate the friction force. It has been assumed that the friction force does not affect the bending and unbending force, therefore, this force can be calculated by considering the coefficient of friction equal to zero in the simulation.

The FE simulations were done using MSC Marc software. First the strip was bent over the roll, then the back force was applied and finally the strip was drawn for 50 mm. Five elements in the thickness and fine elements in the deformation zone with 0.5 mm in the length direction and 1mm in the width direction were selected after performing a mesh sensitivity analysis for strain results. BUT test simulations were conducted for a coarser mesh size (1 mm by 1 mm) and also a finer mesh size (0.5 mm by 0.5 mm). It has been seen that the strain results of different simulations converged by reducing the mesh size. But the contact pressure results are mesh size dependent. A mesh size with 0.5 mm in the length direction and 1 mm in the width direction was chosen for the FE simulations.

Design of Experiments. Experiments were designed to see the effects of different parameters. Three levels were considered for each variable. A central design with defined parameters was selected (strip in rolling direction; roll in room temperature; 2 kN back force; 1 g/m² lubricant). In each test, the level of only one variable is changed. All tests were repeated at least once to ensure the repeatability of the results. Fig. 3 depicts all the conducted experiments with the number of experiments conducted at each point (number in parentheses). The test order was selected completely random.

<figure><img src="image_1214.png" /><figcaption>Fig. 3. Design of experiments and all tests and repetitions done.</figcaption></figure>
Surface topography of the sheet before and after the test are measured using confocal microscope with the resolution of 0.64 µm/pixel. The real contact area of the surface that was in contact with the roll at the end of test, is calculated using the height probability density distribution histogram. It is assumed that the maximum height with the maximum in probability is the flattened height, for a background see [16].

## Results and Discussions

In order to validate the FE model, von Mises equivalent strain results from DIC measurements and simulations were compared for two cases with 2 kN and 4 kN back forces. Fig. 4 shows the results after drawing the sample for 26.7 mm to the left. Edges of the samples are not included in the DIC measurements. There are also some points, the white holes in the strain map, where software was unable to calculate the strain. This was due to the painting pattern of the samples. Since the strain deviation along the width is quite small, the strain at those points can be considered to be the same as the neighborhood points.

<figure><img src="image_1213.png" /><figcaption>Fig. 4. Von Mises equivalent strain comparison from the DIC and simulation.</figcaption></figure>

The results of contact pressure for different back forces are illustrated in Fig. 5. In these simulations, the material properties of AA5182 have been used and a frictionless contact is assumed. The contact pressure increases with increasing back force from 1 kN to 2 kN but decreases with increasing back force from 2 kN to 4 kN. The decrease in contact pressure is due to an increase in contact area, as it is evident in the contact pressure map.

<figure><img src="image_1214.png" /><figcaption>Fig. 5. Contact pressure results from simulations for BUT test of AA5182 sheets.</figcaption></figure>
Surface topography of the sheet before and after the test are measured using confocal microscope with the resolution of 0.64 µm/pixel. The real contact area of the surface that was in contact with the roll at the end of test, is calculated using the height probability density distribution histogram. It is assumed that the maximum height with the maximum in probability is the flattened height, for a background see [16].

## Results and Discussions

In order to validate the FE model, von Mises equivalent strain results from DIC measurements and simulations were compared for two cases with 2 kN and 4 kN back forces. Fig. 4 shows the results after drawing the sample for 26.7 mm to the left. Edges of the samples are not included in the DIC measurements. There are also some points, the white holes in the strain map, where software was unable to calculate the strain. This was due to the painting pattern of the samples. Since the strain deviation along the width is quite small, the strain at those points can be considered to be the same as the neighborhood points.

<figure><img src="image_1215.png" /><figcaption>Fig. 4. Von Mises equivalent strain comparison from the DIC and simulation.</figcaption></figure>

The results of contact pressure for different back forces are illustrated in Fig. 5. In these simulations, the material properties of AA5182 have been used and a frictionless contact is assumed. The contact pressure increases with increasing back force from 1 kN to 2 kN but decreases with increasing back force from 2 kN to 4 kN. The decrease in contact pressure is due to an increase in contact area, as it is evident in the contact pressure map.

<figure><img src="image_1216.png" /><figcaption>Fig. 5. Contact pressure results from simulations for BUT test of AA5182 sheets.</figcaption></figure>
The delta-force-displacement (delta-force is the difference between drawing force and back-force) curves for different back forces are depicted in Fig. 6 for AA5182-EDT. These results show that the delta-force will increase with increasing back force. This happens due to mainly change in the bending and unbending force and also variations in the friction force, caused by the contact pressure changes (shown in Fig. 5). In order to see the effect of friction force, the effect of bending and unbending force must be subtracted from the total delta-force. The draw force result of FE simulation without friction, can be interpreted to be equal to bending and unbending force. Effects of different back forces (therefore different contact pressures) on friction force can be seen by subtracting the draw force results of FE simulations without friction from the draw force results of experiments. At 40 mm displacement the initially bent area has already passed the deformation zone. Therefore, the average draw force between 40 mm and 50 mm displacement was used to compare the data. Table 1 compares the results of simulations and experiments in different conditions.

<figure><img src="image_1215.png" /><figcaption>Fig. 6. Effect of different back forces on difference between draw force and back force.</figcaption></figure>

<table><caption>Table 1. Effect of different back forces on draw force and friction force results.</caption><thead><tr><td>Back force (kN)</td><td>ΔF (kN) experimental results</td><td>ΔF (kN) simulation results with μ=0</td><td>Friction force (N) of experiments</td><td>Average Coulomb's friction coefficient*</td></tr></thead><tbody><tr><td>1</td><td>1.520</td><td>1.005</td><td>515</td><td>0.226</td></tr><tr><td>2</td><td>2.646</td><td>1.770</td><td>876</td><td>0.204</td></tr><tr><td>4</td><td>3.204</td><td>2.514</td><td>690</td><td>0.090</td></tr></tbody></table>

*Friction force of the experiments divided by the total normal force to the contact calculated from FE analyses.

Considering a constant coefficient of friction for the BUT test, the friction force will increase with increasing back force from 1 kN to 4 kN due to increasing the normal force. However the experiments imply that the friction force increases from 1 kN back force to 2 kN, but decreases from 2 kN and 4 kN, even though the normal force has been increased. Hence, the results indicate that the coefficient of friction depends on pressure distribution at the contact and decreases with increase in contact pressure [1].

Test results for different lubricant amounts, orientation of strip with respect to rolling direction and roll temperature are depicted in Fig. 7. The amount of lubricant in the selected range (0.5 g/m² to 2 g/m²), appears to have no significant effect on the draw force. One explanation can be related to not having hydrodynamic pressure and distribution of the hot-melt solid lubricant on the surface. If hydrodynamic pressure does not build up due to low sliding velocity and the fact that lubricant is not fluid, asperity ploughing, and shear of boundary layers determine the coefficient of friction.
The delta-force-displacement (delta-force is the difference between drawing force and back-force) curves for different back forces are depicted in Fig. 6 for AA5182-EDT. These results show that the delta-force will increase with increasing back force. This happens due to mainly change in the bending and unbending force and also variations in the friction force, caused by the contact pressure changes (shown in Fig. 5). In order to see the effect of friction force, the effect of bending and unbending force must be subtracted from the total delta-force. The draw force result of FE simulation without friction, can be interpreted to be equal to bending and unbending force. Effects of different back forces (therefore different contact pressures) on friction force can be seen by subtracting the draw force results of FE simulations without friction from the draw force results of experiments. At 40 mm displacement the initially bent area has already passed the deformation zone. Therefore, the average draw force between 40 mm and 50 mm displacement was used to compare the data. Table 1 compares the results of simulations and experiments in different conditions.

<figure><img src="image_1217.png" /><figcaption>Fig. 6. Effect of different back forces on difference between draw force and back force.</figcaption></figure>

<table><caption>Table 1. Effect of different back forces on draw force and friction force results.</caption><thead><tr><td>Back force (kN)</td><td>ΔF (kN) experimental results</td><td>ΔF (kN) simulation results with μ=0</td><td>Friction force (N) of experiments</td><td>Average Coulomb's friction coefficient*</td></tr></thead><tbody><tr><td>1</td><td>1.520</td><td>1.005</td><td>515</td><td>0.226</td></tr><tr><td>2</td><td>2.646</td><td>1.770</td><td>876</td><td>0.204</td></tr><tr><td>4</td><td>3.204</td><td>2.514</td><td>690</td><td>0.090</td></tr></tbody></table>

*Friction force of the experiments divided by the total normal force to the contact calculated from FE analyses.

Considering a constant coefficient of friction for the BUT test, the friction force will increase with increasing back force from 1 kN to 4 kN due to increasing the normal force. However the experiments imply that the friction force increases from 1 kN back force to 2 kN, but decreases from 2 kN and 4 kN, even though the normal force has been increased. Hence, the results indicate that the coefficient of friction depends on pressure distribution at the contact and decreases with increase in contact pressure [1].

Test results for different lubricant amounts, orientation of strip with respect to rolling direction and roll temperature are depicted in Fig. 7. The amount of lubricant in the selected range (0.5 g/m² to 2 g/m²), appears to have no significant effect on the draw force. One explanation can be related to not having hydrodynamic pressure and distribution of the hot-melt solid lubricant on the surface. If hydrodynamic pressure does not build up due to low sliding velocity and the fact that lubricant is not fluid, asperity ploughing, and shear of boundary layers determine the coefficient of friction.
The lubricant might cover both valleys and asperities instead of just filling the valleys. In that case the shear of lubricant layer plays an important role in determining the friction forces. Further study needs to be done to understand the lubricant behavior and effects. The sheet orientation regarding to the rolling direction also did not affect the force significantly, although further investigation needs to be done to draw a conclusion. Using different roll temperatures, RT, 40°C, 80°C, appears to affect the friction force. The draw forces for roll in room temperature and 40°C are almost the same while that for roll in 80°C is slightly higher. The increase in the draw force can be explained by the increase of the friction force due to reduction in viscosity of lubricant since its melting temperature is approximately 40°C.

<figure><img src="image_1216.png" /><figcaption>Fig. 7. The effect of lubricant amount, rolling direction and roll temperature on difference between draw force and back force.</figcaption></figure>

Real area of contact has been calculated using the surface height probability density histogram [16]. Fig. 8 shows the surface topographies and height probability density histograms of the BUT samples with 1 kN, 2 kN and 4 kN back forces. The red lines show the heights with maximum probability and the numbers (α) are the percentage of area below the curve to the right which are the real area of contact. The real area of contact for different test repetitions and conditions are shown in Fig. 9. The real area of contact for samples with 4 kN appears to be smaller than samples with 1 kN and 2 kN. This is in agreement with FE simulation results, which show that the contact pressure for 4 kN is lower than contact pressure for 2 kN, however, the contact area in the case of 4kN is larger than the one from 2kN case.

<figure><img src="image_1217.png" /><figcaption>Fig. 8. Surface topographies and height probability density histograms of BUT samples.</figcaption></figure>
The lubricant might cover both valleys and asperities instead of just filling the valleys. In that case the shear of lubricant layer plays an important role in determining the friction forces. Further study needs to be done to understand the lubricant behavior and effects. The sheet orientation regarding to the rolling direction also did not affect the force significantly, although further investigation needs to be done to draw a conclusion. Using different roll temperatures, RT, 40°C, 80°C, appears to affect the friction force. The draw forces for roll in room temperature and 40°C are almost the same while that for roll in 80°C is slightly higher. The increase in the draw force can be explained by the increase of the friction force due to reduction in viscosity of lubricant since its melting temperature is approximately 40°C.

<figure><img src="image_1218.png" /><figcaption>Fig. 7. The effect of lubricant amount, rolling direction and roll temperature on difference between draw force and back force.</figcaption></figure>

Real area of contact has been calculated using the surface height probability density histogram [16]. Fig. 8 shows the surface topographies and height probability density histograms of the BUT samples with 1 kN, 2 kN and 4 kN back forces. The red lines show the heights with maximum probability and the numbers (α) are the percentage of area below the curve to the right which are the real area of contact. The real area of contact for different test repetitions and conditions are shown in Fig. 9. The real area of contact for samples with 4 kN appears to be smaller than samples with 1 kN and 2 kN. This is in agreement with FE simulation results, which show that the contact pressure for 4 kN is lower than contact pressure for 2 kN, however, the contact area in the case of 4kN is larger than the one from 2kN case.

<figure><img src="image_1219.png" /><figcaption>Fig. 8. Surface topographies and height probability density histograms of BUT samples.</figcaption></figure>
<figure><img src="image_1218.png" /><figcaption>Fig. 9. Real area of contact from height distribution histograms for different BUT tests.</figcaption></figure>

**Conclusions**

The BUT test was used to examine the effects of different parameters on the friction force. The bending and unbending force contribution to the difference between draw force and back force can be determined by FE simulations of the experiment with the friction coefficient of zero. The FE simulation was validated using DIC. The contact pressure distribution over the width is not uniform and close to edges there are contact pressure peaks.

The force-displacement results imply that with increasing back force, friction force will not necessarily increase. Increasing the back force from 2 kN to 4 kN causes the strip to follow the roll curvature better than increases the contact area and consequently reduces the local contact pressure (element level). This results in a friction force decrease. In other words, the average coefficient of friction decreases with increasing back-force. By looking at the real area of contact, it can also be seen that for 4 kN back force the real area of contact is smaller (due to lower contact pressure) and therefore, the coefficient of friction is smaller. There was no significant difference in the draw force results regarding different lubricant amounts and rolling directions of the sheet. However, for the roll at 80°C, the draw force is slightly higher than RT and 40°C. This can be explained by melting the lubricant at high temperature and reduction in drylube viscosity.

**Acknowledgments**

The authors would like to acknowledge the partners in FORMALUB project. This work has been financially supported by the FORMALUB Project.

**References**

[1] M. Shisode, J. Hazrati, T. Mishra, M. de Rooij, C. ten Horn, J. van Beeck, T. van den Boogaard. Modeling boundary friction of coated sheets in sheet metal forming. Tribology International. 2021;153:106554. https://doi.org/10.1016/j.triboint.2020.106554

[2] S.C. Tung, M. Wenner, Z. Guo, Z. Li, X. Dong. An in-situ tribotest method designed for predicting wear life and frictional performance during the aluminum forming process. Tribology and Interface Engineering Series. 2005;48:187-205. https://doi.org/10.1016/S0167-8922(05)80021-5

[3] R. Zhou, J. Cao, Q.J. Wang, F. Meng, K. Zimowski, Z.C. Xia. Effect of EDT surface texturing on tribological behavior of aluminum sheet. Journal of Materials Processing Technology. 2011;211(10):1643-9. https://doi.org/10.1016/j.jmatprotec.2011.05.004

[4] S. Dou, J. Xia. Analysis of Sheet Metal Forming (Stamping Process): A Study of the Variable Friction Coefficient on 5052 Aluminum Alloy. Metals. 2019;9(8):853. https://doi.org/10.3390/met9080853
<figure><img src="image_1220.png" /><figcaption>Fig. 9. Real area of contact from height distribution histograms for different BUT tests.</figcaption></figure>

**Conclusions**

The BUT test was used to examine the effects of different parameters on the friction force. The bending and unbending force contribution to the difference between draw force and back force can be determined by FE simulations of the experiment with the friction coefficient of zero. The FE simulation was validated using DIC. The contact pressure distribution over the width is not uniform and close to edges there are contact pressure peaks.

The force-displacement results imply that with increasing back force, friction force will not necessarily increase. Increasing the back force from 2 kN to 4 kN causes the strip to follow the roll curvature better than increases the contact area and consequently reduces the local contact pressure (element level). This results in a friction force decrease. In other words, the average coefficient of friction decreases with increasing back-force. By looking at the real area of contact, it can also be seen that for 4 kN back force the real area of contact is smaller (due to lower contact pressure) and therefore, the coefficient of friction is smaller. There was no significant difference in the draw force results regarding different lubricant amounts and rolling directions of the sheet. However, for the roll at 80°C, the draw force is slightly higher than RT and 40°C. This can be explained by melting the lubricant at high temperature and reduction in drylube viscosity.

**Acknowledgments**

The authors would like to acknowledge the partners in FORMALUB project. This work has been financially supported by the FORMALUB Project.

**References**

[1] M. Shisode, J. Hazrati, T. Mishra, M. de Rooij, C. ten Horn, J. van Beeck, T. van den Boogaard. Modeling boundary friction of coated sheets in sheet metal forming. Tribology International. 2021;153:106554. https://doi.org/10.1016/j.triboint.2020.106554

[2] S.C. Tung, M. Wenner, Z. Guo, Z. Li, X. Dong. An in-situ tribotest method designed for predicting wear life and frictional performance during the aluminum forming process. Tribology and Interface Engineering Series. 2005;48:187-205. https://doi.org/10.1016/S0167-8922(05)80021-5

[3] R. Zhou, J. Cao, Q.J. Wang, F. Meng, K. Zimowski, Z.C. Xia. Effect of EDT surface texturing on tribological behavior of aluminum sheet. Journal of Materials Processing Technology. 2011;211(10):1643-9. https://doi.org/10.1016/j.jmatprotec.2011.05.004

[4] S. Dou, J. Xia. Analysis of Sheet Metal Forming (Stamping Process): A Study of the Variable Friction Coefficient on 5052 Aluminum Alloy. Metals. 2019;9(8):853. https://doi.org/10.3390/met9080853
[5] S. Dou, X. Wang, J. Xia, L. Wilson. Analysis of sheet metal forming (Warm stamping process): A study of the variable friction coefficient on 6111 aluminum alloy. Metals. 2020;10(9):1-16. https://doi.org/10.3390/met10091189

[6] J.S. Wu, Y.H. Jiang, W.R. Wang, X.C. Wei. High-temperature friction of 7075 aluminum alloy sheet during hot stamping. Gongcheng Kexue Xuebao/Chinese Journal of Engineering. 2020;42(12):1631-8.

[7] A. Shafiee Sabet, J. Domitner, K.I. Öksüz, E. Hodžić, H. Torres, M. Rodríguez Ripoll, C. Sommitsch. Tribological investigations on aluminum alloys at different contact conditions for simulation of deep drawing processes. Journal of Manufacturing Processes. 2021;68:546-57. https://doi.org/10.1016/j.jmapro.2021.05.050

[8] M. Meiler, M. Pfestorf, M. Geiger, M. Merklein. The use of dry film lubricants in aluminum sheet metal forming. Wear. 2003;255(7-12):1455-62. https://doi.org/10.1016/S0043-1648(03)00087-5

[9] M. Meiler, H. Jaschke, editors. Lubrication of aluminium sheet metal within the automotive industry. Advanced Materials Research; 2005: Trans Tech Publ. https://doi.org/10.4028/0-87849-972-5.551

[10] T. Trzepiecinski. A Study of the Coefficient of Friction in Steel Sheets Forming. Metals. 2019;9(9):988. https://doi.org/10.3390/met9090988

[11] Y.S. Kim, M.K. Jain, D.R. Metzger. Determination of pressure-dependent friction coefficient from draw-bend test and its application to cup drawing. International Journal of Machine Tools and Manufacture. 2012;56:69-78. https://doi.org/10.1016/j.ijmachtools.2011.12.011

[12] H.G. Lemu, T. Trzepieciński. Numerical and Experimental Study of Frictional Behavior in Bending Under Tension Test. Strojniski Vestnik/Journal of Mechanical Engineering. 2013;59(1). https://doi.org/10.5545/sv-jme.2012.383

[13] D.W. Vallance, D.K. Matlock. Application of the bending-under-tension friction test to coated sheet steels. Journal of Materials Engineering and Performance. 1992;1(5):685-93. https://doi.org/10.1007/BF02649250

[14] N. Nanayakkara, G. Kelly, P. Hodgson, editors. Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming. Materials forum; 2005: IMEA.

[15] T. Trzepieciński, H.G. Lemu. Proposal for an Experimental-Numerical Method for Friction Description in Sheet Metal Forming. Strojniski Vestnik/Journal of Mechanical Engineering. 2015;61(6). https://doi.org/10.5545/sv-jme.2015.2404

[16] M.P. Shisode, J. Hazrati, T. Mishra, M.B. de Rooij, A.H. van den Boogaard. Semi-analytical contact model to determine the flattening behavior of coated sheets under normal load. Tribology International. 2020;146:106182. https://doi.org/10.1016/j.triboint.2020.106182
[5] S. Dou, X. Wang, J. Xia, L. Wilson. Analysis of sheet metal forming (Warm stamping process): A study of the variable friction coefficient on 6111 aluminum alloy. Metals. 2020;10(9):1-16. https://doi.org/10.3390/met10091189

[6] J.S. Wu, Y.H. Jiang, W.R. Wang, X.C. Wei. High-temperature friction of 7075 aluminum alloy sheet during hot stamping. Gongcheng Kexue Xuebao/Chinese Journal of Engineering. 2020;42(12):1631-8.

[7] A. Shafiee Sabet, J. Domitner, K.I. Öksüz, E. Hodžić, H. Torres, M. Rodríguez Ripoll, C. Sommitsch. Tribological investigations on aluminum alloys at different contact conditions for simulation of deep drawing processes. Journal of Manufacturing Processes. 2021;68:546-57. https://doi.org/10.1016/j.jmapro.2021.05.050

[8] M. Meiler, M. Pfestorf, M. Geiger, M. Merklein. The use of dry film lubricants in aluminum sheet metal forming. Wear. 2003;255(7-12):1455-62. https://doi.org/10.1016/S0043-1648(03)00087-5

[9] M. Meiler, H. Jaschke, editors. Lubrication of aluminium sheet metal within the automotive industry. Advanced Materials Research; 2005: Trans Tech Publ. https://doi.org/10.4028/0-87849-972-5.551

[10] T. Trzepiecinski. A Study of the Coefficient of Friction in Steel Sheets Forming. Metals. 2019;9(9):988. https://doi.org/10.3390/met9090988

[11] Y.S. Kim, M.K. Jain, D.R. Metzger. Determination of pressure-dependent friction coefficient from draw-bend test and its application to cup drawing. International Journal of Machine Tools and Manufacture. 2012;56:69-78. https://doi.org/10.1016/j.ijmachtools.2011.12.011

[12] H.G. Lemu, T. Trzepieciński. Numerical and Experimental Study of Frictional Behavior in Bending Under Tension Test. Strojniski Vestnik/Journal of Mechanical Engineering. 2013;59(1). https://doi.org/10.5545/sv-jme.2012.383

[13] D.W. Vallance, D.K. Matlock. Application of the bending-under-tension friction test to coated sheet steels. Journal of Materials Engineering and Performance. 1992;1(5):685-93. https://doi.org/10.1007/BF02649250

[14] N. Nanayakkara, G. Kelly, P. Hodgson, editors. Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming. Materials forum; 2005: IMEA.

[15] T. Trzepieciński, H.G. Lemu. Proposal for an Experimental-Numerical Method for Friction Description in Sheet Metal Forming. Strojniski Vestnik/Journal of Mechanical Engineering. 2015;61(6). https://doi.org/10.5545/sv-jme.2015.2404

[16] M.P. Shisode, J. Hazrati, T. Mishra, M.B. de Rooij, A.H. van den Boogaard. Semi-analytical contact model to determine the flattening behavior of coated sheets under normal load. Tribology International. 2020;146:106182. https://doi.org/10.1016/j.triboint.2020.106182
# Effect of micro-plasto-hydrodynamic lubrication on strip surface in steel cold rolling

ELHAJJ Cynthia¹,²,*, LAHOUIJ Imène¹, LUONG Linh Phuong² and MONTMITONNET Pierre¹

¹Centre de Mise en Forme de Matériaux, MINES Paris | PSL Research University, CNRS UMR7635, France

²R&D research center, Aperam Stainless Europe, France

ªcynthia.elhajj@minesparis.psl.eu

**Keywords:** MPHDL Lubrication, Numerical Modelling, Steel Cold Rolling, Surface Finish

**Abstract.** This study employs numerical calculations based on the micro-plasto-hydrodynamic lubrication (MPHDL) theory to analyze the evolution of oil pits during the stainless-steel cold rolling process. The model is enhanced by incorporating lubricant temperature variations caused by its contact with the heated roll and strip, as well as variations in pit slope. The findings show the significant impact and relevance of considering these additional parameters in assessing the performance of the MPHDL mechanism. Notably, the model demonstrates good agreement with experimental measurements conducted on a Stainless-Steel grade undergoing multiple passes.

**Introduction**

Controlling friction in Stainless Steel (SS) cold rolling leads to a better surface finish resulting in superior product quality and more favorable economic outcomes, to reduced roll load (smaller tooling deformation, hence easier strip profile and flatness control) and torque (reduced power required from motors). In cold rolling, prioritizing lubrication modeling is a fundamental factor to address the challenging notion of effective friction control. Nonetheless, it is crucial to note that lubrication involves two distinct subproblems [1]: global lubrication, involving the feeding of lubricant to the process entry point, and local micro-scale lubrication, diving into the interactions unfolding at the local scale of asperity.

Hot-rolled stainless steel, ready for cold rolling, is first subjected to shot-blasting and pickling operations. The sheets are therefore left with craters (Fig. 1) which must be smoothed out during cold rolling to obtain a bright, glossy surface finish. But they form oil pits which resist smoothing [2], compromising the gloss of high-quality stainless-steel products. This emphasizes the significance of a microscale lubrication mechanism that facilitates both pit closure, particularly focusing on its impact at the local (pit) scale. The pits (diameter ~80-100µm, depth ~10-20µm) form oil reservoirs. Due to macroscopic plastic deformation of the strip, as the free volumes between the strip and the roll surface is reduced, the lubricant is pressurized in the pits. At a certain point, due to a hydrodynamic effect, the lubricant will escape to form a micro-film (< 3 µm thick) on the adjacent plateau, a 2-scale lubrication mechanism. This promotes a relation between the asperity crushing rate (reduction of the pits) and the quantity of escaping lubricant from the micro-pits. This mechanism is called Micro Plasto-Hydro-Dynamic Lubrication (MPHDL) [3].

A lot of experimental and numerical work has been done on the MPHDL mechanism. Bech et al. [4] conducted experiments using a transparent tool in a strip drawing configuration. As they observed and confirmed the escape phenomenon of the lubricant, the more important revelation was the demonstration of the influence of various parameters on the tendency for either backward or forward escape (it was also more developed by Bay et al. [5]). Due to this escape, Ahmed and Sutcliffe [6] were interested to observe the reduction of pit under this mechanism in SS strip

<figure><img src="image_1219.png" /></figure>
# Effect of micro-plasto-hydrodynamic lubrication on strip surface in steel cold rolling

ELHAJJ Cynthia¹,²,*, LAHOUIJ Imène¹, LUONG Linh Phuong² and MONTMITONNET Pierre¹

¹Centre de Mise en Forme de Matériaux, MINES Paris | PSL Research University, CNRS UMR7635, France

²R&D research center, Aperam Stainless Europe, France

ªcynthia.elhajj@minesparis.psl.eu

**Keywords:** MPHDL Lubrication, Numerical Modelling, Steel Cold Rolling, Surface Finish

**Abstract.** This study employs numerical calculations based on the micro-plasto-hydrodynamic lubrication (MPHDL) theory to analyze the evolution of oil pits during the stainless-steel cold rolling process. The model is enhanced by incorporating lubricant temperature variations caused by its contact with the heated roll and strip, as well as variations in pit slope. The findings show the significant impact and relevance of considering these additional parameters in assessing the performance of the MPHDL mechanism. Notably, the model demonstrates good agreement with experimental measurements conducted on a Stainless-Steel grade undergoing multiple passes.

**Introduction**

Controlling friction in Stainless Steel (SS) cold rolling leads to a better surface finish resulting in superior product quality and more favorable economic outcomes, to reduced roll load (smaller tooling deformation, hence easier strip profile and flatness control) and torque (reduced power required from motors). In cold rolling, prioritizing lubrication modeling is a fundamental factor to address the challenging notion of effective friction control. Nonetheless, it is crucial to note that lubrication involves two distinct subproblems [1]: global lubrication, involving the feeding of lubricant to the process entry point, and local micro-scale lubrication, diving into the interactions unfolding at the local scale of asperity.

Hot-rolled stainless steel, ready for cold rolling, is first subjected to shot-blasting and pickling operations. The sheets are therefore left with craters (Fig. 1) which must be smoothed out during cold rolling to obtain a bright, glossy surface finish. But they form oil pits which resist smoothing [2], compromising the gloss of high-quality stainless-steel products. This emphasizes the significance of a microscale lubrication mechanism that facilitates both pit closure, particularly focusing on its impact at the local (pit) scale. The pits (diameter ~80-100µm, depth ~10-20µm) form oil reservoirs. Due to macroscopic plastic deformation of the strip, as the free volumes between the strip and the roll surface is reduced, the lubricant is pressurized in the pits. At a certain point, due to a hydrodynamic effect, the lubricant will escape to form a micro-film (< 3 µm thick) on the adjacent plateau, a 2-scale lubrication mechanism. This promotes a relation between the asperity crushing rate (reduction of the pits) and the quantity of escaping lubricant from the micro-pits. This mechanism is called Micro Plasto-Hydro-Dynamic Lubrication (MPHDL) [3].

A lot of experimental and numerical work has been done on the MPHDL mechanism. Bech et al. [4] conducted experiments using a transparent tool in a strip drawing configuration. As they observed and confirmed the escape phenomenon of the lubricant, the more important revelation was the demonstration of the influence of various parameters on the tendency for either backward or forward escape (it was also more developed by Bay et al. [5]). Due to this escape, Ahmed and Sutcliffe [6] were interested to observe the reduction of pit under this mechanism in SS strip

<figure><img src="image_1221.png" /></figure>
drawing and cold rolling. They also established experimental method, using a three-dimensional profilometry data, to identify pits using different criteria [7]. In the same area, Sutcliffe and Georgiades [8] characterized and determined the pit features : depth, diameter and slope. The forward (HydroStatic, MPHSL) escape was addressed numerically as a cavity problem using a finite element method with a Darcy interfacial medium, following the model developed by Stephany et al. [9] and Caretta et al. [10]. The backward (HydroDynamic, MPHDL) escape was treated by Lo and Wilson[11] who assumed a workpiece consisting of triangular asperities transverse to the forming direction, compressed by a smooth tool ; they set up equations coupling strip plastic deformation, lubricant extraction and pit closure. Sutcliffe et al. [12] applied Lo and Wilson theory for a SS strip rolling and drawing case.

<figure><img src="image_1220.png" /><figcaption>Fig. 1 Scanning Electron Microscope (SEM) observation of a stainless-steel strip surface subjected to shot blast and pickling.</figcaption></figure>

This paper considers only MPHDL permeation without consideration of MPHSL or the global Plasto hydrodynamic lubrication (PHL). Its purpose is to rely on the methodology of Lo and Wilson model, incorporating additional parameters such as the effect of temperature or the pit slope variation, which have not been addressed previously, and assessing their impact on the effectiveness of this mechanism after a few passes.

## Model Description

The purpose of this model is to show the influence of pit oil escape (quantified by $h_1$, the oil film thickness formed at the edge of an asperity) on the evolution of pit closure (quantified by $(1 - A)$, where A is the actual contact area). Thus, the main idea is to find equations linking $h_1$ and A.

**Asperity crushing:** Studies have shown that asperities on the surface of the strip are crushed and flattened progressively while the strip is plastically deforming under the action of rolling, showing the influence of the macroscopic strain $\epsilon$. At the same time, the asperity is locally deforming with its own strain $\epsilon_a$ and strain rate (extension rate) $\dot{\epsilon}_a$ considered uniform and distinct from the strip elongation rate $\dot{\epsilon}$ (the difference is due to the flattening, so that $\dot{\epsilon}_a > \dot{\epsilon}$). Mathematically, both macroscopic and microscopic deformation can be shown by expressing the asperity crushing velocity $v_f$ using the time derivative of the mean depth of the asperity.

Fig. 2 shows the schematic of a triangular asperity. The geometry is described by the actual contact area A, the length between two consecutive asperities (the period) L and the slope of the asperity $\theta$. In the present paper, the latter is allowed to vary, contrary to previous models of the literature. Considering small asperity slope $\theta$, the depth of the asperity can be expressed as:

$$ \delta = \frac{(1-A)L\theta}{2} \qquad (1) $$
drawing and cold rolling. They also established experimental method, using a three-dimensional profilometry data, to identify pits using different criteria [7]. In the same area, Sutcliffe and Georgiades [8] characterized and determined the pit features : depth, diameter and slope. The forward (HydroStatic, MPHSL) escape was addressed numerically as a cavity problem using a finite element method with a Darcy interfacial medium, following the model developed by Stephany et al. [9] and Caretta et al. [10]. The backward (HydroDynamic, MPHDL) escape was treated by Lo and Wilson[11] who assumed a workpiece consisting of triangular asperities transverse to the forming direction, compressed by a smooth tool ; they set up equations coupling strip plastic deformation, lubricant extraction and pit closure. Sutcliffe et al. [12] applied Lo and Wilson theory for a SS strip rolling and drawing case.

<figure><img src="image_1222.png" /><figcaption>Fig. 1 Scanning Electron Microscope (SEM) observation of a stainless-steel strip surface subjected to shot blast and pickling.</figcaption></figure>

This paper considers only MPHDL permeation without consideration of MPHSL or the global Plasto hydrodynamic lubrication (PHL). Its purpose is to rely on the methodology of Lo and Wilson model, incorporating additional parameters such as the effect of temperature or the pit slope variation, which have not been addressed previously, and assessing their impact on the effectiveness of this mechanism after a few passes.

## Model Description

The purpose of this model is to show the influence of pit oil escape (quantified by $h_1$, the oil film thickness formed at the edge of an asperity) on the evolution of pit closure (quantified by $(1 - A)$, where A is the actual contact area). Thus, the main idea is to find equations linking $h_1$ and A.

**Asperity crushing:** Studies have shown that asperities on the surface of the strip are crushed and flattened progressively while the strip is plastically deforming under the action of rolling, showing the influence of the macroscopic strain $\epsilon$. At the same time, the asperity is locally deforming with its own strain $\epsilon_a$ and strain rate (extension rate) $\dot{\epsilon}_a$ considered uniform and distinct from the strip elongation rate $\dot{\epsilon}$ (the difference is due to the flattening, so that $\dot{\epsilon}_a > \dot{\epsilon}$). Mathematically, both macroscopic and microscopic deformation can be shown by expressing the asperity crushing velocity $v_f$ using the time derivative of the mean depth of the asperity.

Fig. 2 shows the schematic of a triangular asperity. The geometry is described by the actual contact area A, the length between two consecutive asperities (the period) L and the slope of the asperity $\theta$. In the present paper, the latter is allowed to vary, contrary to previous models of the literature. Considering small asperity slope $\theta$, the depth of the asperity can be expressed as:

$$ \delta = \frac{(1-A)L\theta}{2} \qquad (1) $$
<figure><img src="image_1221.png" /><figcaption>Fig. 2 Schematic of flattening of asperity with lubricant escape at the edge of the pit.</figcaption></figure>

Before deriving, A and L are replaced in Eq.(1) using their expression in Appendix, thus the asperity crushing velocity (Fig. 11) $v_f = -\frac{1}{2}\frac{d\bar{\delta}}{dt}$, becomes:

$$v_f = -\frac{\theta L(\dot{\epsilon} - A\dot{\epsilon}_a)}{4} - \frac{\dot{\theta}(1-A)L}{4} \quad (2)$$

Where $\dot{\theta}$ is the asperity slope variation rate.

The local dimensionless crushing rate W is then defined for a better representation of the flattening process:

$$W = \frac{2v_f}{\dot{\epsilon}L} \quad (3)$$

Combining Eq.(2) and Eq.(3) gives:

$$W = -\frac{\theta(\dot{\epsilon} - A\dot{\epsilon}_a)}{2\dot{\epsilon}} - \frac{\dot{\theta}(1-A)}{2\dot{\epsilon}} \quad (4)$$

A few hardness models [13,14,15,16] have been established to express the crushing rate function of the area of contact and the effective hardness $\Delta = \frac{p_p - p_v}{Y}$, where Y is the plane strain yield stress of the strip metal. The aim of those model is to compute the evolution of plateau and valley pressure respectively $p_p$ and $p_v$. Between those models, we select Sutcliffe [17] correlation, thus W can be expressed as:

$$W = A(1 - A)(C_1(\Delta) + C_2(\Delta)A + C_3(\Delta)A^2) \quad (5)$$

Where $C_1$, $C_2$ and $C_3$ are functions of $\Delta$ [17].

The plateau and valley pressure can be expressed as:

$$p_p = \bar{p} + (1 - A)Y\Delta \quad (6)$$

$$p_v = \bar{p} - AY\Delta \quad (7)$$

In the previous equations $A = f(\dot{\epsilon}_a)$, so the only unknowns are $\dot{\epsilon}_a$ and $\Delta$. Combining Eq.(4) and Eq.(5) gives the first nonlinear equations in the system to solve. The second equation is derived in the next subsection. It describes the relation between the thickness $h_1$ of the oil film escaping through the edge of the pit, the asperity strain rate $\dot{\epsilon}_a$ and effective hardness $\Delta$.
<figure><img src="image_1223.png" /><figcaption>Fig. 2 Schematic of flattening of asperity with lubricant escape at the edge of the pit.</figcaption></figure>

Before deriving, A and L are replaced in Eq.(1) using their expression in Appendix, thus the asperity crushing velocity (Fig. 11) $v_f = -\frac{1}{2}\frac{d\bar{\delta}}{dt}$ becomes:

$$v_f = -\frac{\theta L(\dot{\epsilon} - A\dot{\epsilon}_a)}{4} - \frac{\dot{\theta}(1-A)L}{4} \quad (2)$$

Where $\dot{\theta}$ is the asperity slope variation rate.

The local dimensionless crushing rate W is then defined for a better representation of the flattening process:

$$W = \frac{2v_f}{\dot{\epsilon}L} \quad (3)$$

Combining Eq.(2) and Eq.(3) gives:

$$W = -\frac{\theta(\dot{\epsilon} - A\dot{\epsilon}_a)}{2\dot{\epsilon}} - \frac{\dot{\theta}(1-A)}{2\dot{\epsilon}} \quad (4)$$

A few hardness models [13,14,15,16] have been established to express the crushing rate function of the area of contact and the effective hardness $\Delta = \frac{p_p - p_v}{Y}$, where Y is the plane strain yield stress of the strip metal. The aim of those model is to compute the evolution of plateau and valley pressure respectively $p_p$ and $p_v$. Between those models, we select Sutcliffe [17] correlation, thus W can be expressed as:

$$W = A(1 - A)(C_1(\Delta) + C_2(\Delta)A + C_3(\Delta)A^2) \quad (5)$$

Where $C_1$, $C_2$ and $C_3$ are functions of $\Delta$ [17].

The plateau and valley pressure can be expressed as:

$$p_p = \bar{p} + (1 - A)Y\Delta \quad (6)$$

$$p_v = \bar{p} - AY\Delta \quad (7)$$

In the previous equations $A = f(\dot{\epsilon}_a)$, so the only unknowns are $\dot{\epsilon}_a$ and $\Delta$. Combining Eq.(4) and Eq.(5) gives the first nonlinear equations in the system to solve. The second equation is derived in the next subsection. It describes the relation between the thickness $h_1$ of the oil film escaping through the edge of the pit, the asperity strain rate $\dot{\epsilon}_a$ and effective hardness $\Delta$.
**Flow of lubricant escaping the pits:** In this process, pits function as oil reservoirs. So, using Fig. 2, the oil volume in the triangle pit per unit width is defined as:

$$v = \frac{\delta^2}{2\theta} = \frac{\theta L^2 (1-A)^2}{4} \qquad (8)$$

The fluid is assumed incompressible. Consider the control volume “lubricant + edge of the pit,” the lubricant exits with a mean velocity $\bar{u}_1$ expressed in Appendix while the edge of the pit is moving in accordance with the asperity deformation rate $\dot{\epsilon}_a$. Using the conservation of mass, the mass flow of the lubricant exiting the reservoir is equal to the volume change in the reservoir per unit time. Differentiating Eq.(8) with respect to time gives:

$$\frac{dv}{dt} = \frac{\theta L^2 (1-A)(\dot{\epsilon}-A\dot{\epsilon}_a)}{2} + \frac{\dot{\theta} L^2 (1-A)^2}{4} = -h_1 \left( \frac{\bar{u}_1 + \frac{AL\dot{\epsilon}_a}{2}}{2} \right) \qquad (9)$$

Arranging Eq.(9) gives a first expression of the oil film thickness, based on geometrical arguments:

$$h_1 = - \frac{2\theta L^2 (1-A)(\dot{\epsilon}-A\dot{\epsilon}_a)}{2\bar{u}_1 + AL\dot{\epsilon}_a} - \frac{\dot{\theta} L^2 (1-A)^2}{2\bar{u}_1 + AL\dot{\epsilon}_a} \qquad (10)$$

Note that in Eq.(4) and Eq.(10), if we consider the slope of the asperity unchanged during the stretching of the asperity (so that $\dot{\theta} = 0$) as in former approaches, Lo and Wilson equations are retrieved [11].

At this stage, $h_1$ is a function of $\dot{\epsilon}_a$ : we need a second equation which will be found using another expression of $h_1$.

**Pressure distribution using Reynolds equation:** The surface is subjected to a mean pressure $\bar{p}$ resulting in the reduction of the pit volume. The latter will be pressurized to the point of escape due to hydrodynamic action. This will change the redistribution of the pressure map; notice in Fig. 2 how the pressure on the plateau becomes higher than the mean pressure while in the valley it decreases below it. This redistribution can be determined solving the Reynolds equation. Thus, the 1-D simplified Reynolds equations for an incompressible fluid is given by:

$$\frac{dQ}{dh} = - \frac{12\eta[p(x),T(x)]\alpha\bar{u}_1}{\theta} \frac{h-h_0}{h^3} = - \frac{12\eta_0[T(x)]\alpha\bar{u}_1}{\theta} \frac{h-h_0}{h^3} \qquad (11)$$

Where $Q = 1 - e^{-\alpha p}$ is the reduced pressure, $\alpha$ is the pressure viscosity coefficient and $h_0$ is a constant, the (unknown at this stage) thickness at the point where the pressure gradient becomes zero. The viscosity of the lubricant $\eta$ is always taken in such models as a function of the pressure only, neglecting the temperature effect, e.g. $\eta = \eta_0 e^{\alpha p}$. However, in a steady cold rolling state, the roll and strip surface can be heated up to 200°C which will logically affect the temperature of the lubricant in contact with both surfaces and hence its viscosity. For this reason, the viscosity in the present model will be expressed as [18]:

$$\eta = \eta_0 e^{-\beta(T_{lub} - T_0)} \qquad (12)$$

Where $\beta$ is the temperature viscosity coefficient, $T_{lub} = \frac{T_{r,b}+T_{s,b}}{2}$ is the lubricant local temperature (where r stands for roll, s for strip and b for bite region) and $T_0$ is the temperature at which the viscosity $\eta_0$ is given (often 40°C). The expression of the viscosity can now be replaced
**Flow of lubricant escaping the pits:** In this process, pits function as oil reservoirs. So, using Fig. 2, the oil volume in the triangle pit per unit width is defined as:

$$v = \frac{\delta^2}{2\theta} = \frac{\theta L^2 (1-A)^2}{4} \qquad (8)$$

The fluid is assumed incompressible. Consider the control volume “lubricant + edge of the pit,” the lubricant exits with a mean velocity $\bar{u}_1$ expressed in Appendix while the edge of the pit is moving in accordance with the asperity deformation rate $\dot{\epsilon}_a$. Using the conservation of mass, the mass flow of the lubricant exiting the reservoir is equal to the volume change in the reservoir per unit time. Differentiating Eq.(8) with respect to time gives:

$$\frac{dv}{dt} = \frac{\theta L^2 (1-A)(\dot{\epsilon}-A\dot{\epsilon}_a)}{2} + \frac{\dot{\theta} L^2 (1-A)^2}{4} = -h_1 \left( \frac{\bar{u}_1 + \frac{AL\dot{\epsilon}_a}{2}}{2} \right) \qquad (9)$$

Arranging Eq.(9) gives a first expression of the oil film thickness, based on geometrical arguments:

$$h_1 = - \frac{2\theta L^2 (1-A)(\dot{\epsilon}-A\dot{\epsilon}_a)}{2\bar{u}_1+AL\dot{\epsilon}_a} - \frac{\dot{\theta} L^2 (1-A)^2}{2\bar{u}_1+AL\dot{\epsilon}_a} \qquad (10)$$

Note that in Eq.(4) and Eq.(10), if we consider the slope of the asperity unchanged during the stretching of the asperity (so that $\dot{\theta} = 0$) as in former approaches, Lo and Wilson equations are retrieved [11].

At this stage, $h_1$ is a function of $\dot{\epsilon}_a$: we need a second equation which will be found using another expression of $h_1$.

**Pressure distribution using Reynolds equation:** The surface is subjected to a mean pressure $\bar{p}$ resulting in the reduction of the pit volume. The latter will be pressurized to the point of escape due to hydrodynamic action. This will change the redistribution of the pressure map; notice in Fig. 2 how the pressure on the plateau becomes higher than the mean pressure while in the valley it decreases below it. This redistribution can be determined solving the Reynolds equation. Thus, the 1-D simplified Reynolds equations for an incompressible fluid is given by:

$$\frac{dQ}{dh} = - \frac{12\eta[p(x),T(x)]\alpha\bar{u}_1}{\theta h^3} = - \frac{12\eta_0[T(x)]\alpha\bar{u}_1}{\theta h^3} \qquad (11)$$

Where $Q = 1 - e^{-\alpha p}$ is the reduced pressure, $\alpha$ is the pressure viscosity coefficient and $h_0$ is a constant, the (unknown at this stage) thickness at the point where the pressure gradient becomes zero. The viscosity of the lubricant $\eta$ is always taken in such models as a function of the pressure only, neglecting the temperature effect, e.g. $\eta = \eta_0 e^{\alpha p}$. However, in a steady cold rolling state, the roll and strip surface can be heated up to 200°C which will logically affect the temperature of the lubricant in contact with both surfaces and hence its viscosity. For this reason, the viscosity in the present model will be expressed as [18]:

$$\eta = \eta_0 e^{-\beta(T_{lub} - T_0)} \qquad (12)$$

Where $\beta$ is the temperature viscosity coefficient, $T_{lub} = \frac{T_{r,b}+T_{s,b}}{2}$ is the lubricant local temperature (where r stands for roll, s for strip and b for bite region) and $T_0$ is the temperature at which the viscosity $\eta_0$ is given (often 40°C). The expression of the viscosity can now be replaced
in Eq.(11). Integrating Eq.(11) with respect to h gives $Q = f(h) + Q_0$. The film thickness $h_1$ is considered small in front of the film thickness in the pit (equal to the depth of the pit), so that the pressure gradient becomes zero at the edge of the valley, resulting in $h_0 = h_1$. The boundary conditions are expressed as:

* At $h_1 = 0, Q_0 = 1 - e^{-\alpha p_v}$

* At $h = h_1 \neq 0, Q = 1 - e^{-\alpha p_v} = f(h_1) + Q_0$

The expression of the oil film thickness becomes:

$$h_1 = - \frac{6\eta_0 e^{-\beta(T_{tub} - T_0)} \alpha \bar{u}_1}{\theta(e^{-\alpha p_v} - e^{-\alpha p_p})} \quad (13)$$

Combining the two expressions of $h_1$ in Eq.(10) and Eq.(13) leads to the second nonlinear equation to complete our system.

**Implementation:** The system of equations has been solved in Python using general nonlinear solvers. The microscale lubrication model cannot be solved without data coming from the macroscale. Namely, the strain $\epsilon$, the strain rate $\dot{\epsilon}$, the mean pressure $\bar{p}$ and the relative velocity $u_1$ are separately computed in the strip, here using a slab method. The roll and strip surface temperature are calculated using a 2D finite difference method [19]. The expression of $p_p$ and $p_v$ given in Eq.(6) and Eq.(7) are replaced in the above equations. Therefore, the equations are solved in each slab to find $\dot{\epsilon}_a$ and $\Delta$ with an initial guess [$\dot{\epsilon}_a > \frac{\dot{\epsilon}}{A}$ and $\Delta > 0$]. The evolution of the area of contact A and the oil film thickness $h_1$ at the edge of the pit are then deduced, which closes the solution.

## Results and parameters study

This section presents the numerical results of the model, and the effects of several parameters on the efficacy of MPHDL. Rolling parameters for a chosen stainless-steel grade are summarized in Table 1. $A_0, L_0$ and $\theta_0$ are to be determined experimentally (see next section), however, for now, theoretical representative values will be used. Fig. 3 shows the result after one pass. The pits shrink (A increases) as the lubricant escapes and form a film at the edge, relubricating partially the plateau. The pressure at the valley increases along the bite while the plateau pressure decreases; they meet where $\Delta = 0$ at the exit of the bite region. An early cold rolling pass (initial thickness 5 mm) is selected because this is where the pit/plateau morphology of Fig. 1, hence the present model, applies.

**Number of passes:** Considering a schedule of reductions for three passes, $r = [18\%, 17\%, 17\%]$, Fig. 4 shows A reaches 90%, i.e. pits are almost closed after only three passes. Therefore, the MPHDL mechanism occurs only in the first passes.

**Strip thickness reduction:** A higher reduction rate will result in more pronounced plastic deformation of the strip. This leads to a faster flattening of the asperity thus closing of the pits. Fig. 5 shows that A evolves more with a higher reduction. Note that the length of contact (bite) changes with the reduction rate.

**Pit slope:** A pit with a smaller slope is easier to crush, this also leads to a higher evolution of the area of contact (Fig. 6).
in Eq.(11). Integrating Eq.(11) with respect to h gives $Q = f(h) + Q_0$. The film thickness $h_1$ is considered small in front of the film thickness in the pit (equal to the depth of the pit), so that the pressure gradient becomes zero at the edge of the valley, resulting in $h_0 = h_1$. The boundary conditions are expressed as:

* At $h_1 = 0, Q_0 = 1 - e^{-\alpha p_v}$

* At $h = h_1 \neq 0, Q = 1 - e^{-\alpha p_v} = f(h_1) + Q_0$

The expression of the oil film thickness becomes:

$$h_1 = - \frac{6\eta_0 e^{-\beta(T_{lub} - T_0)} \alpha \bar{u}_1}{\theta(e^{-\alpha p_v} - e^{-\alpha p_p})} \quad (13)$$

Combining the two expressions of $h_1$ in Eq.(10) and Eq.(13) leads to the second nonlinear equation to complete our system.

**Implementation:** The system of equations has been solved in Python using general nonlinear solvers. The microscale lubrication model cannot be solved without data coming from the macroscale. Namely, the strain $\varepsilon$, the strain rate $\dot{\varepsilon}$, the mean pressure $\bar{p}$ and the relative velocity $u_1$ are separately computed in the strip, here using a slab method. The roll and strip surface temperature are calculated using a 2D finite difference method [19]. The expression of $p_p$ and $p_v$ given in Eq.(6) and Eq.(7) are replaced in the above equations. Therefore, the equations are solved in each slab to find $\dot{\varepsilon}_a$ and $\Delta$ with an initial guess [$\dot{\varepsilon}_a > \frac{\dot{\varepsilon}}{A}$ and $\Delta > 0$]. The evolution of the area of contact A and the oil film thickness $h_1$ at the edge of the pit are then deduced, which closes the solution.

## Results and parameters study

This section presents the numerical results of the model, and the effects of several parameters on the efficacy of MPHDL. Rolling parameters for a chosen stainless-steel grade are summarized in Table 1. $A_0, L_0$ and $\theta_0$ are to be determined experimentally (see next section), however, for now, theoretical representative values will be used. Fig. 3 shows the result after one pass. The pits shrink (A increases) as the lubricant escapes and form a film at the edge, relubricating partially the plateau. The pressure at the valley increases along the bite while the plateau pressure decreases; they meet where $\Delta = 0$ at the exit of the bite region. An early cold rolling pass (initial thickness 5 mm) is selected because this is where the pit/plateau morphology of Fig. 1, hence the present model, applies.

**Number of passes:** Considering a schedule of reductions for three passes, $r = [18\%, 17\%, 17\%]$, Fig. 4 shows A reaches 90%, i.e. pits are almost closed after only three passes. Therefore, the MPHDL mechanism occurs only in the first passes.

**Strip thickness reduction:** A higher reduction rate will result in more pronounced plastic deformation of the strip. This leads to a faster flattening of the asperity thus closing of the pits. Fig. 5 shows that A evolves more with a higher reduction. Note that the length of contact (bite) changes with the reduction rate.

**Pit slope:** A pit with a smaller slope is easier to crush, this also leads to a higher evolution of the area of contact (Fig. 6).
<table><caption>Table 1 Typical rolling parameters</caption><thead><tr><td>Parameters</td><td>Values</td></tr></thead><tbody><tr><td>Entry strip thickness z<sub>0</sub></td><td>5 [mm]</td></tr><tr><td>Lubricant temperature T<sub>0</sub></td><td>40[°C]</td></tr><tr><td>Lubricant viscosity μ<sub>0</sub></td><td>0.08 [Pa.s]</td></tr><tr><td>Pressure viscosity coefficient α</td><td>1.5 × 10<sup>-8</sup> [m<sup>2</sup>/N]</td></tr><tr><td>Roll diameter D</td><td>60 [mm]</td></tr><tr><td>Roll speed u<sub>r</sub></td><td>2.5 [m/s]</td></tr><tr><td>Temperature viscosity coefficient β</td><td>0.08 [°C<sup>-1</sup>]</td></tr></tbody></table>

<figure><img src="image_1222.png" /><figcaption>Fig. 3 (a) Variation of the contact area ratio A and the film thickness $h_1$ across the bite region; (b) Variation of plateau and valley pressure across the bite region, $A_0 = 0.4$, $L_0 = 300 \mu m$, $\theta_0 = 10°$ and $r = 18\%$. X = 0 is bite inlet, bite outlet is at X ~ 5 mm.</figcaption></figure>

<figure><img src="image_1223.png" /><figcaption>Fig. 4 Variation of area of contact A through the bite after three passes, $\theta_0 = 10°$.</figcaption></figure>

**Lubricant viscosity and thermal effect:** Lubricant viscosity plays a crucial role in the lubrication process, especially in the initial stages. Fig. 7.a shows how, as the lubricant temperature increases (Fig. 7.d), the lubricant viscosity decreases through the bite. However, it is the entry viscosity that sets the lubrication regime and the thickness of film formed by the escaping lubricant. Fig. 7.b shows that the consideration of thermal effect has an important influence on the performance of the MPHDL mechanism: the decreasing viscosity results in smaller $h_1$, i.e. more oil staying in the pits and delaying their crushing. Considering variations in temperature, the pit closure is decelerated by 12.5%, an effect not accounted for when this parameter is neglected. This difference in result can be even higher depending on the temperature viscosity coefficient of the lubricant as shown in Fig. 7.c ($\beta = 0$ represents the scenario where there is no thermal effect).
<table><caption>Table 1 Typical rolling parameters</caption><thead><tr><td>Parameters</td><td>Values</td></tr></thead><tbody><tr><td>Entry strip thickness z<sub>0</sub></td><td>5 [mm]</td></tr><tr><td>Lubricant temperature T<sub>0</sub></td><td>40[°C]</td></tr><tr><td>Lubricant viscosity μ<sub>0</sub></td><td>0.08 [Pa.s]</td></tr><tr><td>Pressure viscosity coefficient α</td><td>1.5 × 10<sup>-8</sup> [m<sup>2</sup>/N]</td></tr><tr><td>Roll diameter D</td><td>60 [mm]</td></tr><tr><td>Roll speed u<sub>r</sub></td><td>2.5 [m/s]</td></tr><tr><td>Temperature viscosity coefficient β</td><td>0.08 [°C<sup>-1</sup>]</td></tr></tbody></table>

<figure><img src="image_1224.png" /><figcaption>Fig. 3 (a) Variation of the contact area ratio A and the film thickness $h_1$ across the bite region; (b) Variation of plateau and valley pressure across the bite region, $A_0 = 0.4$, $L_0 = 300 \ \mu m$, $\theta_0 = 10°$ and $r = 18\%$. X = 0 is bite inlet, bite outlet is at X ~ 5 mm.</figcaption></figure>

<figure><img src="image_1225.png" /><figcaption>Fig. 4 Variation of area of contact A through the bite after three passes, $\theta_0 = 10°$.</figcaption></figure>

**Lubricant viscosity and thermal effect:** Lubricant viscosity plays a crucial role in the lubrication process, especially in the initial stages. Fig. 7.a shows how, as the lubricant temperature increases (Fig. 7.d), the lubricant viscosity decreases through the bite. However, it is the entry viscosity that sets the lubrication regime and the thickness of film formed by the escaping lubricant. Fig. 7.b shows that the consideration of thermal effect has an important influence on the performance of the MPHDL mechanism: the decreasing viscosity results in smaller $h_1$, i.e. more oil staying in the pits and delaying their crushing. Considering variations in temperature, the pit closure is decelerated by 12.5%, an effect not accounted for when this parameter is neglected. This difference in result can be even higher depending on the temperature viscosity coefficient of the lubricant as shown in Fig. 7.c ($\beta = 0$ represents the scenario where there is no thermal effect).
<figure><img src="image_1224.png" /><figcaption>Fig. 5 Variation of area of contact A for different reductions, $\theta_0 = 10^\circ$.</figcaption></figure>

<figure><img src="image_1225.png" /><figcaption>Fig. 6 Variation of area of contact A for different pit angles $\theta$, $r = 18^\circ$.</figcaption></figure>

<figure><img src="image_1226.png" /><figcaption>Fig. 7 (a) Variation of lubricant viscosity through the bite; (b) Effect of lubricant temperature change on the elimination of pits; (c) Effect of the temperature viscosity coefficient $\beta$ on the elimination of pits; (d) Lubricant temperature variation through the bite.</figcaption></figure>
<figure><img src="image_1226.png" /><figcaption>Fig. 5 Variation of area of contact A for different reductions, $\theta_0 = 10^\circ$.</figcaption></figure>

<figure><img src="image_1227.png" /><figcaption>Fig. 6 Variation of area of contact A for different pit angles $\theta$, $r = 18^\circ$.</figcaption></figure>

<figure><img src="image_1228.png" /><figcaption>Fig. 7 (a) Variation of lubricant viscosity through the bite; (b) Effect of lubricant temperature change on the elimination of pits; (c) Effect of the temperature viscosity coefficient $\beta$ on the elimination of pits; (d) Lubricant temperature variation through the bite.</figcaption></figure>
## Experimental validation

This section compares numerical results with experimental tests on a series of strip subjected to up to three passes of cold rolling. In both cases, the required input parameters are $A_0$, $L_0$ and $\theta_0$, to be found experimentally. The experiment consists in the extraction of data using a profilometer. The observation surface was chosen to be $2 \times 2 \text{ mm}$ with a pitch step of $2 \times 2 \text{ µm}$. The extracted file was treated and corrected using the Gwyddion software. Fig. 8 shows the result for the initial strip. The next important step is to define at which depth a feature is a pit since the assumption $\delta \gg h_1$ is made in the model. To do so, a 3D height matrix (taken transverse to the rolling direction) was processed in Python to calculate the depth of features:

$$d[i, j] = H[i, j] - H_0 \qquad (14)$$

Where $d[i, j]$ is the depth matrix, $h[i, j]$ the height matrix and $H_0$ the reference height at which a plateau is considered. In the following, $H_0$ is chosen, for the best representation of the surface, at a cumulative probability of 90% of the surface profile height.

<figure><img src="image_1227.png" /><figcaption>Fig. 8 Height distribution profile of the initial shot blasted strip surface.</figcaption></figure>

Now, Ahmed and Sutcliffe [20] criterion can be used to identify the pits:

$$\left| \frac{d[i, j]}{R_q} \right| > \delta_p \qquad (15)$$

Where $\delta_p = 1$ is the tolerance for a roll roughness of $0.4 - 0.6 \text{ µm}$ and $R_q$ is the roll RMS roughness. So now, the depth of features that does not validate the criterion are set to zero in $d[i, j]$. Finally, $A$ is simply the percentage of plateau ($d[i, j] = 0$) in the matrix, $L$ is the period between two consecutive mean pits and $\theta$ is calculated through the mean depth and length of consecutive pits. The results are shown in Table 2 and Fig. 9. The results verify that the slope of asperity during the flattening process does not remain unchanged, contrary to the hypothesis in the literature models. Fig. 10 shows the numerical results agrees reasonably with the experimental data.

<figure><img src="image_1228.png" /><figcaption>Fig. 9 3D height representation of (a) initial strip; (b) strip after three passes.</figcaption></figure>
## Experimental validation

This section compares numerical results with experimental tests on a series of strip subjected to up to three passes of cold rolling. In both cases, the required input parameters are $A_0$, $L_0$ and $\theta_0$, to be found experimentally. The experiment consists in the extraction of data using a profilometer. The observation surface was chosen to be $2 \times 2$ mm with a pitch step of $2 \times 2$ µm. The extracted file was treated and corrected using the Gwyddion software. Fig. 8 shows the result for the initial strip. The next important step is to define at which depth a feature is a pit since the assumption $\delta \gg h_1$ is made in the model. To do so, a 3D height matrix (taken transverse to the rolling direction) was processed in Python to calculate the depth of features:

$$d[i, j] = H[i, j] - H_0 \qquad (14)$$

Where $d[i, j]$ is the depth matrix, $h[i, j]$ the height matrix and $H_0$ the reference height at which a plateau is considered. In the following, $H_0$ is chosen, for the best representation of the surface, at a cumulative probability of 90% of the surface profile height.

<figure><img src="image_1229.png" /><figcaption>Fig. 8 Height distribution profile of the initial shot blasted strip surface.</figcaption></figure>

Now, Ahmed and Sutcliffe [20] criterion can be used to identify the pits:

$$\left| \frac{d[i, j]}{R_q} \right| > \delta_p \qquad (15)$$

Where $\delta_p = 1$ is the tolerance for a roll roughness of $0.4 - 0.6$ µm and $R_q$ is the roll RMS roughness. So now, the depth of features that does not validate the criterion are set to zero in $d[i, j]$. Finally, $A$ is simply the percentage of plateau ($d[i, j] = 0$) in the matrix, $L$ is the period between two consecutive mean pits and $\theta$ is calculated through the mean depth and length of consecutive pits. The results are shown in Table 2 and Fig. 9. The results verify that the slope of asperity during the flattening process does not remain unchanged, contrary to the hypothesis in the literature models. Fig. 10 shows the numerical results agrees reasonably with the experimental data.

<figure><img src="image_1230.png" /><figcaption>Fig. 9 3D height representation of (a) initial strip; (b) strip after three passes.</figcaption></figure>
<table><caption>Table 2 Characterization of pit parameter</caption><thead><tr><th>Parameters</th><th>Initial strip</th><th>First Pass</th><th>Second Pass</th><th>Third Pass</th></tr></thead><tbody><tr><td>A<sub>0</sub></td><td>0.43</td><td>0.58</td><td>0.75</td><td>0.88</td></tr><tr><td>L<sub>0</sub></td><td>210 µm</td><td>270 µm</td><td>310 µm</td><td>380 µm</td></tr><tr><td>θ<sub>0</sub></td><td>13°</td><td>11.3°</td><td>8.5°</td><td>5°</td></tr></tbody></table>

<figure><img src="image_1229.png" /><figcaption>Fig. 10 Experimental Data to Numerical result comparison.</figcaption></figure>

## Conclusion

This paper presents a numerical model detailing the progression of oil pit closure during cold rolling through the application of the MPHDL theory. Notably, the outcomes reveal the practical suitability of this theory during the initial stages of a rolling schedule, wherein up to 90% of pits are effectively closed after three passes. A significant result of this study underscores the role of temperature variation in influencing the mechanism efficacy. The temperature impact on lubricant viscosity is identified as a key factor, introducing a nuanced perspective as it contributes to a less optimistic outcome, resulting in fewer pits being closed. Conclusively, our study enhanced its reliability by incorporating experimental data as input for the numerical model. This additional step not only validated the accuracy of our computational approach but also showed fair agreement between the numerical simulations and experimental results.

## Acknowledgements

The authors gratefully acknowledge grant CIFRE 2022/1447 from ANRT, and Aperam Stainless Europe for their generous support in providing materials and data for both experimental and numerical testing, which greatly enriched the scope and outcomes of this research. We extend our gratitude for Frederic Georgi for his invaluable help and assistance in operating the profilometer.

## Appendix

This Appendix presents the equations of the MPHDL model derived by Lo and Wilson [11].

<figure><img src="image_1230.png" /><figcaption>Fig. 11 Asperity flattening rate.</figcaption></figure>

The current asperity spacing, contact area and mean oil velocity at the asperity edge becomes:

$$L = L_0 e^{\epsilon} \qquad (A 1)$$

$$A = A_0 e^{\epsilon_a - \epsilon} \qquad (A 2)$$

$$\bar{u}_1 = \frac{u_1 - \frac{AL\epsilon_a}{2}}{2} \qquad (A 3)$$
<table><caption>Table 2 Characterization of pit parameter</caption><thead><tr><th>Parameters</th><th>Initial strip</th><th>First Pass</th><th>Second Pass</th><th>Third Pass</th></tr></thead><tbody><tr><td>A<sub>0</sub></td><td>0.43</td><td>0.58</td><td>0.75</td><td>0.88</td></tr><tr><td>L<sub>0</sub></td><td>210 µm</td><td>270 µm</td><td>310 µm</td><td>380 µm</td></tr><tr><td>θ<sub>0</sub></td><td>13°</td><td>11.3°</td><td>8.5°</td><td>5°</td></tr></tbody></table>

<figure><img src="image_1231.png" /><figcaption>Fig. 10 Experimental Data to Numerical result comparison.</figcaption></figure>

## Conclusion

This paper presents a numerical model detailing the progression of oil pit closure during cold rolling through the application of the MPHDL theory. Notably, the outcomes reveal the practical suitability of this theory during the initial stages of a rolling schedule, wherein up to 90% of pits are effectively closed after three passes. A significant result of this study underscores the role of temperature variation in influencing the mechanism efficacy. The temperature impact on lubricant viscosity is identified as a key factor, introducing a nuanced perspective as it contributes to a less optimistic outcome, resulting in fewer pits being closed. Conclusively, our study enhanced its reliability by incorporating experimental data as input for the numerical model. This additional step not only validated the accuracy of our computational approach but also showed fair agreement between the numerical simulations and experimental results.

## Acknowledgements

The authors gratefully acknowledge grant CIFRE 2022/1447 from ANRT, and Aperam Stainless Europe for their generous support in providing materials and data for both experimental and numerical testing, which greatly enriched the scope and outcomes of this research. We extend our gratitude for Frederic Georgi for his invaluable help and assistance in operating the profilometer.

## Appendix

This Appendix presents the equations of the MPHDL model derived by Lo and Wilson [11].

<figure><img src="image_1232.png" /><figcaption>Fig. 11 Asperity flattening rate.</figcaption></figure>

The current asperity spacing, contact area and mean oil velocity at the asperity edge becomes:

$$L = L_0 e^{\epsilon} \qquad (A 1)$$

$$A = A_0 e^{\epsilon_a - \epsilon} \qquad (A 2)$$

$$\bar{u}_1 = \frac{u_1 - \frac{AL\epsilon_a}{2}}{2} \qquad (A 3)$$
## References

[1] M. Laugier, R. Boman and Y. Carretta, Micro-Plasto-Hydrodynamic Lubrication a Fundamental Mechanism in Cold Rolling, Adv. Mater. Res. 966-967 (2014) 228-241. https://doi.org/10.4028/www.scientific.net/AMR.966-967.228

[2] J. Bech, N. Bay and M. Eriksen, A Study of Mechanisms of Liquid Lubrication in Metal Forming, CIRP Ann. 47 (1998) 221-226. https://doi.org/10.1016/S0007-8506(07)62822-4.

[3] H. Kudo, M. Tsubouchi, H. Takada and K. Okamura, An Investigation into Plasto-Hydrodynamic Lubrication with a Cold Sheet Drawing Test, CIRP Ann. 31 (1982) 175-180. https://doi.org/10.1016/S0007-8506(07)63292-2

[4] J. Bech, N. Bay and M. Eriksen, Entrapment and escape of liquid lubricant in metal forming, Wear 232 (1999) 134-139. https://doi.org/10.1016/S0043-1648(99)00136-2

[5] N. Bay, J. I. Bech, J. L. Andreasen and I. Shimizu, Studies on Micro Plasto Hydrodynamic Lubrication in Metal Forming, Metal Forming Science and Practice, Elsevier, 2002, pp. 115-134. https://doi.org/10.1016/B978-008044024-8/50007-2

[6] R. Ahmed and M. P. F. Sutcliffe, An Experimental Investigation of Surface Pit Evolution During Cold-Rolling or Drawing of Stainless Steel Strip, J. Tribol. 123 (2001) 1-7. https://doi.org/10.1115/1.1327580

[7] R. Ahmed and M. P. F. Sutcliffe, Identification of surface features on cold-rolled stainless steel strip, Wear 244 (2000) 60-70. https://doi.org/10.1016/S0043-1648(00)00442-7

[8] M. P. F. Sutcliffe and F. Georgiades, Characterisation of pit geometry in cold-rolled stainless steel strip, Wear 253 (2002) 963-974. https://doi.org/10.1016/S0043-1648(02)00247-8

[9] A. Stephany, H. R. Le and M. P. F. Sutcliffe, An efficient finite element model of surface pit reduction on stainless steel in metal forming processes, J. Mater. Process. Technol. 170 (2005) 310-316. https://doi.org/10.1016/j.jmatprotec.2005.05.008

[10] Y. Carretta, J. Bech, N. Legrand, M. Laugier, J.-P. Ponthot and R. Boman, Numerical modelling of micro-plasto-hydrodynamic lubrication in plane strip drawing, Tribol. Int. 110 (2017) 378-391. https://doi.org/10.1016/j.triboint.2016.10.046

[11] S.-W. Lo and W. R. D. Wilson, A Theoretical Model of Micro-Pool Lubrication in Metal Forming, J. Tribol. 121 (1999) 731-738. https://doi.org/10.1115/1.2834129

[12] M.P.F Sutcliffe, H.R. Le and R. Ahmed, Modeling of Micro-Pit Evolution in Rolling or Strip-Drawing, J. Tribol. 123 (2001) 791-798. https://doi.org/10.1115/1.1352741

[13] W.R.D Wilson, Friction and Lubrication in Sheet Metal Forming, in: Koistinen, D.P., Wang, NM. (eds), Mechanics of Sheet Metal Forming. Springer, Boston, 1978, pp. 157-174. https://doi.org/10.1007/978-1-4613-2880-3_7

[14] D. A. Korzekwa, P. R. Dawson and W. R. D. Wilson, Surface asperity deformation during sheet forming, Int. J. Mech. Sci. 34 (1992) 521-539. https://doi.org/10.1016/0020-7403(92)90028-F

[15] D. Adeleke, D. Kalumba, L. Nolutshungu, J. Oriokot and A. Martinez, The Influence of Asperities and Surface Roughness on Geomembrane/Geotextile Interface Friction Angle, Int. J. Geosynth. Ground Eng. 7 (2021). https://doi.org/10.1007/s40891-021-00265-y

[16] W. R. D. Wilson and S. Sheu, Real area of contact and boundary friction in metal forming, Int. J. Mech. Sci. 30 (1988) 475-489. https://doi.org/10.1016/0020-7403(88)90002-1
## References

[1] M. Laugier, R. Boman and Y. Carretta, Micro-Plasto-Hydrodynamic Lubrication a Fundamental Mechanism in Cold Rolling, Adv. Mater. Res. 966-967 (2014) 228-241. https://doi.org/10.4028/www.scientific.net/AMR.966-967.228

[2] J. Bech, N. Bay and M. Eriksen, A Study of Mechanisms of Liquid Lubrication in Metal Forming, CIRP Ann. 47 (1998) 221-226. https://doi.org/10.1016/S0007-8506(07)62822-4.

[3] H. Kudo, M. Tsubouchi, H. Takada and K. Okamura, An Investigation into Plasto-Hydrodynamic Lubrication with a Cold Sheet Drawing Test, CIRP Ann. 31 (1982) 175-180. https://doi.org/10.1016/S0007-8506(07)63292-2

[4] J. Bech, N. Bay and M. Eriksen, Entrapment and escape of liquid lubricant in metal forming, Wear 232 (1999) 134-139. https://doi.org/10.1016/S0043-1648(99)00136-2

[5] N. Bay, J. I. Bech, J. L. Andreasen and I. Shimizu, Studies on Micro Plasto Hydrodynamic Lubrication in Metal Forming, Metal Forming Science and Practice, Elsevier, 2002, pp. 115-134. https://doi.org/10.1016/B978-008044024-8/50007-2

[6] R. Ahmed and M. P. F. Sutcliffe, An Experimental Investigation of Surface Pit Evolution During Cold-Rolling or Drawing of Stainless Steel Strip, J. Tribol. 123 (2001) 1-7. https://doi.org/10.1115/1.1327580

[7] R. Ahmed and M. P. F. Sutcliffe, Identification of surface features on cold-rolled stainless steel strip, Wear 244 (2000) 60-70. https://doi.org/10.1016/S0043-1648(00)00442-7

[8] M. P. F. Sutcliffe and F. Georgiades, Characterisation of pit geometry in cold-rolled stainless steel strip, Wear 253 (2002) 963-974. https://doi.org/10.1016/S0043-1648(02)00247-8

[9] A. Stephany, H. R. Le and M. P. F. Sutcliffe, An efficient finite element model of surface pit reduction on stainless steel in metal forming processes, J. Mater. Process. Technol. 170 (2005) 310-316. https://doi.org/10.1016/j.jmatprotec.2005.05.008

[10] Y. Carretta, J. Bech, N. Legrand, M. Laugier, J.-P. Ponthot and R. Boman, Numerical modelling of micro-plasto-hydrodynamic lubrication in plane strip drawing, Tribol. Int. 110 (2017) 378-391. https://doi.org/10.1016/j.triboint.2016.10.046

[11] S.-W. Lo and W. R. D. Wilson, A Theoretical Model of Micro-Pool Lubrication in Metal Forming, J. Tribol. 121 (1999) 731-738. https://doi.org/10.1115/1.2834129

[12] M.P.F Sutcliffe, H.R. Le and R. Ahmed, Modeling of Micro-Pit Evolution in Rolling or Strip-Drawing, J. Tribol. 123 (2001) 791-798. https://doi.org/10.1115/1.1352741

[13] W.R.D Wilson, Friction and Lubrication in Sheet Metal Forming, in: Koistinen, D.P., Wang, NM. (eds), Mechanics of Sheet Metal Forming. Springer, Boston, 1978, pp. 157-174. https://doi.org/10.1007/978-1-4613-2880-3_7

[14] D. A. Korzekwa, P. R. Dawson and W. R. D. Wilson, Surface asperity deformation during sheet forming, Int. J. Mech. Sci. 34 (1992) 521-539. https://doi.org/10.1016/0020-7403(92)90028-F

[15] D. Adeleke, D. Kalumba, L. Nolutshungu, J. Oriokot and A. Martinez, The Influence of Asperities and Surface Roughness on Geomembrane/Geotextile Interface Friction Angle, Int. J. Geosynth. Ground Eng. 7 (2021). https://doi.org/10.1007/s40891-021-00265-y

[16] W. R. D. Wilson and S. Sheu, Real area of contact and boundary friction in metal forming, Int. J. Mech. Sci. 30 (1988) 475-489. https://doi.org/10.1016/0020-7403(88)90002-1
[17] M. P. F. Sutcliffe, Flattening of Random Rough Surfaces in Metal-Forming Processes, J. Tribol. 121 (1999) 433-440. https://doi.org/10.1115/1.2834086

[18] A. Azushima, Lubrication in steel strip rolling in Japan, Tribol. Int. 20 (1987) 316-321. https://doi.org/10.1016/0301-679X(87)90059-4

[19] A. A. Tseng, A Numerical Heat Transfer Analysis of Strip Rolling, J. Heat Transf. 106 (1984) 512-517. https://doi.org/10.1115/1.3246708

[20] R. Ahmed and M. P. F. Sutcliffe, Identification of surface features on cold-rolled stainless steel strip, Wear 244 (2000) 60-70. https://doi.org/10.1016/S0043-1648(00)00442-7
[17] M. P. F. Sutcliffe, Flattening of Random Rough Surfaces in Metal-Forming Processes, J. Tribol. 121 (1999) 433-440. https://doi.org/10.1115/1.2834086

[18] A. Azushima, Lubrication in steel strip rolling in Japan, Tribol. Int. 20 (1987) 316-321. https://doi.org/10.1016/0301-679X(87)90059-4

[19] A. A. Tseng, A Numerical Heat Transfer Analysis of Strip Rolling, J. Heat Transf. 106 (1984) 512-517. https://doi.org/10.1115/1.3246708

[20] R. Ahmed and M. P. F. Sutcliffe, Identification of surface features on cold-rolled stainless steel strip, Wear 244 (2000) 60-70. https://doi.org/10.1016/S0043-1648(00)00442-7
# Analysis of wear behavior of powder metallurgy tools in shear cutting of electrical steels

KUMAR SUNDARAJAN Praveen¹,ª, ŞELTE Aydın²,ᵇ*, HOENEN Niklas¹,ᶜ, CLAUSMEYER Till¹,ᵈ and TEKKAYA A. Erman¹,ᵉ

¹Institute of Forming Technology and Lightweight Components, TU Dortmund University, Baroper Str. 303, D-44227 Dortmund, Germany

²Uddeholm s AB, SE-683 85 Hagfors, Sweden

ªPraveen.kumar-sundarajan@thermic-energy.com, ᵇAydin.Selte@uddeholm.com,

ᶜniklas.hoenen@iul.tu-dortmund.de, ᵈtill.clausmeyer@iul.tu-dortmund.de,

ᵉerman.tekkaya@iul.tu-dortmund.de

**Keywords:** Shear Cutting, Electrical Steel, Tool Steels, Wear

**Abstract.** The shear-cutting process of electrical steels for electrical engines' rotors and stators influences the properties of the shear-cut edges. The properties such as geometry and mechanical and electromagnetic properties of shear-cut edges depend on the wear behavior of the tools. This study examines tool wear in three powder (PM1, PM8, PM10) metallurgical tool steels during shear cutting of electrical steel. PM1 is intended for high-performance applications owing to its unique mixture of boride and carbide precipitates. PM8 is a high alloyed Cr-Mo-V tool steel tailored for abrasive wear applications with a certain amount of ductility, and PM10 is a nitrogen alloyed tool steel specifically designed for applications where adhesive wear resistance is required. Tool wear and shear-cut edge properties were analyzed at four different intervals of punch strokes for 8% and 16% cutting clearances. The experimental study found that the 8% clearance caused excessive chipping in punch corners for all three materials, mainly PM10, which chipped in all corners at the end of 108,000 strokes. In contrast, PM1 demonstrated better chipping resistance, particularly at 16% clearances. Furthermore, PM1 showed superior resistance to edge wear for various punch strokes and clearances.

**Introduction and Background**

Blanking efficiently produces sheet metal parts without chip formation, relying on factors like punch-die clearance (c), sheet thickness (t), and punch radius ($R_p$) for accuracy [1]. The guideline VDI 2906 identifies four key edge characteristics: rollover from bending, burnishing, and angular fractures caused by sharp punches and burr formation from excessive clearance or dull tools [2]. The clearance significantly impacts tool wear and sheared edge quality; an excessive clearance causes burrs and rough fracture zones, complicating further processing.

Wear on the tool surface while blanking leads to alterations in the quality of the cut surface. The cutting-edge radius significantly influences energy consumption during blanking [3]. Wear typically occurs on the tool's outer surface, rounding the cutting edge, attributed to adhesion, abrasion, fatigue, and tribochemical wear processes [1]. According to [4], due to repeated impact loads or thermal shocks, the punch experiences some micro crushes, fragments, and breaking on the cutting edges, and mechanical or thermal fatigue during blanking creates irregular microcracks that propagate and produce chipping or macro fracture with a further increase in punch strokes.

[5] stated that electrical steels are the most commonly utilized soft magnetic materials. Non-oriented electrical steel is vital for motor components like rotors and stators. Although blanking is the favored method due to its efficiency and cost-effectiveness, it introduces high stress and strain near the sheared edge. [6] conducted a silicon steel blanking experiment, revealing gradual cutting-

<figure><img src="image_1231.png" /></figure>
# Analysis of wear behavior of powder metallurgy tools in shear cutting of electrical steels

KUMAR SUNDARAJAN Praveen¹,ª, ŞELTE Aydın²,ᵇ*, HOENEN Niklas¹,ᶜ, CLAUSMEYER Till¹,ᵈ and TEKKAYA A. Erman¹,ᵉ

¹Institute of Forming Technology and Lightweight Components, TU Dortmund University, Baroper Str. 303, D-44227 Dortmund, Germany

²Uddeholm s AB, SE-683 85 Hagfors, Sweden

ªPraveen.kumar-sundarajan@thermic-energy.com, ᵇAydin.Selte@uddeholm.com,

ᶜniklas.hoenen@iul.tu-dortmund.de, ᵈtill.clausmeyer@iul.tu-dortmund.de,

ᵉerman.tekkaya@iul.tu-dortmund.de

**Keywords:** Shear Cutting, Electrical Steel, Tool Steels, Wear

**Abstract.** The shear-cutting process of electrical steels for electrical engines' rotors and stators influences the properties of the shear-cut edges. The properties such as geometry and mechanical and electromagnetic properties of shear-cut edges depend on the wear behavior of the tools. This study examines tool wear in three powder (PM1, PM8, PM10) metallurgical tool steels during shear cutting of electrical steel. PM1 is intended for high-performance applications owing to its unique mixture of boride and carbide precipitates. PM8 is a high alloyed Cr-Mo-V tool steel tailored for abrasive wear applications with a certain amount of ductility, and PM10 is a nitrogen alloyed tool steel specifically designed for applications where adhesive wear resistance is required. Tool wear and shear-cut edge properties were analyzed at four different intervals of punch strokes for 8% and 16% cutting clearances. The experimental study found that the 8% clearance caused excessive chipping in punch corners for all three materials, mainly PM10, which chipped in all corners at the end of 108,000 strokes. In contrast, PM1 demonstrated better chipping resistance, particularly at 16% clearances. Furthermore, PM1 showed superior resistance to edge wear for various punch strokes and clearances.

**Introduction and Background**

Blanking efficiently produces sheet metal parts without chip formation, relying on factors like punch-die clearance (c), sheet thickness (t), and punch radius ($R_p$) for accuracy [1]. The guideline VDI 2906 identifies four key edge characteristics: rollover from bending, burnishing, and angular fractures caused by sharp punches and burr formation from excessive clearance or dull tools [2]. The clearance significantly impacts tool wear and sheared edge quality; an excessive clearance causes burrs and rough fracture zones, complicating further processing.

Wear on the tool surface while blanking leads to alterations in the quality of the cut surface. The cutting-edge radius significantly influences energy consumption during blanking [3]. Wear typically occurs on the tool's outer surface, rounding the cutting edge, attributed to adhesion, abrasion, fatigue, and tribochemical wear processes [1]. According to [4], due to repeated impact loads or thermal shocks, the punch experiences some micro crushes, fragments, and breaking on the cutting edges, and mechanical or thermal fatigue during blanking creates irregular microcracks that propagate and produce chipping or macro fracture with a further increase in punch strokes.

[5] stated that electrical steels are the most commonly utilized soft magnetic materials. Non-oriented electrical steel is vital for motor components like rotors and stators. Although blanking is the favored method due to its efficiency and cost-effectiveness, it introduces high stress and strain near the sheared edge. [6] conducted a silicon steel blanking experiment, revealing gradual cutting-

<figure><img src="image_1233.png" /></figure>
edge wear at 0% clearance, increased plastic deformation zone and cutting-edge rounding with an 8% clearance. [7] studied tool wear in 22MnB5 boron steel blanking, noting minimal wear in S390 material, manufactured through powder metallurgic processes, compared to K340, which is cold work tool steel manufactured from electro slag remelting. Tool wear directly impacts sheared edge quality. Studies by [8] link tool wear to crucial burr length assessment for product quality.

[9] found high stroke counts (40,000 to 60,000) significantly increase burrs due to intense punch strokes. [10] discovered that clearance (5-20%) affects sheared edges, altering zones and reducing tool life. Inadequate clearance causes secondary shear, demanding more energy [11]. [6] noted microhardness testing analyzes work hardening in sheared edges; punch wear widens blanking gaps, raising shear stress changes in tool geometry impact microhardness, reducing Shear-Affected Zones (SAZ) with smaller clearances. [12] demonstrated intensified work hardening near edges due to tool wear.

Powder Metallurgy (PM) High-Speed Steels offer an alternative to conventionally produced tool steels, showcasing unique attributes like heightened hardness and toughness, distinguishing them from traditional tool steels. While extensive research has centered on analyzing tool wear on electrical sheets, there remains a notable gap in exploring powder metallurgical (PM) tools in the blanking process of electrical steels. This study thoroughly examines tool wear analysis using three distinct PM tool steels for varying clearances. Furthermore, it examines the properties of sheared edges resulting from different punch strokes.

## Procedure

A TruPunch 5000 was used for experimental blanking with a 1000 mm x 1000 mm blank. A total of 108,000 strokes are performed using a 10 mm x 10 mm punch and two dies (10.16 mm and 10.32 mm), as shown in Fig. 1.

No lubricant or BHF was used. The analysis was conducted after 9,000, 45,000, 81,000, and 108,000 strokes.

<figure><img src="image_1232.png" /><figcaption>Figure 1: Schematic diagram of square punch with different die dimensions.</figcaption></figure>

## Tool Steel

This work uses three powder metallurgical tool steel, namely, PM1 (X50MoCoCr17-4), PM8 (X230VCrMo8-5), and PM10 (X130VMoN10-2). PM8 is abrasive-resistant with a lower hard phase content than PM1, while PM10 has enhanced anti-galling properties and it contains 1.8% of Ni. PM1 is an abrasive-resistant material with higher compressive strength. Chemical composition and properties are given in Tables 1 and 2.

<table><caption>Table 1: Chemical composition of three punch materials.</caption><thead><tr><th>Grade</th><th>C, %</th><th>Si, %</th><th>Mn, %</th><th>Cr, %</th><th>Mo, %</th><th>V, %</th></tr></thead><tbody><tr><td>PM1</td><td>0.5</td><td>1.0</td><td>0.3</td><td>4.2</td><td>17.3</td><td><strong>0.25</strong></td></tr><tr><td>PM8</td><td>2.3</td><td>0.4</td><td>0.4</td><td>4.8</td><td>3.6</td><td><strong>8</strong></td></tr><tr><td>PM10</td><td>1.3</td><td>0.5</td><td>0.4</td><td>0.4</td><td>1.8</td><td><strong>10</strong></td></tr></tbody></table>
edge wear at 0% clearance, increased plastic deformation zone and cutting-edge rounding with an 8% clearance. [7] studied tool wear in 22MnB5 boron steel blanking, noting minimal wear in S390 material, manufactured through powder metallurgic processes, compared to K340, which is cold work tool steel manufactured from electro slag remelting. Tool wear directly impacts sheared edge quality. Studies by [8] link tool wear to crucial burr length assessment for product quality.

[9] found high stroke counts (40,000 to 60,000) significantly increase burrs due to intense punch strokes. [10] discovered that clearance (5-20%) affects sheared edges, altering zones and reducing tool life. Inadequate clearance causes secondary shear, demanding more energy [11]. [6] noted microhardness testing analyzes work hardening in sheared edges; punch wear widens blanking gaps, raising shear stress changes in tool geometry impact microhardness, reducing Shear-Affected Zones (SAZ) with smaller clearances. [12] demonstrated intensified work hardening near edges due to tool wear.

Powder Metallurgy (PM) High-Speed Steels offer an alternative to conventionally produced tool steels, showcasing unique attributes like heightened hardness and toughness, distinguishing them from traditional tool steels. While extensive research has centered on analyzing tool wear on electrical sheets, there remains a notable gap in exploring powder metallurgical (PM) tools in the blanking process of electrical steels. This study thoroughly examines tool wear analysis using three distinct PM tool steels for varying clearances. Furthermore, it examines the properties of sheared edges resulting from different punch strokes.

## Procedure

A TruPunch 5000 was used for experimental blanking with a 1000 mm x 1000 mm blank. A total of 108,000 strokes are performed using a 10 mm x 10 mm punch and two dies (10.16 mm and 10.32 mm), as shown in Fig. 1.

No lubricant or BHF was used. The analysis was conducted after 9,000, 45,000, 81,000, and 108,000 strokes.

<figure><img src="image_1234.png" /><figcaption>Figure 1: Schematic diagram of square punch with different die dimensions.</figcaption></figure>

## Tool Steel

This work uses three powder metallurgical tool steel, namely, PM1 (X50MoCoCr17-4), PM8 (X230VCrMo8-5), and PM10 (X130VMoN10-2). PM8 is abrasive-resistant with a lower hard phase content than PM1, while PM10 has enhanced anti-galling properties and it contains 1.8% of Ni. PM1 is an abrasive-resistant material with higher compressive strength. Chemical composition and properties are given in Tables 1 and 2.

<table><caption>Table 1: Chemical composition of three punch materials.</caption><thead><tr><th>Grade</th><th>C, %</th><th>Si, %</th><th>Mn, %</th><th>Cr, %</th><th>Mo, %</th><th>V, %</th></tr></thead><tbody><tr><td>PM1</td><td>0.5</td><td>1.0</td><td>0.3</td><td>4.2</td><td>17.3</td><td><strong>0.25</strong></td></tr><tr><td>PM8</td><td>2.3</td><td>0.4</td><td>0.4</td><td>4.8</td><td>3.6</td><td><strong>8</strong></td></tr><tr><td>PM10</td><td>1.3</td><td>0.5</td><td>0.4</td><td>0.4</td><td>1.8</td><td><strong>10</strong></td></tr></tbody></table>
<table><caption>Table 2: Properties of three punch materials.</caption><thead><tr><th>Grade</th><th>Compressive strength (MPa)</th><th>Conductivity at 200°C (W/m°C)</th><th>Hardness (HRC)</th></tr></thead><tbody><tr><td>PM1</td><td>3600</td><td>-</td><td>68-69</td></tr><tr><td>PM8</td><td>2800</td><td>25</td><td>63-64</td></tr><tr><td>PM10</td><td>3000</td><td>25</td><td>63-65</td></tr></tbody></table>

## Electrical Steel

Tool wear in PM1, PM8, and PM10 was analyzed when blanking against non-grain-oriented electrical steel of 1 mm thickness. This material is commonly employed in blanking operations. The electrical steel contains 1.25% of the mass content Si. The yield and ultimate tensile strength are 250 MPa and 370 MPa, respectively.

## Tool Wear Measurement

The Keyence VR5000 profilometer, with 2 µm accuracy, quantifies punch tool wear. A 3D-printed fixture has been designed to ensure precise placement and capturing of corner and edge wear. Imaging is done at 80x magnification after 9,000, 45,000, 81,000, and 108,000 strokes. Corner chipping depth and width are measured using 10 equidistant lines spaced 30 µm apart to quantify the wear. Average values for corners with extensive chipping and maximum values for those with minimal wear enable effective comparisons across clearances and punch materials. A significant variation of wear is observed between different punch sides, which leads to the omission of an error plot, which causes higher error deviation. The quantification of tool wear in the punch involves measuring the change in its edge radius, with an initial radius of 15 µm. This process employs a profilometer to scan all four sides of the punch using 10 horizontal measurement lines spaced 1050 µm apart. Analyzing the edge profile for each line determines the edge radius. Notably, an increase in strokes correlates with an increase in the radius.

## Sheared Properties Measurement

The blank is evaluated for sheared properties at the initial state and the beginning of 45,000, 81,000, and 108,000 strokes on all sides. The red marking is done at the initial point of the sheet to distinguish the different sides after blanking (Fig. 2a). The collected samples are embedded and polished to achieve a fine surface finish to measure sheared properties and microhardness.

A microscope with a magnification of 100x according to VDI 2906 is used to assess parameters like rollover ($h_r$), burnish ($h_b$), fracture ($h_f$), and burr height (Fig. 2b). Sheared properties are evaluated on all sides, and the average is calculated for each stroke.

<figure><img src="image_1233.png" /><figcaption>Figure 2 a): Marking on the sides of the sheared blank, b): Measurement of sheared properties according to VDI guidelines 2906.</figcaption></figure>
<table><caption>Table 2: Properties of three punch materials.</caption><thead><tr><th>Grade</th><th>Compressive strength (MPa)</th><th>Conductivity at 200°C (W/m°C)</th><th>Hardness (HRC)</th></tr></thead><tbody><tr><td>PM1</td><td>3600</td><td>-</td><td>68-69</td></tr><tr><td>PM8</td><td>2800</td><td>25</td><td>63-64</td></tr><tr><td>PM10</td><td>3000</td><td>25</td><td>63-65</td></tr></tbody></table>

## Electrical Steel

Tool wear in PM1, PM8, and PM10 was analyzed when blanking against non-grain-oriented electrical steel of 1 mm thickness. This material is commonly employed in blanking operations. The electrical steel contains 1.25% of the mass content Si. The yield and ultimate tensile strength are 250 MPa and 370 MPa, respectively.

## Tool Wear Measurement

The Keyence VR5000 profilometer, with 2 µm accuracy, quantifies punch tool wear. A 3D-printed fixture has been designed to ensure precise placement and capturing of corner and edge wear. Imaging is done at 80x magnification after 9,000, 45,000, 81,000, and 108,000 strokes. Corner chipping depth and width are measured using 10 equidistant lines spaced 30 µm apart to quantify the wear. Average values for corners with extensive chipping and maximum values for those with minimal wear enable effective comparisons across clearances and punch materials. A significant variation of wear is observed between different punch sides, which leads to the omission of an error plot, which causes higher error deviation. The quantification of tool wear in the punch involves measuring the change in its edge radius, with an initial radius of 15 µm. This process employs a profilometer to scan all four sides of the punch using 10 horizontal measurement lines spaced 1050 µm apart. Analyzing the edge profile for each line determines the edge radius. Notably, an increase in strokes correlates with an increase in the radius.

## Sheared Properties Measurement

The blank is evaluated for sheared properties at the initial state and the beginning of 45,000, 81,000, and 108,000 strokes on all sides. The red marking is done at the initial point of the sheet to distinguish the different sides after blanking (Fig. 2a). The collected samples are embedded and polished to achieve a fine surface finish to measure sheared properties and microhardness.

A microscope with a magnification of 100x according to VDI 2906 is used to assess parameters like rollover ($h_r$), burnish ($h_b$), fracture ($h_f$), and burr height (Fig. 2b). Sheared properties are evaluated on all sides, and the average is calculated for each stroke.

<figure><img src="image_1235.png" /><figcaption>Figure 2 a): Marking on the sides of the sheared blank, b): Measurement of sheared properties according to VDI guidelines 2906.</figcaption></figure>
# Result and Discussions

## Wear Analysis

### PM8

PM8 punch is analyzed for 8% and 16% clearances to determine chipping depth, width, and edge radius changes after 9,000, 45,000, 81,000, and 108,000 strokes. Wear increases with stroke count, with more explicit chipping observed at 108,000 strokes compared to 9,000 strokes. Corner chipping is more prominent than edge chipping. For PM8 with 8% clearance, corners 1 and 2 exhibit predominant chipping, while corners 3 and 4 show minor or no chipping. Chipping starts at 45,000 strokes and gradually widens. Corner 2 has the maximum chipping depth and width after 108,000 strokes, while corner 4 shows minimal chipping. Chipping depth and width in corner 4 after 108,000 strokes.

Fig. 3 compares corner 2, with maximum chipping, to corner 4, where there is no considerable chipping after 9,000 and 108,000 strokes, respectively. SEM images reveal cracks at punch edges (Fig. 4a), indicating an increased chipping with more strokes. Wear is mainly abrasive, with minimal galling. Fig. 4b shows a significant crack above the chipped corner that will expand with more strokes. Compared to 8% clearance, 16% clearance exhibits minimal chipping on all corners but significant wear on side 3 of the punch.

<figure><img src="image_1234.png" /><figcaption>Figure 3: PM8 punch for 8% clearance for a): Corner 2 after 45,000 strokes, b): Corner 4 after 45,000 strokes, c): Corner 2 after 108,000 strokes, d): Corner 4 after 108,000 strokes.</figcaption></figure>

<figure><img src="image_1235.png" /><figcaption>Figure 4: SEM images of PM8 for 8% clearance at the end of 108,000 strokes at the a): punch edge and b): chipped corner.</figcaption></figure>
# Result and Discussions

## Wear Analysis

### PM8

PM8 punch is analyzed for 8% and 16% clearances to determine chipping depth, width, and edge radius changes after 9,000, 45,000, 81,000, and 108,000 strokes. Wear increases with stroke count, with more explicit chipping observed at 108,000 strokes compared to 9,000 strokes. Corner chipping is more prominent than edge chipping. For PM8 with 8% clearance, corners 1 and 2 exhibit predominant chipping, while corners 3 and 4 show minor or no chipping. Chipping starts at 45,000 strokes and gradually widens. Corner 2 has the maximum chipping depth and width after 108,000 strokes, while corner 4 shows minimal chipping. Chipping depth and width in corner 4 after 108,000 strokes.

Fig. 3 compares corner 2, with maximum chipping, to corner 4, where there is no considerable chipping after 9,000 and 108,000 strokes, respectively. SEM images reveal cracks at punch edges (Fig. 4a), indicating an increased chipping with more strokes. Wear is mainly abrasive, with minimal galling. Fig. 4b shows a significant crack above the chipped corner that will expand with more strokes. Compared to 8% clearance, 16% clearance exhibits minimal chipping on all corners but significant wear on side 3 of the punch.

<figure><img src="image_1236.png" /><figcaption>Figure 3: PM8 punch for 8% clearance for a): Corner 2 after 45,000 strokes, b): Corner 4 after 45,000 strokes, c): Corner 2 after 108,000 strokes, d): Corner 4 after 108,000 strokes.</figcaption></figure>

<figure><img src="image_1237.png" /><figcaption>Figure 4: SEM images of PM8 for 8% clearance at the end of 108,000 strokes at the a): punch edge and b): chipped corner.</figcaption></figure>
Corner 4 shows the most wear, reaching 57 µm depth and 127 µm width after 108,000 strokes. Corners 4 and 2 wear more in 45,000 strokes at 8% clearance than in 81,000 strokes. Fig. 5 compares corners 2 and 4 at 16% clearance, with corner 2 showing the least wear (14 µm depth, 53 µm width) even after 108,000 strokes. No chipping is observed on the punch corners compared to 8%. Wear gradually increases with more strokes, with a 56.30% depth increase from 9,000 to 108,000 strokes. The width increases by 168% from 9,000 to 45,000 strokes and only 6.78% from 45,000 to 108,000 strokes, primarily at the corner tip.

Compared to 8% clearance, 16% clearance exhibits minimal chipping on all corners but significant wear on side 3 of the punch. Corner 4 shows the most wear, reaching 57 µm depth and 127 µm width after 108,000 strokes. Corners 4 and 2 wear more in 45,000 strokes at 8% clearance than in 81,000 strokes. Fig. 6 compares the chipping depth for PM8 for the clearance values of 8% and 16%, respectively. Up to 9,000 strokes, 16% have slightly more chipping, but from 45,000 to 108,000 strokes, 8% dominate due to earlier chipping onset. and 431% for 16%, while chipping width increases by 265.93% and 323.82% for 8% and 16%, respectively.

Chipping depth increases by 1811.76% for 8%. Chipping depth remains consistent from 45,000

<figure><img src="image_1236.png" /><figcaption>Figure 5: PM8 for 16% clearance for a): Corner 2 after 45,000 strokes, b): corner 4 after 45,000 strokes, c): corner 2 after 108,000 strokes, d): corner 4 after 108,000 strokes.</figcaption></figure>

to 108,000 strokes, with a slight 10 µm width increase, indicating wear progression with more strokes. Punch tool wear is quantified by monitoring edge radius changes for different clearances and strokes. Unlike corner chipping, edges show minimal variation. Fig. 7a and Fig. 7c compare side 1 for 8% clearance at 9,000 and 108,000 strokes, and Figure 7 b) and d) for side 4. After 9,000 strokes, sides 1 and 4 have edge values of 21.97 µm and 20.47 µm, respectively. The edge radius linearly increases with strokes, reaching 31.44 µm and 36.277 µm for sides 1 and 4 at 108,000

strokes. The average edge radius stays near 21 µm at 9,000 strokes, increasing by 10.68% to 45,000 strokes and 51.79% to 108,000 strokes, remaining consistent after 81,000 strokes. For 16% clearance, Side 3 experiences significant edge wear from 45,000 to 108,000 strokes (Fig. 8).

<figure><img src="image_1237.png" /><figcaption>Figure 6: Comparison for PM8 between 8% and 16% clearance for chipping depth.</figcaption></figure>
Corner 4 shows the most wear, reaching 57 µm depth and 127 µm width after 108,000 strokes. Corners 4 and 2 wear more in 45,000 strokes at 8% clearance than in 81,000 strokes. Fig. 5 compares corners 2 and 4 at 16% clearance, with corner 2 showing the least wear (14 µm depth, 53 µm width) even after 108,000 strokes. No chipping is observed on the punch corners compared to 8%. Wear gradually increases with more strokes, with a 56.30% depth increase from 9,000 to 108,000 strokes. The width increases by 168% from 9,000 to 45,000 strokes and only 6.78% from 45,000 to 108,000 strokes, primarily at the corner tip.

Compared to 8% clearance, 16% clearance exhibits minimal chipping on all corners but significant wear on side 3 of the punch. Corner 4 shows the most wear, reaching 57 µm depth and 127 µm width after 108,000 strokes. Corners 4 and 2 wear more in 45,000 strokes at 8% clearance than in 81,000 strokes. Fig. 6 compares the chipping depth for PM8 for the clearance values of 8% and 16%, respectively. Up to 9,000 strokes, 16% have slightly more chipping, but from 45,000 to 108,000 strokes, 8% dominate due to earlier chipping onset. and 431% for 16%, while chipping width increases by 265.93% and 323.82% for 8% and 16%, respectively.

Chipping depth increases by 1811.76% for 8%. Chipping depth remains consistent from 45,000

<figure><img src="image_1238.png" /><figcaption>Figure 5: PM8 for 16% clearance for a): Corner 2 after 45,000 strokes, b): corner 4 after 45,000 strokes, c): corner 2 after 108,000 strokes, d): corner 4 after 108,000 strokes.</figcaption></figure>

to 108,000 strokes, with a slight 10 µm width increase, indicating wear progression with more strokes. Punch tool wear is quantified by monitoring edge radius changes for different clearances and strokes. Unlike corner chipping, edges show minimal variation. Fig. 7a and Fig. 7c compare side 1 for 8% clearance at 9,000 and 108,000 strokes, and Figure 7 b) and d) for side 4. After 9,000 strokes, sides 1 and 4 have edge values of 21.97 µm and 20.47 µm, respectively. The edge radius linearly increases with strokes, reaching 31.44 µm and 36.277 µm for sides 1 and 4 at 108,000

strokes. The average edge radius stays near 21 µm at 9,000 strokes, increasing by 10.68% to 45,000 strokes and 51.79% to 108,000 strokes, remaining consistent after 81,000 strokes. For 16% clearance, Side 3 experiences significant edge wear from 45,000 to 108,000 strokes (Fig. 8).

<figure><img src="image_1239.png" /><figcaption>Figure 6: Comparison for PM8 between 8% and 16% clearance for chipping depth.</figcaption></figure>
<figure><img src="image_1238.png" /><figcaption>Figure 7: PM8 for 8% clearance for a): side 1 after 9,000 strokes, b): side 4 after 9,000 strokes, c): side 1 after 108,000 strokes, d): side 4 after 108,000 strokes.</figcaption></figure>

<figure><img src="image_1239.png" /><figcaption>Figure 8: Punch side 3 of PM8 for 16% clearance after a): 9,000 strokes, b): 45,000 strokes, c): 108,000 strokes.</figcaption></figure>

At 9,000 strokes, minimal wear keeps the corner edge intact, but wear blunts the corner, increasing its radius with more strokes. Fig. 9 displays the average edge radius for all sides, with Side 3's excessive wear causing significant variation. The average edge radius increases by 46% from 9,000 to 45,000 strokes and by 115% to 108,000 strokes, reaching a peak of around 56 µm.

<figure><img src="image_1240.png" /><figcaption>Figure 9: Average edge radius of PM8 for 16% clearance for different numbers of strokes.</figcaption></figure>
<figure><img src="image_1240.png" /><figcaption>Figure 7: PM8 for 8% clearance for a): side 1 after 9,000 strokes, b): side 4 after 9,000 strokes, c): side 1 after 108,000 strokes, d): side 4 after 108,000 strokes.</figcaption></figure>

<figure><img src="image_1241.png" /><figcaption>Figure 8: Punch side 3 of PM8 for 16% clearance after a): 9,000 strokes, b): 45,000 strokes, c): 108,000 strokes.</figcaption></figure>

At 9,000 strokes, minimal wear keeps the corner edge intact, but wear blunts the corner, increasing its radius with more strokes. Fig. 9 displays the average edge radius for all sides, with Side 3's excessive wear causing significant variation. The average edge radius increases by 46% from 9,000 to 45,000 strokes and by 115% to 108,000 strokes, reaching a peak of around 56 µm.

<figure><img src="image_1242.png" /><figcaption>Figure 9: Average edge radius of PM8 for 16% clearance for different numbers of strokes.</figcaption></figure>
## PM10

PM10 is examined for chipping and corner wear at various clearances and stroke counts. At 8% clearance, extensive chipping is evident across all corners of the punch. Corner 4 experiences comparatively less chipping than corners 1 and 2. Corner 1 shows substantial chipping at 108,000 strokes, with an average chipping depth and width of 1009.5 µm and 275.21 µm, respectively. Chipping initiates at 45,000 strokes, gradually increasing to 81,000 strokes before peaking at 108,000 strokes. After 45,000 and 81,000 strokes, the chipping depth is approximately 52.83 µm and 77.59 µm, while the chipping width remains around 68 µm. A visible crack appears after

81,000 strokes, indicating further width extension. Unlike PM8, PM10 experiences significant chipping at all corners for an 8% clearance, with corners 1 and 2 particularly impacted. PM10, unlike PM8, exhibits chipping at a 16% clearance. The maximum chipping occurs at corners 1 and 2, while corners 3 and 4 remain minimally affected. Chipping width is crucial, showing a significant increase, indicating the expanded chipping area on the punch surface. For a 16% clearance, the average chipping depth peaks at 110.02 µm after 45,000 strokes, a 3348% increase from 9,000 strokes, remaining constant at 108,000 strokes. Average chipping width increases by 350% between 9,000 and 45,000 strokes, gradually expanding with stroke count. Both chipping depth and width experience substantial increases of 3254% and 436% from 9,000 to 108,000 strokes.

Regarding edge wear, PM10 behaves consistently across all punch sides, unlike PM8, which displays variation. Wear is slightly higher, with 8% clearance compared to 16%. At 8% clearance, side 2 exhibits higher wear at 108,000 strokes with an edge radius of 42 µm, while other sides average around 37 µm. Similarly, at 16% clearance, side 2 shows less wear with an edge radius under 22 µm, around 10 µm less than the other sides. Fig. 10 illustrates the average edge radius for 8% and 16% clearances, with 8% consistently outperforming 16%.

## PM1

PM1, like PM8 and PM10, was examined for chipping and edge radius changes with increasing strokes. Chipping was minimal until 108,000 strokes, primarily occurring at corner 2 with maximum depth and width of 19 µm and 58 µm after 9,000 strokes. Widespread chipping began at 45,000 strokes, with a depth and width of 528 µm and 160 µm. Chipping depth remained consistent, but width increased to around 172 µm at 108,000 strokes.

<figure><img src="image_1241.png" /><figcaption>Figure 10: Comparison of average edge radius for PM10 material for two different clearances across different punch strokes.</figcaption></figure>
## PM10

PM10 is examined for chipping and corner wear at various clearances and stroke counts. At 8% clearance, extensive chipping is evident across all corners of the punch. Corner 4 experiences comparatively less chipping than corners 1 and 2. Corner 1 shows substantial chipping at 108,000 strokes, with an average chipping depth and width of 1009.5 µm and 275.21 µm, respectively. Chipping initiates at 45,000 strokes, gradually increasing to 81,000 strokes before peaking at 108,000 strokes. After 45,000 and 81,000 strokes, the chipping depth is approximately 52.83 µm and 77.59 µm, while the chipping width remains around 68 µm. A visible crack appears after

81,000 strokes, indicating further width extension. Unlike PM8, PM10 experiences significant chipping at all corners for an 8% clearance, with corners 1 and 2 particularly impacted. PM10, unlike PM8, exhibits chipping at a 16% clearance. The maximum chipping occurs at corners 1 and 2, while corners 3 and 4 remain minimally affected. Chipping width is crucial, showing a significant increase, indicating the expanded chipping area on the punch surface. For a 16% clearance, the average chipping depth peaks at 110.02 µm after 45,000 strokes, a 3348% increase from 9,000 strokes, remaining constant at 108,000 strokes. Average chipping width increases by 350% between 9,000 and 45,000 strokes, gradually expanding with stroke count. Both chipping depth and width experience substantial increases of 3254% and 436% from 9,000 to 108,000 strokes.

Regarding edge wear, PM10 behaves consistently across all punch sides, unlike PM8, which displays variation. Wear is slightly higher, with 8% clearance compared to 16%. At 8% clearance, side 2 exhibits higher wear at 108,000 strokes with an edge radius of 42 µm, while other sides average around 37 µm. Similarly, at 16% clearance, side 2 shows less wear with an edge radius under 22 µm, around 10 µm less than the other sides. Fig. 10 illustrates the average edge radius for 8% and 16% clearances, with 8% consistently outperforming 16%.

## PM1

PM1, like PM8 and PM10, was examined for chipping and edge radius changes with increasing strokes. Chipping was minimal until 108,000 strokes, primarily occurring at corner 2 with maximum depth and width of 19 µm and 58 µm after 9,000 strokes. Widespread chipping began at 45,000 strokes, with a depth and width of 528 µm and 160 µm. Chipping depth remained consistent, but width increased to around 172 µm at 108,000 strokes.

<figure><img src="image_1243.png" /><figcaption>Figure 10: Comparison of average edge radius for PM10 material for two different clearances across different punch strokes.</figcaption></figure>
Other corners had minor wear, increasing the chipping width slightly. Corners 1 and 4 had average chipping widths of 32 µm and 21 µm, respectively. PM1 outperformed other materials in wear resistance. Fig. 11 compares average edge radius values for 8% and 16% for two clearances. Notably, the 8% clearance exhibits a linear increase in edge radius with stroke count, while the 16% clearance maintains a stable value until 81,000 strokes before rising to approximately 29 µm at 108,000 strokes. The 8% and 16% clearances differ by around 12 µm at 81,000 strokes and about 6 µm at 45,000 and 108,000 strokes. Minimal variations exist between punch sides, with a maximum difference of 4-5 µm. Side 3 influences the edge radius more at 45,000 strokes, and side 1 exhibits less wear. This trend is consistent for both clearances, with side 4 dominating the edge radius at 8% clearance. Overall, the average edge radius increases by 42% and 46% between 9,000 and 108,000 strokes for 8% and 16% clearances.

In terms of edge radius, side 3 increased from 18 µm to 28 µm (16% clearance) or 33 µm (8% clearance) after 9,000 strokes, with slightly more wear at 8% clearance. PM8 demonstrates minimal chipping at an 8% clearance,

with a depth of approximately 65 µm after 108,000 strokes. Initially, PM10 surpasses PM1, but by 108,000 strokes, PM10 experiences extensive chipping. At a 16% clearance, PM8 and PM1 exhibit minimal wear, with PM1 showing superior chipping and wear resistance among the materials. Regarding edge wear, PM1 demonstrates superior wear resistance over PM8 and PM10 (Fig. 12). After 9,000 strokes, their edge radius measures 21 µm, increasing to 33 µm, 38 µm, and 32 µm after 108,000 strokes. At 8% clearance, PM8 shows 6 µm more wear than PM1 and PM10. However, at 16% clearance, both PM1 and PM10 exhibit minimal wear with a final edge radius of 28 µm, while PM8's side 3 experiences extensive wear, increasing the edge radius to 56 µm after 108,000 strokes.

<figure><img src="image_1242.png" /><figcaption>Figure 11: Comparison of average edge radius for PM1 material for two clearances across different punch strokes.</figcaption></figure>

<figure><img src="image_1243.png" /><figcaption>Figure 12: Edge radius comparison for 16% clearance between different punch materials across various strokes.</figcaption></figure>
Other corners had minor wear, increasing the chipping width slightly. Corners 1 and 4 had average chipping widths of 32 µm and 21 µm, respectively. PM1 outperformed other materials in wear resistance. Fig. 11 compares average edge radius values for 8% and 16% for two clearances. Notably, the 8% clearance exhibits a linear increase in edge radius with stroke count, while the 16% clearance maintains a stable value until 81,000 strokes before rising to approximately 29 µm at 108,000 strokes. The 8% and 16% clearances differ by around 12 µm at 81,000 strokes and about 6 µm at 45,000 and 108,000 strokes. Minimal variations exist between punch sides, with a maximum difference of 4-5 µm. Side 3 influences the edge radius more at 45,000 strokes, and side 1 exhibits less wear. This trend is consistent for both clearances, with side 4 dominating the edge radius at 8% clearance. Overall, the average edge radius increases by 42% and 46% between 9,000 and 108,000 strokes for 8% and 16% clearances.

In terms of edge radius, side 3 increased from 18 µm to 28 µm (16% clearance) or 33 µm (8% clearance) after 9,000 strokes, with slightly more wear at 8% clearance. PM8 demonstrates minimal chipping at an 8% clearance,

with a depth of approximately 65 µm after 108,000 strokes. Initially, PM10 surpasses PM1, but by 108,000 strokes, PM10 experiences extensive chipping. At a 16% clearance, PM8 and PM1 exhibit minimal wear, with PM1 showing superior chipping and wear resistance among the materials. Regarding edge wear, PM1 demonstrates superior wear resistance over PM8 and PM10 (Fig. 12). After 9,000 strokes, their edge radius measures 21 µm, increasing to 33 µm, 38 µm, and 32 µm after 108,000 strokes. At 8% clearance, PM8 shows 6 µm more wear than PM1 and PM10. However, at 16% clearance, both PM1 and PM10 exhibit minimal wear with a final edge radius of 28 µm, while PM8's side 3 experiences extensive wear, increasing the edge radius to 56 µm after 108,000 strokes.

<figure><img src="image_1244.png" /><figcaption>Figure 11: Comparison of average edge radius for PM1 material for two clearances across different punch strokes.</figcaption></figure>

<figure><img src="image_1245.png" /><figcaption>Figure 12: Edge radius comparison for 16% clearance between different punch materials across various strokes.</figcaption></figure>
# Sheared Edge Analysis

## PM8

The PM8 sheared edge properties were investigated with 8% and 16% clearance values, focusing on burr height as a crucial indicator of blank quality. For PM8 with an 8% clearance, burr height remained below 2% of thickness until 108,000 strokes. Sheared characteristics had a limited impact on stroke numbers compared to varied clearances [8]. Fig. 13 displays the average values of rollover ($h_r$), burnish zone ($h_b$), fracture zone ($h_f$), and burr height for PM8 with 8% clearance across different stroke counts. Rollover increased by roughly 3% of sheet thickness over 108,000 strokes.

In contrast, with 16% clearance, burr height exceeded 4% of sheet thickness and reached nearly 8% at 45,000 strokes. The

increase in $h_r$ was substantial, around 13%, from the initial state to 108,000 strokes for 16% clearance. Similarly, $h_b$ decreased with more strokes, from 42% to 32.33% at 108,000 strokes.

<figure><img src="image_1244.png" /><figcaption>Figure 13: Sheared edge properties of PM8 for 8% clearance for different strokes.</figcaption></figure>

## PM10

PM10 exhibits more stable sheared properties than PM8 with varying stroke numbers. The rollover region remains consistent at approximately 22% of sheet thickness up to 108,000 strokes. This pattern holds for both burnish and fracture zones, at around 42% and 36%, respectively. Burr height varies slightly as strokes increase, rising from 1% to 2.5% for 8% clearance, likely due to chipping. In contrast, the 16% clearance maintains nearly constant burr height across strokes, with only slight changes at 45,000 strokes, as illustrated in Fig. 14.

## PM1

The material PM1 exhibits more significant burr formation at 8% clearance compared to PM8 and PM10. Throughout all punch strokes, a notable burr forms, averaging about 1.5% of the sheet thickness. The fracture zone expands from 33% to around 39% of the sheet thickness at 108,000 strokes, while the burnish zone remains at approximately 40%. Initially, at 42%, the burnish zone reduces to around 39%. At 108,000 strokes, deviation increases notably, reaching 8.31% for burnish and 6.33% for the fracture zone. Burr formation is evident only at 8% clearance in PM1, absent in other materials. At 16% clearance, burr height further increases to over 5% of the sheet thickness. PM1 shows a higher deviation between its sides than other materials, impacting properties like $h_b$ and $h_f$. Fig. 15 illustrates PM1's predominant burr formation at 16% clearance compared to 8%, with an average difference of around 4% across all strokes, displaying minimal variation in burr height.
# Sheared Edge Analysis

## PM8

The PM8 sheared edge properties were investigated with 8% and 16% clearance values, focusing on burr height as a crucial indicator of blank quality. For PM8 with an 8% clearance, burr height remained below 2% of thickness until 108,000 strokes. Sheared characteristics had a limited impact on stroke numbers compared to varied clearances [8]. Fig. 13 displays the average values of rollover ($h_r$), burnish zone ($h_b$), fracture zone ($h_f$), and burr height for PM8 with 8% clearance across different stroke counts. Rollover increased by roughly 3% of sheet thickness over 108,000 strokes.

In contrast, with 16% clearance, burr height exceeded 4% of sheet thickness and reached nearly 8% at 45,000 strokes. The

increase in $h_r$ was substantial, around 13%, from the initial state to 108,000 strokes for 16% clearance. Similarly, $h_b$ decreased with more strokes, from 42% to 32.33% at 108,000 strokes.

<figure><img src="image_1246.png" /><figcaption>Figure 13: Sheared edge properties of PM8 for 8% clearance for different strokes.</figcaption></figure>

## PM10

PM10 exhibits more stable sheared properties than PM8 with varying stroke numbers. The rollover region remains consistent at approximately 22% of sheet thickness up to 108,000 strokes. This pattern holds for both burnish and fracture zones, at around 42% and 36%, respectively. Burr height varies slightly as strokes increase, rising from 1% to 2.5% for 8% clearance, likely due to chipping. In contrast, the 16% clearance maintains nearly constant burr height across strokes, with only slight changes at 45,000 strokes, as illustrated in Fig. 14.

## PM1

The material PM1 exhibits more significant burr formation at 8% clearance compared to PM8 and PM10. Throughout all punch strokes, a notable burr forms, averaging about 1.5% of the sheet thickness. The fracture zone expands from 33% to around 39% of the sheet thickness at 108,000 strokes, while the burnish zone remains at approximately 40%. Initially, at 42%, the burnish zone reduces to around 39%. At 108,000 strokes, deviation increases notably, reaching 8.31% for burnish and 6.33% for the fracture zone. Burr formation is evident only at 8% clearance in PM1, absent in other materials. At 16% clearance, burr height further increases to over 5% of the sheet thickness. PM1 shows a higher deviation between its sides than other materials, impacting properties like $h_b$ and $h_f$. Fig. 15 illustrates PM1's predominant burr formation at 16% clearance compared to 8%, with an average difference of around 4% across all strokes, displaying minimal variation in burr height.
<figure><img src="image_1245.png" /><figcaption>Figure 14: Burr height comparison of PM10 material for 8% and 16% clearance across different punch strokes.</figcaption></figure>

<figure><img src="image_1246.png" /><figcaption>Figure 15: Burr height comparison of PM1 material for 8% and 16% clearance across different punch strokes.</figcaption></figure>

## Conclusion

This study investigated electrical steel blanking with PM1, PM8, and PM10 punch materials, yielding the following formal findings:

1. At an 8% clearance, all materials experienced chipping, with PM1 demonstrating superior chipping resistance. PM10 exhibited chipping at all corners, while PM8 displayed variable chipping effects.

2. At a 16% clearance, PM1 and PM8 showed no chipping, whereas PM8 exhibited minor corner wear, and PM10 chipped at corners 1 and 2.

3. Tool wear, assessed through edge radius, was most pronounced in PM10, followed by PM8 and PM1 at 8% clearance. However, PM8 outperformed the others at 16% clearance.

4. The Sheared edge analysis found varying burr heights for different materials and clearances. At 8% clearance, all punch materials had burr heights below 2.5% of sheet thickness, with PM1 slightly higher. At 16% clearance, all materials exceeded 5% burr height, with PM8 having the most due to side 3 wear. Side 4 had higher burr at 16% clearance, increasing standard deviation compared to 8%

The analysis of tool wear and sheared properties shows that different corners of the punch and blank sides behave differently for both clearance values. Chipping at the punch corners is more predominant in 8% clearance than in 16%. Both corners at the front face are prone to chipping compared to the other corners. In terms of blank, side 4 has a higher burr and side 1 has a comparatively lesser burr blank side could be due to the misalignment between the punch and die, which causes unequal clearances on four sides.

## Acknowledgment and disclaimers

NH, TC and AET appreciate funding provided to TU Dortmund by Uddeholms AB for this study. PS is thankful for the funding of his M.Sc. thesis related to the work. The authors used the software Grammarly for language polishing.
<figure><img src="image_1247.png" /><figcaption>Figure 14: Burr height comparison of PM10 material for 8% and 16% clearance across different punch strokes.</figcaption></figure>

<figure><img src="image_1248.png" /><figcaption>Figure 15: Burr height comparison of PM1 material for 8% and 16% clearance across different punch strokes.</figcaption></figure>

## Conclusion

This study investigated electrical steel blanking with PM1, PM8, and PM10 punch materials, yielding the following formal findings:

1. At an 8% clearance, all materials experienced chipping, with PM1 demonstrating superior chipping resistance. PM10 exhibited chipping at all corners, while PM8 displayed variable chipping effects.

2. At a 16% clearance, PM1 and PM8 showed no chipping, whereas PM8 exhibited minor corner wear, and PM10 chipped at corners 1 and 2.

3. Tool wear, assessed through edge radius, was most pronounced in PM10, followed by PM8 and PM1 at 8% clearance. However, PM8 outperformed the others at 16% clearance.

4. The Sheared edge analysis found varying burr heights for different materials and clearances. At 8% clearance, all punch materials had burr heights below 2.5% of sheet thickness, with PM1 slightly higher. At 16% clearance, all materials exceeded 5% burr height, with PM8 having the most due to side 3 wear. Side 4 had higher burr at 16% clearance, increasing standard deviation compared to 8%.

The analysis of tool wear and sheared properties shows that different corners of the punch and blank sides behave differently for both clearance values. Chipping at the punch corners is more predominant in 8% clearance than in 16%. Both corners at the front face are prone to chipping compared to the other corners. In terms of blank, side 4 has a higher burr and side 1 has a comparatively lesser burr blank side could be due to the misalignment between the punch and die, which causes unequal clearances on four sides.

## Acknowledgment and disclaimers

NH, TC and AET appreciate funding provided to TU Dortmund by Uddeholms AB for this study. PS is thankful for the funding of his M.Sc. thesis related to the work. The authors used the software Grammarly for language polishing.
## References

[1] K. Lange (1986) Handbook of metal forming. McGraw-Hill, New York

[2] S. Golovashchenko, W. Zhou, S. Nasheralahkami, N. Wang, 2017. Trimming and Sheared Edge Stretchability of Light Weight Sheet Metal Blanks. Procedia Eng 207, 1552-1557. https://doi.org/10.1016/j.proeng.2017.10.1077

[3] W. Klingenberg, & T.W. de Boer, (2008). Condition-based maintenance in punching/blanking of sheet metal. International Journal of Machine Tools and Manufacture, 48(5), 589-598. https://doi.org/10.1016/j.IJMACHTOOLS.2007.08.013

[4] S. Luo, Effect of the geometry and the surface treatment of punching tools on the tool life and wear conditions in the piercing of thick steel plate. Journal of Materials Processing Technology, (1999), 122-133, 88(1-3). https://doi.org/10.1016/S0924-0136(98)00375-6

[5] S. Fortunati, S. Cicalè, J. Schneider, A. Franke, R. Kawalla, 2016. Developments in the Field of Electrical Steels over the Last Years.

[6] J. Mucha, 2010. An experimental analysis of effects of various material tool's wear on burr during generator sheets blanking. The International Journal of Advanced Manufacturing Technology 50, 495-507. https://doi.org/10.1007/s00170-010-2554-1

[7] S. Vogt, F. Neumayer, I. Serkyov, G. Jesner, R. Kelsch, M. Geile, A. Sommer, R. Golle, W. Volk, 2017. Experimental evaluation of tool wear throughout a continuous stroke blanking process of quenched 22MnB5 ultra-high-strength steel. J Phys Conf Ser 896, 012057. https://doi.org/10.1088/1742-6596/896/1/012057

[8] H. Makich, L. Carpentier, G. Monteil, X. Roizard, J. Chambert, P. Picart, 2008. Metrology of the burr amount - correlation with blanking operation parameters (blanked material – wear of the punch). International Journal of Material Forming 1, 1243-1246. https://doi.org/10.1007/s12289-008-0167-0

[9] J. Mucha, J. Tutak, 2019. Analysis of the Influence of Blanking Clearance on the Wear of the Punch, the Change of the Burr Size, and the Geometry of the Hook Blanked in the Hardened Steel Sheet. Materials 12, 1261. https://doi.org/10.3390/ma12081261

[10] R. Wiedenmann, P. Sartkulvanich, and T. Altan, "Finite element analysis on the effect of sheared edge quality in blanking upon hole expansion of advanced high strength steel," International Deep Drawing Research Group (IDDRG) Conference, 2009, Golden, CO, USA.

[11] D. Ammar, 2019. PhD thesis. Characterization of blanking induced magneto-mechanical cut edge defects in non-oriented electrical steel. The University of Sheffield

[12] H.A. Weiss, N. Leuning, S. Steentjes, K. Hameyer, T. Andorfer, S. Jenner, W. Volk, 2017. Influence of shear cutting parameters on the electromagnetic properties of non-oriented electrical steel sheets. J Magn Magn Mater 421, 250-259. https://doi.org/10.1016/j.jmmm.2016.08.002
## References

[1] K. Lange (1986) Handbook of metal forming. McGraw-Hill, New York

[2] S. Golovashchenko, W. Zhou, S. Nasheralahkami, N. Wang, 2017. Trimming and Sheared Edge Stretchability of Light Weight Sheet Metal Blanks. Procedia Eng 207, 1552-1557. https://doi.org/10.1016/j.proeng.2017.10.1077

[3] W. Klingenberg, & T.W. de Boer, (2008). Condition-based maintenance in punching/blanking of sheet metal. International Journal of Machine Tools and Manufacture, 48(5), 589-598. https://doi.org/10.1016/j.IJMACHTOOLS.2007.08.013

[4] S. Luo, Effect of the geometry and the surface treatment of punching tools on the tool life and wear conditions in the piercing of thick steel plate. Journal of Materials Processing Technology, (1999), 122-133, 88(1-3). https://doi.org/10.1016/S0924-0136(98)00375-6

[5] S. Fortunati, S. Cicalè, J. Schneider, A. Franke, R. Kawalla, 2016. Developments in the Field of Electrical Steels over the Last Years.

[6] J. Mucha, 2010. An experimental analysis of effects of various material tool's wear on burr during generator sheets blanking. The International Journal of Advanced Manufacturing Technology 50, 495-507. https://doi.org/10.1007/s00170-010-2554-1

[7] S. Vogt, F. Neumayer, I. Serkyov, G. Jesner, R. Kelsch, M. Geile, A. Sommer, R. Golle, W. Volk, 2017. Experimental evaluation of tool wear throughout a continuous stroke blanking process of quenched 22MnB5 ultra-high-strength steel. J Phys Conf Ser 896, 012057. https://doi.org/10.1088/1742-6596/896/1/012057

[8] H. Makich, L. Carpentier, G. Monteil, X. Roizard, J. Chambert, P. Picart, 2008. Metrology of the burr amount - correlation with blanking operation parameters (blanked material – wear of the punch). International Journal of Material Forming 1, 1243-1246. https://doi.org/10.1007/s12289-008-0167-0

[9] J. Mucha, J. Tutak, 2019. Analysis of the Influence of Blanking Clearance on the Wear of the Punch, the Change of the Burr Size, and the Geometry of the Hook Blanked in the Hardened Steel Sheet. Materials 12, 1261. https://doi.org/10.3390/ma12081261

[10] R. Wiedenmann, P. Sartkulvanich, and T. Altan, "Finite element analysis on the effect of sheared edge quality in blanking upon hole expansion of advanced high strength steel," International Deep Drawing Research Group (IDDRG) Conference, 2009, Golden, CO, USA.

[11] D. Ammar, 2019. PhD thesis. Characterization of blanking induced magneto-mechanical cut edge defects in non-oriented electrical steel. The University of Sheffield

[12] H.A. Weiss, N. Leuning, S. Steentjes, K. Hameyer, T. Andorfer, S. Jenner, W. Volk, 2017. Influence of shear cutting parameters on the electromagnetic properties of non-oriented electrical steel sheets. J Magn Magn Mater 421, 250-259. https://doi.org/10.1016/j.jmmm.2016.08.002